Mathematics SPM_Sasbadi_ChrisMun_Topical Assessment Total Pro SPM 4-5

rTl('F)JAml7i7iCW .,J.l /^

SASBADI

lot %&A IJRZAI

athematics

Chris Mun

on

m

it Is of'03106 Ana\y c, q t

ADHERES TO THE LATEST SPM FORmAT

Sasbadi Sdn . Bhd. (139288-X) Lot 12, Jalan Teknologi 3/4, Taman Sains Selangor 1, Kota Damansara, 47810 Petaling Jaya, Selangor Darul Ehsan, Malaysia. Tel: +603-6145 1188 Fax: +603-6145 1199 Laman web: www.sasbadi.com e-mel: [email protected]

Hak cipta terpelihara. Tidak dibenarkan memetik atau mencetak kembali mana-mana bahagian isi buku ini dalam bentuk apa jua dan dengan cara apa pun, baik secara elektronik, fotologi, mekanik, rakaman, atau yang lain-lain sebagainya sebelum mendapat izin bertulis daripada Penerbit. © Sasbadi Sdn. Bhd. (139288-X) Cetakan 2007

ISBN 978-983-59-3350-9

Dicetak di Malaysia oleh Summit Print Sdn. Bhd. (410861-A)

The TOTAL PRO SPM Topical Assessment MATHEMATICS series has been published specifically to fulfil the urgent needs of students who are preparing to sit for the SPM public examination: These exam-oriented assessment materials are intensive and comprehensive, covering all the topics prescribed in the KBSM syllabus for Forms 4 and 5. They also include model papers which conform to the current SPM format. The book is systematically organised according to topics and subtopics as in the textbooks, it also meets all the requirements of the SPM and the KBSM syllabus. The questions in this book are both original and challenging, incorporating a variety of questioning techniques and levels of difficulty to meet the actual standard.of the SPM papers. Moreover, the number of questions set on each topic is determined by the popularity or the frequency of recurrence of the topic in the SPM examination as indicated by the trend observed in the past three to five years. Students who work consistently and systematically, using the TOTAL PRO SPM Topical Assessment MATHEMATICS will be able to improve their understanding of the subjects and evaluate their own performance. Consequently, this motivation will boost their confidence in facing the real challenges of the public exam with greater success.

SUPERIOR ADVANTACESS OF THE TOTAL PRO. SPM TOPI4AL, ASSESSMENTMATHEMATICS; Cover all the topics prescribed in the KBSM syllabus for Forms 4 and 5 and focus on popular examination topics in the SPM.

Enables students to predict the type and allocation of questions based on a careful study of the past years' SPM papers.

Comprises challenging questions which incorporate a variety of questioning techniques and levels of difficulty and conforms to the current SPM format.

Consist of two complete sets of SPM-quality Model Papers set in accordance with the actual format and standard of the public exam.

Provide plausible answers to questions for students to check and evaluate their own understanding and performance in the subject.

THE PUBLISHER

(iii)

• ANALYSIS OF SPM PAPERS(2003 -2006)

(vi)

• MATHEMATICAL FORMULAE ( vii) - (viii)

5.2 Gradient of a Straight Line in Cartesian Coordinates 5.3 Intercepts 5.4 Equation of a Straight Line 5.5 Parallel Lines

FORM 4

Statistics III

1.1 Significant Figures 1.2 Standard Form

Quadratic Expressions and Equations

6.1 Class Intervals 6.2 Mode and Mean of Grouped Data 6.3 Histograms 6.4 Frequency Polygons 6.5 Cumulative Frequency 6.6 Measures of Dispersion

2.1 Quadratic Expressions 2.2 Factorisation of Quadratic Expressions. 2.3 Quadratic Equations 2.4 Roots of Quadratic Equations

7.1 Sample Spaces 7.2 Events 7.3 Probability of an Event

Sets 3.1 Sets 3.2 Subset, Universal Set and Complement of a Set 3.3 Operations on Sets

Circles Ill 8.1 Tangents to a Circle 8.2 Angles between Tangents and Chords 8.3 Common Tangents

Mathematical Reasoning 4.1 Statements 4.2 Quantifiers "All" and "Some" 4.3 Operations on Statements 4.4 Implications 4.5 Arguments 4.6 Deduction and Induction

9.1 The Values of Sin e, Cos 9 and Tan 0 9.2 Graphs of Sine, Cosine and Tangent

The Straight Line 5.1 Gradient of a Straight Line 1 10.1 Angles of Elevation and Depression

(iv)

Lines and Planes in 3-Dimensions

"14,

11.1 Angles between Lines and Planes 11.2 Angles between Two Planes

Gradient and Area under IT a Graph 17.1 Quantity Represented by the Gradient of a Graph 17.2 Quantity Represented by the Area under a Graph

1] Probability II 18.1 Probability of an Event 18.2 Probability of the Complement of an Event 18.3 Probability of a Combined Event

12.1 Numbers in Bases Two, Eight and Five

Graphs of Functions II 13.1 Graphs of Functions 13.2 Solution of an Equation by the Graphical Method 13.3 Region Representing Inequalities in Two Variables

19.1 Bearings

Transformations III 20.1 Longitudes 20.2 Latitudes 20.3 Location of a Place 20.4 Distance on the Surface of the Earth

14.1 Combination of Two Transformations

Matrices 15.1 Concept of Matrices 15.2 Concept of Equal Matrices 15.3 Addition and Subtraction of Matrices 15.4 Multiplication of a Matrix by a Number 15.5 Multiplication of Two Matrices 15.6 Concept of Identity Matrices 15.7 Concept of Inverse Matrices 15.8 Solve Simultaneous Linear Equations. Using Matrices

21.1 Orthogonal Projections 21.2 Plans and Elevations

SPMMODELTESTI Variations 16.1 Direct Variations 16.2 Inverse Variations 16.3 Joint Variations

.(V)

N , !A ^ ILIVY'S11$ 0F`'S M^PA E- 15^ ((l 00 )' I -j 'am' 0

1-3

Number of Questions 2006 2005 2004 2003 1 2 1 2 2 2 2 2 1 1 I 1 1 1 1 1 3 1 2 2 2 2 2 3 1 2 2 2 1 1 2 2 1 1 -

Topic

Form Polygons I& II Algebraic Expressions Linear Equations Algebraic Formulae Statistics I & II Transformations I & 11 Indices Linear Inequalities Trigonometry I

4

Standard Form Sets The Straight Line Statistics III Probability I Circles III Trigonometry II Angles of Elevation and Depression Lines and Planes in 3-Dimensions

4 3 1 2 1 2 1 1

4 3 2 1 1 2 2 1

3 3 2 1 2 1 3 1 1

4 3 2 1 1 2 2 1

5

Number Bases Graphs of Functions II Matrices Variations Probability II Bearings Earth as a Sphere

2 1 3 2 1 1

2 1 1 2 2 1 1

2 1 2 3 1 2

2 1 2 3 I 1 1

PAPER 2 Section

1-3

A

4

5

4 B

Topic

Form

5

Solid Geometry Circles I&II Linear Equations Quadratic Expressions and Equations Sets Mathematical Reasoning The Straight Line Lines and Planes in 3-Dimensions Graphs of Functions II Matrices Gradient and Area under a Graph Probability II Statistics III Graphs of Functions II Transformations III Earth as a Sphere Plans and Elevations (Vi)

Number of Questions 2006 2005 2004 2003 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 I 1 1

1 I 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1

The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.

RELATIONS I am x an = am+n 2 am+an=am-n 3 (am)n =a mn

4 A-'= 1 (d_b\ ad-bc -c a) 5 P(A) = n(A) n(S) 6 P(A') =1- P(A) 7 Distance = (x2-x)2 + (y2 -y1)2

8 Midpoint, (x, y) = x1

+ x2

y1 + y2

2 2

9 Average speed = distance travelled time taken 10 Mean- sum of data number of data 11 Mean = sum of (class mark x frequency) sum of frequencies 12 Pythagoras' Theorem &=a2+b2

a b

13 m =

2 -x1

Y

X2 -X1

14 m=- y-intercept x-intercept

(xl> Y1)

y-intercept

x-intercept x

0 (x2, YZ)

(vii)

SHAPES AND SPACE 1 Area of trapezium = 2 x sum of parallel sides x height

2 Circumference of circle = TO = 2nr

3 Area of circle = nr2

4 Curved surface area of cylinder = 2inrh

5 Surface area of sphere = 4nr2

6 Volume of right prism = cross sectional area x length

7 Volume of cylinder = itr2h

8 Volume of cone = 1 nrzh 3

9 Volume of sphere = 3 nr3

10 Volume of right pyramid = 3 x base area x height 11 Sum of interior angles of a polygon = (n - 2) x 180° 12 arc length - angle subtended at centre circumference of circle 360°

13

area of sector _ angle subtended at centre area of circle 3600 sector

14 Scale factor, k = PA

15 Area of image = kz x area of object

(viii)

I

1.1 Significant Figures

1.2 Standard Form

SECTION A Objective Questions This section consists of 40 questions. Answer all the questions. For each question, choose only one answer. You may use a non -programmable scientific calculator.

Subtopic 1.1 1 Round off 2 794 to two significant figures. A 2 700 B 2790 C 2 800 D 2 810 2 Round off 300 257 , to four significant figures. A 3 003 B 300 200 C 300 300 D 300 357 3 Round off 4.17572 to three significant figures. A 4.18 B 4.175 C 4.176 D 4.1757 4 Round off 0.060813 to three significant figures. A 0.06 B 0.060 C 0.0608 D 0.06081 5 Round off 0.006197 to three significant figures. A 0.006 B 0.0061 C 0.0062 D 0.00620 6 Round off 92.6142 to three significant figures. A 92.6 C 92.614 B 92.61 D 93.0

7 Round off 0.00436 to two significant figures. A 0.004 B 0.0043 C 0.0044 D 0.00436 8 Round off 73 208 to three significant figures. A 732 B 73 200 C 73 210 D 732 100 9 Convert 3 285 km to in and round off the answer to three significant figures. A 32 850 in B 32900m C 329 000 in D 3290000m

10 Calculate the value of 5.801 - 9 x 0.417 and round off the answer to two significant figures. A 2 B 2.0 C 2.01 D 2.1

11 Calculate the value of 71.82 + 16.2 - 0.03 and round off the answer to two significant figures. A 61 B 610 C 6 100 D 6 200

1

12 Calculate the value of (5.19)2 and round off the answer to two significant figures. A 26.93 C 27 B 26.94 D 28 13 Calculate the value of 0.915 - 0.01 x 2.4 and round off the answer to three significant figures. A 22 C 221 B 220 D 221.6 14 The volume of a cube is 50 cm3. Find the length, in cm, of the edge of the cube. Give the answer correct to two significant figures. A 3.6 C 7.1 B 3.7 D 7.2 15 The diagram shows a circle with diameter 11.2 cm.

Calculate the area, in cm2, of the circle and give the ans wer correct to three significa nt figures. Use it = 72) A B C D

35.2 98.5 98.6 99.0

16 Mr Lee saves RM36 000 in a bank at an interest rate of 3.2% per annum. After one year, his total interest, correct to two significant figures, is A RM1 100 B RM1 150 C RM1 152 D RM1 200

23 Find the value of 0.00008 x 0.0045 and express the answer in the standard form. A 3.6 x 10-a B 3.6 x 10-' C 3.6 x 10' D 3.6 x 108

31 Find the value of 3.6 x 10-4 - 7.8 x 10-5 and express the answer in the standard form. A 4.98 x 10-5 B 4.98 x 10-4 Y 2.82 x 10-5 D 2.82 x 10-4

24 Calculate the value of

32 Calculate the value of

0.00063 an d express th e 9 000 answer in standard form. A 7 x 10-8 B 7x10-' C 7 x 10-6 D 7x108

65 600 and ex p ress the 0.8 x 10-6 answer in the standard form.

Subtopic 1.2 17 Express 0.000000305 in the standard form. A 3.05 x 10-6 B 3.05x10-' C 3.05 x 10-8 D 30.5 x 10-8 18 Express 218 000 in the standard form. A 218 x 103 B 2.18 x 105 C 21.8 x 10-4 D 2.18 x 10-5

19 Express 0.00436 in the standard form. A 0.043 x 10-2 B 0.436 x 10-3 C 4.36 x 10-3 D 4.36 x 103

20 3.18x106= A 3180 B 31 800 C 318 000 D 3 180 000 21 7.3 x 10-4 = A 0.0000073 B 0.000073 C 0.00073 D 0.0073 22 Express 2.438 x 10-5 as a single number. A 0.002438 B 0.0002438 C 0.00002438 D 0.000002438

B 8.2 x 109 C 8.2 x 1010 D 8.2 x 1011

25 Calculate the value of 6.5x108x8x10-13and express the answer in the standard form. A 5.2 x 10'5 B 5.2 x 10-4 C 5.2 x 104 D 5.2 x 105

33 Calculate the value of 4 x 109+8.7x 1010 and express the answer in the standard form. A 4.87 x 109 B 4.87 x 1010 C 9.1 x 109 D 9.1 x 1010

26 7.6 x 10-6 + 9.44 x 10-5 = A 1.704 x 10 -s B 1.02 x 10-5 C 1.704 x 10-4 D 1.02 x 10-4

34 5.9 x 104 + 480 000 = A 1.07 x 105 B 1.07 x 106 C 5.39 x 104 D 5.39 x 105

27

24 000 = 6 x 10-4 A 4x107 B 4x108 C 0.4 x 10' D 0.4 x 109

28 4.5 x 106 x 5 000 = A 2.25 x 1010 B 2.25 x 109 C 2.25x108 D 2.25 x 106 29 3.7x1012-8.9x10"= A 3.611 x 1012 B 3.611 x 1011 C 2.81x1012 D 2.81 x 1011 30 (5 x 10-3)2 = A 25 x 10-6 B 2.5 x 10-' C 2.5 x 1b-5 D 2.5 x 10-4

2

r

A 8.2 x 108

35

12.28 x 105 = (4 x 10'3)2 A 3.07 x 1010 B 3.07 x 1011 C 7.675 x 109 D 7.675x1010

36 A motorcycle moved at a speed of 120 km h-'. Find the distance, in m, travelled by the motorcycle in 90 minutes. A 3x103 B 1.08x104 C 1.8 x 105 D 1.08 x 10' 37 The area of a rectangular piece of land is 8.4 km2. If its length is 3 500 m, find its width, in m. A 2.4 x 103 B 2.4 x 103 C 2.94 x 101 D 2.94x103

38 The wheel of a car has a radius of 28 cm. How many rotations does the wheel make if the car travels a distance of 88 km? Use it = 72) A 5 x 104 B 5x105 C 5 x 106 D 5 x 10-$

SECTION B

39 Given 1 g of metal Y contains 5.8 x 1020 atoms, Calculate the number of atoms in 2.5 kg of metal Y and express the answer in the standard form. A 1.45 x 1021 B 1.45 x 1024 C 2.32 x 1017 D 2.32 x 1020

40 A rectangular floor has a length of 3 600 cm and a width of 2 000 cm. The floor needs to be covered with square tiles, measuring 20 cm x 20 cm. Calculate the number of tiles needed to cover the whole floor. A 1.8 x 103 C 3.6 x 103 B 1.8x104. D 3.6x104

Subjective Questions

This section consists of 20 questions. Answer all the questions. You may use a non-programmable scientific calculator. 5 Calculate the value of 7.13 - 10 x 6.2 and round off the answer to three significant figures.

Subtopic 1.1 1 Round off the following numbers correct to two significant figures. (a) 0.07006 (b) 49 815

Answer:

6 (a) Calculate the value of 13.02 + 5.3 x 90. (b) Round off the answer in (a) to four significant figures.

Answer:

Answer: (a)

2 Round off the following numbers correct to three significant figures. (a) 50.761 (b) 83 249

(b)

Answer: 7 (a) Calculate the value of 200 - 146.28 _ 16. (b) Round off the answer in (a) to four significant figures.

(a) (b)

Answer: (a)

3 Calculate the value of each of the following and round off the answer to one significant figure. (a) 5 418 - 2 970 (b) 3.8 _ 800

(b)

Answer: 8 The diagram shows a right-angled triangle. X CM

4 (a) Calculate the value of 57 007 - 24 518 + 3 107. (b) Round off the answer in (a) to three significant figures. Answer: (a)

9 cm

7 cm

Calculate the value of x correct to two significant figures.

(b)

Answer:

3

14 Find the value of 7.5 x 10-6 - 9.1 x 10-7 and express the answer in the standard form.

9 A sphere has a radius of 8 cm. Find its total surface area, in cm2, and round off the answer to three significant figures. (Use is = 3.142)

Answer:

Answer:

15 Find the value of 9.4 x 10-4 + 8 x 10-5 and express the answer in the standard form.

Subtopic 1.2

Answer: 10 State the following numbers in the standard form. (a) 0.00076 (c) 359 (b) 0.0000204 (d) 8 003 000 Answer: 16 Find the value of 9 660 and express the 7x109 answer in the standard form.

(a)

(b)

Answer:

(c)

(d) 17 Find the value of 6.3 x 104 x 2.5 x 10-9 and express the answer in the standard form.

11 Write each of the following as a single number. (a) 1.8 x 10-3 (c) 6 x 105

Answer:

(b) 5.04 x 10-4 (d) 9.815 x 106

Answer: (a) 18 Find the value of 6.8 x 7 x 106 and express the answer in the standard form.

(b)

Answer:

(c) (d)

19 The thickness of a wooden plank is 5.4 x 10-5 m. Calculate the total thickness, in m, of 500 pieces of such planks and express the answer in the standard form.

12 Find the value of 5.8 x 1012 - 5 x 1011 and express the answer in the standard form. Answer:

Answer:

13 Find the value of 3.78 x 106 and express the 0.007 answer in the standard form.

20 The scale of a map is 1: 400 000. Find the actual length, in cm, of a river which measures 8.4 cm on the map. Express the answer in the standard form.

Answer:

Answer:

4

Form 4

Quadratic Expressions and Equations

2.1 Quadratic Expressions 2.3 Quadratic Equations 2.2 Factorisation of Quadratic Expressions 2.4 Roots of Quadratic Equations

SECTION A

Objective Questionsyx

This section consists of 16 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 2.1 1 Expand 3y(y + 2). A 3y+2 C 3y2+6 B 3y + 6y D 3y2 + 6y 2 (2p - 1) (p - 5) _ A 2p2 + 5 B 2p2+5p+5 C 2p2-5p+5 D 2p2 - 11p + 5 3 Expand (5q - 2)2. A 5q2 +4 B 5q2 - 10 C 25g2 - 20q + 4 D 25q2 - 10q + 2 4 The diagram shows a trapezium. ❑

6 Factorise 3x2 - llx + 6. A (3x - 3) (x + 2) B (3x-2)(x-3) C (3x - 2) (x + 3) D (3x+2)(x+3)

7 Factorise 4r2 - 49 completely. A (2r + 7)2 B (2r - 7)2 C (2r + 7)(2r - 1) D (2r + 7 )(2r - 7)

8 Factorise 3h2 - 18h + 15 completely . A (h-1)(h-5) B (h - 2)(h - 3) C 3(h - 1) (h - 5) D 3(h - 2)(h - 3)

Subtopic 2.4 11 The roots of the equation 8 - 3p2 = 2p are A -2 and 3 B -2 and 4 C -3 and2 D 3 and 2 12 Solve the quadratic equation 3x(x - 5) = 0. A x=-5orx=3 B x=-5orx=5 C x=Oorx=5 D x=3 orx=5 13 Solve the quadratic equation 4k2 = k.

p cm

A k= 4 ork=1 4p cm

Subtopic 2.3 n (p + 5) cm

Express the area, in cm2, of the trapezium in terms of p. A 4p2 + p C 8p2 + 20 B 4p2+ 10p D 8p2 + 20p

B k=Oork=

9 Which of the following is not a quadratic equation? A 2(m + l) = 8m2 B 2=(f-2)2 C 3a2 - 2ab = 5 D w2 = w 2 3

C k=Oork=4 D k=fork=4 14 Solve the quadratic equation 2y2 - 5 =Y A y = -5 or y

Subtopic 2.2 5 Factorise 4 + 5t - 9t2. A (2 + 3t)(2 - 3t) B (4+9t)(1-t) C (4 + t)(1 - 9t) D (4 + t)(1 + 9t)

10 2n2 + 3(n - 1)2 = 0 when written in the general form is A 2n2-3n+3=0 B 2n2+3n+3=0 C 5n2-6n+1=0 D 5n2-6n+3=0

5

1 2

B y -2 or y=1 C y=-1 ory= 2 D y=-2 ory=5

The area of the triangle KLM is equal to the area of a square with sides of 5 cm. Find the possible value of h. A 2 C 10 B 5 D 15

15 The diagram shows a triangle KLM.

(h + 5) cm

16 To prepare a bucket of cement, Encik Kadir needs

(2x - 3) kg of sand and 2 kg of cement. Encik Kadir prepares x buckets of the mixture with a total mass of 66 kg of cement and sand. Find the value of x. A 3 C 6 B 5 D 7

SECTION B Subjective Questions} This section consists of 15 questions. Answer all the questions. You may use a non-programmable scientific calculator. Answer:

Subtopic 2.1 1 Determine whether each of the following is a quadratic expression. (a) 4x2 - y (c) p(p - 3) (b) 5-h-4h2

(a)

(c)

(b)

(d)

Answer: (a)

(b)

(c)

2 Expand each of the following. (a) 6y(y - 1) (c) (3k + 1)2 (d) (1 - 2q)2 (b) (2 - m)(m + 3) Answer: (a)

5 Factorise the following completely. (a) n2 + n - 6 (b) 3m (m 5) - (m - 5) (c) 2(5p2 - 1) - p (d) 3q2 + 4q - 7 Answer: (a)

(c)

(b)

(d)

(b) (c)

(d) 3 A salesperson sold y packets of book marks costing RM2 each and y cups costing RM(y + 3) each. Express the total sales of the salesperson in terms of y. Answer:

6 Factorise the following completely. (a) a2 - 49 (b) 6b(3b + 1) - 2(3b + 1) (c) 16 + (k + 2) (k - 8)

(d) h2 - 2(3h - 4) Answer: (a)

(c)

(b)

(d)

Subtopic 2.2 4 Factorise completely each of the following quadratic expressions. (a) 8p2 + 6 (c) 64h2 - 1 (b) 27y - 9y2 (d) 2t2 - 32

11 Solve each of the following quadratic equations. (a) 4p2 + . 12p = 0 ( c) 3k 2 + 4k = 5

Subtopic 2.3 7 Determine whether each of the following is

k+2

a quadratic equation.

(a) h2 - 2hk = 0

(b) (y - 5)2 = 9

(c) (y - 2)2 = 9

(d )

x

36

= 1 4x

(b) x = 3 Answer: Answer: (a)

(b)

(a)

( )

(b)

( d)

(c)

8 Write each of the following quadratic equations in the general form. 12 Determine the roots of the following quadratic equations. (a) (p - 1)(p+3)=5(p+3) (b) 3(2 - q) = 10 - q2

(a) r2 = 7(r + 1) (b) (w + 1)(4w - 3) = 1

Answer: (c) x +x=2 Answer:

13 Solve the quadratic equation 3p2 - 5 = 7p. 2

(a)

(b) (c)

9

14 Solve the quadratic equation 2x 3- 1) = x + 4. Answer:

A taxi travels from the station to town P at an average speed of 20x km/h. The journey of 120 km takes (2x - 4) hours.

15 In the diagram, ABCD and AEFG are rectangles. (4 + x) cm

Form a quadratic equation from the information given tbove. Answer:

E 2 cmi B

F

x cm

C

(a) Express the following in terms of x. (i) Length of AE, in cm. (ii) Area of the shaded region, in cm2.

Subtopic 2.4

(b) Given that the area of the shaded region is 27 cm2, find the length of AG, in cm.

10 Determine whether -3 and 2 are the roots of each of the following quadratic equations. (a) x2-2x-6=0 (c) 3(x2+1)=x (b) x(x + 1) = 6

Answer: (a) (i)

Answer: (a) (b)

(b)

(c)

7

3.3 Operations on Sets

3.1 Sets 3.2 Subset, Universal Set and Complement of a Set

SECTION A Objective Questions This section consists of 35 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 3.1 1 Given P is a set of prime numbers between 10 and 30. The elements of set P are A {11, 13, 19) B (11, 15, 19, 23, 29) C {11, 13, 17, 19, 23, 291 D {11, 13, 17, 19, 21, 23, 27, 29) 2 Given that Q = (factors of 18), find n(Q).

A B

5 6

C D

7 8

3 Given X = {colours of the Malaysian flag). Which of the following is false? A white E X B red E X C blue E X D green E X

5 Given setP={4,6,7),setQ= 13, 4, 5, 7) and set R = (4, 5, 7), which of the following is true? A PCQ C RcP B QCP D RCQ 6 Givens= {x :5-- x-- 20,x is an integer} and P = (x : x is a multiple of 5), find n(P). A 4 C 10 B 8 D 12 7 Given= {x :36 -- x 0.33

3 Which of the following is a false statement? A pis a consonant. B 6 is a factor of 258. C 2 is a prime number. D A trapezium is a regular polygon.

5 Which of the following is a true statement? A All even numbers are multiples of 4. B Some birds have wings. C All fish eat meat. D Some polygons have 5 sides.

9 Which of the following are implications for the sentence "h > k if and only if h + 5 > k+5."?

I If h > k, then h + 5 > k + 5. II Ifh 5k. III If h + 5 > k + 5, then h > k. 'A I only B III only

Subtopic 4.3 6 Which of the following is a true statement? A 52=10 or 72=8=6. B 8 + 9 = 17 and 8 x 4 =32. C 5 is a factor of 20 and 7 is a factor of 10. D Hexagons have 8 sides and octagons have 9 sides.

C I and III only D II and III only

Subtopic 4.5 10

7 Which of the following is a true statement? A (42)4 = 46 or 6 - (-5) = 1.

Form a conclusion based on the two given premises. A 122> 10 B 122> 100 C 144> 10 D 144 < 100

B 4 = 0.75 and sin 60° = 0.5.

Subtopic 4.2 4 Which of the following is a false statement? A Some odd numbers are prime numbers. B All multiples of 6 are multiples of 3. C Some perfect squares are negative numbers. D Some pyramids have a square base.

C { } C {2, 3} or -4(-4) = 8. D A trapezium has four sides of equal length and two of its sides are parallel. 11

Subtopic 4.4 8 "If m = -7, then m2 = 49" - The antecedent in the above implication is A m=-7 C m2=-49 B m=7 D m2=49

14

Premise 1: If x > 10, then x2 > 100. Premise 2: 12 > 10

Premise 1 : If 4x < 20, then x < 5. Premise 2: ............................ Conclusion: 4x > 20 Premise 2 in the above argument is A x20

12

Which of the following is the conclusion for the above argument? A All squares have four sides of equal length. B All quadrilaterals are EFGH. C EFGH has four sides of equal length. D EFGH has four right angles. 13

Which of the following is Premise 2 in the argument given? A 42 is a multiple of 12. B 42 is a multiple of 18. C 72 is a multiple of 6. D 7 is a multiple of 12.

Premise 1: All squares have four sides of equal length. Premise 2: EFGH is a square.

Premise 1:

All multiples of 12 are multiples of 6. Premise 2: ........................ is a Conclusion: 42 multiple of 6.

15 Given a number sequence, 5, 14, 29, 50, ..., has the following pattern. 5=3(12)+2 14=3(22)+2 29 = 3(32) + 2 50 = 3(42) + 2 The general conclusion by induction for the number sequence is

Subtopic 4.6 14

All acute angles are less than 90 °. ZKLM is an acute angle. The conclusion by deduction for the argument above is A ZKLM = 900 B LKLM > 900 C LKLM < 900 D LKLM a 90°

A n2, where n = 0, 1, 2, 3, ... B 3n2, where n = 1, 2, 3, 4,...

C n2 + 2, where n = 0, 1, 2, 3,... D 3n2 + 2, where n = 1, 2, 3, 4,...

SICM N B Subjective Questions This section consists of 25 questions. Answer all the questions . You may use a non-programmable scientific calculator. 3 Construct true mathematical statements by using the following numbers and symbols. (a) -12, -11 and >

Subtopic 4.1 1 Determine whether each of the following is a statement. (a) Help me! (b) Kuantan is in Pahang. (c) (-3)3 = 27

(b) 0.25, and < (c) {3, 6, 9}, 3 and E Answer:

Answer:

(a)

(a) (b)

(b) (c)

(c) 2 Complete the following mathematical sentences by using the symbol > or < in the empty box to form

4 Determine whether each of the following statements is true or false. (a) 47 is a perfect square. (b) The highest common factor of 18 and 27 is 9. (c) Some tigers can live in water.

(a) a true statement, (b) a false statement. Answer: (a) -15 (b) 7

J -8 2 3

15

8 Combine the following pair of statements to Answer: (a) (c) form a true statement. Statement 1: -8 x (-3) = 11 (b) Statement 2: 35 is a multiple of 7. Answer:

Subtopic 4.2 5 Determine whether each of the following statements is true or false. (a) All even numbers are multiples of 4. (b) All factors of 12 are factors of 60.

Subtopic 4.4 9 State the antecedent and consequent in each of the following implications.

(a) If k = -4, then k3 = -64.

Answer:

(b) If it rains today, then the football match will be cancelled. Answer: (a)

6 Construct a true statement using the quantifier "all" or "some" based on the given object and property in each of the following. (a) Object: regular polygons Property: 8 sides of equal length (b) Object: workers in a factory-

(b)

Property: wear spectacles (c) Object: triangles Property: right angles

10 State the antecedent and consequent in each of the following implications. (a) If Ismail 's father comes to school late, then Ismail will go home late.

(d) Object: trapeziums Property: two parallel sides

(b) If > 8, then m > 82.

Answer:

Answer:

(a)

(a)

(b) (b)

(c)

(d) 11 Write two implications from each of the following sentences. (a) x > y if and only if 3x > 3y. (b) p is a negative number if and only if p3 is a negative number.

Subtopic 4.3 7 Determine whether each of the following statements is true or false. (a) A cat has four legs and a chicken has four legs. (b) 32 + 52 > 42 and -0.43 < -0.34. (c) 30 is a multiple of 4 and 6. (d) 53= 125 or 25=9=3

Answer: (a) Implication 1: Implication 2:

Answer: (b) Implication 1: Implication 2:

16

18 Form a conclusion by induction for the number sequence, 0, 3, 8, 15, ..., which follows the pattern: 0=12-1 3=22-1 8=32-1 15=42- 1

Subtopic 4.5 12 Form a conclusion based on the following premises. Premise 1: All students of the Form 5K class passed the SPM examination. Premise 2: Azlina is a student of the Form 5K class.

Answer:

Conclusion: ................................................................ 19 Form a conclusion by deduction for the following statements.

Answer:

All parallelograms have opposite sides that are parallel. (general statement)

13 Complete the premise in the following argument: Premise 1 : All regular pentagons have five sides of equal length.

ABCD is a parallelogram. (specific case) Answer:

Premise 2: ................................................................... Conclusion: PQRST have five sides of equal length.

Subtopics 4.1- 4.6 20 (a) Complete the premise in the following argument: Premise 1:If the length of each side of a square is x cm, then the area of the square is x2 cm.

Answer: 14 Complete the conclusion in the following argument: Premise 1: If 5x = 20, then x = 4. Premise 2: x # 4 Conclusion: ................................................................ Answer:

(b)

15 Complete the premise in the following argument: Premise 1: If a number is a factor of 18, then the number is a factor of 54. Premise 2: .................................................................. Conclusion: 6 is a factor of 54.

Premise 2: .......................................................... Conclusion: The area of the square PQRS is 25 cm2. Write down two implications based on the following sentence. "pq>0ifandonly ifp>0andq>0."

Answer: (a) Premise 2:

Answer: (b) Implication 1: 16 Complete the premise in the following argument: Premise 1: ................................................................... Premise 2: p < 6 Conclusion : p + 4 < 10

Implication 2: 21 (a) Complete the premise in the following argument: Premise 1: ...................... 0 ................................... Premise 2: Jamal is not Juliana 's brother. Conclusion: Juliana is not a doctor. (b) Given (Xm)n = x mn, where m, n and x are positive numbers. Find the value of

Answer:

Subtopic 4.6 17 Form a conclusion by induction for the number sequence , 5, 17, 37, 65, ..., which follows the pattern: 5=4(12)+1 17 = 4(22) + 1 37 = 4(32) + 1 65 = 4(42) + 1

(i)

(24)2,

(ii ) (7 4 )8

Answer: (a) Premise 1:

(b) (i) (ii) Answer:

17

(b) Write down Premise 2 to complete the following argument: Premise 1 : If y is less than zero , then y is a negative number. Premise 2 : ......... i ................................................ Conclusion : - 2 is a negative number. (c) Write down two implications based on the following sentence.

22 (a) Complete the conclusion in the following argument: Premise 1: All triangles have the sum of interior angles of 180°. Premise 2: ABC is a triangle. Conclusion: .......... .............................................. (b) Form a conclusion by induction for the number sequence, 3, 10, 21, 36, ..., which follows the pattern: 3=2(12)+1 10=2(22)+2 21=2(32)+3 36 = 2(42) +4

5p > 20 if only if p > 4. Answer: (a) (i) (ii)

(b) Premise 2:

Answer: (a) Conclusion:

(c) Implication 1:

(b) Implication 2:

23 (a) State whether the following statement is true or false.

25 (a) Complete each statement in the answer space with the quantifier "all" or "some" so that it will become a true statement. (b) State the converse of the following statement and hence, determine whether its converse is true or false.

5>3or21=6. (b) Write down two implications based on the following sentence. x'= 64 if only ifx=4.

Ifx>7,then x>4.

(c) Complete the premise in the following argument: Premise 1: All pentagons have five sides. Premise 2: .......................................................... Conclusion: ABCDE has five sides.

(c) Complete the premise in the following argument: Premise 1 : If set P is a subset of set Q, then P fl Q = P. Premise 2 : ........................................................... Conclusion : Set P is not a subset of set Q.

Answer: (a)

Answer: (a) (i) ................... of the multiples of 5 are even numbers.

(b) Implication 1: 4

(ii) ................... hexagons have six sides. Implication 2:

(b) (c) Premise 2:

24 (a) State whether each of the following statements is true or false. (i) 4x2= 8and52=10. (ii) The elements of set P = ( 10, 15 , 20) are divisible by 5 or the elements of set Q = (1, 2, 3) are factors of 4.

(c) Premise 2:

18

5.1 Gradient of a Straight Line 5.2 Gradient of a Straight Line in Cartesian Coordinates

5.3 Intercepts 5.4 Equation of a Straight Line 5.5 Parallel Lines

Objective Questions

SECTION A

This section consists of 25 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 5.1 1 In the following, which straight line PQ has a gradient of 4 ? A

Q

3 Given the gradient of a straight line which passes through points (1, 4) and (2, k) is -3. The value of k is A -7 C 0 B -i D 1 4 The diagram shows a straight line PQ on a Cartesian plane.

6 The coordinates of point Q are (-1, 2) and the gradient of the straight line QR is 3. The coordinates of point R could be A (2, -11) C (2, 9) B (2, -9) D (2, 11) 7 In the diagram, 0 is the origin.

B 5 cm

P

D

The gradient of PQ is A -2

C 1 2

The straight line which has the largest gradient is A PQ C TU B RS D VW

B -2 D 2

Subtopic 5.3

Subtopic 5.2 2 The diagram shows a straight line AB on a Cartesian plane.

5 In the diagram , PQR is a straight line on a Cartesian plane.

8 In the diagram, PQ is a straight line on a Cartesian plane. y

y

y B(6,3) ^x

01 10 Qx A(-2, -5) f

^x

0

The gradient of AB is A -1 C 1 B 2 D 2

The gradient of PQ is

The value of h is Al C 5 B 3 D 7

19

A

-5 3

C

3 5

B

-3 D 5 .5 3

9 In the diagram, FG is a straight line.

13 The diagram shows two straight lines, MN and NP, on a Cartesian plane.

y

18 The gradient of the straight line 3x-5y= 15 is A

-3

C

3 5

y

B - 3 D 5

P(3, 3)

*x

Cc 0

+x

What is the gradient of FG? A -3 C 1 3 B

-3

D

M O The gradient of NP is -3 and the distance of MN is 13 units. Find the x -intercept of MN. A -12 C _ 13 5

3

10 In the diagram, RSTis a straight line on a Cartesian plane. y \R(0, P)

19 Find the y-intercept of the straight line 2x - 5y = 20. A

-5

B

-4

y

14 In the diagram , OPQR is a trapezium. Given 2PQ = OR. y OI L(4, 0)

OI P(6, 0) .x T(2, -3) The x-intercept of the straight line QR is

A B

11 The gradient of a straight line VW is 3. If they-intercept of the straight line VW is 12, the x-intercept is A -36 C 4 B -4 D 36 12 In the diagram, PQ is a straight line with the gradient 1 3

8 C 12 10 D 16

Subtopic 5.4 15 Which of the following points does not lie on the straight line y = 3x - 5? A (-2, -1) C (0, -5) B (-1, -8) D (1, -2) 16 The equation of a straight line which has a gradient of and passes through point (0, -3) is A y= 2x-2 B y= 2x+3 C 2y=x-6 D 2y=x-3

Find the x-intercept of the

straight line PQ. 4

A -12

C

B

D _ 1 12

-4

3

17 The equation of a straight line which passes through points (-3, -3) and (4, 11) is A y=-2x-3 B y=-2x+3 C y=2x-3 D y=2x+3

20

I

D

B -5 D -12 5

^x

The value of p is A 2 C 4 B 3 D 6

2 5 10

20 In the diagram , the straight line HK intersects the straight line KL at K.

R(0, 8) S(1, 0)

C

x

The equation of the straight line KL is 3 A y=-4x3 3 B y=-4x+3

C y=-1 2x-2 1x+2 D y=-2

Subtopic 5.5 21 Which of the following pairs of straight lines are parallel? A y=5+1 y=0.4x+2 B y=-2x+1 2y=4x+2 C 3y+9x=-3 3x - y = 9 D x + Y =5 2 3 2y + 3x = 2 22 Given the straight line y = mx - 5 is parallel to the straight line 4x + 6y = 8. The

value of m is A -3 2

C

2 3

B

D

3 2

-2 3

23 In the diagram, OKLM is a parallelogram. Given the gradient of the straight line OK is 3.

24 In the diagram, PQRS is a parallelogram and RST is a straight line.

25 Which of the following straight lines is parallel to the straight line 3y = x + 6 and passes through point (-6, -4)? A y= 3+2

y

B y= Z+3 C 3y=x-6 D 3y=x-3

O The value of t is A 5 C 7 B 6 D 8

The coordinates of point Tare A (-12, 0) C (0, -6) B (-6, 0) D (0, -12)

SECTION B Subjective Questionsy This section consists of 20 questions. Answer all the questions. You may use a non-programmable scientific calculator.

Subtopic 5.1

Subtopic 5.3 4

Im, Based on the diagram, find the gradient of the straight line MN.

Based on the diagram, state (a) the x-intercept, (b) the y-intercept, of the straight line RS.

Answer:

Answer: (a)

Subtopic 5.2 (b)

2 Find the gradient of the straight line that passes through points (-4, 2) and (-8, 6). Answer:

5 A straight line PQ intersects the y-axis at point R. If the x-intercept of the straight line PQ is 4 and its gradient is -2, find the coordinates of point R. Answer:

3 Given points (1, -7), (4, k) and (6, 4) lie on a straight line. Find the value of k. Answer:

21

10 Find the equation of the straight line which is parallel to y = 4 - 6x and passes through point (-1, 1).

Subtopic 5.4 6 On the diagram in the answer space, draw the

Answer:

straight line y = -ix + 1. Answer:

Subtopics 5.1 - 5.5 In the diagram, the straight line MN is parallel to the x-axis and the length of OK is 2 units.

11

7 Find the points of intersection of the following pairs of straight lines by solving the simultaneous linear equations. (a) y=x+5 (b) 3x+2y=12

Find (a) the y-intercept of the straight line MN, (b) the gradient of the straight line KN. Answer:

y= 1x+4 2x-y=1

(b)

(a) Answer:

12 The diagram shows a rectangle PQRS drawn on a Cartesian plane. y

8 Find the equation of a straight line which passes through each of the following pairs of points. (a) (0, -7) and (3, 2) (b) (-2, 4) and (-8, 1) P(-1, 0) 0

Answer:

(a) Calculate the gradient of the straight line PR. (b) Find the y-intercept of the straight line QS. Answer:

(b)

(a)

In the diagram, the gradient of the straight

13

Subtopic 5.5 9 Determine whether each of the following pairs of straight lines are parallel. (a) y=x-3 (b) 2x-5y=1 3y=x-6 5y=2x+3

line KLM is - 2. Find

M

(a) the value of p, x (b) the x-intercept of the straight line MN.

Answer:

(a)

(b)

I Answer: (a)

22

(b)

y

14

In the diagram, 0 is the origin. The gradient of

18 y G

the straight line ST is 2

S(4, -10)

Find (a) the gradient of the straight line ROS,

^x

O

(b) the y-intercept of

H(10 , -6)

the straight line ST. Answer: (a)

(b)

In the diagram , EF, FG and GH are straight lines. OE is parallel to FG and EF is parallel to GH. Given the equation of EF is 2x+y=6. (a) State the equation of the straight line FG. (b) Find the equation of the straight line GH and hence, state its y-intercept.

Answer:

(b)

(a) In the diagram, 0 is the origin. OPQR is a parallelogram. Find (a) the equation of the straight line PQ, (b) the coordinates of .x point Q.

(a)

16

19 In the diagram, 0 is the origin. Q lies on the x-axis and P lies on the y-axis. The straight line PT is parallel to the x-axis and the straight line PQ is parallel to the straight line RS. The equation of the straight PQ is x + 2y = 10. y

(b)

In the diagram, the straight line PQ is parallel to the straight line OR. Find (a) the gradient of the straight line OR, (b) the y-intercept of the straight line QR.

(a) State the equation of the straight line PT. (b) Find the equation of the straight line RS and hence, state its x-intercept. Answer:

Answer: (a)

(b)

(a)

(b) 20

M(2, 10)

In the diagram, OPQR is a parallelogram and 0 is the origin. Find (a) the equation of the straight line QR. (b) the y-intercept of the straight line PQ.

17

E(0, 6)

0 F(3, 0)

Answer: (a)

y

.x N

The diagram shows a straight line EF and a straight line MN drawn on a Cartesian plane. EF is parallel to MN. Find (a) the equation of the straight line MN, (b) the x-intercept of the straight line MN.

Answer:

(b)

(a)

23

(b)

6.4 Frequency Polygons 6.5 Cumulative Frequency 6.6 Measures of Dispersion

6.1 Class Intervals 6.2 Mode and Mean of Grouped Data 6.3 Histograms

SECTION A

Objective Questions

This section consists of 16 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 6.1

Questions 4 and 5 are based on the following frequency table.

Age Group (years

Score

Frequency

11-20

1-10

5

21-30

11 - 20

15

31 -40

21 - 30

41-50

31-40

Height (cm)

Frequency

10

101 - 110

2

8

111 - 120

5

121-130

6

131 - 140

9

141-150

4

151-160

3

161 - 170

1

Based on the frequency table, the lower limit of the class interval 31 - 40 is A 30.5 C 39.5 B 31 D 40

4 Calculate the size of the class interval in the table. A 7 C 9 B 8 D 10

Length of Rope (m)

5 State the lower boundary of the class interval 11 - 20. C 11 A 10 D 11.5 B 10.5

0.4-0.8

In the table, the missing class interval is A 1.3 - 1.8 B 1.3 - 1.9 C 1.4 - 1.8 D 1.4 - 1.9 3 The largest value in a data is 38 and the smallest value is 12. If the number of class intervals required is 6, then the suitable size of the class interval is A 4 C 6 B 5 D 7

The midpoint of the modal class is A 135 C 136 B 135 .5 D 136.5

0.9 - 1.3 1.9-2.3

7 The frequency table shows the heights of 30 students in a class.

Subtopic 6.2 6 The frequency table shows the lengths of 30 ribbons. Length (cm)

Frequency

40 - 44

3

45 - 49

8

50 - 54

10

55-59

9

The modal class is A 45 - 49 B 49.5 - 54.5 C 50 - 54 D 50.5 - 54.5

24

8 The frequency table shows the marks obtained by 20 students in a game. Marks

Frequency

11 - 15

3

16-20

5

21 - 25

6

26-30

4

31-35

2

Calculate the mean mark. A 20.55 C 21.65 B 21.55 D 22.25

9 The frequency table shows the masses of 20 baskets of mangoes collected by a farmer. Mass of Frequency Mangoes ( kg) 9-11

3

12-14

6

15-17

5

18-20

4

21-23

2

Calculate the mean mass, in kg, of a baseket of mangoes. A 14.4 C 16.4 B 15.4 D 30.8

Subtopic 6.3 Questions 10 and 11 are based on the following histogram. The histogram shows the distribution of the ages of a group of participants in a competition.

Subtopic 6.4 Questions 12 and 13 are based on the following frequency polygon. The frequency polygon shows the thickness of 100 books in a library.

Thickness of book (mm)

12 The modal class is A 10.5 - 15.5 B 11 - 15 C 12 - 15 D 12.5 - 15.5 13 Of the total number of books with a thickness of between

Iq

0 0 0 0 Age (years) ,

10 The mean age, in years, of the group is A 32.0 B 36.8 C 37.3 D 38.6 11 The percentage of the number of participants who are more than 40 years old is A 17 B 20 C 32 D 34

1

Frequency

6 12 10 18 2

Mass of Sugar (kg)

them are written in Malay and the rest are in English. The number of English books with a thickness of between 5 mm and 20 mm is A 32 C 48 B 40 D 60 kr L

Mass of Sugar (kg)

2

3

4 5

Based on the table above, a cumulative frequency table is constructed as follows:

5 mm and 20 mm each, 5 of

0

15 The table shows the distribution of the masses of sugar sold in a market on a certain day.

Upper Cumulative Boundary Frequency

0

0.5

0

1

1.5

6

2

2.5

18

3

3.5

x

4

4.5

46

5

5.5

48

The value of x is 10 B 22 C 28 D 30

Subtopic 6.6 16 The ogive shows the total donation that is collected from 100 donors. Cumulative frequency

Subtopic 6.5 14 Which Of the following is not a step to draw an ogive? A Add one class interval with a cumulative frequency of 0 before the first class interval. B Find the upper boundary of each class interval. C Find the cumulative frequency of each class interval. D Plot the graph of frequency against the upper boundary.

25

The first quartile is A 25 B 30 C 35 D 40

SECTION B Subjective Questions' This section consists of 16 questions. Answer all the questions. You may use a non-programmable scientific calculator. Subtopic 6.1

Subtopic 6.2

1 The data shows the masses, in kg, of 40 boxes that are shipped by a transport company.

3 The data shows the circumferences, in cm, of 30 rubber tree trunks that are sent to a factory to be processed to produce furniture wood.

68 11 59 34 22

42 52 43 61 60

67 45 25 20 36

55 28 46 33 58

56 48 52 42 23

44 26 24 18 48

53 35 44 32 35

56 45 37 57 47

140 165 152 153 157 160 148 143 133 146 127 157 135 140 122 142 151 161 128- 147 137 142 163 131 139 149 141 145 162 150

Construct a frequency table for the data by using the class intervals, 11 - 20, 21 - 30, 31 40 and so on. State the size of the class interval.

(a) Construct a grouped frequency table for the data by using the class intervals, 120 - 129, 130 - 139, 140 - 149 and so on. (b) (i) State the size of the class interval. (ii) State the modal class. (iii) Calculate the mean circumference, in cm, of the trunks.

Answer:

Answer: (a)

2 The data shows the time, in minutes, required by 25 students to solve the mathematical problems in a set of questions. 8 24 15 17 28 7 12 8 11 14 16 12 16 7 21 11 10 13 14 8 26 27 18 30 20

4 The frequency table shows the distribution of the masses of _40 watermelons harvested by a farmer.

Construct a frequency table for the data by using the class intervals, 6 - 10, 11 - 15, 16 - 20 and so on.

Mass (kg)

Frequency

1.5- 1.9

6

Answer:

2.0-2.4

10

2.5 - 2.9

12

3.0-3.4

8

3.5 -3.9

4

(a) State the modal class. (b) Calculate the mean mass, in kg. Answer: (a) (b)

26

8 The frequency table shows the masses of the baskets of prawns transported by a fisherman's boat.

Subtopic 6.3 5 The frequency table shows the distribution of the periods of complete oscillation of 55 pendulums.

Mass (kg)

Frequency

12 - 15

5

16 - 19

7

Period of Oscillation (minutes)

Frequency

20-23

8

2.5 -2.9

6

24-27

12

3.0-3.4

5

28-31

4

3.5 - 3.9

18

32-35

3

4.0-4.4

11

36 - 39

6

4.5 - 4.9

10

5.0 -5.4

5

Construct a frequency polygon based on the frequency table.

Based on the frequency table, draw a histogram.

Subtopic 6.5 6 The frequency table shows the heights of 100 students in a school.

9 Complete the cumulative frequency table below.

Height ( cm)

Frequency

120- 124

8

125 - 129

10

3-5

4

130 - 134

22

6-8,

5

135 - 139

13

9-11

6

140 - 144

12

12 - 14

10

145 - 149

20

15 - 17

8

15

18-20

2

150 - 154

Distance Cumulative Upper Frequency Frequency Boundary (km)

Based on the frequency table, draw a histogram.

Subtopic 6.6 Subtopic 6.4

10 The frequency table shows the distribution of the masses of 45 watermelons in a stall.

7 The frequency table shows the distances travelled by a group of students to school. Distance ( km)

Frequency

31 - 40

7

41-50

8

51 - 60

12

61 - 70

16

71-80

9

81 - 90

5

91-100

3

Mass (kg)

Frequency

1.6 - 2.0

5

2.1 - 2.5

8

2.6 -3.0

9

3.1 - 3.5

12

3.6 -4.0

7

4.1 -4.5

4

(a) Draw an ogive based on the data given. (b) From the ogive, find (i) the median, (ii) the first quartile, (iii) the third quartile.

(a) Draw a histogram. (b) Construct a frequency polygon based on the histogram in (a).

27

Subtopics 6.1- 6.6 13 The data shows the number of foreign workers employed by 40 factories in an industrial area. 24 21 50 33

11 The frequency table shows the lengths of 42 pieces of ribbon used to tie presents. Length (cm)

Frequency

61-63

2

64-66

3

67 - 69

8

70- 72

10

73-75

7

76- 78

6

79 - 81

5

82-84

1

22 25 33 15 65 48 28 11 32 17 48 17 5 28 44 54

43 58 29 37 16 35 68 22

(a) Class Frequency Mid- Cumulative Interval point Frequency 1 - 10

(ii) (iii) 12 The table shows the scores obtained by a group of shooters in a shooting competition. Frequency x Score

10

30

12

60

14

x

16

48

18

36

20

20

42 28 56 1 57

Answer:

(b) (i)

Score

2 65 38 34

(a) Based in the data and using a class interval of 10, complete the table in the answer space. (b) Based on the table in (a), (i) state the modal class, (ii) calculate the estimated mean number of foreign workers in each factory. (c) For this part of the question, use graph paper. Using a scale of 2 cm to 10 foreign workers on the horizontal axis and 2 cm to 5 factories on the vertical axis, draw an ogive for the data. From the ogive, find (i) the median, (ii) the third quartile.

(a) Draw an ogive based on the data given. (b) From the ogive, find (i) the median, (ii) the first quartile, (iii) the third quartile. Answer:

34 28 13 23

(b) (i)

If the total frequency is 20, find the value of x. Answer:

28

Upper Boundary

14 The data shows the volume, in me, of water that is collected in each bottle by 50 participants in a telematch. 142 142 151 154 146

160 148 151 144 158

152 154 137 147 163

145 141 155 154 164

146 152 151 145 157

156 149 140 157 146

151 152 153 158 152

150 138 141 137 153

142 147 138 140 157

Answer: (a)

153 149 139 151 152

Marks

Midpoint

40 - 44

42

Frequency

45-49 50-54 55-59 60 - 64 65-69

(a) Construct a grouped frequency table for the data by using the class intervals, 130 - 134, 135 - 139 and so on. (b) For this part of the question, use graph paper. Using a scale of 2 cm to 5 me on the horizontal axis and 2 cm to 5 participants on the vertical axis, draw an ogive for the data. (c) From the ogive, find (i) the median, (ii) the interquartile range.

16 The data shows the monthly savings, in RM, of 40 students. 46 45 52 47 50

Answer:

60 56 54 45 64 66

68 63 40 58 69 56

59 55 60 46 61 65

61 44 57 67 50 58

44 54 34 40 58

60 32 45 48 51

42 46 52 45 36

38 56 35 42 48

41 40 50 53 56

55 60 36 44 32

(a) Based on the data and using a class interval of 5, complete the table in the answer space. (b) Based on the table in (a), calculate the estimated mean of the monthly savings of each student. (c) For this part of the question, use graph paper. Using a scale of 2 cm to RM5 on the horizontal axis and 2 cm to 1 student on the vertical axis, draw a frequency polygon to represent the data. (d) Based on the frequency polygon in (c), state one piece of information about the montly savings.

15 The data shows the marks scored by 36 students in a monthly mathematics test. 51 65 58 62 68 48

53 37 40 38 44

48 59 49 62 55 64

Answer:

(a) Using the data and a class interval of 5 marks, complete the table in the answer space. (b) Based on the table in (a), (i) state the modal class, (ii) calculate the mean score of the group and give the answer correct to 2 decimal places. (c) For this part of the question, use graph paper. Using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 1 student on the vertical axis, draw a histogram for the data.

(a)

Class Interval

Midpoint

Frequency

31 - 35

33

4

36-40

(b) (d)

29

7.3 Probability of an Event

7.2 Events

7.1 Sample Spaces

Objective Questions=,, This section consists of 25 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 7.1

Subtopic 7.2

Subtopic 7.3

1 A letter is selected at random from the word `MALAYSIA'. Which of the following outcomes is not possible? A A vowel is selected. B A consonant is selected. C Letter S is selected. D Letter T is selected.

5 A letter is selected at random from the word JASMANI'. The elements in the sample space excluding the letter A are A J, S, M, I B J, S, M, N C J, S, M, N, I D J, A, S, M, N, I

8 A factory produces 3 000 computers in a year. 60 of the computers are defective. If a computer is selected at random from the factory, find the probability that the computer is defective.

2 A colour is selected at random from the colours of the traffic lights. All the possible outcomes are A yellow, red, blue B yellow, green, white C green, red, yellow D red, green, blue

3 A prime number less than 13 is selected at random. The sample space is A (3, 5, 7, 11} B {2,3,5,7,11) C {2, 3, 5, 7, 11, 13) D {2,3,5,7,9,11,13}

4 A coin is tossed twice. If H represents heads and T represents tails, the sample space is A {H, T} B {HH, TT, HT} C {HH, TT, HT, TH} D {H, T, HH, TT}

6 Two dice are rolled. M is the event of obtaining two numbers with a sum of 6. The elements of M are A {(2, 3), (3, 2)) B {(1, 6), (2, 3), (3, 2)) C {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)) D {(3, 3), (5, 1), (2, 4), (0, 6), (4, 2))

7 A basket has a green apple and two red apples. Two apples are selected at random from the basket. Which of the following is a possible event? A Two green apples are selected. B An apple and an orange are selected. C A red apple is not selected. D A green apple and a red apple are selected.

30

A 1 60

C 1 40

B 1 50

D

1 30

9 A survey on the monthly expenses of 1 000 residents is carried out in a residential garden. The results are shown in the frequency table below. Monthly Expenses (RM)

Frequency

1 000

180

1 200 1 400

420

1 600

190

210

Find the probability that a resident selected at random has expenses of more than RM1 200. A 3 8 B 2 5 C 3 5 D 3 4

10 The table shows the ages of 4 000 tourists who visited Tioman Island in a certain month. Age (years)

Frequency

25 - 31

160

32 - 38

800

39 - 45

1 250

46 - 52

1 790

If a tourist is selected at random, find the probability that the tourist's age is less than 39 years. A

6 C 3 25 10

B

3 D 2 20 5

11 A dice is tossed 2 400 times. The probability of obtaining a number 4 is 6. Find the number of times that the number 4 can be obtained. A 200 C 400 B 300 D 600 12 In a survey on the sizes of shoes worn by a group of women, it is found that 360 women wear shoes of size 5. If a woman is selected at random from the group, the probability that the woman wears shoes of size 5 is 3. Find the total number of women in the group. A 300 C 480 B 360 D 540 13 There are 16 boys and some girls in a class. If a student is chosen at random from the class, the probability that a girl is chosen is

11 Find the number of girls in the class. A 24 C 32 B 28 D 36

14 A bag contains 6 yellow balls and x red balls. A ball is chosen at random from the bag and the probability of choosing a yellow ball is 1. The value of x is 3 A 12 C 16 B 14 D 18 15 A basket contains 8 mangoes and some mangosteens. If a fruit is selected at random from the basket, the probability of selecting a mangosteen is 1. Find the number of 5 mangosteens in the basket. A 12 C 14 B 13 D 15 16 A box contains 5 red pens and a number of green pens. If a pen is selected at random from the box, the probability of selecting a red pen is 3 . Three additional red pens are added into the box. If a pen is selected at random from the bag, find the probability of selecting a red pen.

18 A cupboard is filled with 35 science books and History books. If a book is selected at random from the cupboard, the probability of selecting a History book is . Then 10 science books and 5 History books are added into the cupboard. A, book is selected at random from the cupboard. State the probability of selecting a Science book. A 1 7 2 B 7 C 2 5 3 D 5 19 A box contains nine cards as shown below.

9

A9 U 9N K❑ A number of cards marked U are added into the box. If a card is selected at random from the box, the probability of selecting a card marked L is 8 . How many cards

A 2 9

marked U are added into the box? A 4 B 5 C 6 D 7

B 1 4 C 4 9 D 3 4 17 There are 20 male workers and 25 female workers *in a factory. 6 of the male workers have cars. If a worker is selected at random from the factory, the probability of selecting a worker who has a car is 5-. The number of female workers who have cars is A 8 B 12 C 16 D 18

31

20 A bag contains 20 pens which are either blue or red. If a pen is selected at random from the box, the probability of selecting a blue pen is 5. Then 8 blue pens are added into the bag. If a pen is selected at random from the box, the probability of selecting a red pen is A 2 C 4 5 7 B

2 D 5 7 7

21 The following number cards are put in a bag. 2

3

6

7

8

10

Then all the cards with numbers that are multiples of 3 are taken out. If a card is chosen at random from the bag, the probability that the number is a multiple of 2 is A 1 3 B 3 5 C 2 3 D 4 5 22 A box contains 40 sheets of paper. 24 of them are red and the rest are orange in colour. Then 10 sheets of orange coloured paper are used up. If a sheet is selected at random from the bag, the probability of selecting an orange sheet is A

3 C 8 20 15 B 1 D 13 5 20

23 The table shows the results of a group of candidates in an examination. Grade

A

B

C

D

E

Number

of Candi- 8 1 dates

11 10 5

Given that grade D is considered fail, if a candidate is selected at random from the group, the probability of selecting a candidate with a pass is C 7 A 11 50 10 D 39 B 13 25 50

25 The incomplete table shows bank notes of four denominations in a bag. Value of RM1 RM2 RM5 RM10 Notes Number of Notes

10

6

12

If a bank note is taken out at random from the bag, the probability of selecting a RM2 note is 61-. The number of bank notes of more than RM2 value is A 8 B 20 C 24 D 36

24 A container has 12 blue beads, 20 green beads and some yellow beads. If a bead is selected at random from the container, the probability of selecting a green bead is 12. The number of yellow beads in the container is A 10 C 16 B 12 D 48

SECTION B Subjective Questions This section consists of 10 questions. Answer all the questions. You may use a non-programmable scientific calculator.

Subtopic 7.1

Subtopic 7.2

1 An even number is chosen at random from the numbers, 6, 7, 8, 9, 10, 11 and 12. Write all the outcomes of the experiment.

3 A letter is selected at random from the word 'ENGLISH' Write the following events. (a) A vowel is selected. (b) A consonant is selected.

Answer: Answer: (a) 2 Box P contains a red card and a yellow card. Box Q contains a red card and a blue card. A card is selected at random from each box. By using a suitable letter to represent each coloured card, write the sample space for the experiment.

(b)

Answer:

32

4 A bag is filled with six cards numbered 20, 22, 24, 26, 28 and 30. Two cards are selected at random. Determine whether each of the following events is possible.

7 A box contains 24 green cards, 30 yellow cards and 26 white cards. If a card is selected at random from the bag, find the probability that the card is (a) a white card.

(a) Two multiples of 4 are selected. (b) Two prime numbers are selected.

(b) not a yellow card.

(c) At least one multiple of 5 is selected.

Answer:

Answer: (a)

8 All the cards in the diagram are put into an empty box.

(b)

G

(c)

0 G

R

A

H

Y

If a card is selected at random from the box, find the probability that the card is marked with (a) the letter H, (b) a vowel.

Subtopic 7.3

Answer:

5 A school has 1 200 students. If a student is selected at random, the probability of selecting a prefect is 4U . Find the number of prefects 9 A box contains 24 fifty sen coins and a number of ten sen coins. If a coin is selected at random from the box, the probability of selecting a ten

in the school. Answer:

sen coin is 5 (a) Find the total number of coins in the box. (b) If 8 fifty sen coins are added into the box, find the probability a coin selected at random is a fifty sen coin.

6 The table shows the marks scored by 160 students in a mathematics test. Marks

Number of Students

51 - 55

16

56 - 60

50

61 - 65

72

66- 70

22

Answer:

10 There are 72 red chairs and blue chairs in a class. If a chair is selected at random from the class the probability of selecting a blue chair

If a student is selected at random from the group, find the probability that his score is (a) in the class interval 61 - 65, (b) less than 61 marks.

is 2. 3 (a) Find the number of blue chairs in the class. (b) If 4 red chairs and 2 blue chairs are taken out from the class, find the probability that a chair selected at random is a red chair.

Answer: (a)

Answer:

(b)

33

8.1 Tangents to a Circle 8.2 Angles between Tangents and Chords

8.3 Common Tangents

SECTION A Objective Questions ` This section consists of 30 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 8.1 1 The diagram shows a circle with centre O. FH and GH are tangents to the circle.

The value of y is A 10 C 20 B 15 D 35

Subtopic 8.2 6 In the diagram, PQR is a tangent to the circle QST at Q.

4 In the diagram, PQ is a tangent to the circle with centre O. PO is parallel to the straight line QR.

P

Which of the following is not true? A FH = GH B p° = q° C r°=s° D LOFH # 90° 2 In the diagram, PQ and PR are tangents to the circle with centre O.

Q

The value of x is

A B P 5cm Q

The radius, in cm, of the circle is A 4.46 C 5.65 B 5.32 D 6.12

25 65

C D

72 82

7. In the diagram, ABC is a tangent to the circle BDEF at B.

5 In the diagram , XY and ZY are tangents to the circle with centre O. The value of x is A 48 C 56 B 54 D 59

R

The value of x is A 25 C 60 B 50 D 65 3 In the diagram, JL and KL are tangents to the circle with centre O.

8 In the diagram, PUV and PQR are tangents to the circle QSTU. The length of XY, in cm, correct to two decimal places is A 10.39 B 11.24 C 12.69 D 12.81

34

ZSQR is equal to 12 In the diagram, PQ and PS 16 In the diagram, the tangent are tangents to the circle QRS MPN touches the circle PQRS A ZPQU C ZQTU B LQSU D LQUS with centre O. with centre 0 at P. R

9 In the diagram , JKL is a tangent to the circle KFGH at K. S

P

The value of y is A 45 C 60 B 50 D 65 The value of q is A 55 C 70 B 65 D 75

13 In the diagram, the tangents QR and SR touch the circle PQS at Q and S respectively. Q

10 In the diagram, JKN is a tangent to the circle KLM with centre O. JLOM is a straight line.

The value of x + y is A 50 C 70 B 60 D 80 17 The diagram shows a circle PQRS with diameter PTR. The tangent PU touches the circle at P. QTS is a straight line.

The value of x is A 25 C 35 B 30 D 40 14 In the diagram , PQS is a circle with centre O. The tangent RST touches the circle at S. POQR is a straight line. The value of x is A 29 B 32 C 34 D 35 11 In the diagram , ABF is a tangent to the circle BCDE with centre O. BOD and COEF are straight lines.

18 In the diagram , ABC and ADE are tangents to the circle BDF. E

The value of x is A 15 C 45 B 30 D 60 15 In the diagram , MPN is a tangent to the circle PQRS at P. PTR and QTS are straight lines.

Calculate the values of x and y. A x=25,y=40 B x=25,y=65 C x=25,y=75 D x=30,y=50

The value of y is A 70 C 90 B 80 D 100

A-

B,

The value of x is A 50 C 60 B 55 D 65 19 In the diagram , PQR and TSR are tangents to the circle QVUS.

P

The value of x is A 30 C 55 B 45 D 65

35

The value of x + y is A 124 C 132 B 128 D 144

20 In the diagram, QRS is a circle with centre O. PST is a tanget to the circle at S. PQOR is a straight line.

24 In the diagram , PQR is a tangent to the circle QST at Q. P

The length, in cm, of AB is A 2.47 C 3.17 B 2.67 D 3.47 28 In the diagram, MN is a common tangent to the two circles with centres 0 and C respectively.

R

The value of x is A 20 C 40 B 30 D 60 21 In the diagram, JKL is a tangent to the circle KMNP at K.

The length of arc QS is equal to the length of arc ST. Find the value of x.

A B

28 34

C D

56 68

25 In the diagram, SRT is a tangent to the circle with centre 0 at R. OQT, OUR and PUQ are straight lines.

29 In the diagram, PQ is a common tangent to the two circles with centres 0 and C respectively.

1'The value of y is C 95 A 55 B 85 D 125 22 In the diagram, QRS is a circle with centre O. PQT is a tangent to the circle at Q.

Find the value of x. A 15 C 35 B 20 D 55

Subtopic 8.3 26 In the diagram, HG is a common tangent to the two circles with centres E and F respectively.

P

The value of x is A 30 C 60 B 40 D 70 23 In the diagram, JKN is a tangent to the circle KLM at K and LMN is a straight line.

If the length of OC is 15 cm, calculate the value Qf LMOC. A 81°40' C 84°10' B 82°20' D 85°20'

G Calculate the length, in cm, of HG. A 14.96 C 15.67 B 15.45 D 15.87

Find the area, in cm2, of quadrilateral COPQ. A 104.4 C 110.2 B 108.6 D 120.4 30 In the diagram , PQR is a common tangent to the two circles with centres M and N respectively. LSR is a tangent to the circle with centre N. LMNQ is a straight line and MN = 4 cm.

27 The diagram shows two circles with centres 0 and C respectively. PQ is a common tangent to the two circles. OABC is a straight line. P Calculate the length, in cm, of QR. A 5.12 C 6.28 B 5.66 D 6.64

The value of y is A 20 C 40 B 30 D 50

36

SECTION B Subjective Questions This section consists of 10 questions. Answer all the questions. You may use a non-programmable scientific calculator. In the diagram, ABC is a tangent to the circle BDEF at B. BGE and DGF are straight lines. Calculate the value of

Subtopic 8.1 In the diagram, RS is a tangent to the circle with centre 0 and ROV is a diameter of the circle. STV is a straight line. Calculate R 10 cm'

D (a) x

b (c) Z.

(a) ZTRS,

Answer:

(b) the length, in cm, of VT.

(a)

(c)

Answer: (a)

(b)

(b) 5

2

In the diagram, QRST is a circle with centre 0. The tangent PQ touches the circle at Q. Calculate the value of (a) x, (b) y, (c) Z.

In the diagram, KL and KM are tangents to the circle with centre O. Calculate (a) ZKOL,

(b) the length, in cm, of KO.

Answer: (a)

Answer: (a)

(c)

(b)

(b)

In the diagram, the circle BCD with centre D O has a radius of 5 cm. AB and AC are tangents to the circle. Calculate (a) the value of x, (b) the value of y, (c) the length, in cm, of AC.

Subtopic 8.2 3

In the diagram , PQR is a tangent to the circle QST. Calculate the value of (a) x, (b) y. P Q

R

Answer:

Answer:

(a)

(a)

(b)

(b)

37

(c)

Subtopics 8.1 - 8.3

Subtopic 8.3

9 In the diagram, PQ is a common tangent to the two circles with centres 0 and C respectively.

7 In the diagram, PQ is a common tangent to the two circles with centres 0 and R respectively.

Given OP = 8 cm and RQ = 6 cm, calculate (a) the length , in cm, of PQ, (b) LPOR. Answer:

Given OP = 5 cm and CQ = 3 cm, calculate (a) the value of x, (b) the length, in cm, of PQ.

(a)

Answer: (a)

(b) (b)

8 The diagram shows, two circles with diameters OK and MK respectively. 0 is the centre of the big circle. KL is a common tangent to the circles.

10 In the diagram, ABD is a common tangent to the two circles with centres 0 and C respectively. OBC is a straight line.

M

Given OK = 7 cm, calculate (a) the length, in cm, of KL, (b) the area, in cm2, of the shaded region. ) (Use It = 272 7

Calculate (a) LB CD, (b) the radius, in cm, of the circle with centre C. Answer: (a)

Answer: (a)

(b)

(b)

38

9.1 The Values of Sin 0, Cos 6 and Tan 8

9.2 Graphs of Sine, Cosine and Tangent

SECTION A Objective Questions `^ This section consists of 35 questions . Answer all the questions . For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 9.1 1 In the diagram, 0 is the centre of the semicircle PQRS. y Q(-0.5, 0.866)

\X. Which of the following is not true? A sin x° 0.866 B cos x° = 0.5 C tan 180° = 0 D sin 90° = 1 2 2 cos 60° - tan 45° _ A -1 C 0 B - -L D 1 2 2 3 4 cos 180° + 2 sin 90° _ A -6 B -2 C 2 D 6 4 6 sin 30° - 3 tan 360° _ A -3 B 0 C 3 D 6 5 Given cos x° = -0.2079 and 0° , x° < 360°. The values of x are A 78 and 102. B 78 and 282. C 102 and 258. D 102 and 282.

6 Given tan 8 = 0.7265 and 180° -_ 8 , 360°, the value of 6 is A 216° C 306° B 234° D 324° 7 Given sin 8 = -0.9205 and 0° -- 8 , 360°, the values of 8 are A 67° and 113°. B 113° and 247°. C 113° and 293°. D 247° and 293°. 8 Given tan p° = -7.12 and 0° , p° -- 360°, find the values of p. A 82 and 262 B 98 and 262 C 98 and 278 D 262 and 278 9 Given cos 6 = -0.8116 and 90° s 6 , 180°, find the value of 8. A 125°45' C 144°15' B 135°45' D 154°15' 10 In the diagram, QRS is a

11 In the diagram , cos LBAC 5 13

B The length, in cm, of BC is A 18 C 24 B 20 D 26 12 In the diagram , ADC is a straight line. A

Given BD = 15 cm, tan LBAD 8 and tan LCBD = 3 , calculate the length, in cm, of ADC. A 18 C 24 B 20 D 34 13 In the diagram, KLM is a straight line.

straight line and cos x° = 4 5, I

12 cm K 15 cm ZZ:

0 L M

Q The value of sin y° is A -4 C 3 5 5 B -3 D 4 5 5

39

What is the value of cos 8? A -12 C 5 13 13 B - 5 D 12 13 13

14 In the diagram , KMN and MLP are straight lines. Given KM : MN = 2: 1 and cos LLKM = 5 .

Find the value of cos LPSR.

A -4 5

C 3 5

B -3 5

4

D

22 In the diagram , QRST is a trapezium and PQR is a

straight line. S T4,*mLI

5

18 In the diagram, DEF is a straight line.

P

a R Q 7 cm

The value of cos 0 is

Find the value of sin LMPN. 1 C 9 A 3 5 B 5 D 9 9 4

R

F The value of tan ZDEG is A -1.376 C -0.5878 B -0.8090 D 0.8090

T 12 cm

cos LSPR = 4 5

S

U Find the value of tan x°. C -4 5 3 4

A -5 3

5 cm P

15 cm

T

Find LQRT. A 67°23' C 157°23' B 112°37' D 161°34'

B Find the length, in cm, of QR. A 8 C 18 B 9 D 25

21 In the diagram , PQRS is a rectangle . Given PT = 3TQ

-3 4

dan tan x° = 4 3 P

D 5 3

It is given that cos x° = 8 17 and tan y° = 2. Calculate the length, in cm, of EFG. A 19 C 38 B 31 D 46 25 In the diagram, R is the midpoint of the straight line QS. Q

T4 cm Q R 18 cm

17 In the diagram, PQRS is a rhombus. RST is a straight line. P 5cm Q

T

F

The length, in cm, of LMN is A 12 C 24 B 18 D 30

A -4 C 4 3 3

24 In the diagram, EFG is a straight line.

K

P

The value of tan x° is

3

20 In the diagram, LMN is a straight line. Given KM = 6 cm.

16 In the diagram, PTR and QTS are straight lines. Given ST 3 cm.

B

23 In the diagram , PQRS is a straight line and PQ = QR.

19 In the diagram, PQR is a straight line. Given

15 In the diagram , PQST is a rectangle. Given QR : RS =1 : 4. Q

A -4 C 3 5 5 B -3 D 4 5 5

x° S

R

S

C 4

The value of cos x° is 3 C 4 A 5 4

5 3

B

Find the value of sin y°.

A 3 5 B

3 4

5

D

40

4 5

D 3 5

26 In the diagram , KMN is a right-angled triangle.

30 In the diagram, PQS is a straight line. Given sin LPST = 5 and

The value of k is A 90° C 270 B 180° D 360°

tan ZQSR = 12. 34 Which of the following represents the graph of y = cos x? A y

P 12 cm T N

It is given that LN = 10 cm, KM = 12 cm and L is the midpoint of KM. Find the value of tan 6.

1 S

0

The length, in cm, of PQ is A 7 C 10

A -5 C -3 4 4

B

B -4 D -4 3 5 27 In the diagram , PQS and RST are straight lines. Given tan x° = 2 and cos y° 5

8

D

13

-1

B

31 In the diagram, ABCD is a rectangle. BEC is a straight

y

0

line and BE = ? BC. 3 12 cm D

A

Y

C 1

6 cm 0 10°

B E C The value of tan LAEC is S 8cm

The length, in cm, of RST is A 12 C 20 B 16 D 24 28 In the diagram, QRS is a straight line. Given tan LPSQ = 1. P

A -4 3

C 4

B -3 4

D

D

32 In the diagram , ABCD is a rectangle . ADF and BEF are straight lines. Given CE = ED

35 Which of the following represents the graph of y=sinxfor0°x 180°? A y A

8 cm 12 cm

Q R 6cmS B C

B

The value of tan LBED is

C 4

A

4 3 B 1 D 4

A 4 C 3

3

29 In the diagram , PST and QRS are straight lines.

-4 B

4 D 4 3

C

Subtopic 9.2

15 cm S

T

33 The diagram shows the graph of y = cos x. y

D

Find the value of cos 0.

A -4 5

B

-2 5

Y

3 3 2

and tan LAFB = 3. 4

The value of tan LPRQ is

C 5 4 D 3 2

41

11

X

0° 11

SECTION B

Subjective Questions

This section consists of 10 questions. Answer all the questions . You may use a non-programmable scientific calculator. 4 (a), Given sin 8 = 0.9397 and 0° 8 = 360°, find the values of 8. (b) Given cos a = 0.4352 and 0° a 360°, find the values of a. (c) Given tan f3 = -3.354 and 00 , P - 360°, find the values of P.

Subtopic 9.1 1 In the diagram , 0 is the centre of the circle PQRST.

Answer:

O >W1 Q(0.866, -0.5)

State the values of (a) sin w°, (b) tan 270°, (c) cos 180°.

In the diagram, EFG is a straight line. Find the values of (a) sin x°, (b) cos y°.

Answer:

(b) Answer: (a) 2 Without using a scientific calculator, calculate the values of (a) sin 30° + cos 180°, (b) 4 tan 45° - 3 sin 270°, (c) -5 cos 60° - sin 90°.

(b)

Answer: 6

(a)

G

(b) (c) 3 Find the values of (a) sin 143°, (c) tan 310°, (b) cos 307°15', (d) tan 207.4°.

Answer: (a)

Answer:

(b)

42

In the diagram, DEF and DHG are straight lines. (a) State the values of sin x°. (b) Calculate the cm, length, in of FG.

7 In the diagram , ACD is a straight line.

Subtopic 9.2 9 On the axes in the answer space, sketch the graph of each of the following functions. (a) y = sin x for 0° x 3600 (b) y = cos x for 0° x 3600 (c) y = tan x for 00 x 360° Answer:

Given sin LACB = 3 , find the values of (a) cos x°,

(a) Y

(b) y.

Answer:

0•x

(a)

(b) x

(c) 8 In the diagram , PQST is a rectangle and 2QR = RS.

y A

0

12 cm

10 The diagram shows the graphs of y = sin x and y = cos X. y

Find the values of (a) cos x°,

)- x

(b) tan y°.

Answer: (a) Find the coordinates of (a) point P, (b) point Q.

(b)

Answer: (a)

(b)

43

Form 4

Angles of Elevation and Depression

10.1 Angles of Elevation and Depression

SECTION A Objective Questions This section consists of 20 questions . Answer all the questions . For each question , choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 10.1 1 In the diagram, JKL and MN are two vertical poles on a horizontal plane.

I K 11

L

The height, in m, of the flag pole is A 3.56 C 3.72 B 3.68 D 3.82 4 In the diagram, K, L and M are three points on a horizontal plane. MN is a vertical tower. Given KLM is a straight line and L is the midpoint of KM.

N

The angle of elevation of point I from point M is

A LJMK C LKJM B LJML D LLMN 2 In the diagram , KL and MN are two vertical poles on a horizontal plane. P is a point on KL and MN = PL. K M

3 In the diagram, EG is a vertical flag pole on a horizontal plane. The angle of elevation of G from F is 24°. G

7 In the diagram, PQ and RS are two vertical poles on a horizontal plane. The angle of elevation of S from Q is 35°. S

The angle of elevation of N from K is A 50°10' C 51°47' B 50°24' D 53°57' 5 In the diagram , X and Y are two points on a horizontal plane. YZ is a vertical pole.

L N The angle of depression of M from K is

A LKML C LNKP B LMKP D LPMK

The angle of elevation of T from P is A 37°52' C 51°3' B 38°57' D 52°7'

Z 8m X

12

m

Q

it

Calculate the value of x. A 5.4 C 14.0 B 11.0 D 18.0 8 In the diagram, EF and GH are two vertical poles on a horizontal plane. E

y 30 m

The angle of depression of X from Z is A 26°24' C 32°24' B 28°46' D 33°41' 6 In the diagram, QS and RT are two vertical poles on a horizontal plane. PQR and PST are two straight lines.

44

20 m

G F 40 m r

The angle of depression of peak G from peak E is 25°. Calculate the height , in m, of the pole GH. A 9.33 C 18.65 B 11.35 D 25.34

9 The diagram shows two vertical poles, PQ and RS, on a horizontal plane. R

The angle of depression of peak P from peak R is 32°. Calculate the angle of elevation of peak P from S. A 28°57' C 41°19' B 41°11' D 61°3' 10 In the diagram, FG is a vertical flag pole on a horizontal plane EF. G

12 In the diagram, F, G and H are three points on a horizontal plane, forming an equilateral triangle FGH. GK and HL are vertical poles. The angle of elevation of K from F is 65°.

Find the angle of elevation of L from G. A 41°16' C 43°12' B 42°35' D 44°14' 13 In the diagram , EH and FG are two vertical poles on a horizontal plane. The angle of depression of G from H is 30°.

15 In the diagram, PRS is a vertical pole on a horizontal plane. The angle of elevation of R from Q is 20°.

The height, in in, of the pole is A 14.46 C 23.10 B 16.28 D 50.21 16 In the diagram, P, Q and R are three points on a horizontal plane. RS is a vertical pole.

H

Q E 25 m F

5m

The angle of elevation of G from E is 48°. The height, in in, of the flag pole is A 16.73 C 22.51 B 18.58 D 27.77 11 In the diagram, P and Q are two points on a horizontal plane. PS is a ladder which leans on a vertical wall QR.

E 8m ^F The height, in in, of the pole EH is

A 9.14 C 9.54 B 9.26 D 9.62 14 In the diagram, P, Q and R are three points on a horizontal plane. RS is a vertical pole.

Given the angle of elevation of S from Q is 40°. The height, in in, of the pole RS is A 4.06 C 4.20 B 4.12 D 4.28 17 In the diagram, K, L and M are three points on a horizontal plane. KP and LQ are two vertical poles. Given ZKLM = 90° and the angle of elevation of Q from P is 25°.

P 10 m

s

3m K

13 m 12 m

Given the angle of depression of P from S is 60°. Find the length, in in, of RS. A 2.3 C 6.9 B 3.1 D 7.7

Given ZPQR = 90°, find the angle of elevation of S from P. A 26°34' C 28°12' B 27°14' D 29°31'

45

The height, in in, of the pole LQ is A 5.10 C 5.33 B 5.16 D 5.68

18 In the diagram, PU, QT and RS are three vertical poles on a horizontal plane . The angle of elevation of T from U is 15° and the angle of depression of S from T is 35°.

19 In the diagram, E, F and G are three points on a horizontal plane where EFG is a straight line. FH is a vertical lamp post. The angle of elevation of H from E is 42° and the angle of depression of G from H is 50°.

20 In the diagram , PS and RT are two vertical poles on a horizontal ground . The angle of elevation of S from . Q is 60° and the angle of depression of Q from T is 35°.

H [

Calculate the distance, in m, of QR. A 4.08 C 4.24 B 4.14 D 4.39

E 10m F G The distance, in m, of FG is

A 6.45 B 7.56

C 10.73 D 13.24

The difference in distance, in m, between PQ and QR is A 1.61 C 6.19 B 3.34 D 18.65

SECTION B Subjective Questions This section consists of 8 questions. Answer all the questions. You may use a non-programmable scientific calculator. Answer:

Subtopic 10.1

(b)

(a) 1

In the diagram, Q and R are two points on horizontal ground. PR is m a vertical pole. Q Find (a) the angle of elevation of P from Q, (b) the distance of QR in m.

12 m

Answer: (a)

2 e

(b)

In the diagram, E, F and G are three points on a horizontal plane where EFG is a straight line. GT is a vertical pole. Given the angle of elevation of T from F is 65° and EF = FG.

Calculate (a) the length, in m, of FG, (b) the angle of elevation of T from E.

In the diagram, P and Q are two points on a horizontal plane. PR is a vertical flag pole. The angle of depression of Q from R is 48°.

Answer: (a)

Find (a) the height, in m, of the flag pole, (b) the length, in m, of QR.

46

(b)

4

L 10m

In the diagram, K, L and M are three points on a horizontal plane where KLM is a straight line. KN is a vertical tower. Given the angle of elevation of N from M is 58° and KL = LM.

Calculate (a) the angle of depression of T from U, (b) the height, in m, of the pole SV. Answer:

(b)

(a)

Calculate (a) the height, in m, of the tower,

(b) the angle of elevation of N from L. Answer: (a)

(b) 7

In the diagram, A, B and C are three points on a horizontal plane and LACB = 90°. BE and CD E are two vertical poles. 5m 20 m

5

B

Calculate (a) the angle of elevation of D from A, (b) the angle of depression of E from D.

In the diagram, U and V are two points on a horizontal plane. UX and VW are two vertical flag poles. The angle of elevation of W from X is 24°.

Answer:

(a)

(b)

Calculate (a) the height, in m, of the flag pole UX, (b) the angle of depression of V from X. Answer: (a)

8

(b)

E 6m F 5mG

In the diagram, E, F and G are three points on a horizontal plane where EFG is a straight line. EP and GQ are two vertical poles.

Calculate

(a) the angle of elevation of P from F, (b) the height, in m, of the pole GQ. Answer:

6 U 7m

In the diagram, R, S and T are three points on a horizontal plane and ZRTS = 90°. RU and SV are two vertical poles. Given the angle of elevation of U from V is 20°.

Form 4

I

I

Lines and Planes in 3-Dimensions

11.1 Angles between Lines and Planes

SECTION A

11.2 Angles between Two Planes

Objective Questions

This section consists of 20 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator. Subtopic 11.1 1 The diagram shows a right prism with a horizontal rectangular base ABCD.

3 The diagram shows a right pyramid with a rectangular base PQRS.

F

6 The diagram shows a right prism with a horizontal rectangular base PQRS. The isosceles triangle PQW is the uniform cross section of the prism. M is the midpoint of PQ. V

Q

Which of • the following is not true? A BCFE is an inclined plane. B ABE is a vertical plane. C Line AB is normal to the plane ADFE. D Line DF is the orthogonal projection of line CF on the plane ABCD.

What is the angle between line NQ and the base PQRS? A ZNQR C LNSQ B LNQS D LQNS 4 The diagram shows a cuboid.

The angle between line SW and the base PQRS is A LMSR C LMWS B LMSW D LRSW 7 The diagram shows a right prism with a horizontal rectangular base PQRS.

w 2 The diagram shows a right prism with a horizontal rectangular base PQRS. The vertex V is vertically above point O.

The angle between line KR and the plane KNSP is A ZNKR C LRKS B LNRK D LSKN 5 The diagram shows a cube.

P

Q

Name the angle between line RV and the plane RSW. A LPRV C LRVW B LQRV D LVRW 8 The diagram shows a cuboid with a horizontal base JKLM.

F

The angle between line SV and the plane PRV is A LOPS C LOSV B LOSR D LOVS

G

The angle between line FN and the plane KLMN is A LFLN C ZFNL B LFNK D LHFN

48

S

R

Name the angle between line JP and the plane JMQ. A LPJM C LPMQ B LPJQ D LPQ J 9 The diagram shows a cuboid with a horizontal rectangular base the KLMN.

12 The diagram shows a pyramid with a horizontal square base ABCD. The vertex E is vertically above point O. M is the midpoint of AB.

B

The angle between line KR and the base KLMN is A 26°34' C 63°26' B 53°8' D 68°12' 10 The diagram shows a right prism with an isosceles triangle PQR as its horizontal base. M and N are the midpoints of, QR and TU respectively.

C

The angle between the planes ABE and ABCD is A LEMO C LEAO B LEBO D LBAE 13 The diagram shows a right prism with a horizontal rectangular base ABCD. P and Q are the midpoints of BC and AD respectively.

15 The diagram shows a right pyramid. The vertex E is vertically above point D. E

Name the angle between the plane BCE and the base ABCD. A LADE B LEAD C LEBC D LECD 16 The diagram shows a cuboid with a rectangular base EFGH.

5 cm

Q Calculate the. angle between line PN and the plane QRUT. A 26°34' C 63°26' B 32°24' D 68°12'

The angle between the planes BCE and BCF is A LEPF C LPEF B LEPQ D LPEQ 14 The diagram shows a cuboid. M is the midpoint of DH.

The angle between the plane EFM and the base EFGH is A LEFG C LFMG B LFEM D LGFM 17 The diagram shows a right prism with an isosceles triangle as its horizontal base. M and N are the midpoints of SU and PR respectively.

Subtopic 11.2 11 The diagram shows a cuboid. W

Q

Name the angle between the planes PQVW and PQRS. A LVPQ C L VQR B LVPR D LWPR

Name the angle between the plane BCM and the base ABCD. A LBCD C LDBM B LBCM D LDCM

49

R

Name the angle between the planes PQR and QSU. A LMQN C LRQU B LNMQ D LSQN

18 The diagram shows a cuboid with a horizontal base PQRS. T

W

19 The diagram shows a cuboid with a horizontal base PQRS.

20 The diagram shows a right prism with a rectangular base ABCD. The right- angled triangle BCF is the uniform cross section of the prism.

P Q Name the angle between the planes PSWV and PSTU.

A LRWS B LSWT C ZSWU D ZTSW

SECTION B

P 12 cm

Q

Calculate the angle between the planes SUV and TUVW. A 33°41' C 63°26' B 56°19' D 74°32'

Calculate the angle between the planes BCE and BCF. A 16°42' C 73°18' B 33°24' D 84°21'

Subjective Questions

This section consists of 20 questions. Answer all the questions. You may use a non-programmable scientific calculator. 2 The diagram shows a right prism with a horizontal rectangular base ABCD. M and N are the midpoints of the BC and AD respectively.

Subtopic 11.1 1 The diagram shows a right prism with a rectangular base KLMN.

Name (a) the angle between line BE and the base ABCD, (b) the angle between line EM and the base ABCD.

Name (a) the horizontal planes, (b) the vertical planes, (c) the inclined planes, (d) the normals to the plane KLMN, (e) the orthogonal projection of line KP on the base KLMN.

Answer:

Answer: 3 The diagram shows a pyramid with a horizontal square base PQRS. The vertex V is vertically above point S.

(a)

(b) (c)

(d) (e)

Name (a) the angle between line QV and the base PQRS,

50

(b) the angle between line RV and the base PQRS.

Identify and calculate the angle between line KR and the base KLMN.

Answer:

Answer:

(b)

(a)

4

The diagram shows a right prism with a rectangular base ABCD. Trapezium BCGF is the uniform cross section of the prism.

K

The diagram shows a right prism . The base KLMN is a horizontal rectangle . The right10 cm angled triangle LMQ is J '^ the uniform cross L 7 cm M section of the prism.

Identify and calculate the angle between line KQ and the base KLMN.

B

Name (a) the angle between line AG and the base ABCD, (b) the angle between line AG and the plane CDHG.

Answer:

Answer: 8

The diagram shows a pyramid. The right-angled triangle BCE is a horizontal plane and the square ABCD is a vertical plane. Given CE = 12 cm.

5 The diagram shows a pyramid VEFGH. E

Identify and calculate the angle between line DE and the base BCE. Answer:

E 24 cm F The base EFGH is a horizontal rectangle. N is the midpoint of EH. The apex V is 10 cmvertically above point N. Calculate the angle between line FV and the base EFGH.

Answer:

9

6 The diagram shows a cuboid with a rectangular base KLMN.

The diagram shows a pyramid with a rectangular base PQRS. The vertex E is vertically above point S.

Identify and calculate the angle between line QV and the base PQRS.

R

Answer:

51

13 The diagram shows a right prism. The rightangled triangle JKL is the uniform cross section of the prism.

Subtopic 11.2 The diagram shows a right pyramid with a triangular base ABC. M is the midpoint of AB. The vertex D is vertically above point C.

10

L

Name (a) the angle between the planes ABD and ABC, (b) the angle between the planes BCD and ACD.

Identify and calculate the angle between the plane JPQ and the plane PQLK.

Answer:

Answer:

(b)

11 The diagram shows a cuboid. V

W

14 The diagram shows a right prism with the triangle PQU as its uniform cross section. M and N are the midpoints of PQ and RS respectively. V

Name (a) the angle between the plane RSTU and the base PQRS, (b) the angle between the plane PQV and the base PQRS, (c) the angle between the planes PTV and PSWT.

Identify and calculate the angle between the plane PQV and the base PQRS. (c)

Answer:

12 The diagram shows a right prism with a horizontal square base EFGH. The trapezium FGML is the uniform cross section of the prism. The rectangular surface GHNM is vertical while the rectangular surface EFLK is inclined. K

15 The diagram shows a cuboid.

N

S

K 8 cm L

Identify the angle between the plane KLS and the base KLMN.

F 12 cm G

Calculate the angle between the plane EFN and the base EFGH.

Answer:

Answer:

52

16 The diagram shows a right pyramid with a horizontal square base ABCD. M is the midpoint of BC. E

Subtopics 11.1, 11.2 19 The diagram shows a cuboid. H 12 cm G

AL

Identify and calculate the angle between the plane BCE and the base ABCD. Answer:

Calculate (a) the length, in cm, of BH, (b) the angle between the line BH and the base ABCD, (c) the angle between the planes BHG and EFGH. Answer: (a)

17 The diagram shows a cuboid. M is the midpoint of AB.

(b)

(c)

20 The diagram ' shows a right prism with an equilateral triangle ABC as its uniform cross section . M, N and P are the midpoints of DF, AC and BC respectively.

Calculate the angle between the planes GHM and EFGH.

Answer:

18 The diagram shows a right prism with a rectangular base PQRS.

P

8 cm

B

(a) Calculate the length, in cm, of MP. (b) Calculate the angle betweerf line MP and the base ABC. (c) Name the angle between the planes MNP and ACFD.

Q

Answer:

Identify and calculate the angle between the planes QSV and RSVW.

(a)

Answer: (b)

(c)

53

12.1 Numbers in Bases Two, Eight and Five

SECTION A Objective Questions This section consists of 35 questions. Answer all the questions. For each question, choose only one answer. You are may use a non-programmable scientific calculator.

Subtopic 12.1 1 State the value of digit 3 in base ten in the number 5368. A 8 C 24 B 11 D 192 2 What is the value of digit 2 in base ten in the number 20415? A 50 C 127 B 125 D 250

7 Given the value of digit 4 in a certain number is 100. The possible number is A 3425 C 14015 B 4178 D 240810 8 Express 4710 as a number in base two. A 1010102 B 1011112 C 1101002 D 1110102

3 4768 = A 84+8'+86 B 4x8°+7x81+6x82 C 4x82+7x81+6x8° D 4x83+7x82+6x81

9 Express 23810 as a number in base five. A 13435 B 14135 C 14235 D 14535

4 In which of the following does digit 1 have the highest value? A 1445 B 21910 C 71528 D 1000002 4

10 Express 41710 as a number in base eight. A-6418 B 6468 C 7128 D 7148

5 In which of the following does digit 3 have the value of 7510? A 3145 B 5308 C 34025 D 43168 6 The value of digit 7 in the number 41718 is 7 x 8,,. The value of n is A 1 B 2 C 3 D 4

11 Express 11102 as a number in base ten. A 810 B 1010 C 1210 D 141Q 12 Express 2435 as a number in base ten. A 6910 B 7310 C 7810" D 8110

54

13 Express 11418 as a number in base ten. A 59210. C 60910 B 59810 D 61410 14 Express 101010112 as a number in base eight. A 2538 C 2738 B 2718 D 3168 15 Convert 378 to a number in base two. A 11112 B 101112 C 111102 D 111112

16 Express 2318 as a number in base five. A 10235 C 11045 B 11035 D 11135 17 Express 11435 as a number in base eight. A 2558 C 2758 B 2658 D 3158 18 Convert 100112 to a number in base five. A 215 B 235 C 315 D 345 19 Convert 1235 to a number in base two. A 1001012 B 1001102 C 1010012 D 1011012

20 Express 23 + 2 as a number in base two. A 1012 B 10012 C 10102 D 100012

25 Express 2(84) + 8 as a number in base eight. A 10108 B 20108 C 100108 D 200108

21 Express 24 + 23 + 1 as a number in base two. A 11012 B 110002 C 110012 D 1100012

26 Express 82 + 6 as a number in base two. A 1001102 B 10001102 C 10011002 D 11001102

22 Express 54. + 4 as a number in base five. A 10045 B 40045 C 100045 D 400045

27 Given 2k48 is a three-digit number in base eight. Find the value of k if 2k48 = 101011002. A 4 C 6 B 5 D 7

23 Express 55 + 2(54) + 52 as a number in base five. A 1201005 B 1201105 C 1201205 D 1210105

28 1012 + 11112= A 101002 B 101102 C 110002 D 111002

24 Express 83 + 6 as a number in base eight. A 20068 C 100068 B 10068 D 100168

29 1011012 + 1112 = A 1100102 B 1101002 C 1101102 D 1110002

30 110112 + 11102= A 1010012 B 1011012 C 1100012 D 1110012 31 10112 - 1012= A 112 C 101 2 B 1002 D 1102 32 101012 - 10112 = A 1102 C 10102 B 10002 D 11002 33 1100102 - 11012= A 101012 B 1001012 C 1001112 D 1011012 34 Given that 1112 + P= 101102, find the value of P. A 10112 B 11002 C 11102 D 11112 35 Given that M - 101112 =10112, find the value of M. A 11002 B. 1000102 C 100100.2 D 1100102

SIOWN d Subjective Questions This section consists of 15 questions. Answer all the questions. You may use a non-programmable scientific calculator. 2 State the value of the underlined digit in base ten in each of the following. (a) 578 (b) 1638 (c) 41228

Subtopic 12.1 1 State the value of the underlined digit in base ten in each of the following. (a) 11012 (c) 110010112 (b) 1010112

Answer: (a)

Answer: (a)

(b) (b) (c) (c)

55

9 Express 1008 as a number in (a) base two, (b) base five.

3 State the value of the underlined digit in base ten in each of the following. (c) 11345 (a) 435 (b) 2105

Answer:

Answer: (a)

(a)

(b)

c) 10 Express 1015 as a number in (a) base two, (b) base eight.

(b)

A nswer: (a)

4 Express 2910 as a number in (c) base five. (a) base two, (b) base eight, Answer: (a)

(b)

11 (a) Express 7210 as a number in base five. (b) Express 1115 as a number in base eight.

(c)

Answer: (a)

(b)

12 (a) Express 4 x 83 + 3 x 8° as a number in base eight. (b) Express 628 as a number in base two.

5 Express 11011002 as a number in (a) base ten, (b) base eight. Answer:

Answer:

6 Express 24 +2 2 + 2 + 1 as a number in (a) base two, (b) base eight.

13 Given 1k18 is a three-digit number in base eight. Find the value of k in each of the following. (a) M. = 8910 (b) 1k18 = 11000012

Answer: (a)

(b)

(b)

Answer: (a) 7 Express 53 + 3 as a number in (a) base five, (b) base eight.

14 Find the value of each of the following. (a) 100112 + 10112 (b) 111002 - 1102

Answer: (a)

(b)

(b)

Answer: 8 (a) The value of digit 4 in the number 24325 is 4 x 5^. State the value of n. (b) Express 50810 as a number in base five. 15 Solve each of the following. (a) 10012 + 101112 (b) 110002 - 112

Answer: (a)

(b)

I Answer:

56

13.1 Graphs of Functions 13.3 Region Representing Inequalities in 13.2 Solution of an Equation by the Graphical Method Two Variables

SECTION A Objective Questions This section consists of 20 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator. 3 The diagram shows the graph of the function y = k - 2x".

Subtopic 13.1 1 The diagram shows four straight lines drawn on a Cartesian plane.

Y

T- r1 Y

Find the values of n and k. A n=-2andk=2 B n=-2andk=4 C n=2andk=2 D n=2andk=4

Which straight line is the graph of the function y = 2x - 5? A PQ C PS D PT B PR

6 The diagram shows the graph ofy=x2+2.

4 In the diagram , the equation of the straight line PQR is y = -2x" + c. Y

From the graph, find the value ofywhen x=-2. A 2 C 6 B 5 D 8 7 The diagram shows the graph ofy=8- x3.

P Q(1, 3) R

2 The diagram shows the graph of the function y = 2 - x". Y

0

The value of c is A 4 C 6 B 5 D 7 5 The diagram shows the graph of y = 4x". Y

(2, p)

The value of n is A -1 B 1 C 2 D 3

01 The value of p is

A -2 C 2 B

-1

D

57

4

From the graph, find the value of x when = 0. A 0 C 4 B 2 D 8

8 Which of the following graphs represents y = ax", where n = 3 and a < 0? A Y

Subtopic 13.2

Subtopic 13.3

10 The diagram shows the graph of the function y = x2 - 6.

13 Which of the following is not true? A Point (0, -6) satisfies the equation y = -3(x + 2). B Point (-2, 0) satisfies the equation y = -3(x + 2). C Point (- 1, -4) satisfies the inequality y < -3(x + 2). D Point (-3, 2) satisfies the inequality y > -3(x + 2).

C B

Y x

A suitable straight line is drawn to find the value of x which satisfies the equation x2-x- 6=0. Which of the following is the line? A y=-x C y=2x B y=x D 2y=x

2 D

14 Which of the following shaded regions satisfies the inequalities y > x + 2, x+y -- 5 and y < 5?

A Y

11 The graph represents the

Y

function 6 Y=x

C

9 Which of the following graphs represents y = x2 - 4?

A

Y

From the graph, the value of x which satisfies the equation

D

Y =x+2 5

x - 3x=0is B

A B

1 2

C D

3 6

12 The graph represents the function y = x2 - 4x + 4.

0

15

x 5

Y

Y..

C x

D

Y

0

From the graph, the values of x which satisfy the equation x2 - 3x = 0 are A 0 and 1 C land 4 B Oand3 D 3and4

58

The shaded region in the diagram is defined by the following inequalities except A y,0 B y-2x C x -5. (b) Write down two implications based on the following statement: p3 = 8 if and only if p = 2. (c) Complete the premise in the following argument: Premise 1

..................................................................................................................................... .......................

Premise 2 : J * 3 Conclusion : x 0 9 [5 marks]

106

8 Five cards in Diagram 5 are put into a box. S

C

L

E

DIAGRAM 5 Two cards are selected at random from the box. The first card is returned to the box before the second card is selected. Calculate the probability of selecting (a) the letter L on the first card or a vowel on the second card, (b) a consonant on the first card and the letter E on the second card. [5 marks] 9 Given matrix M = 1 -2 , find 2 5 (a) the inverse matrix of.M. (b) hence, using matrices, the values of u and v that satisfy the following simultaneous equations: u-2v=8 2u + 5v = 7 [6 marks] 10

In Diagram 6, 0 is the centre of a semicircle with a diameter of 28 cm. OPM is a quadrant of a circle with centre O. Given M is the midpoint of OB. Using it _ 22 , find (a) the area, in cm2, of the shaded region, (b) the perimeter, in cm, of the shaded region. [6 marks]

11

Diagram 7 shows the speed-time graph of the movement of a particle for a period of 24 seconds. (a) State the uniform speed, in m s-1, of the particle. (b) If the distance travelled in the first four seconds is 56 m, calculate (i) the value of v, (ii) the total distance, in m, travelled by the particle. [6 marks] 4 10 24 ' Time (s)

Speed (m s-1) A v 12 9

0

DIAGRAM 7

Section B [48 marks] Answer four questions from this section. 12 (a) Complete Table 1 with the values of y for the function y = 2x2 - 3x - 7. x

-2

y

7

-1.5

-1

0

1

-2

-7

-8

2

3

[3 marks]

4

2

TABLE 1 (b) For this part of the question, use graph paper. You may use a flexible curve rule. Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, draw the graph of y=2x2-3x-7for-2_- x,4. [4 marks] (c) From your graph, find (i) the value of y when x = 2.8, (ii) the values of x which satisfy 2(x2 - x) = x + 7. [3 marks] (d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation 2x2 - 4x - 5 = 0 for -2 , x , 4. State these values of x. [2 marks]

107

13 (a) Transformation P is a reflection in the line x = 2 and transformation R is an anticlockwise rotation of 900 about the centre (1, 0). State the coordinates of the image of point (4, 2) under each of the following transformations: (i) R (ii) PR (iii) RP [5 marks] PTUV, PQRS and ABCD, Diagram 8 shows three quadrilaterals, (b) drawn on a Cartesian plane. (i) PQRS is the image of ABCD under the combined transformation WV. Describe in full the transformation: (a) V (b) W (ii) It is given that quadrilateral ABCD represents a region with an area of 14 cmz. Calculate the area, in cmz, of the region represented by the shaded region. [7 marks]

DIAGRAM 8

14 The data in Diagram 9 shows the marks obtained by 60 students in a test. 43 58 66 24 35 54

54 64 31 28 47 35

27 75 64 34 56 64

24 56 58 27 50 64

67 64 49 63 57 54

57 56 41 49 26 34

46 48 29 28 52 75

46 24 34 29 54 64

45 42 63 45 32 51 53 73 60 37 27 46

DIAGRAM 9 (a) Based on the data in Diagram 9 and using a class interval of 10, complete Table 2. [3 marks]

Marks

Frequency

Lower Boundary

Upper Boundary

21 - 30

11

20.5

30.5

TABLE 2 [3 marks] (b) Based on Table 2 in ( a), calculate the estimated mean mark obtained by a student. (c) For this part of the question , use graph paper. Using a scale of 2 cm to 10 marks on the horizontal axis and 2 cm to 2 students on the vertical axis, [6 marks] draw a histogram and a frequency polygon on the same diagram to represent the data .

108

15 You are not allowed to use graph paper to answer this question. (a) Diagram 10(i) shows a solid with a rectangular base ABCD on a horizontal plane. The triangle FGH is an inclined plane and the triangle EFG is a horizontal plane. The edges AF, BH, CG and DE are vertical and BH = 2 cm.

DIAGRAM 10(i) Draw to full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X. [3 marks] (b) A solid right prism is joined to the solid in Diagram 10(i) at the vertical plane BCKH to form a combined solid as shown in Diagram 10(ii ). The right-angled triangle BCM is its uniform cross section. The base ABMCD is on a horizontal plane.

L 2 cm M

DIAGRAM 10(ii) Draw to full scale (i) the plan of the combined solid, [4 marks] (ii) the elevation of the combined solid on a vertical plane parallel to AD as viewed from Y. [5 marks]

16 P(21°S, 67°W), Q and R are three points on the surface of the earth. Q is due north of P and arc PQ subtends an angle of 56° at the centre of the earth. PR is a diameter of the common parallel of latitude. (a) Find (i) the latitude of Q, (ii) the longitude of R. [4 marks] (b) An aeroplane took off from Q and flew due south along the longitude 67°W until it reached P. Then it flew due east along the parallel of latitude of P until it reached R. (i) Find the total distance, in nautical miles, travelled by the aeroplane. (ii) If the average speed of the aeroplane is 800 knots, calculate the time, in hours and minutes, taken for the whole journey. [8 marks]

109

Time : One hour and fifteen minutes

PAPER 1

This question paper consists of 40 questions. Answer all the questions. Each question is followed by four options, A, B, C and D. For each question, choose only one answer. You may use a non-programmable scientific calculator. 1 Round off 88 450 to three significant figures. C 88 400 A 884 B 885 D 88 500

7 Diagram 2 is drawn on a grid of squares.

10 In Diagram 4, ABC is a straight line and AD = BD.

2 Express 0.0043 in the standard form. A 4.3 x 104 C 4.3 x 10-4 B 4.3 x 10-3 D 4.3 x 10-5 3 Express 83+4x8'+3 as a number in base eight. A 1438 C 10438 B 10318 D 14318

4 Express 245 as a number in base two. A 1102 C 11102 B 10102 D 11112 5 4.3 x 10-5 + 2.4 x 10-6 = A 4.54 x 10-6 B 4.54 x 10-5 C 4.54 x 10-2 D 4.54 x 10-'

DIAGRAM 2 Shape P' is the image of shape P under a translation. Which of the points, A, B, C or D, is the image of point Q under the same translation? 8 In Diagram 3, ABC is a tangent to the circle with centre 0, at B. CDOE is a straight line.

6 In Diagram 1, J, K, L and M are some vertices of a regular polygon. KLN is a straight line.

K L

N

DIAGRAM 1 The number of sides of the polygon is A 11 B 12 C 13 D 15

The value of x is

A B

75 80

C D

85 90

11 In Diagram 5, ABCDEF is a regular hexagon and DEGH is a parallelogram. G

DIAGRAM 5 DIAGRAM 3

M,

DIAGRAM 4

The value of x is A 22 C 56 B 34 D 87 9 Given the formula H = mq2, find the value of m if H = 4.6 x 107 and q = 2.5 x 102. A 1.84 x 103 B 1.84 x 102 C 7.36x102 D 7.36 x 103

110

Calculate the value of x. A 80 B 55 C 40 D 20 12 Given cos x° = -0.2588 and 90° , x° , 180°, find the value of x. A 75 B 105 C 125 D 175

13 In Diagram 6, PQR is a straight line and sin x° = 3 5 S

17 Diagram 9 shows a right prism with a horizontal rectangular base ABCD. The right-angled triangle EAB is the uniform cross section of the prism. M and N are the midpoints of EF and AD respectively.

Q DIAGRAM 6

F

Calculate the length, in cm, of QS.

3cmB

DIAGRAM 7

DIAGRAM 9 The angle between the plane CMN and the plane ADFE is A ZCMF B ZCND C LDNF D ZDNM 18 Diagram 10 shows the position of a car and a tower which are on a horizontal plane.

Calculate the value of sin LDCE. A -12 C 5 13 12 5 12 B D 13 13 15 D(32°N, 60°W) and F(p°N, 120°E) are two points on the surface of the earth. Given the shortest distance of DF is 4 920 nautical miles. Calculate the value of p. A 32 C 82 B 66 D 114 16 In Diagram 8, P, Q and R are three points on a horizontal plane.

C D

6 8

A p-'q-3 C pq3 B pq-3 D pq6 23 Given that 81 = 3", find the value of n. A -4 B -3

C D

2 3

24 Given 1 p , 6 and 3 , q 10, find the maximum value of q - p. A 4 C 9 B 7 D 10

an, '100 M,

DIAGRAM 10 The angle of elevation of the peak of the tower from the car is 24°. The height, in m, of the tower is A 41.01 B 44.52 C 89.43 D 137.03

A h= 1

B h=

The bearing of R from Q is A 115° C 335° B 133° D 342°

then p = A 3 B 5

25 Diagram 11 shows the graph ofy=nx3-6.

1 19 Given that h - h = k' k express h in terms of k.

DIAGRAM 8

21 Given P 3 7 - (1 -p)=8,

22 p2q3 - (pq2)3 =

A 4.47 C 10 B 7.21 D 13

14 In Diagram 7, ACE is a straight line.

20 p2+(3q +p)(3q-p)= A 9q2 B 2p2 + 9q2 C 2p2 - 6pq D 2p2 + 6pq + 9q2

C h=

2k k-1

D h=2k-1

111

DIAGRAM 11 The value of n is A -3 C 2 B -2 D 3 26 Given t ={x: 10,x 8 Consequent: m > 82 11 (a) Implication I: If x > y, then 3x > 3y. Implication 2: If 3x > 3y, then x>y. (b) Implication 1: If p is a negative number, then p3 is a negative number. Implication 2: If p3 is a negative number, then p is a negative number. 12 Azlina passed the SPM examination. 13 PQRSTis a regular pentagon. 14 5x m 20 15 6 is a factor of 18. 16 If p < 6, then p + 4 < 10. 17 4n2+1,n=1,2,3,4,... 18 n2-1,n=1,2,3,4,... 19 ABCD has opposite sides that are parallel. 20 (a) The length of each side of the square PQRS is 5 cm. (b) Implication 1: If pq > 0, then p>0andq>0. Implication 2: If p > 0 and q > 0, then pq > 0.

21 (a)

If Juliana is a doctor, then Jamal is Juliana's brother. (b) (i) 28 = 256 (ii) 72=49 22 (a) Triangle ABC has a sum of interior angles of 180°. (b) 2n2 + n, n =1, 2,3,4,... 23 (a) True (b) Implication 1: If x3 = 64, then x = 4. Implication 2: If x = 4, then x3 = 64. (c) ABCDE is a pentagon. 24 (a) (i) False (ii) True (b) -2 is less than zero.

19 (a) y=S (b) y=-2 -3;-6 20

(a) y = -2x + 14 (b) 7

TOPICAL ASSESSMENT 6 Section A : Objective Questions 3 B 1 B 2 C 4 D 8 D 9 B 7 B 6 C 11 D 12 B 14 D 13 C 16 B Section B : Subjective Questions

(c) Implication 1: If 5p > 20, then p>4. Implication 2: If p > 4, then

5p>20. 25 (a) (i) Some (ii) All (b) If x > 4, then x > 7. False (c) PfQ*P

Mass (kg)

Tally

Frequency

11 -20 21 - 30 31-40 41 - 50 51 - 60 61 - 70

III Hill 411111 4fl1flif l 4ft1 8ftf III

3 6 7 11 10 3

Size of the class interval = 10 2

TOPICAL ASSESSMENT 5 Section A : Objective Questions 1 C 2 C 3 D 4- B 6 D 7 D 9 D 8 B 11 B 12 C 13 B 14 C 16 C 17 D 18 C 19 B 21 D 22 B 23 C 24 C Section B : Subjective Questions 3 1 4 2 -1 3

5B 10 C 15 C

5 10 15 20 25

Time (minutes )

Tally

6-10 11 - 15 16-20 21-25 26 - 30

1411 101111 1+1 II 1111

D B A B C 3 (a)

--2-

5 4 (a) -3

(b) -2

Frequency 6 8 5 2 4

Circumference (cm)

Tally

Frequency

120-129 130 -139 140 -149 150 -159 160-169

III aflt 44914111 R1 .191

3 5 11 6 5

(b) (i) 10 (ii) 140 - 149 (iii) 146.17 cm 4 (a) 2.5-2.9 (b) 2.625 kg

5 (0, 8) 6

5 Frequency

O

-em u'-:..

20

(b) (2, 3)

10

7 (a) (-2, 3) 8 (a) y=3x-7

15+

(b) y= 2 x+5 (b) Parallel 9 (a) Not parallel 10 y=-6x-5 11 (a) 8 (b) 2 12 (a) 2 (b) 12 13 (a) p=5 (b) 10 14 (a) - 2 (b) -12

2.45 2.95 3.45 3.95 4.45 4.95 5.45 Period of oscillation (minutes) 6 Frequency 25i

15 (a) y=2x- 18 (b) (12,6) 16 (a) 2

(b) 5 17 (a) y=2x-18 (b) 12 18 (a) x=3 (b) y=-2x+ 14;14

119

0 1 9.5 124.5 129.5134.5 139.5 144.5 149.5 154.5 Height (cm)

14 (a)

11 (a)

7 (a), (b) Frequency

Length (cm)

Frequency

20

58 - 60 61 - 63 64-66 67 - 69 70 - 72 73 - 75 76-78 79 - 81 82 - 84

0 2 3 8 10 7 6 5 1

40.5 50.5 60.5 70.5 80.5 90.5 100.5 110.5 Distance (km)

Cumulative Upper Frequency Boundary 0 2 5 13 23 30 36 41 42

60.5 63.5 66.5 69.5 72.5 75.5 78.5 81.5

Volume (mt)

Frequency

130 - 134 135 - 139 140 -144 145 - 149 150 - 154 155 -159 160 - 164

0 5 8 10 17 7 3

Cumulative Upper Frequency Boundary 0 5 13 23 40 47 50

134.5 139.5 144.5 149.5 154.5 159.5 164.5

84.5

Cumulative frequency 8 Frequency 12 10 8 6 4

/

2 0 7.5 11.5 15.5 19.5 23.5 27.5 31.5 35.5 39.5 43.5 Mass (kg)

5

0'

9 Cumulative Upper Frequency Boundary

Distance (km)

Frequency

3 -5 6-8 9-11

4 5 6

4 9 15

5.5 8.5 11.5

12 - 14

10

25

14.5

15 - 17 18 - 20

8 2

33 35

17.5 20.5

10 (a) Mass (kg)

Frequency

1.1-1.5 1.6-2.0 2.1-2.5 2.6-3.0 3.1-3.5 3.6-4.0 4.1-4.5

0 5 8 9 12 7 4

Cumulative Upper Frequency Boundary 0 5 13 22 34 41 45

1.55 2.05 2.55 3.05 3.55 4.05 4.55

Ii

'

f4

60.5 63.5 66.5 69.5 72.5 75.5 78.5 81.5 84.5 Length (cm)

(b) (i) 72 cm (ii) 68.5 cm (iii) 76 cm 12 x=84 13 (a) Class Interval

Frequency

Midpoint

1- 10 11-20 21- 30 31-40 41-50 51 - 60 61- 70

3 5 11 8 6 4 3

5.5 15.5 25.5 35.5 45.5 55.5 '65.5

0:'- + i +-Yi 134.5 139.5 144.5 149 .5 154.5 159.5 164.5 Volume (ml) Upper Cunwlative frequency Boundary

3 8 19 27 33 37 40

10.5 20.5 30.5 40.5 50.5 60.5 70.5

(b) (i) 21 - 30 (ii) 33.75

(c) (i) 150.25 mP (ii) 9.75 mP 15 (a)

Marks

Midpoint

Frequency

40 - 44 45 - 49 50 - 54 55 - 59 60 - 64 65 - 69

42 47 52 57 62 67

2 5 3 10 9 7

(b) (i) 55 - 59 (ii) 57.56 marks (c)

Cumulative frequency 4

Frequency

40 10+ 35 9+

10i

1.55 2.05 2.55 3.05 3.55 4.05 4.55 Mass (kg)

(b) (i) 3.1 kg (ii) 2.4 kg (iii) 3.5 kg

51 0.5 10.5 20.5 30.5 40.5 50.5 60.5 70.5 Number of foreign workers

I (c) (i) 31.5 (ii) 44.75

120

39.5 44.5 49.5 54.5 59.5 64.5 69.5 Marks

16 (a) Class Interval 31-35 36 - 40 41 - 45 46 - 50 51- 55 56 - 60

Midpoint Frequency 33 38 43 48 53 58

4 8 9 7 7 5

(b) RM45.50 (c)

Section B: Subjective Questions 1 (a) 25° (b) 19.43 cm 2 (a) 54° (b) 13.61 cm 3 (a) 70 (b) 66 4 (a) 28 (b) 28 (c) 5 (a) 60 (b) 60 (c) 6 (a) 124 (b) 56 (c) 7 (a) 13.86 cm (b) 81°47' 8 (a) 11.75 cm (b) 63 cm' 9 (a) 35

58 90 9.40 cm

(b) 7.75 cm 10 (a) 58° (b) 7.5 cm

TOPICAL ASSESSMENT 9 Section A: Objective Questions 1 B 2 C 3 B 4 C 5 6 A 7 D 8 C 9 C 10 11 C 12 D 13 B 14 B 15 16 A 17 B 18 A 19 B 20 21 A 22 B 23 D 24 C 25 26 B 27 C 28 D 29 A 30 31 B 32 A 33 B 34 B 35

Monthly savings (RM)

(,i) 19 students whose monthly savings is more then RM45. (Accept other possible answers.)

TOPICAL ASSESSMENT 7 Section A: Objective Questions 1 D 2 C 3 B 4 C 6 C 7 D 8 B 9 B 11 C 12 D 13 B 14 A 16 C 17 B 18 D 19 C 21 B 22 B 23 C 24 C

5C 10 A 15 A 20 B 25 B

Section B : Subjective Questions 1 (6,8, 10, 12) 2 S = {(RP, RQ), (Re, BQ), (Y,, RQ), (Ye, BQ)} 3 (a) {E, I} (b) (N, G, L, S, H) 4 (a) Possible (c) Possible (b) Not possible 5 390 33 6 (a) 9 (b) 20 80 5 7 (a) 13 (b) 40 8 1 1 8 (a) (b) 9 3 8 9 (a) 60 (b) 17 10 10 (a) 48 (b) 33

Section B : Subjective Questions 1 (a) -0.5 (b) Undefined (c) -1 2 (a) 0.5 (b) 7 (c) -3.5 3 (a) 0.6018 (c) -1.1918 (b) 0.6053 (d) 0.5184 4 (a) 70° and 110° (b) 64°12' and 295°48' (c) 106°36' and 286°36' 5 (a) 0.7660 (b) -0.1736 3 6 (a) (b) 9.6 cm 5 7 7 (a) (b) 128°56' 9 3 3 8 (a) (b) 5 4 9 (a) y

5 10 15 20 25 30

A A C B B B

(b)

Z/'180- 20K360°

10 (a) (45 °, 0.7071) (b) (225°,-0.7071)

121

5 10 15 20

D D A B

Section B: Subjective Questions 1 (a) 36 (b) 5.51 m 2 (a) 33.32 m (b) 44.83 m 3 (a) 5.6 m (b) 46°58' 4 (a) 32 m (b) 72°39' 5 (a) 3.66 m (b) 16°58' 6 (a) 30°15' (b) 2.27 m 7 (a) 33°41' (b) 10°37' 8 (a) 53°8' (b) 1.52 m

TOPICAL ASSESSMENT 11 Section A : Objective Questions 1 D 2 D 3 B 4 C 5 C 6 B 7 D 8 B 9 C 10 A 11 C 12 A 13 A 14 D 15 D 16 D 17 A 18 D 19 A 20 C

. v=tanx,.

TOPICAL ASSESSMENT 8 Section A : Objective Questions 1 D 2 B 3 C 4 B 6 C 7 D 8 D 9 B 11 A 12 B 13 C 14 B 16 B 17 B 18 B 19 C 21 B 22 B 23 B 24 D 26 D 27 A 28 B 29 C

C C C B B A A

TOPICAL ASSESSMENT 10 Section A: Objective Questions 1 A 3 A 4 D 2 D 6 A 7 D 8 B 9 B 11 B 12 B 13 D 14 A 16 C 17 C 18 D 19 B

x

Section B : Subjective Questions 1 (a) KLMN (b) KNP, LMQ MNPQ (c) KLQP (d) MQ, NP (e) KN 2 (a) ZEBN (b) LEMN 3 (a) LSQV (b) ZSRV 4 (a) LCAG (b) ZAGD 5 21°48' 6 LRKM=28°18' 7 LQKM=21°48' 8 LDEC = 22°37' 9 LVQS=35° 10 (a) ZDMC (b) ZACB 11 (a) LPST or LQRU (b) LVQR (c) LVTW 12 36°52' 13 LJPK = 51°21' 14 ZVMN = 21 °48' 15 LSKN=33°41' 16 LEMO = 41°25' 17 33°41' 18 ZQSR = 36°52' 19 (a) 13 cm (b) 13°21' (c) 36°52' 20 (a) 5 cm (b) 36°52' (c) ZCNP

FORM 5 TOPICAL ASSESSMENT 12 Section A: Objective Questions

-'i i4 ;if ,11,1411""' •

y=x'-3x

lul 11 N Section B : Subjective Questions 1 (a) 4 (b) 32 (c) 64 2 (a) 7 (b) 48 (c) 2048 3 (a) 20 (b) 50 (c) 125 4 (a) 111012 (b) 358 (c) 1045

1.5

(b) 1548

6.7

6 (a) 101112

:M1,11 M % 4"k

(b) k=6 (b) (-3, 0)

3 (a) n=-1 4 (a) n=3 5 (a)

5 (a) 10810

iff

5

8

2

.: Ft .

0 TV

a .u

1.3

a'

5

(b) 278 7 (a) 10035 (b) 2008

4-111

3t }

u x

10

8 (a) n=2 (b) 40135

-lit

9 (a) 10000002

(c) Draw the straight line y =x + 5; X=-2.65,2.55

E r

(b) 2245 10 (a) 110102

^

t

a

i

(b) 328

t a

8 y> 2x,x--5,y--2x

y

r`

TO,

9 yx-3,4x+3y 12,xa'0 10 y--x+5,y+2x0,x 0

11 (a) 2425 (b) 378 12 (a) 40038

_

r

(b) 1100102

h 17

l} a 4

:

tV

13 (a) k=3 (b) k=4

2

14 (a) 111102 (b) 101102

t

t;

fi 8

15 (a) 1000002 (b) 101012

(c) (i) y=2.2 6 (a)

TOPICAL ASSESSMENT 13 Section A: Objective Questions 1 B 2 D 3 D 4 B 5 C 8 D 9 A 10 B 6 C 7 D 11 C 12 B 13 D 14 C 15 D 16 A 17 C 18 B 19 A 20 C

x

x

(ii) x =1.65

-0.5 2 3

12

y 2.3 -4 -3

(b) y rr H

.r!

Section B : Subjective Questions 1 (a) y x-2y=4 ^^ x 4

13

r t^ i s , 1 r ^,

(b) 14

0

x

122

"TI

44,

14 (a)

-2

1

2.5

-2

7

1.4

4

15 (a) (i) (5, -3) (ii) (a) (5, -1) (b) (2,-3) (b) (i) (a) R : A reflection in the line y = 4 (b) S : An enlargement of scale factor 2 with centre (1, 4) (ii) 41.1 cm2 16 (a) (i) (1,2) (ii) (0, 4) (iii) (-4, 7) (b) (i) (a) V : A reflection in the line x = -2

i IA

5

(b) W : An enlargement of scale factor 3 with centre (1, 7)

(ii) 192 m2 TOPICAL ASSESSMENT 15 Section A : Objective Questions 1 B 2 A 3 C 4 A 6 B 7 B 8 D 9 B 11 B 12 B 13 A 14 C 16 D 17 D 18 B 19 B 21 C 22 B 23 D 24 C 26 B 27 D 28 D 29 C

6

(c) (i) y = 5 (ii) x=-2.3,-0.35,2.6 (d) Draw the straight line y = x + 1; x = -2.15, -0.2, 2.3 15 (a) 1 1.5 9

1

0.9

(b), (d)

(c) Draw the straight line y = x + 5; x=-2.35,0,2.4 TOPICAL ASSESSMENT 14 Section A: Objective Questions 1 D 2 C 3 B 4 A 5 B 6 C 7 D 8 A 9 C 10 B Section B: Subjective Questions 1 (a) 4CBE (b) ABCE 2 (a) MURK (b) LtVRK 3 y

7 (a) (1, 4) 8 (a) (4, 0) 9 (a) (1, 2)

(b) (3, -2) (b) (1, 2) (b) (5, 6)

123

A A B B A C

Section B : Subjective Questions 1 (a) 3 (b) 2 (c) 3x2 2 (a) -3 (b) 9 (c) 8 3 (a) p= l (b) q=2 4 (a) x= -3 (b) y= l (c) z=4 5 (a) ( 4 3 ) (c)

10 (a) V : A translation ( 4) 0 W : A rotation of 180 about the centre (5, 3) (b) A rotation of 180° about the centre (3, 3) 11 (a) P A reflection in the line EHM (y=2) Q An enlargement of scale factor 3 with centre E(1, 2) (b) 72 unite 12 (a) (i) (4, 0) (ii) (7, 1) (iii) (10, 0) (b) (i) (a) U An anticlockwise rotation of 90° about the centre A (2, 3) V An enlargement of scale factor 3 with centre A(2, 3) (ii) 9 cm2 13 (a) (i) (-6, 5) (ii) (-6, 9) (b) (i) A reflection in the line AD (ii) A clockwise rotation of 90° about the centre (-6, 6) (c) (i) (-6, 3) (ii) 45.8 unite 14 (a) (i) (2, -1) (ii) (0, -1) (b) (i) T : A clockwise rotation of 90° about the centre (0,5) V An enlargement of scale factor 2 with centre E(-3, 1) (ii) 60 m2

5 10 15 20 25 30

(3) (b) 3 6 (a) p=-2

(10)

(b) q=3

7 (a) 4 6 / 8 (a) (-2) 0 9 (a)

2 \ -1 4 /

(b)

8 1 6 2 )

10 •(a)

(b)

(c)

11

( -2 3 ) 2 1 9 5 ^--y 2 -1 ) 3 -1 2

(a)

3 5 2 2 2 -3

(b)

2 3 1 31

(c)

(b)

\ -6 77 /

(b) m=3,n=-5

2 -2 3 2)

(c)

( -1 1 -1 3 /

TOPICAL ASSESSMENT 17 Section A : Objective Questions 1 D 2 C 3 B 4 C 5 B 6 B 7 A 8 C 9 C 10 D

12 (a) \3/

(b)

1-4/

9 (a) 10 (a)

(c)

Section B : Subjective Questions 1 (a) 60 km (b) 45 minutes (c) 80 km h-' 2 (a) 45 m (c) 4.5 m s-' (b) 90m 3 (a) 80m (b) 3 seconds (c) 2 m s-' 4 (a) 105 km (c) 35 km (b) 0800 hours (d) 42 km h-' 5 (a) d=90 (c) 3.6 ms-' (b) 4.5 m s-' 6 (a) 0.4 hour (b) 70 km h-' (c) (i) 60 km (ii) 1.2 hours 7 (a) 30 seconds (c) 150 m

31 13 (a) p=3,q=1 (b) m=2,n=-2 (c) x=-l,y=-5 14 (a) 4 2 -3 2 (b) m=3,n=-1 15 (a) p =-5,q=-3 (b) x=3,y=-1 16 (a) e=-15 } (b)

(-2 2 -3 (c) h=-2,k=2 17 (a) r=- 2

(b) 10 m s_2

2 (b) 11 52 (c) v=-1,w=-3

(c) 50 km h-'

TOPICAL ASSESSMENT 16 Section A : Objective Questions 1 A 2 C 3 A 4 D 5 6 C 7 B 8 C 9 C 10 11 B 12 B 13 B 14 B 15 16 A 17 D 18 C 19 D 20 21 A 22 D 23 D 24 B 25 26 B 27 C 28 B 29 D 30

Section B : Subjective Questions (b) 48

2 (a) P= (b) h=4

D A C A C C

9 (a) v = 14 (b) 580 m (c) 14.5 ms-' 10 (a) 8 m s-2 (b) u=8 11 (a) T,=8 (b) 3.75 m s-1 (c) Tz =15 12 (a) 2 3 m s-2 (b) 2 100 m (c) T=42.5 13 (a) v=23 (b) v=30 14 (a) ' 1 m s-2 (b) 144 m (c) T=25 15 (a) 20 m s-1 (b) (i) t = 32 (ii) 20.75 m s-1

13 (a) 14 (a)

(b)

15 (a)

(b)

TOPICAL ASSESSMENT 19 Section A : Objective Questions 1 C 2 C 3 C 4 A 5 D 6 C 7 B 8 C 9 C 10 D 11 B 12 C 13 C 14 A 15 D 16 D 17 C 18 D 19 B 20 D

(i) r=2 2 (ii) 3 5 (a) A = B60 (b) C=9

TOPICAL ASSESSMENT 18 Section A : Objective Questions 1 B 2 D 3 C 4 D 5 B 6 C 7 D 8 B 9 D 10 C 11 C 12 B 13 D 14 C 15 B 16 B 17 C 18 C 19 B 20 A Section B : Subjective Questions

(b) 1

6 (a) a=2 ,b=-3

(b) (b) s 612

10 7 10

(b) 8

7 (a) y = 32x2 (b) k=2 2

(b) (b) M=75 (b)

9 (a) y=4. (b) r=1 3

2 9 4 17

(b) 20

10 (a) (i) n = 1 (ii) n = --L 5 6

124

160° 230° 105° 305° 185°

TOPICAL ASSESSMENT 20 Section A: Objective Questions 1 B 2 D 3 A 4 C 5 D 8 D 9 B 10 D 6 C 7 C 11 C 12 A 13 A 14 A 15 A 16 D 17 C 18 C 19 D 20 A

3 (a)

8 (a) h=2

12 (a)

Section B : Subjective Questions 1 (a) 340° (b) 310° (c) 2 (a) 290° (b) 170° (c) 3 (a) 000° (b) 210° (c) 4 (a) 090° (b) 215° (c) 5 (a) 005° (b) 030° (c) 6 (a) 290° (b) 050° 7 (a) 185° (b) 330(c) 020° 8 (a) 040° (b) 2209 (a) 085° (b) 240° 10 (a) 105° (b) 322.5°

(b) 600 km

(b) v=2,w=-1

1 (a) E= 4F

11 (a)

8 (a) 20 km h-2

18 (a) p = 2

(b)

8 (a)

Section B: Subjective Questions 1 (a) 60°W (b) 5°W 2 (a) 38°W (b) 7°E 3 (a) 18°S (b) 40°S 4 (a) 60°N (b) 4°N 5 (a) 84°W (b) 4°E (c) (44°N, 40°W) 6 (a) x=52 (b) (52°N, 93°W) (c) (0°, 130°W) 7 (a) 3 000 n.m. (b) 927. 05 n.m. (c) 4 320 n.m. 8 (a) 180° (b) 8 400 n.m. 9 (a) 8 025 . 96 n.m. (b) 5 760 n.m.

F

10 (a) 3 300 n.m. (b) 1 650 n.m. (c) 1 800 n.m. 11 (a) 8=66 (b) 4 392.76 n.m. 12 (a) WE (b) (i) (38°S, 36°E) (ii) 9 hours 36 minutes 13 (a) 120°W (b) (i) 5°N (ii) 5 196.15 n.m. (iii) 810.7 knots 14 (a) 60°S

7 (a)

5 (a) J/K/E

G/F

L/D 12 cm

7 cm / V 4 cm 20 cm 1/B

4 cm

H/A

14 cm

C

3cm

(b) 4 900 cm3 8 (a)

(b) H/G

U/P

4cm

T/N

I//

(b) 4 cm K

L

5 cm M

Q

3 cm

3 cm 4 cm B/E 3cm C/D

A/F

(c) 1 800 n.m. (d) (i) 3 600 n.m. (ii) 100°E 15 (a) 140°E (b) 3 600 n.m. (c) 2 760 n.m. (d) 7.2 hours

R/K

(C)

UH

S/L

4cm //G

(b) R

S

2 cm L/K

3 cm

5 cm

2 cm C/B/A

D/E/F K/Q/P

6 (a) Section B : Subjective Questions 1 T/S W

T

U

3 cm

TOPICAL ASSESSMENT 21 Section A: Objective Questions 1 D 2 B 3 B 4 B 5 C 6D

F/E

6 cm

G/A

4 cm

L/M/N

(c) SIR

R

3 cm 6 cm V

U/P 3cm

4 cm

5 cm

T/U

Q 2 cm

2

I/C

E/D

L/K 3cm H/B

3 cm

C

3 cm

M/Q 4cm

N/P

I

4 cm

9 (a)

(b)

U/T H/G

K/S

I/F

6 cm

H/B

F/A 2 cm G 3cm

4cm

3

V

U/T

4 cm

2 cm V/P

3 cm W/Q

N/W B/A

3cm

C

(b)

3 cm

2 cm

V/U I (C)

P/S

4

4 cm

Q/R

I/H

2 cm

F/G

W/K

V 2 cm

6 cm 4 cm 4 cm

L/T

K/U

r L

2 cm C/B Q/P

5 cm

6 cm

R/S

125

E/A

P/T

3cm Q/S R

(c)

V

(b)

4 cm

V/U

WIT

N 2 cm

2 cm L

W

K

KIN

3 cm

3 cm HID

4 cm

GIC P/S

2 cm Q/P

K

SIT

R

Q/R

6 cm

L V 2.12 cm U

T 2 cm

10 (a) T'S

2 cm

R

M/W

4 cm

EIA

FIB

M

2.12 cm

N

3 cm 4 cm

12 (a) E

F P 4.24 cm QIS 4.24 cm 2 cm

UIP

3 cm

NIV

3 cm

Q AID

(b)

B/C

14 (a) FIE

GIH

N/M 4cm 6 cm 5 cm

PIS

Q/R

(b) (i) PIS

Q/R

6 cm

AID

(b) (i) 2cm

D

C

3 cm

2 cm A/P

T

r ------------- i

B/Q

U 1 cm V

2 cm

1 cm SIR

B/C

FIR

E/S

N

(c) M

4 cm

5 cm

P/Q

4 cm

11 (a)

HIE

GIF

FIE

LIK

2 cm K 1 cm N

FIE 6 cm

3 cm

3 cm

BIA

5 cm

MIBIA

CID

4 cm

Q/P

4cm

CID

RIS

P

(b) (i) K

A

15 (a) 13 (a)

L

RIK

4 cm

Q2cmP/N

UIR

TIS 2 cm

EIH

FIG

3 cm

6 cm

6 cm 6 cm

V/N

3 cm 3 cm A/D/M

4 cm

BICIN

W/M/P

6 cm

126

K/Q

S/L

T

U/M

R

(b) (i) DIE

4 cm

T/Q/F 2 cm U/P

2 cm SIR

16 21 26 31 36

B B C B A

17 22 27 32 37

D D C B B

18 23 28 33 38

C D B B B

19 24 29 34 39

D B C B D

20 25 30 35 40

B D A C C

5 cm 3 cm

L/K/I

H/G M/N

Paper 2 1 (a) x=7 (b) 31 2 1021.15 cm3 3 LAGH=53°8' 4 k= 2,2 5 p=2,q=6

PIQID 2 cm

U/T

F/E

R 5 cm

3 cm

M/L

6 cm

N/H/K GII

16 (a)

(b) 4y=-3x+27

7 (a) True (b) Implication 1

2 cm S

6 (a) - 4

N/K

7 cm

If p3 = 8, then p=2. Implication 2: If p = 2, then p3=8. (c) If x = 9, then f = 3.

8 (a) 13 25 (b) 3 25 _5 9 (a) 9 2 9

(b) (i) (a) V : A translation (6) 1 (b) W: An enlargement of scale factor 3 with centre P(2,4) (ii) 112 cm2 14 (a) Lower Upper Marks Frequency Boundary Boundary 11

20.5

30.5

31- 40

8

30.5

40.5

41- 50

13

40.5

50.5

51-60

15

50.5

60.5

61-70

10

60.5

71-80

3

70.5

70.580.5

21-30

(b) 47.83 marks (c)

2 9 1 9

(b) u = 6,v = -1 10 (a) 269 2 cm2 (b) 83 cm 11 (a) 9 m s-' (b) (i) v =16 (ii) 257 m

6 cm

FIE

G/H

12 (a)

(b) (i) 4 cm

K/H

-1.5 2

10.5 20.5 30.5 40.5 50.5 60.5 Marks

2

4

-5 13

15 (a)

FIE

70.5 80.5 90.5

G

P/U 2 cm T/G

(b)

4 cm 6 cm

6 cm

H 2 cm AID 3cm B/C

LIE

Q/R

S/F

(ii) K

P

F/A

H/B

B/A

5 cm

2 cm E/H

FIG

SPM MODEL TEST 1 Paper 1 1 C 2 A 3 C 4 B 5 D 6 A 7 D 8 B 9 C 10 B 11 D 12 D 13 D 14 B 15 C

(c) (i) y = 0.2 (ii) x = -1.3, 2.7 (d) Draw the straight line y = x - 2; x = -0.9,2.9 13 (a) (i) (- 1, 3) (iii) (-1, -1) (ii) (5, 3)

127

MICID

(d)

(b)

16 (a) (i) 35°N (ii) 113°E

Frequency

(b) (i) 13442.67 n.m. (ii) 16 hours 48 minutes

SPM MODEL TEST 2 Paper 1 3 C 2 B 1 D 8 A 7 A 6 D 12 B 13 B 11 B 18 B 17 B 16 D 21 B 22 A 23 A 26 A 27 C 28 A 33 A 31 D 32 B 37 D 38 A 36 C

4 9 14 19 24 29 34 39

C C D C C D C C

10+

5B 10 C 15 $ 20 A 25 A 30 A 35 C 40 B

6f

2+

Paper 2 1 (a)

49.5 59.5 69.5 79.5 89.5 99.5 109.5 Age (years)

15 (a)

(c) (i) y = -9.2 (ii) x = 0.65

MIN

(d) Draw the straight line y = -2x + 4; x = -2.4, -0 .4, 2.85

(b) 4

E/F

4cm

2 452.16 cm2 3 t=-2 3 4 p=-1,9=2 5 31°36' 6 (a) (i) Some (ii) All (b) Ify 0 and y , 0, that satisfy all the given constraints. (b) Draw and shade the region R that satisfies all the given constraints. (c) Based on the graph, answer the following questions. (i) If there are 30 boys, find the maximum number of girls that can go for the trip. (ii) Calculate the amount of subsidy needed for the number of students in (c)(i).

Subtopics 21.1 & 21.2 1 A grocery shop has 5 kg of grade A peanuts and 8 kg of grade B peanuts. He wants to pack them into packets of two types, P and Q, as shown in the table.

Type

Mass of grade A peanuts

Mass of grade B peanuts

P

25g

75g

Q

50 g

50g

3 A factory has 200 workers. The employer provides not more than 4 big buses and a few mini buses to ferry the workers to and from work. A big bus has a capacity of 40 passengers and a mini bus has a capacity of 20 passengers. The costs to operate a big bus and a mini bus are RM50 and RM30 respectively. The employer can only afford to employ at most 9 drivers. Given x big buses and y mini buses are used per day. (a) Write down all the linear inequalities, other than x , 0 and y , 0, that satisfy all the above conditions. (b) Draw and shade the region R that satisfies all the above conditions. (c) Use the graph in (b) to find the number of big and mini buses used to keep the cost a minimum.

Given x is the number of packets of type P and y is the number of packets of type Q that he obtained. (a) Write down all the linear inequalities, other than x , 0 and y , 0, which satisfy the above constraints. (b) Draw and shade the region R that satisfies all the above constraints. (c) Given the profits from a packet of type P and a packet of type Q are 15 sen and 25 sen respectively. Use your graph from part (b) to estimate the maximum profit possible. 2 A nature club wants to take students for a field trip. Given x boys and y girls are joining the trip. The number of students is based on the following constraints. I : The total number of students should be at least 20. II : The sum of twice the number of boys and three times the number of girls is at most 120. III: The club subsidies RM3 for a boy and RM2 for a girl. The total expenditure is at most RM120.

4 A factory produces two types of electronic components, A and B. The costs of producing 1 unit of component A and 1 unit of component B are RM20 and RM10 respectively. The production of the electronic components A and B per day is based on the following conditions. I : The total production is not more than 80 units. II : The number of units of component A is at most three times the number of units of component B. III: The daily capital is not more than RM1 000.

97

(b) Draw and shade the region R that satisfies the constraints. (c) Based on the graph in (b), find the maximum - profit in a week if the profits from each unit of baskets A and B are RM20 and RM10 respectively.

Given the factory produces x units of component A and y units of component B each day.

(a) Write down three inequalities, other than x - 0 and y - 0, which satisfy all the given conditions. Using suitable scales for both axes, draw and shade the region R that satisfies the given conditions. (c) The selling prices of components A and B are RM30 and RM20 per unit respectively. Use the graph from (b) to find the minimum and maximum profits made if the production of component A is 30 units per day.

(b)

7 A bakery makes two types of cakes, A and B. A unit of cake A takes 1 hour to prepare and 20 minutes to bake while a unit of cake B takes 20 minutes to prepare and 40 minutes to bake. In a day, the bakery can make x units of cake A and y units of cake B according to the following conditions. I : The maximum preparation time is 12 hours. II : The total time to bake is at least 6 hours. III: The number of units of cake A to the number of units of cake B is in the ratio not more than 2 : 1.

5 A shop sells type A and type B food every day. It sells x plates of food A and y plates of food B. The sale of the two types of food follows the following conditions. I The amount of food A exceeds the amount of food B by at least 10 plates.

(a) Write down three inequalities, other than x - 0 and y - 0, that satisfy all the above conditions. (b) Draw and shade the region R that satisfies all the above conditions. (c) Based on the graph in (b), answer the following questions. (i) Find the minimum and maximum number of units of cake B made if 8 units of cake A are made on a certain day. (ii) The bakery earns a profit of RM20 and RM16 respectively for each unit of cakes A and B sold. Find the maximum profit possible.

II Double the amount of food A and triple the amount of food B produce a total of at least 60 plates. III: The amount of food B is less than or equal to double the amount of food A. (a) Write down three inequalities, other than x - 0 and y - 0, that satisfy all the above conditions. Draw and shade the region R that satisfies all the above conditions. (c) Given the profits from 1 plate of food A and 1 plate of food B are RM1.50 and RM1.20 respectively. Use the graph from part (b) to determine the minimum and maximum profits if the shop sells 14 plates of food B.

(b)

8 In a nursery, a farmer decides to plant two types of flowers as shown in the table.

6 A factory produces two types of baskets, A and B. In one week, it produces x units of basket A and y units of basket B, using machines P and Q. Machine P needs 60 minutes and 40 minutes to produce one unit of basket A and one unit of basket B respectively. Machine Q needs 20 minutes and 80 minutes to produce one unit of basket A and one unit of basket B respectively. The production of the factory is limited by the following constraints. I The running time for machine P is not more than 4 800 minutes. II : The running time for machine Q is not less than 2 400 minutes. III: The number of basket A produced is not more than twice the number of basket B.

Flower

Land use

Cost

P

0.4 m2

RM16

Q

0.6 m2

RM4

The land he uses is only 600 m2 and he has an allocation of RM8 000 to spend on the flowers. He plants x units of flower P and y units of flower Q. The number of units of flower P exceeds the number of units of flower Q by at least 200. (a) Write down three inequalities, other than x , 0 and y - 0, that satisfy all the given constraints. (b) Draw and shade the region R that satisfies the above constraints.

(a) Write down three inequalities, other than x - 0 and y - 0, that satisfy all the above constraints.

98

(c) Based on the graph in (b), answer the following questions.

(ii) If the profits from one unit of cake A and one unit of cake B sold are RM6 and RM8 respectively, find the maximum profit possible.

(i) If the cost to buy the flowers is maximum and the total number of units of flowers planted is minimum, find the area of the land used. (ii) If each unit of flower P and flower Q can bring in profits of RM4 and RM3 respectively, find the maximum profit possible.

11 Given x and y represent the number of Form 5 and Form 6 students respectively who are chosen for scholarship awards. The conditions for the awards are as follows. I : The number of Form 6 recipients exceeds the number of Form 5 recipients by at most 200. II : The number of Form 6 recipients must be

9 A retail shop buys shirts and blouses from a supplier at a price of RM12 and RM8 per piece respectively. The number of shirts is at least twice the number of blouses. The retail shop has a capital of only RM6 000. The shop sells each shirt and each blouse for RM20 and RM16 respectively and gets a profit of not less than RM1 800. Given the shop sells x shirts and y blouses. (a) Write down three inequalities, other than x - 0 and y - 0, that satisfy all the above conditions. (b) Draw and shade the region R that satisfies all the above conditions. (c) Based on the graph in (b), find (i) the maximum number of shirts that can be sold. (ii) the minimum profit if the shop sells 150 blouses.

at least 3 of the number of Form 5 recipients. III: The total number of recipients is less than or equal to 500. (a) Write down three inequalities, other than x - 0 and y - 0, that satisfy all the above conditions. (b) Draw and shade the region R that satisfies all the above conditions. (c) From the graph in (b), answer the following questions. (i) If the amounts given to each Form 5 recipient and each Form 6 recipient are RM30 and RM40 per month respectively, find the maximum amount spent per month. (ii) Find the minimum and maximum amounts given out monthly if the number of Form 6 recipients is fixed at 250.

10 A housewife wants to start a small business by selling two types of cakes, A and B. The table shows the ingredients used to make the cakes.

Cake

Butter

Flour

A

120 g

300 g

B

240 g

200 g

12 A factory produces toys of two models, A and B. The time taken to cut and weld a toy of each model is shown in the table.

She has only 8.4 kg of butter and 12 kg of flour to make x units of cake A and y units of cake B. The ratio of the number of units of cake A to the number of units of cake B that she makes is not more than 3 : 1. (a) Write down all the linear inequalities, other than x - 0 and y - 0, that satisfy all the above constraints. (b) Draw and shade the region R that satisfies all the above constraints. (c) Use the graph in (b) to answer the following questions. (i) If the housewife makes twice as many units of cake B than cake A, find the maximum number of units of the cakes she could make.

Model

Time for cutting (minutes)

Time for welding (minutes)

A

45

50

B

30

70

The factory can spend at the most 10 hours to cut and at least 5 hours 50 minutes to weld the toys. The number of units of model A is not more than 5 the number of units of model B. Given the factory produces x units of model A and y units of model B. (a) Write down three inequalities, other than x - 0 and y - 0, that satisfy all the above conditions.

99

(a) Write down all the linear inequalities, other than x , 0 and y ' 0, satisfying all the given conditions. (b) Draw and shade the region R that satisfies all the given conditions.

(b) Draw and shade the region R that satisfies all the conditions. (c) Based on the graph in (b), answer the following questions. (i) Find the minimum number of units of model B that can be produced if 3 units of model A have been produced. (ii) If the profits from the sale of each unit of model A and model B are RM14 and RM8 respectively, find the maximum profit possible.

(c) Use the graph to find the maximum profit, if the profits from each packet of curry powder P and curry powder Q are 18 sen and 24 sen respectively. 14 A courier service company uses two types of vans, A and B, for delivery. Each van A can take 9 big boxes and 3 small boxes of goods. Each van B can take 3 big boxes and 10 small boxes of goods. On a certain day, the company wants to deliver 36 big boxes and 30 small boxes of goods. It has a maximum of 8 vans available on that day altogether. Given the number of van A and the number of van B available are x and y respectively.

13 A factory produces two types of curry powder, P and Q, containing two basic ingredients, A and B, which are mixed in certain proportions as shown in the table. Pe

Ingredient A (units)

Ingredient B (units)

P

20

40

Q

30

20

(a) Write down all the linear inequalities, other than x , 0 and y , 0, that satisfy all the above constraints.

(b)

Draw and shade the region R that satisfies all the above constraints. (c) Use the graph to find the number of van A and of van B necessary to keep the cost a minimum, given that van A needs RM60 each and van B needs RM80 each to operate.

The total amount of ingredient A used is 18 000 units and the total amount of ingredient B used is 22 000 units. The minimum production of curry powder Q is 250 packets per day. It is given that the factory produces x packets of curry powder P and y packets of curry powder Q per day.

100

i

Time : Two hours

PAPER 1

This paper consists of 25 questions . Answer all the questions. Write your answers clearly in the spaces provided. Show your working. It may help you to get marks . The marks allocated for each question are shown in brackets. You may use a non-programmable scientific calculator. 1

Set A

Set B

Diagram 1 shows the relation between set A and set B. (a) State the type of the relation. (b) Using function notation, write the relation between the two sets. [2 marks]

Answer: (a) ................................................. DIAGRAM 1

(b) .................................................

X g k-2x x+1

2

Diagram 2 shows the function g : x k - 2x ,x# -l,wherekis x +1 a constant. Find the value of k. [2 marks]

2 1 3

Answer: k = .................................................

DIAGRAM 2

3 A quadratic equation x2 + px + 4 = x has two equal roots. Find the possible values of p.

[3 marks]

Answer: p = ................................................. Diagram 3 shows the graph of a 'quadratic function y = g(x). The

4

straight line y = 24 is a tangent to the curve y = g(x). (a) Write the equation of the axis of symmetry of the curve. (b) Express g(x) in the form a (x + b)2 + c, where a, b and c are constants. [3 marks] Answer: (a) ................................................. DIAGRAM 3

(b) .................................................

5 Find the range of values of x for 2x(x - 5) a 3(x - 5). [2 marks]

Answer: .......................................................

101

[3 marks]

6 Solve the equation 9-11 -1 = 9 1 _s.

Answer: x = ................................................. [4 marks]

7 Given that 2 log5 y = 2 + 4 logs x, express y in terms of x.

Answer: ....................................................... [3 marks]

8 Solve the equation 3 ' + log2 (x - 10) = log2 3x.

Answer: x = .................................................. 9 The sixth term of an arithmetic progression is 6 + p.and the sum of the first six terms is 8p - 6, where p is [3 marks] a constant. Given that the common difference of the progression is 2, find the value of p.

Answer: p = ............. ..................................... 10 The third term of a geometric progression is 81. The sum of the second and third terms is 189. Find (a) the common ratio and the first term of the progression. (b) the sum to infinity of the progression. [4 marks] Answer: (a) ................................................. (b) ................................................. Y Diagram 4(a) shows a curve y = 2x2 - 9. Diagram 4(b) shows the straight line graph obtained when y = 2x2 - 9 is expressed in the linear form Y = -9X + c. Express X and Y in terms of x and/or y. [3 marks]

11

-* X 0

DIAGRAM 4(a)

DIAGRAM 4(b) Answer: X = ................................................ Y = ................................................ Diagram 5 shows a straight line AB and a straight line BC are

12

perpendicular at point B. The equation of BC is y = 2 x + 1. Find the coordinates of B.

[3

marks]

01 A(3, 0) DIAGRAM 5

Answer: .......................................................

102

13

Diagram 6 shows two vectors, OA and BA, drawn on a Cartesian plane. Express (a) OA in the form (Y x). (b) AB in the form xi + yj. [2 marks] Answer: (a) ................................................. (b) .................................................

DIAGRAM 6

14 The points A, B and C are collinear. It is given that AB ='3a + 4b and AC = ka + (2 + k)b, where k is a constant. Find (a) the value of k. (b) the ratio AB : BC.

[4 marks] Answer : ( a) k = ..........................................

(b) ............................................ 15 Solve the equation 3 cost x = 7 cos x - 4 cos 60° for 0° -- x , 360°.

[4 marks]

Answer: x = ................................................. 16

Diagram 7 shows sectors OAB and BPQ with centres 0 and B respectively. Given that OB = 6 cm, arc AB 10 cm, BP : PO = 1 : 2 and ZPBQ = 0.5 radian, calculate (a) the value of 0, in radians. (b) the perimeter, in cm, of the shaded region. [4 marks] Answer: ( a) 0 = ......................................... (b) .................................................

17 A point Q lies on the curve y = 3x2 - 4x + 1. Given that the gradient of the normal to the curve at Q is 1, find the coordinates of Q. [3 marks] Answer: 18 It is given that y - - 5 u5 , where u = 3 - x2 . Find

in term s o f x.

Answer: 19 Given that y

.......................................................

[3 marks]

.......................................................

2x2 - x - 1,

(a) find the value of when x = 2. (b) express the approximate change in y, in terms of h, when x changes from 2 to 2 + h, where h is a small value. [4 marks] Answer: (a) .................................................

(b) .................................................

103

Diagram 8 shows a curve y = f (x). Given the area of region A is 2 unite and the area of region B is 5 unite. Find the value of

20

f a 3 f (x) dx. [2 marks]

Answer: .......................................................

DIAGRAM 8 21 Given that f 23 g(x) dx = 5, find

(a) the value of - f z g(x) dx. (b) the value of k

if f2 3

[kx - g(x)] dx = -15. [4 marks)

Answer: ( a) ................................................. (b) ................................................. 22

S

0

C

N

Diagram 9 shows six letter cards. A three-letter code is to be formed using three of these cards . Find the number of different three-letter

D

codes that

DIAGRAM 9

(a) can be formed. (b) end with a vowel. [4 marks] Answer: ( a) ................................................. (b) .................................................

23 The probability that Siva qualifies for a debate is 4 while the probability that Chin qualifies is 5 Find the probability that (a) both of them do not qualify for the debate. (b) only one of them qualifies for the debate. [3 marks] Answer: ( a) ................................................. (b) .................................................

24 A set of positive integers consists of. 2, 6 and h. The variance' for this set of integers is 3 . Find the value of h.

[4

marks]

Answer: h = ................................................. 25

f (z) A

z 0

Diagram 10 shows a standard normal distribution graph. The probability represented by the area of the shaded region is 0.4656. (a) Find the value of k. (b) Given X is a continuous random variable which is normally distributed with a mean of 48 and a standard deviation of 5. Find the value of X when the z-score is k. [4 marks]

k

DIAGRAM 10

Answer: (a) k = ......................................... (b) X = ........................................

104

PAPER 2 Time: Two hours and thirty minutes This paper consists of three sections: Section A, Section B and Section C. Answer all the questions in Section A, four questions from Section B and two questions from Section C. Show your working. It may help you to get marks. The marks allocated for each question and sub-part of a question are shown in brackets. You may use a non -programmable scientific calculator. Section A [40 marks] Answer all the questions in this section. 1 Solve the simultaneous equations 3x - 5y = 1 and x2 - 3xy + 2y2 = 0. [5 marks] 2 Given that f:x-44x-1and g:x-) 4 +3, find

(a) f_'(x).

[2 marks]

(b) f-'g(x)•

[2 marks]

(c) h(x) such that hg(x)

=

x2.

[2

marks]

3 Two salesmen , A and B, start to sell a certain health product at the same time. (a) Salesman A sells k bottles in the first month and his sales increase constantly by h bottles every subsequent month. He sells 52 bottles on the fifth month and his total sales for the first 12 months are 678 bottles. Find the values of k and h. [5 marks] (b) Salesman B sells 10 bottles in the first month and his sales increase constantly by 5 bottles every subsequent month. If both of them sell the same number of bottles in the nt'' month, find the value of n. [2 marks] 4 (a) Sketch the graph of y = -2 sin x for 0 s x _- 2n.

[4 marks]

(b) Hence, using the same axes , sketch a suitable graph to find the number of solutions to the equation x + 2 sin x = 1 for 0 , x , 2n. State the number of solutions. It

[3 marks]

5 Given p = (k + 1)i + 41, q = 2 i + (k - 4) j and p is parallel to q. (a) Find the possible values of k.

[3

marks]

(b) Using the positive value of k from (a), find the unit vector in the direction of p - q.

[3 marks]

6 Table 1 shows the frequency distribution of the marks of a group of students in an examination. Marks

Number of students

20-29

13

30 - 39

22

40 - 49

35

50-59

57

60-69

20

70 - 79

3 TABLE 1

105

(a) Find the mean mark.

[2 marks]

(b) Find the median mark.

[2 marks]

(c) Use graph paper to answer this sub-part of the question. Using a scale of 2 cm to 10 marks on the horizontal axis and 2 cm to 10 students on the vertical axis, draw a histogram to represent the frequency distribution of the marks. Hence, find the mode mark. [4 marks] (d) What is the mode mark if the marks of each student is increased by 5? [1 mark]

Section B [40 marks] Answer four questions from this section. 7 Use graph paper to answer this question. Table 2 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are related by the equation y = ax3 + bx, where a and b are constants. x

1.0

1.5

2.0

2.5

3.0

y

7.0

16.1

32.0

56.9

93.0

TABLE 2 (a) Plot Y against x2, using a suitable scale for each axis. Hence, draw the line of best fit. X (b) Use your graph from (a) to find (i) the value of a.

[5 marks]

(ii) the value of b. [5 marks]

8 y=x2-2x+2

1

0

2

x

Diagram 1 shows the straight line AB intersecting the curve y = x2 - 2x + 2 at points A and B. Find (a) the equation of -line AB.

[2 marks]

(b) the area of the shaded region P.

[5 marks]

(c) the volume generated, in terms of it, when the shaded region Q' [3 marks] is revolved through 360° about the x-axis.

DIAGRAM 1

9 Solutions to this question by scale drawing will not be accepted. Diagram 2 shows three points, P, Q and R, lies on the line 2y = x + 6 such that PQ : PR= 1 : 4. Find

y I

2) =x + 6 (a) the coordinates of point R.

[2 marks]

Q(2, 4) (b) the equation of the straight line that is perpendicular to PR and passes through point Q. [3 marks] X

0

(c) A point A moves such that the angle PAR is always 90°. Find the equation of the locus of point A. [5 marks]

DIAGRAM 2

106

10

Diagram 3 shows a sector ABCD with centre A drawn on a Cartesian plane. The equation of BD is x + 2y = 8. Find (a) the radius of sector ABCD.

[2 marks]

(b) the angle 9, in radians.

[3 marks]

(c) the area of the shaded region .

[5 marks]

DIAGRAM 3

11 The mass of a packet of biscuits is normally distributed with a mean of 95 g and a standard deviation of 6.2 g. (a) Find the probability that a packet of biscuits chosen at random has a mass of less than 92 g or more than 98 g. [5 marks] (b) If 80% of the packets of biscuits chosen at random have masses of less than x g, find the value of x.

[5 marks]

Section C [20 marks] Answer two questions from this section. 12 A particle moves in a straight line and passes througi a fixed point 0. Its velocity, v m s-1, is given by v = 2t2 - 3t, where t is the time in seconds after leaving 0. (Assume the motion to the right is positive.) (a) Find

(i) the maximum velocity of the particle. (ii) the time interval during which the particle moves to the left. (iii) the time interval during which the acceleration is positive. [5 marks] (b) Sketch the velocity-time graph of the motion of the particle for 0 _- t , 3. [2 marks] (c) Calculate the total distance travelled in the first 3 seconds after leaving 0.

[3 marks]

Diagram 4 shows a trapezium ABCD where AB is parallel to DC. Calculate

13

11 cm 25°

DIAGRAM 4

(a) the length of AC.

[2 marks]

(b) the length of AD.

[2 marks]

(c) the area of trapezium ABCD. [3 marks] (d) the perpendicular distance from A to DC. [3 marks]

107

14 Use graph paper to answer this question. A factory manufactures two types of shelves, A and B. The production of each type of shelf involves two processes, sawing the wood and assembling the parts. Table 3 shows the time taken to saw and to assemble a unit of shelf A and a unit of shelf B.

Time taken (minutes) Sh elf

Sawing

Assembling

A

30

15

B

10

20

TABLE. '3 The factory produces x units of shelf A and y units of shelf B based on the following constraints. I : The maximum total time for sawing is 360 minutes. II The total time for assembling is at least 180 minutes. III: The ratio of the number of units of shelf A to the number of units of shelf B is at least 1 : 3. (a) Write down three inequalities, other than x , 0 and y 0, which satisfy all the above constraints. [3 marks] (b) Using a scale of 2 cm to 2 shelves on the x-axis and 2 cm to 5 shelves on the y-axis, construct and [3 marks] shade the region R which satisfies all the above constraints. (c) Using your graph from (b), find (i) the minimum number of units of shelf B if 4 units of shelf A are produced per day. (ii) the maximum profit per day, if the profit from one unit of shelf A is RM12 and from one unit of shelf B is RM16. [4 marks]

15 Table 4 shows the price indices and weightages of items A, B, C and D used to make a sofa chair.

Item

Price index for the year 2006 based on the year 2004

Weightage

A

110

y

B

80

2y

C

X

3

D

150

2

TABLE 4 (a) Given the price of item C in the year 2004 is RM40 and it increases to RM52 in the year 2006. Find [2 marks] the value of x. (b) If the composite index for the prices of the -items is 120, find the value of Y. [3 marks] (c) Calculate the price of a sofa chair in the year 2006 if its corresponding price in the year 2004 [2 marks] is RM750. (d) If the price index of each item is expected to increase by 10% from the year 2006 to 2008, find the [3 marks] new composite index for the year 2008 based on the year 2004.

108

i

Time : Two hours

PAPER 1

This paper consists of 25 questions. Answer all the questions. Write your answers clearly in the spaces provided. Show your working. It may help you to get marks. The marks allocated for each question are shown in brackets. You may use a non -programmable scientific calculator. 1

Diagram 1 shows two functions , f and g. Find (a) f_'(5). (b) fg-'(-2).

z -( g x f 1, y

[2 marks]

-3 5

-2

Answer: (a) .................................................

(b) .................................................

DIAGRAM 1

[2 marks]

2 Given that h-' : x -* 2x - 1, find h-lh(x).

Answer: ....................................................... 3 A quadratic equation x2 - 2a(x + 1) = 0, where a is a constant has no real roots. Find the range of values of a. [3 marks] Answer: ....................................................... 4 Given 2 and - 3 are the roots of an equation axe + bx = 4, where a and b are constants. Find the values of a and b.

[3

marks] Answer: a = ................................................. b = .................................................

5 Given that f(x) = x(x - 5), find the range of the values of x such that f(x) - 4 > 10.

[2 marks]

Answer: ....................................................... 6 The points P(0, 4), Q(5, 1) and R(2, k) are the vertices of a triangle. If the area of triangle PQR is 8 unite, find the possible values of k. [3 marks]

Answer: k = ................................................. 7 Given that logo x2y = p and log2 xy2 = t, express loge (xy)2 in terms of p and t.

[4 marks]

Answer: .......................................................

109

[3 marks]

8 Solve the equation logo (log,, 30x) = 1. Give your answer correct to four significant figures.

Answer: x = .................................................. Diagram 2 shows part of a curve y = p(x + q)2 + r, where p, q and r are constants and B is the maximum point. Find (a) the value of q.

(b) the values of r and p. [3 marks] Answer: (a) q = ......................................... (b) r= .......................................... DIAGRAM 2

p = ......................................... Diagram 3 shows two sectors, AOB and APQ, with centres 0 and P respectively. Given OP = 4 cm and P is the midpoint of OA. The area of the shaded region is 18 cm2. Find the area of sector AOB. [4 marks]

10

0

B DIAGRAM 3

Answer:

Y,. 11

.......................................................

Diagram 4 shows a straight line graph which is obtained by plotting

x

(q, 14) x against x. It is known that x is related to y by the equation [3 marks]

y = 5x2 + U. Find the values of p and q. (0, P) 0

b.x

Answer: p = ................................................. q = ................................. .. . .. ...........

DIAGRAM 4

12 The tangent to a curve y = + at the point (-1, 5) is perpendicular to the straight line y = - 4 + 3. Calculate the values of a and b.

[3

marks] Answer: a = ................................................. b = .................................................

-4 -a -4 Diagram 5 shows two vectors, AB and BC. Given that AB = 5i + 2j, express ( x). (b) O in the form xi + yj . (a) AC in the form

13

[2 marks]

Answer: (a). ................................................. DIAGRAM 5

(b) .................................................

110

i

14 Given that 11 , x and 19 are three consecutive terms of an arithmetic progression. ( a) Find the value of x and the common difference. ( b) If x is the sixth term of the progression , find the first term.

[4 marks] Answer: (a) .................................................

(b) ................................................. 15 Differentiate 5x2(1 - 2x)3 with respect to x.

[3 marks]

Answer: 16 Solve the equation 4 tan 2 x - sect x = 2 for 0° , x , 360°.

....................................................... [4 marks]

Answer: x = ................................................. 17 The radius of a spherical bubble increases at a rate of 0.08 cm s-1. Find the rate of change of the surface area , in terms of x, when the volume of the bubble is 36x cm3. [3 marks]

Answer: ....................................................... 18 Find f

a (2x - 1)(2x +

1) dx in terms of a.

[3 marks]

Answer: ....................................................... 19

P(1, 9)

Diagram 6 shows part of a curve y = 2x2 + 1 and a rectangle PQRS. Find (a) the coordinates of point Q. (b) the area of the shaded region.

[4 marks]

Answer: ( a) ................................................. DIAGRAM 6

(b) .................................................

20 Given the median for the set of numbers 7, 6, 4, x, 10 and 9 is 8. If x is an integer and 1 , x -- 10, state the possible values of x. [2 marks]

Answer: x = .................................................

111

21 Given that

J

f(x) dx = 4 and

JZ g(x) dx = 2, find

(a) the valuez of J? [f(x) + g(x)] dx. (b) the value of k if jz [f(x) + 2 g(x) - k] dx = 2. [4 marks]

Answer: ( a) ................................................. (b) ................................................. 22 Find the number of ways of arranging the letters of the word QUALIFY if ( a) all the letters are arranged in a row. (b) the letters are arranged in two rows with three vowels in the first row and four consonants in the second row. [4 marks]

Answer : (a) .................................................

(b) ................................................. 23 The probability of choosing a red ball from a bag is 5 - . If the action is repeated 150 times, find (a) the mean, (b) the standard deviation, of the number of times a red ball is chosen.

[4 marks]

Answer: (a) ................................................. (b) ................................................. 24 A first-aid committee consisting of 5 persons is chosen from 6 medical officers and 4 first-aid students. Find the number of ways of forming a committee with (a) exactly 2 medical officers. (b) not more than 2 medical officers. [4 marks]

Answer: (a) .................................................

(b) ................................................. 25 If Z is the score for a standard normal distribution and P(k < Z < 0.5) = 0.148, find (a) the value of k. (b) P(Z > k). [4 marks]

Answer: ( a) ................................................. (b) .................................................

112

PAPER 2

Time : Two hours and thirty minutes

This -paper consists of three sections: Section A, Section B and Section C. Answer all the questions in Section A, four questions from Section B and two questions from Section C. Show your working. It may help you to get marks. The marks allocated for each question and sub-part of a question are shown in brackets. You may use a non-programmable scientific calculator. Section A [40 marks] Answer all the questions in this section. 1 Solve the simultaneous equations 4 + 2 = 1 and x2 - xy = 10.

[5 marks]

2 The curve y = 1 + 4x + 4x2 has gradients p and q at the points where x = 4 and x = 1 respectively. Find (a) the values of p and q.

[2

marks]

(b) the equation of the tangent to the curve at the point where x = 1. [3 marks]

3 A student arranges some marbles into rows to form a pattern, starting with p marbles in the first row. Every subsequent row has d marbles more than the row before it. After forming the pattern, he finds that the number of marbles in the first, second and fifth rows form the consecutive terms of a geometric progression. (a) Find the common ratio of the geometric progression.

[2 marks]

(b) If he starts with 3 marbles in the first row, find (i) the value of d. (ii) the number of marbles in the tenth row. [4 marks] 4

--------- --- ------- - ---- - --

6

4+---- r--} } 21--

Diagram 1 is a histogram which represents the distribution of marks obtained by 26 students in a test. (a) Without using an ogive, calculate the median mark. [3 marks]

(b)

Calculate the standard deviation of the distribution. [4 marks]

0' I I I I I 120.5 30.5 40.5 50.5 60.5 70.5 80.5 Marks

DIAGRAM 1 5

Diagram 2 shows a triangle OAB. Point C divides OA in the ratio 2 3 and point D divides AB in the ratio 1 : 2. Given OA = 5a, --3 --3 -.3 -3 -4

OB=b, OE = pOD and CE = qCB. (a) Express OE in terms of (i) p, k and b.

(ii) q, q and b. [3 marks]

(b) Hence, find the values of p and q. [3 marks] DIAGRAM 2

(c) State the ratio OE : ED. [2 marks]

113

[3 marks]

6 (a) Prove that 1 + sect x = 4 cosec2 2x. sin 2 x

Sketch the graph of y 1 - 2 1 sin x I for 0 , x , 2n. Hence, using the same axes , draw a suitable straight line y = k such that there are only two solutions to the equation 2 1 sin x I = 1 - k for 0 , x , 2n. [6 marks]

Section B [40 marks] Answer four questions from this section.

7 Use graph paper to answer this question. Table 1 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are related by the equation b(x + y) - ab = ax2, where a and b are constants. x

1

2

3

4

5

y

0.5

0.5

1.5

3.5

6

TABLE 1 (a) Plot x + y against x2, using a scale of 2 cm to 5 units on the x2-axis and 2 cm to 2 units on the [5 marks] (x + y)-axis. Hence, draw the line of best fit. (b) Use the graph from (a) to find (i) the value of a.

(ii) the value of b.

[5 marks]

Diagram 3 shows a rectangle OABC and part of the-curve y = x2 + k. Given that the two shaded regions are equal in area, find

8

(a) the value of k.

[3 marks]

(b) the area of region P.

[3 marks]

(c) the volume generated, in terms of x, when region P is revolved [4 marks] through 360° about the y-axis.

9 Solutions to this question by scale drawing will not be accepted. y Diagram 4 shows a straight line AB joining two points , A(-4, -8) and B(4, 4) B(4, 4). Find

T P(-1, 3)•

(a) the equation of the straight line that is perpendicular to AB and [3 marks] passing through point P. (b) the coordinates of point Q, where Q is the point of intersection [4 marks] of the line in (a) and line AB. [3 marks]

(c) the ratio of AQ to QB. A(-4, -8)

DIAGRAM 4

114

i

Diagram 5 shows a sector AOB with centre 0 and a semicircle ORQ with centre P. Given OP = 2 cm and the shaded region ARQB is equal in area to the shaded region ORQP. Find

10

(a) the length of radius OA. [2 marks] [4 marks]

(b) the area of the shaded region ARQB.

(c) the perimeter of the shaded region ARQB. [4 marks]

11 (a) In a survey, it is found that 25% of the students in a school are short-sighted. If 10 students are chosen at random from the school, calculate the probability that (i) exactly 3 of them are short-sighted. (ii) less than 3 students are short-sighted. [4 marks] (b) The thickness of a monthly magazine follows a normal distribution with a mean of 0.8 cm and a standard deviation of 0.25 cm. Find (i) the probability that a magazine chosen at random from all the magazines has a thickness of not more than 0.9 cm. (ii) the value of t if 15% of the magazines have a thickness of more than t cm. [6 marks]

Section C [20 marks] Answer two questions from this section. Diagram 6 shows a triangle PQR.

12

(a) Calculate the length, in cm, of PR.

[2 marks]

(b) A quadrilateral PQRS is now formed so that PR is a diagonal, ZPRS = 35° and PS = 15 cm. Calculate the two possible values of LPSR. [3 marks] Q (c) Using the obtuse angle PSR from (b), calculate (i) the length, in cm, of RS. (ii) the area, in cm2, of quadrilateral PQRS.

R

DIAGRAM 6

[5 marks]

13 Table 2 shows the prices and price indices of four items, P, Q, R and S, used to make a computer chip. Diagram 7 is a pie chart which represents the relative amount of the items P, Q, R and S used to make these computer chips.

Price

Item

(RM)

Price index for 2006

Year 2004

Year 2006

based on 2004

P

50.00

60.00

120

Q

18.00

x

110

R

20.50

24.60

y

S

z

42.70

140

TABLE 2

DIAGRAM 7

115

[3 marks]

(a) Find the values of x , y and z.

Calculate the composite index for the cost of making the computer chips for the year 2006 based on the year 2004. Hence, calculate the corresponding cost of making the computer chips in the year 2006 if the cost in the year 2004 is RM200. [4 marks] (c) The cost of making these computer chips is expected to increase by 15 % from the year 2006 to the year 2008. Find the expected composite index for the year 2008 based on the year 2004. [3 marks]

14 Use graph paper to answer this question. Anita wants to plant x pots of orchids and y pots of ferns in her garden , according to the following conditions. I : The total number of pots of plants is not more than 90. II : The number of pots of orchids is equal to or more than half the number of pots of ferns. III: The cost of a pot of orchid is RM3 and a pot of fern is RM1. She is willing to spend at least RM90 to buy the plants. (a) Write down three inequalities , other than x - 0 and y - 0, which satisfy the above conditions. [3 marks] (b) Using a scale of 2 cm to 10 pots of plants on both axes , draw and shade the region R which satisfies the above conditions . [3 marks] (c) Based on the graph in (b), answer the following questions. (i) Find the minimum number of pots of orchids to be planted if there are 20 pots of ferns. (ii) Find the maximum profit if she can sell a pot of orchid and a pot of fern at RM8 and RM12 respectively. [4 marks]

15 Diagram 8 shows a particle moving in a straight line and passing through a fixed point 0.

A

0

B

DIAGRAM 8 Its velocity, v m s-', t seconds after passing through 0 is given by v = 6t - 5 - t2. The particle comes to rest momentarily at points A and B. Find (a) the time interval during which the particle experiences negative acceleration .

[3 marks]

(b) the distance between A and B. [3 marks] (c) the total distance travelled in the first 6 seconds after leaving 0 .

116

[4 marks]

FORM 4 TOPICAL ASSESSMENT 1 Section A: Paper 1 Questions 1 (a) One-to-one relation (b) (a, b, c) 2 (a) 1

(b)

12 (a) m=3,n=1 (b) 1 13 (a) -5 (b) 2 14 (a) 2x2 + 1

(b) x=-1±41

(b) 21-, 1

12 x=4.7,-1.7

15 x+3 16 x2 -3 17 a=1,b=- 8;a=-1,b=-8 18 (a) 5x+3 xm1 2(x - 1) '

3 (a) Y is the square of X. (b) (1,4,9) 4 (a) 5 (b) ((1, 1), (2,3), (3, 4), (4, 2), (5, 5)) 5 (a) 8 1 3 6 (a) a=2,b=1 (b) -1,2 7 (a) 1 (b) 7

(b)

8 (a) f(x)

(b) 2 19 (a) a =-2,b=3 -8

(b)

20 (a) - 5 (b) 2 21 (a) a = 6, b = 4 (b) 5 22 (a) x

2

11 (b) 1

23 (a) 13 - 8x (b) 12x

9

6 a= [,b=-1; -^2_,b=-1 7 (a) 12 (b) 16 8 (a) 5 (b) ±3

-1 f(x) < 3 10 f(x)

9 (a)

2x+1'x# 2

10 (a) a=2,b=-5;a =-2,b=15 (b) 7 11 (a) 3 (b) -8 12 (a) 5 g(x) g(x) = 3x - 3

6 g(x) = -x+ 1

-,2 ;10

(b) 0 , g(x) -- 6

1

i-+x 2 3

_[328 (b) 6 29 (a) ±6 30 (a) - a 2 31 (a) m >4orm 3

Paper 2

{ 0

1 x=-2y=- 'x=2,y=I

(b)

4 v (m } s ') 9i

(c) RM151.50 14 (a) I : 9x + 4y --36 II : 3x+10y '30 III: x+y--8

2 (a) x + 1 4 (b) 16+x 16 (c) 16(x - 3)2 3 (a) k=40,h=3 (b) 16

129

v=2t2-3t

t (s) (c) 16-i m

13 (a) 19.58 cm (b) 8.58 cm (c) 107.57 cm2 (d) 8.27 cm 14 (a) I : 3x+y3

E to +

(b) 10-y-

4 t

2

•^

(c) 15 3 m

+

44

^ TII

(b) 6j + 7j X2

0

5

10

15

130

20

25

E FEATURES Latest SPM Format Totally SPM-oriented Focused on Popular SPM Topics Oganised Topic by Topic Topic Sequence

as in the Textbooks

The TOTAL PRO SPM Meal essment series is the best choice to help you asyeur-;self and identity the areas which require more attention in your preparation for the SM.examination. Each title in the series contains

Titles in the

challenging SPM-oriented questions. The questions are systematically

TOTAL PRO SPM Topical Assessment

organised according to The topics in the Forms 4 and 5 textbooks.

Special emphasis is given to topics that are popular in the examination.

Series • Bahasa Melayu

The panel of writers are teachers with extensive experience in teaching and writing as well as marking examination papers. Their detailed and thorough

Mathematics

analysis of past yews' and the latest SPM papers ensures that the questions

Science

in the books meet the $PM standard. The TOTAL PRO SPM Topical Assessment series will undoubtedly prove to be the perfect complement to your revision programme in preparation for the examination.

Chemt

• Biala,

• Pendiditan Islam: Perdaaanaan Prinsip Perakaunan

AIR

SASBAD! SDN. BHD. c

RM4.90 S em. M 'sia/RM5 .40 Sabah & Saak

X;

Lot 12, Jalan Teknologi 3/4, Taman Sains Selangor 1, Kota Damansara , 47810 Petaling Jaya, Selangor Darul Ehsan. Tel: +603-6145 1188 Fax: +603-6145 1199 Laman web : www.sasbadi.com e-mel: enquiry@ sasbadi.com

ISBN 978 - 983-59-3351-6

9'789835

33516

('272iIiAV

SASBADI

OTAL P

IP .

athematics

Chris Mun

aL

lmw-m

mm

pap r e

ADHERES 70 THE LA TEST SPM FORMAT

SASBADI SON. BHD. t,as2a8-)o PETALING JAYA

Sasbadi Sdn . Bhd. (139288-X) Lot 12, Jalan Teknologi 3/4, Taman Sains Selangor 1, Kota Damansara, 47810 Petaling Jaya, Selangor Darul Ehsan, Malaysia. Tel: +603-6145 1188 Fax: +603-6145 1199 Laman web: www.sasbadi.com e-mel: [email protected]

Hak cipta terpelihara. Tidak dibenarkan memetik atau mencetak kembali mana-mana bahagian isi buku ini dalam bentuk apa jua dan dengan cara apa pun, baik secara elektronik, fotologi, mekanik, rakaman, atau yang lain-lain sebagainya sebelum mendapat izin bertulis daripada Penerbit. © Sasbadi Sdn. Bhd. (139288-X) Cetakan 2007

ISBN 978-983-59-3350-9

Dicetak di Malaysia oleh Summit Print Sdn. Bhd . (410861-A)

The TOTAL PRO SPM Topical Assessment MATHEMATICS series has been published specifically to fulfil the urgent needs of students who are preparing to sit for the SPM public examination. These exam-oriented assessment materials are intensive and comprehensive, covering all the topics prescribed in the KBSM syllabus for Forms 4 and 5. They also include model papers which conform to the current SPM format. The book is systematically organised according to topics and subtopics as in the textbooks, it also meets all the requirements of the SPM and the KBSM syllabus. The questions in this book are both original and challenging , incorporating a variety of questioning techniques and levels of difficulty to meet the actual standard.of the SPM papers. Moreover, the number of questions set on each topic is determined by the popularity or the frequency of recurrence of the topic in the SPM examination as indicated by the trend observed in the past three to five years. Students who work consistently and systematically, using the TOTAL PRO SPM Topical Assessment MATHEMATICS will be able to improve their understanding of the subjects and evaluate their own performance. Consequently, this motivation will boost their confidence in facing the real challenges of the public exam with greater success.

SUPERIOR APVANTA( ES OF ' THE TOTAL PRO, SPMTOPI(°AL A$ SESSM^ENT`MATH EMATKS; Cover all the topics prescribed in the KBSM syllabus for Forms 4 and 5 and focus on popular examination topics in the SPM.

Enables students to predict the type and allocation of questions based on a careful study of the past years' SPM papers.

Comprises challenging questions which incorporate a variety of questioning techniques and levels of difficulty and conforms to the current SPM format.

Consist of two complete sets of SPM-quality Model Papers set in accordance with the actual format and standard of the public exam.

Provide plausible answers to questions for students to check and evaluate their own understanding and performance in the subject.

THE PUBLISHER

(iii)

• ANALYSIS OF SPM PAPERS (2003 -2006) • MATHEMATICAL FORMULAE

(vi) (vii) - (viii)

5.2 Gradient of a Straight Line in Cartesian Coordinates 5.3 Intercepts 5.4 Equation of a Straight Line 5.5 Parallel Lines

FORM 4

Statistics Ill r-l

Standard Form

1.1 Significant Figures 1.2 Standard Form

Quadratic Expressions and

6.1 Class Intervals 6.2 Mode and Mean of Grouped Data 6.3 Histograms 6.4 Frequency Polygons 6.5 Cumulative Frequency 6.6 Measures of Dispersion

4 Equations 2.1 Quadratic Expressions 2.2 Factorisation of Quadratic Expressions 2.3 Quadratic Equations 2.4 Roots of Quadratic Equations

Probability I

7.1 Sample Spaces 7.2 Events 7.3 Probability of an Event

Sets 3.1 Sets 3.2 Subset, Universal Set and Complement of a Set 3.3 Operations on Sets

Circles III 8.1 Tangents to a Circle 8.2 Angles between Tangents and Chords 8.3 Common Tangents

Mathematical Reasoning 4.1 Statements 4.2 Quantifiers "All" and "Some" 4.3 Operations on Statements 4.4 Implications 4.5 Arguments 4.6 Deduction and Induction

9.1 The Values of Sin 0, Cos 9 and Tan 9 9.2 Graphs of Sine, Cosine and Tangent

Angles of Elevation and IJ^ Depression 10.1 Angles of Elevation and Depression

5.1 Gradient of a Straight Line

(iv)

i 't^rj

1a^^

Lines and Planes in -Dimensions

1I / Gradient and Area under (^/ aGraph (^/ 17.1 Quantity Represented by the Gradient of a Graph 17.2 Quantity Represented by the Area under a Graph

11.1 Angles between Lines and Planes 11.2 Angles between Two Planes

I_J, Number Bases 18.1 Probability of an Event 18.2 Probability of the Complement of an Event 18.3 Probability of a Combined Event

12.1 Numbers in Bases Two, Eight and Five

Graphs of Functions 11 13.1 Graphs of Functions 13.2 Solution of an Equation by the Graphical Method 13.3 Region Representing Inequalities in Two Variables

19.1 Bearings

20.1 Longitudes 20.2 Latitudes 20.3 Location of a Place 20.4 Distance on the Surface of the Earth

14.1 Combination of Two Transformations

15.1 Concept of Matrices 15.2 Concept of Equal Matrices 15.3 Addition and Subtraction of Matrices 15.4 Multiplication of a Matrix by a Number 15.5 Multiplication of Two Matrices 15.6 Concept of Identity Matrices 15.7 Concept of Inverse Matrices 15.8 Solve Simultaneous Linear Equations Using Matrices

Plans and Elevations 21.1 Orthogonal Projections 21.2 Plans and Elevations

SPMMODELTEST1 Variations

SPM MODEL TEST 2 16.1 Direct Variations 16.2 Inverse Variations 16.3 Joint Variations

ANSWERS

.(V)

0 .0

J

J

F

J I

\

A

J

P

P E R KS

PAPER 1

1-3

Number of Questions 2003 2004 2005 2006 2 2 1 1 2 2 2 2 1 1 1 1 1 1 1 1 2 2 1 3 2 2 3 2 2 2 2 1 2 2 1 1 1 1 -

Topic

Form Polygons I& II Algebraic Expressions Linear Equations Algebraic Formulae Statistics I & II Transformations I & II Indices Linear Inequalities Trigonometry I

4

Standard Form Sets The Straight Line Statistics III Probability I Circles III Trigonometry II Angles of Elevation and Depression Lines and Planes in 3-Dimensions

4 3 1 2 1 2 1 1

5

Number Bases Graphs of Functions II Matrices Variations Probability II Bearings Earth as a Sphere

2 1 3 2 1 1

4 3 2 1 1 2 2 1 2 1 1 2 2 1 1

3 3 2 I 2 1 3 1 1

4 3 2 1 1 2 2 1

2 1 2 3 1 2

2 1 2 3 1 1 1

PAPER 2 Section

1-3

A

4

5

4 B

Topic

Form

5

Solid Geometry Circles I&II Linear Equations Quadratic Expressions and Equations Sets Mathematical Reasoning The Straight Line Lines and Planes in 3-Dimensions Graphs of Functions II Matrices Gradient and Area under a Graph Probability II Statistics III Graphs of Functions II Transformations III Earth as a Sphere Plans and Elevations

(vi)

Number of Questions 2003 2004 2005 2006 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1

The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.

RELATIONS I am x a

n = am+n

2 am+an=am-n 3 (am )n = amn

d bl 4 A-'= 1 adbc (-c a) 5 P(A) = n(A) n(S) 6 P(A') =1- P(A) 7 Distance = (x 2- x,)2 + (y2 _y,)2

8 Midpoint, (x, y) =

fi. ..--, ........ ............................... ............... .......... ..................... -..-.1.....--. - ............._.. -........ ....._.................. . . . . . ............ -....i._._ ! ......... ....>.... ).......................................

x, + x2 y, + y2 2 2

0

9 Average speed = distance travelled

0

time taken 10 Mean - sum of data number of data 11 Mean = sum of (class mark x frequency) sum of frequencies 12 Pythagoras ' Theorem c2

a

=a2+b2

r b

13m=y2-y, x2-x, 14 m=- y-intercept x-intercept

Y

(x1, Y1)

y-intercept x-intercept ^x

0 (x2, Y)

(vii)

SHAPES AND SPACE 1 Area of trapezium = 2 x sum of parallel sides x height

2 Circumference of circle = TO = 2nr

3 Area of circle = nr'

4 Curved surface area of cylinder = 2nrh

5 Surface area of sphere = 4nr2

6 Volume of right prism = cross sectional area x length

7 Volume of cylinder = nr2h

8 Volume of cone = 1 nr`Lh 3

9 Volume of sphere = 3

nr3

10 Volume of right pyramid = 3 x base area x height 11 Sum of interior angles of a polygon = (n - 2) x 180° 12 arc length _ angle subtended at centre circumference of circle 360° 13 area of sector = angle subtended at centre area of circle 360° sector

PA 14 Scale factor, k = PA 15 Area of image = k2 x area of object

(viii)

SECTION A Objective Questions This section consists of 40 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 1.1 1 Round off 2 794 to two significant figures. A 2 700 B 2790 C 2 800 D 2 810 2 Round off 300 257, to four significant figures. A 3 003 B 300 200 C 300 300 D 300 357 3 Round off 4.17572 to three significant figures. A 4.18 B 4.175 C 4.176 D 4.1757 4 Round off 0.060813 to three significant figures. A 0.06 B 0.060 C 0.0608 D 0.06081 5 Round off 0.006197 to three significant figures. A 0.006 B 0.0061 C 0.0062 D 0.00620 6 Round off 92.6142 to three significant figures. A 92.6 C 92.614 B 92.61 D 93.0

7 Round off 0.00436 to two significant figures. A 0.004 B 0.0043 C 0.0044 D 0.00436 8 Round off 73 208 to three significant figures. A 732 B 73 200 C 73 210 D 732 100 9 Convert 3 285 km to m and round off the answer to three significant figures. A 32 850 m B 32900m C 329 000 m D 3 290 000 m

10 Calculate the value of 5.801 - 9 x 0.417 and round off the answer to two significant figures. A2 B 2.0 C 2.01 D 2.1

11 Calculate the value of 71.82 + 16.2 _ 0.03 and round off the answer to two significant figures. A 61 B 610 C 6 100 D 6 200

1

12 Calculate the value of (5.19)2 and round off the answer to two significant figures. A 26.93 C 27 B 26.94 D 28 13 Calculate the value of 0.915 - 0.01 x 2.4 and round off the answer to three significant figures. A 22 C 221 B 220 D 221.6 14 The volume of a cube is 50 cm3. Find the length, in cm, of the edge of the cube. Give the answer correct to two significant figures. A 3.6 C 7.1 B 3.7 D 7.2 15 The diagram shows a circle with diameter 11.2 cm.

Calculate the area, in cm2, of the circle and give the ans wer correct to three sign ificant figures. Us e it = 72 ) A B C D

35.2 98.5 98.6 99.0

16 Mr Lee saves RM36 000 in a bank at an interest rate of 3.2% per annum. After one year, his total interest, correct to two significant figures, is A RM1 100 B RM1 150 C RM1 152 D RM1 200

Subtopic 1.2 17 Express 0.000000305 in the standard form. A 3.05 x 10-6 B 3.05 x 10-7 C 3.05 x 10-8 D 30.5 x 10-8 18 Express 218 000 in the standard form. A 218 x 103 B 2.18 x 105 C 21.8x10-4 D 2.18 x 10-5 19 Express 0.00436 in the standard form. A 0.043 x 10-2 B 0.436 x 10-3 C 4.36 x 10-3 D 4.36 x 103

20 3.18 x 106 = A 3180 B 31 800 C 318 000 D 3 180 000 21 7.3 x 10-4 = A 0.0000073 B 0.000073 C 0.00073 D 0.0073 22 Express 2.438 x 10-5 as a single number. A 0.002438 B 0.0002438 C 0.00002438 D 0.000002438

23 Find the value of 0.00008 x 0.0045 and express the answer in the standard form. A 3.6 x 10-8 B 3.6 x 10-7 C 3.6 x 107 D 3.6 x 108

31 Find the value of 3.6 x 10-4 - 7.8 x 10-5 and express the answer in the standard form. A 4.98 x 10-5 B 4.98 x 10-4 c 2.82 x 10-5 D 2.82 x 10-4

24 Calculate the value of

32 Calculate the value of

0.00063 and express the 9 000 answer in standard form. A 7 x 10-8

65 600 and express the 0.8x10-6 answer in the standard form. A 8.2 x 108 B 8.2 x 109 C 8.2 x 1010 D 8.2 x 1011

B 7 x 10.7 C 7 x 10-6 D 7 x 108

25 Calculate the value of 6.5 x 108x8x 10-13 and express the answer in the standard form. A 5.2 x 10-5 B 5.2 x 10-4 C 5.2 x 104 D 5.2 x 105

33 Calculate the value of 4 x 109 + 8.7 x 1010 and express the answer in the standard form. A 4.87 x 109 B 4.87 x 1010 C 9.1 x 109 D 9.1 x 1010

26 7.6 x 10-6 + 9.44 x 10-5 = A 1.704 x 10-5 B 1.02 x 10-5 C 1.704 x 10-4 D 1.02 x 10-4

34 5.9 x 104 + 480 000 = A 1.07 x 105 B 1.07 x 106 C 5.39 x 104 D 5.39 x 105

27 24 000 = 6 x 10-4 A 4x107 B 4 x 108 C 0.4 x 107 D 0.4 x 109 28 4.5x106x5000= A 2.25 x 1010 B 2.25 x 109 C 2.25 x 108 D 2.25 x 106 29 3.7 x 1012 - 8.9 x 1011 = A 3.611 x 1012 B 3.611 x 1011 C 2.81 x 1012 D 2.81 x 1011 30 (5 x 10-3)2 = A 25 x 10-6 B 2.5 x 10-7 C 2.5 x lb-5 D 2.5 x 10-4

2

I

1

35

12.28 x 105 (4 x 10-3)2 A 3.07 x 1010 B 3.07 x 1011 C 7.675 x 109 D 7.675 x 1010

36 A motorcycle moved at a speed of 120 km h-1. Find the distance, in in, travelled by the motorcycle in 90 minutes. A 3x103 B 1.08 x 104 C 1.8 x 105 D 1.08 x 10' 37 The area of a rectangular piece of land is 8.4 km2. If its length is 3 500 in, find its width, in in. A 2.4 x 103 B 2.4 x 103 C 2.94 x 101 D 2.94 x 103

38 The wheel of a car has a radius of 28 cm. How many rotations does the wheel make if the car travels a distance of 88 km? Use it = 721l A 5x104 B 5x105 C 5 x 106 D 5 x 10-$

39 Given 1 g of metal Y contains 5.8 x 1020 atoms. Calculate the number of atoms in 2.5 kg of metal Y and express the answer in the standard form. A 1.45 x 1021 B 1.45 x 1024 C 2.32x1017 D 2.32 x 1020

40 A rectangular floor has a length of 3 600 cm and a width of 2 000 cm. The floor needs to be covered with square tiles, measuring 20 cm x 20 cm. Calculate the number of tiles needed to cover the whole floor. A 1.8 x 103 C 3.6 x 103 B 1.8x104. D 3.6x104

SECTION B Subjective Questions, This section consists of 20 questions. Answer all the questions. You may use a non-programmable scientific calculator. 5 Calculate the value of 7.13 _ 10 x 6.2 and round off the answer to three significant figures.

Subtopic 1.1 1 Round off the following numbers correct to two significant figures. (a) 0.07006 (b) 49 815

Answer:

6 (a) Calculate the value of 13.02 + 5.3 x 90. (b) Round off the answer in (a) to four significant figures.

Answer:

Answer:

(b)

(a)

2 Round off the following numbers correct to three significant figures. (a) 50.761 (b) 83 249 Answer:

7 (a) Calculate the value of 200 - 146.28 = 16. (b) Round off the answer in (a) to four significant figures.

(a) (b)

Answer: (a)

3 Calculate the value of each of the following and round off the answer to one significant figure. (a) 5 418 - 2 970 (b) 3.8 = 800

(b)

Answer: (a)

(b)

8 The diagram shows a right-angled triangle. x cm

4 (a) Calculate the value of 57 007 - 24 518 + 3 107. (b) Round off the answer in (a) to three significant figures. Answer: (a)

9 cm

7 cm

Calculate the value of x correct to two significant figures.

(b)

Answer:

3

14 . Find the value of 7.5 x 10-6 - 9.1 x 10-' and express the answer in the standard form.

9 A sphere has a radius of 8 cm. Find its total surface area, in cm2, and round off the answer to three significant figures. (Use it = 3.142)

Answer:

Answer:

15 Find the value of 9.4 x 10-4 + 8 x 10-5 and express the answer in the standard form.

Subtopic 1.2

Answer: 10 State the following numbers in the standard form. (a) 0.00076 (c) 359 (b) 0.0000204 (d) 8 003 000 Answer: 16 Find the value of 9 660 and express the 7x109 answer in the standard form.

(a)

(b)

Answer:

(c)

(d) 17 Find the value of 6.3 x 104 x 2.5 x 10-9 and express the answer in the standard form.

11 Write each of the following as a single number. (a) 1.8 x 10-3 (c) 6 x 105 (b) 5.04 x 10-4 (d) 9.815 x 106

Answer:

Answer: (a) 18 Find the value of 6.8 x 7 x 106 and express the answer in the standard form.

(b)

Answer:

(c)

(d) 19 The thickness of a wooden plank is 5.4 x 10-5 m. Calculate the total thickness, in m, of 500 pieces of such planks and express the answer in the standard form.

12 Find the value of 5.8 x 1012 - 5 x 1011 and express the answer in the standard form. Answer:

Answer:

13 Find the value of 3.78 x 106 and express the 0.007 answer in the standard form.

20 The scale of a map is 1: 400 000. Find the actual length, in cm, of a river which measures 8.4 cm on the map. Express the answer in the standard form.

Answer:

Answer:

4

Form 4

Quadratic Expressions and Equations

2.1 Quadratic Expressions 2.2 Factorisation of Quadratic Expressions

SECTION A

2.3 Quadratic Equations 2.4 Roots of Quadratic Equations

Objective Questions

This section consists of 16 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator. Subtopic 2.1 1 Expand 3y(y + 2). A 3y+2 C 3y2+6 B 3y + 6y D 3y2 + 6y 2 (2p - 1) (p - 5) _ A 2p2 + 5 B 2p2+5p+5 C 2p2-5p+5 D 2p2 - 11p + 5 3 Expand (5q - 2)2. A 5q2+4 B 5q2 - 10 C 25g2 - 20q + 4 D 25q2 - 10q + 2 4 The diagram shows a trapezium.

6 Factorise 3x2 - 11x + 6. A (3x - 3)(x + 2) B (3x - 2)(x - 3) C (3x - 2)(x + 3) D (3x + 2)(x + 3)

7 Factorise 4r2 - 49 completely. A (2r + 7)2 B (2r - 7)2 C (2r + 7)(2r - 1) D (2r + 7)(2r - 7)

8 Factorise 3h2 - 18h + 15 completely . A (h - 1)(h - 5) B (h - 2)(h - 3) C 3(h - 1)(h - 5) D 3(h - 2)(h - 3)

Subtopic 2.4 11 The roots of the equation 8 - 3p2 = 2p are A -2 and 3 B -2 and! C -3 and2 D 3and2 12 Solve the quadratic equation 3x(x - 5) = 0. A x=-5 orx=3 B x=-5 orx=5 C x=Oorx=5 D x=3orx=5 13 Solve the quadratic equation 4k2 = k.

p cm

A k= 4 ork=1 4p cm

Subtopic 2.3 (p + 5) cm

Express the area, in cm2, of the trapezium in terms of p. A 4p2 + p C 8p2 + 20 B 4p2+ 10p D 8p2 + 20p

B k=Oork= 4

9 Which of the following is not a quadratic equation? A 2(m + 1) = 8m2 B 2=(f-2)2 C 3a2-tab=5 D w2 = w 2 3

C k=Oork=4 D k=lork=4 14 Solve the quadratic equation 2y2 -5 3 . = y. A y=-5 ory= 2

Subtopic 2.2 5 Factorise 4 + 5t - 9t2. A (2 + 3t)(2 - 3t) B (4 + 9t)(1 - t) C (4 + t)(1 - 9t) D (4 + t)(1 + 9t)

10 2n2 + 3(n - 1)2 = 0 when written in the general form is A 2n2-3n+3=0 B 2n2+3n+3=0 C 5n2-6n+1=0 D 5n2-6n+3=0

5

B y -2 or y=1 C y=-1 ory= 2 D y=-2 ory=5

The area of the triangle KLM is equal to the area of a square with sides of 5 cm. Find the possible value of h. A 2 C 10 B 5 D 15

15 The diagram shows a triangle KLM.

(h + 5) cm

16 To prepare a bucket of cement, Encik Kadir needs

(2x - 3) kg of sand and 2 kg of cement Encik Kadir prepares x buckets of the mixture with a total mass of 66 kg of cement and sand. Find the value of x. A 3 C 6 B 5 D 7

SECTION B Subjective Questions`, This section consists of 15 questions. Answer all the questions. You may use a non-programmable scientific calculator. Answer:

Subtopic 2.1 1 Determine whether each of the following is a quadratic expression. (a) 4x2 - y (c) p(p - 3) (b) 5 - h - 4h2

(a)

(c)

(b)

(d)

Answer: (a)

(b)

(c) 5 Factorise the following completely. (a) n2 + n - 6 (b) 3m(m 5) (m - 5)

2 Expand each of the following. (a) 6y(y - 1) (c) (3k + 1)2 (d) (1 - 2q)2 (b) (2 - m)(m + 3)

(c) 2(5p2 - 1) - p (d) 3q2 + 4q - 7

Answer:

Answer:

(a)

(a)

(c)

(b)

(d)

(b) (c)

(d) 3 A salesperson sold y packets of book marks costing RM2 each and y cups costing RM(y + 3) each. Express the total sales of the salesperson in terms of y.

6 Factorise the following completely. (a) a2 _ 49 (b) 6b(3b + 1) - 2(3b + 1) (c) 16 + (k + 2)(k - 8) (d) h2 - 2(3h - 4)

Answer:

Answer: (a)

(c)

(b)

(d)

Subtopic 2.2 4 Factorise completely each of the following quadratic expressions. (c) 64h2 - 1 (a) 8p2 + 6 (b) 27y - 9y2 (d) 2t2 - 32

6

11 Solve each of the following quadratic equations. (a) 4p2+12p=0 (c) 3 k2+4k =5

Subtopic 2.3 7 Determine whether each of the following is a quadratic equation.

(a) h2 - 2hk = 0

(b) (y - 5)2 = 9

(c) (y - 2)2 = 9

( d ) 36

4x

(b) 4 x X 3

Answer:

Answer: (a)

(b)

(a)

(c)

(b)

(d)

(c)

8 Write each of the following quadratic equations in the general form. 12 Determine the roots of the following quadratic equations. (a) (p - 1)(p+3)=5(p+3) (b) 3(2-q)=10-q2

(a) r2 = 7(r + 1) (b) (w + 1)(4w - 3) = 1

Answer: (c) z +x=2 Answer:

13 Solve the quadratic equation 3 p2 - 5 = 7p. 2

(a)

(b) (c) 9

14 Solve the quadratic equation 2x 3- 1 ) = x + 4. Answer:

A taxi travels from the station to town P at an average speed of 20x km/h. The journey of 120 km takes (2x - 4) hours.

15 In the diagram , ABCD and AEFG are rectangles.

Form a quadratic equation from the information given fbove.

A 44-+ x) cm G D

Answer:

E

F

x cm

2 cmi

B C (a) Express the following in terms of x. (i) Length of AE, in cm. (ii) Area of the shaded region, in cm2. (b) Given that the area of the shaded region is 27 cm2, find the length of AG, in cm.

Subtopic 2.4 10 Determine whether -3 and 2 are the roots of each of the following quadratic equations. (a) x2-2x-6=0 (c) 3(x2+1)=x (b) x(x + 1) = 6

Answer: (a) (i)

Answer: (a) (b)

(b)

(c)

7

Sets

3.3 Operations on Sets

3.1 Sets 3.2 Subset, Universal Set and Complement of a Set

SECTION A Objective Questions This section consists of 35 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 3.1 1 Given P is a set of prime numbers between 10 and 30. The elements of set P are A {11, 13, 19) B [11, 15, 19, 23, 29) C {11, 13, 17, 19, 23, 29) D {11, 13; 17, 19, 21, 23, 27, 29) 2 Given that Q = {factors of 18), find n(Q). A 5 C 7 B 6 D 8 3 Given X = [colours of the Malaysian flag). Which of the following is false? A white E X B redEX C blue e X D green E X

5 Given set P = {4, 6, 7), set Q = 13, 4, 5, 7) and set R = {4, 5, 7), which of the following is true? A PCQ C RCP B QCP D RCQ 6 Given E=(x:5; = P U Q U R. P

Q

Which of the regions, A, B, C or D , represents the set PnQnR'?

18 The Venn diagram shows the universal set >; = X U Y.

Set X' n Y' is equivalent to set A X C Y B 0 D Y' 19 In which of the following Venn diagrams does the shaded region represent the set P'nQUR?

IGO

B

P

Q

F

H

23 The Venn diagram shows the number of the elements in set P, set Q and set R.

A P Q R

15 Given that the universal set ^ = F U G U H, G C Fand Fn H;6 0, the Venn diagram that represents these relationships is A C F

22 It is given that the universal sett= {x : 1 -- x -- 15,x is an integer), set K = {x : x is a prime number), set L = {x : x is a multiple of 3) and set M = (2, 4, 7, 8). The elements of the set (L U M)' n K are A 1, 11, 13 B 5, 11, 13 C 5, 13, 15 D 1, 5, 11, 13

R

D

It is given that the universal sett= PU Q U R and n(R') = n(P U R). Find the value of x. A 3 C 7 B 4 D 8

G

O

0

16 The Venn diagram shows the universal set >; = X U Y U Z.

20. The Venn diagram shows all the elements of the universal set t, set L, set M and set N.

Cl D

17 The Venn diagram shows the universal set t, set K and set L.

Find the elements of set (MUN)nL. A {6) B {5, 8) C (5, 6, 8) D {4, 5, 8, 91

The region (K n L)' is equivalent to the region A KnL' C KUL' B K'nL' D K'UL'

21 Given= {x:36-- x-- 45,x is an integer), set A = {x : x is a multiple of 31 and set B = {x : x > 411. The elements of set A U B are A {39, 42) B {36, 39, 42, 45) C (36, 39, 41, 42, 43) D {36, 39, 42, 43, 44, 45)

Which of the regions, A, B, C or D, represents the set X n Y'nZ'?

9

24 Given ^ = {x : 6 ' x 15, x is an integer), set P = (x : x is a multiple of 3) and setQ={x :x is an odd number). The elements of set (P n Q)' are A {6, 7, 9, 15) B {6,7,9,12,151 C {6,7,8,9,10,11,121 D (6, 7, 8, 10, 11, 12, 13, 14) 25 The Venn diagram shows the sets X, Y and Z, where 1;=XUYUZ.

The elements of set (X U Z)' are A (2, 4) B {5, 6) C {7, 81 D {3, 5, 61

26 The Venn diagram shows the sets P, Q and R, where C=PUQUR.

30 The Venn diagram shows the universal set :;, set P, set Q and set R.

t

Given ^ = {x : 11 , x 20, x is an integer), Q = (11, 13, 15, 17, 19, 20) and R = {prime numbers ), the elements of set PU (QnR)'are A (11,13,17,19) B ( 12, 14, 16, 18) C 112, 14, 16, 18, 20) D (12, 14 , 15, 16, 18, 20) 27 Given the universal set :;={x:9-- x20,xisan integer), set P = {x : x is a perfect square) and set Q = (x : x is a factor of 36), list all the elements of set P' n Q. A {12, 18) B (9, 16, 18) C {9, 12, 16, 18) D {9, 12, 16, 18, 20) 28 Given i ={x:10-- x_30, x is an integer ), set P = {x : x is a number such that the sum of its digits is 3) and set Q = {x : x is a number such that the digit at tens < the digit at ones ), find n (P' n Q). A 10 C 14 B 12 D 15 29 The Venn diagram shows the number of elements in the universal set :;, set P, set Q and set R.

Which of the following sets represents the shaded region? A PUQ' UR B Pn(QUR) C (P u Q) n R' D P'UQUR

33 Given that the universal set a=XUYU Z, where X= {c, e, p, a, t), Y = (p, i, n, t, a, s) and Z = (c, e, r, d, a, s), find n(XUYnZ'). A 6 C 4 B 5 D 3 34 The Venn diagram shows the universal set ^ = {Form 3 students), set M = {students who like the Mathematics subject) and set S = (students who like the Science subject). t

31 The Venn diagram shows all the elements of the set universal {;, set P and set Q. Given that n(M) = 120, n(S) = 85, n(M fl S) = 36 and the number of students who do not like both subjects is 15, find the total number of Form 3 students. A 148 C 220 B 184 D 256

k

The elements of set (P U Q)' are A {2,7) C (2,7,8) B {6, 8) D {4, 5, 9) 32 The Venn diagram shows the number students in a class who belong to at least one of the three societies. Given the universal set ^ = E U M U S, set E = (members of the

English Society), set M = (members. of the Mathematics Society), set S = (members of the Science Society).

35 The table shows the data obtained from a survey of 100 students. The Venn diagram represents the information given in the table.

Favourite

Number of

Drinks

Students

Tea

56

Coffee

55

Tea and coffee only

15

Tea and milk

8

only Tea only

24

Coffee only

25

Milk

Tea

Find n[(P U Q) n R']. A9 B 10 C 11 D 12

If 22 students are members of at least two societies, find the value of y. A 1 C 11 B 8 D 19

10

Coffee

Find the number of students who like tea or coffee and also milk. A 9 C 15 B 14 D 23

SECTION B Subjective Questions` This section consists of 15 questions. Answer all the questions. You may use a non-programmable scientific calculator. (c)

Subtopic 3.1 1 Given M = {factors of 36}, fill in the boxes with the symbol E or E. Answer: M

(c) 9

M

M

(d) 72

M 4 Find the complement of set for the following pairs of sets.

2 State the number of elements in each of the following sets. (a) J = {the names of days in a week which begin with the letter S} (b) K = (prime factors of 1051 (c) L={x :x is a multiple of4and20-- x 50}

(a) t = {the months in a year} B = {the months that have 31 days) (b) i; = {x : 50 -- x , 65, x is an integer} G = {x : x is a number such that the sum of its digits is an even number} Answer: (a)

(b)

Subtopic 3.2 3 Draw a Venn diagram to show the relationship of each pair of sets in the following. (a) M = {d, u, r, i, a, n} N,= (a, i, u} (b) P = {x : x is a negative integer and -10 < x < -2} Q = {-4, -6, -8) (c) U = (prime numbers which are less than 10) V = (1, 2, 3, 4, 5, 6, 7}

Subtopic 3.3 5 Given ^ = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 121, P = {multiples of 21, Q = {1,2,3,4,5}, R = (factors of 6). List all the elements of the set (a) Q n R, (b) PnQnR, (c) (P n Q)

Answer:

Answer:

(a)

(a)

(b) (b) (c)

11

9 The Venn diagram shows the universal set , set P and set Q.

6 The Venn diagrams in the answer space shows the universal set ^ = P U Q U R. On the diagram, shade the region which represents (a) set P U R, (b) set (P fl R) U Q.

k

(a) Complete the statements in the answer space, using the symbol set fl, U or C to show the relationship between set P and set Q. (b) State the set for Q fl P'. (c) State the set which represents the shaded region.

(b)

Answer: (a) (i) Q 7 The Venn diagrams in.the answer space show the universal sett A U B U C. On the diagram, shade the region which represents (a) set B .U C.

(ii) P

P Q=Q

(b)

(b) set (A fl B)' U C. (c)

Answer:

10 The Venn diagram shows all the elements of the universal set E, set X, set Y and set Z. t

(b)

(a) List all the elements of (X fl Y) U (Y fl Z). (b) Find

Subtopics 3.1 - 3.3

(i) n[(X fl Y) U Z], (ii) n(X' fl Z').

8 It is given that set K = 11, 3, 4], set L = (1, 2, 3, 4, 51 set M = 10, 1, 2, 3, 4, 6, 8, 9) and the universal set = K U L U M. (a) List all the elements of K fl M. (b) Find n(K' fl L).

Answer: (a)

(b) (i)

Answer: (a)

(b)

12

11 Given ^ _ {x : 60 -- x -- 80, x is an integer), P = (x : x is a prime number), Q = (x : x is a number such that the product of its digits is an odd number), R = (x : x is a multiple of 51. (a) List all the elements of set P and set Q. (b) Find n(P U Q). (c) Find n (P' fl R).

14 The Venn diagram shows the number of elements in sets J, K and L. Given the universal sett =JUKUL.

Answer: (a)

Find (a) the value of y when n (K) = n(K' U L), (b) n(J' fl L), (c) n(J U K fl L').

(b)

Answer: (a)

(c)

(b) 12 Given that the universal set = P U Q U R, set P = (s, o, n, a, r}, set Q = (s, o, n, i, c), set R = (t, o, n, i, c). (a) List all the elements of set P fl R. (b) Find n(Q U R').

15 The Venn diagram shows the relationship between the universal set t, set B and set C. Given universal set ^ {Form 3 students), set B = {members of the Red Crescent Society), set C = (members of the Chess Society). Given n(t) = 200, n(B) = 80, n(C) = 110 and n(B f1 C)=30.

Answer: (a)

(b)

t

13 Given that the universal set l; = A U B U C, set E = (x : 10 -- x , 25, x is an integer), set A = {x : x is a factor of 24), set A U B (x : x is a multiple of 31, ACBandBflC=0. (a) List all the elements of set C. (b) Find n (A U C)'.

Find (a) n(C' ), (b) n(B U C), (c) the number of students who are members of the Chess Society but are not members of the Red Crescent Society.

Answer:

Answer:

(a)

(a)

(b) (b) (c)

13

Mathematical Reasoning

4.1 4.2 4.3

4.4 Implications 4.5 Arguments 4.6 Deduction and Induction

Statements Quantifiers "All" and "Some" Operations on Statements

SECTION A

Objective Questions

This section consists of 15 questions. Answer all the questions . For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 4.1 1 Which of the following is a statement? A 3+5 B x+2=5 C sin 60° - cos 30° D 62 k, then h + 5 > k + 5. II If h < k, then 5h > 5k. 'III If h + 5 > k + 5, then

h > k. 2 Which of the following is a true statement? A -6 > -5 B 9 is a prime number. C 16 is a perfect square. D 0.25 > 0.33 3 Which of the following is a false statement? A p is a consonant. B 6 is a factor of 258. C 2 is a prime number. D A trapezium is a regular polygon.

Subtopic 4.2 4 Which of the following is a false statement? A Some odd numbers are prime numbers. B All multiples of 6 are multiples of 3. C Some perfect squares are negative numbers. D Some pyramids have a square base.

A I only B III only C I and III only D II and III only

Subtopic 4.3 6 Which of the following is a true statement? A 52 = 10 or 72 =8 = 6. B 8 + 9 = 17 and 8 x 4 =32. C 5 is a factor of 20 and 7 is a factor of 10. D Hexagons have 8 sides and octagons have 9 sides.

Subtopic 4.5 10

7 Which of the following is a true statement? A (42)4 = 46 or 6 - (-5) = 1.

Form a conclusion based on the two given premises. A 122 > 10 B 122 > 100 C 144> 10 D 144 < 100

B 3 = 0.75 and sin 60° = 0.5. 4 C { } C {2, 3} or -4(-4) = 8. D A trapezium has four sides of equal length and two of its sides are parallel. 11

Subtopic 4.4 8 "If m = -7, then m2 = 49." The antecedent in the above implication is A m=-7 C m2 = -49 B m=7 D m2=49

Premise 1: If x > 10, then x2 > 100. Premise 2: 12 > 10

Premise 1: If 4x < 20, then x < 5. Premise 2: ............................ Conclusion: 4x > 20 Premise 2 in the above argument is A x20

14

i

12

Which of the following is the conclusion for the above argument? A All squares have four sides of equal length. B All quadrilaterals are EFGH. C EFGH has four sides of equal length. D EFGH has four right angles. 13

Which of the following is Premise 2 in the argument given? A 42 is a multiple of 12. B 42 is a multiple of 18. C 72 is a multiple of 6. D 7 is a multiple of 12.

Premise 1 : All squares have four sides of equal length. Premise 2 : EFGH is a square.

Premise 1:

All multiples of 12 are multiples of 6. Premise 2: ........................ Conclusion: 42 is a multiple of 6.

SEO'10N B

15 Given a number sequence, 5, 14, 29, 50, ..., has the following pattern. 5=3(12)+2 14=3(22)+2 29 = 3(32) +2 50 = 3(42) +2 The general conclusion by induction for the number sequence is

Subtopic 4.6 14

All acute angles are less than 90 °. ZKLM is an acute angle. The conclusion by deduction for the argument above is A LKLM = 90° B LKLM > 900 C LKLM < 90° D LKLM , 90°

A n2, where n = 0, 1, 2, 3, ... B 3n2, where n = 1, 2, 3, 4,...

C n2 + 2, where n = 0, 1, 2, 3, ... D 3n2 + 2, where n = 1, 2, 3, 4,...

Subjective Questions

This section consists of 25 questions. Answer all the questions. You may use a non-programmable scientific calculator. 3 Construct true mathematical statements by using the following numbers and symbols. (a) -12, -11 and >

Subtopic 4.1 1 Determine whether each of the following is a statement. (a) Help me! (b) Kuantan is in Pahang. (c) (-3)3 = 27

(b) 0.25, 3 and < (c) {3, 6, 9}, 3 and E Answer:

Answer:

(a)

(a)

(b)

(b) (c)

(c) 2 Complete the following mathematical sentences by using the symbol > or < in the empty box to form (a) a true statement , (b) a false statement. Answer:

4 Determine whether each of the following statements is true or false. (a) 47 is a perfect square. (b) The highest common factor of 18 and 27 is 9. (c) Some tigers can live in water.

(a) -15 n -8

15

8 Combine the following pair of statements to Answer: (a) (c) form a true statement. Statement 1: -8 x (-3) = 11 (b) Statement 2: 35 is a multiple of 7. Answer:

Subtopic 4.2 5 Determine whether each of the following statements is true or false. (a) All even numbers are multiples of 4. (b) All factors of 12 are factors of 60.

Subtonic 4.4 9 State the antecedent and consequent in each of the following implications. (a) If k = -4, then k3 = -64. (b) If it rains today, then the football match will be cancelled.

Answer:

Answer: (a)

6 Construct a true statement using the quantifier "all" or "some" based on the given object and property in each of the following. (a) Object: regular polygons Property: 8 sides of equal length (b) Object: workers in a factory-

(b)

Property: wear spectacles (c) Object: triangles Property: right angles

10 State the antecedent and consequent in each of the following implications. (a) If Ismail's father comes to school late, then Ismail will go home late.

(d) Object: trapeziums Property: two parallel sides

(b) If Fm > 8, then m > 82.

Answer:

Answer: (a)

(b)

11 Write two implications from each of the following sentences. (a) x > y if and only if 3x > 3y. (b) p is a negative number if and only if p3 is a negative number.

Subtopic 4.3 7 Determine whether each of the following statements is true or false. (a) A cat has four legs and a chicken has four legs. (b) 32 + 52 > 42 and -0.43 < -0.34. (c) 30 is a multiple of 4 and 6. (d) 53=125or25-9=3

Answer: (a) Implication 1: Implication 2:

Answer: (b) Implication 1: Implication 2:

16

18 Form a conclusion by induction for the number sequence, 0, 3, 8, 15, ..., which follows the pattern: 0=12-1 3 = 22 - 1 8=32-1 15=42-1

Subtopic 4.5 12 Form a conclusion based on the following premises. Premise 1: All students of the Form 5K class passed the SPM examination. Premise 2: Azlina is a student of the Form 5K class.

Answer:

Conclusion: ................................................................ 19 Form a conclusion by deduction for the following statements. All parallelograms have opposite sides that are parallel. (general statement) ABCD is a parallelogram. (specific case)

Answer:

13 Complete the premise in the following argument: Premise 1: All regular pentagons have five sides of equal length.

Answer:

Premise 2: ................................................................... Conclusion: PQRST have five sides of equal length.

Subtopics 4.1 - 4.6 20 (a) Complete the premise in the following argument: Premise 1:If the length of each side of a square is x cm, then the area of the square is x2 cm.

Answer: 14 Complete the conclusion in the following argument: Premise 1: If 5x = 20, then x = 4. Premise 2: x # 4 Conclusion: ................................................................

Premise 2: .......................................................... Conclusion: The area of the square PQRS is 25 cm2. (b) Write down two implications based on the following sentence. "pq > 0 if and only if p > 0 and q > 0."

Answer: 15 Complete the premise in the following argument: Premise 1: If a number is a factor of 18, then the number is a factor of 54. Premise 2: .................................................................. Conclusion: 6 is a factor of 54.

Answer: (a) Premise 2:

Answer: (b) Implication 1: 16 Complete the premise in the following argument: Premise 1: ................................................................... Premise 2: p < 6 Conclusion : p + 4 < 10

Implication 2: 21 (a) Complete the premise in the following argument: Premise 1: ...................... 0 ................................... Premise 2: Jamal is not Juliana's brother. Conclusion : Juliana is not a doctor. (b) Given (x")" = x "'" where m, n and x are positive numbers. Find the value of

Answer:

Subtopic 4.6 17 Form a conclusion by induction for the number sequence, 5, 17, 37, 65, ..., which follows the pattern: 5=4(12)+1 17 = 4(22) + 1 37 = 4(32) + 1 65 = 4(42) + 1

(i)

(24)2,

(ii ) (7 4 )8.

Answer: (a) Premise 1:

(b) (i) (ii) Answer:

17

(b) Write down Premise 2 to complete the following argument: Premise 1: If y is less than zero , then y is a negative number. Premise 2 : ......... i ................................................ Conclusion : -2 is a negative number. (c) Write down two implications based on the following sentence.

22 (a) Complete the conclusion in the following argument: Premise 1: All triangles have the sum of interior angles of 180°. Premise 2: ABC is a triangle. Conclusion: ........................................................ (b) Form a conclusion by induction for the number sequence, 3, 10, 21, 36, ..., which follows the pattern: 3=2(12)+1 10 = 2(22) + 2 21 = 2(32) + 3 36 = 2(42) +4

5p > 20 if only if p > 4. Answer: (a) (i) (ii) (b) Premise 2:

Answer: (a) Conclusion:

(c) Implication 1:

(b) Implication 2:

23 (a) State whether the following statement is true or false.

25 (a) Complete each statement in the answer space with the quantifier "all" or "some" so that it will become a true statement. (b) State the converse of the following statement and hence, determine whether its converse is true or false.

5>3or21=6 (b) Write down two implications based on the following sentence. x3 = 64 if only if x = 4.

Ifx>'7,then x>4.

(c) Complete the premise in the following argument: Premise 1: All pentagons have five sides. Premise 2 : .......................................................... Conclusion : ABCDE has five sides.

(c) Complete the premise in the following argument: Premise 1 : If set P is a subset of set Q, then P fl Q = P. Premise 2 : ........................................................... Conclusion : Set P is not a subset of set Q.

Answer: (a)

Answer: (a) (i) ................... of the multiples of 5 are even numbers.

(b) Implication 1:

(ii) ................... hexagons have six sides. Implication 2:

(b)

(c) Premise 2:

24 (a) State whether each of the following statements is true or false. (i) 4x2=8and52=10. (ii) The elements of set P = {10, 15, 20) are divisible by 5 or the elements of set Q = 11, 2, 3) are factors of 4.

(c) Premise 2:

18

5.1 Gradient of a Straight Line 5.2 Gradient of a Straight Line in Cartesian Coordinates

5.3 Intercepts 5.4 Equation of a Straight Line 5.5 Parallel Lines

SECTION A Objective Questions This section consists of 25 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 5.1 1 In the following, which straight line PQ has a gradient of 4 ? A

Q 5 cm

3 Given the gradient of a straight line which passes through points (1, 4) and (2, k) is -3. The value of k is A -7 C 0 B -1 D 1 4 The diagram shows a straight line PQ on a Cartesian plane.

P ,3 cm

7 In the diagram, 0 is the origin.

y

B P

6 The coordinates of point Q are (-1, 2) and the gradient of the straight line QR is 3. The coordinates of point R could be A (2, -11) C (2, 9) B (2, -9) D (2, 11)

5 cm

D

The gradient of PQ is A -2

C 1 2

P

1 2

B

The straight line which has the largest gradient is A PQ C TU B RS D VW

D 2

Subtopic 5.3

Subtopic 5.2 2 The diagram shows a straight line AB on a Cartesian plane. y B(6, 3)

5 In the diagram, PQR is a straight line on a Cartesian plane.

8 In the diagram, PQ is a straight line on a Cartesian plane. y

y

^x 0

A(-2, -5) f 0

The gradient of AB is A -1 C 1 B 2 D 2

16

.x

The gradient of PQ is

The value of h is A 1 C 5 B 3 D 7

19

C

A B

3 -5

5 D 3

9 In the diagram, FG is a straight line.

13 The diagram shows two straight lines, MN and NP, on a Cartesian plane.

18 The gradient of the straight line 3x - 5y = 15 is A

-3

C

y

- 5 D 5 3

9

P(3, 3) .x

i

43 0 What is the gradient of FG? A -3 C B

O

The gradient of NP is -3 and the distance of MN is 13 units. Find the x-intercept of MN. A -12 C 13 5

D 3

10 In the diagram, RSTis a straight line on a Cartesian plane. y ^R(0, P)

19 Find the y-intercept of the straight line 2x - 5y = 20.

•x M

1 3

3 5

A

-5

B

-4

C D

2 5 10

20 In the diagram, the straight line HK intersects the straight line KL at K.

B -5 D _ 12 5

y

14 In the diagram, OPQR is a trapezium. Given 2PQ = OR. y R(0, 8)

S(1, 0)

.x

0

T(2, -3)

The value of p is A 2 C 4 B 3 D 6 11 The gradient of a straight line VW is 3. If the y-intercept of the straight line VW is 12, the x-intercept is A -36 C 4 B -4 D 36 12 In the diagram, PQ is a straight line with the gradient

The equation of the straight line KL is O P(6, 0) x The x-intercept of the straight line QR is

A B

A y=-43 3 B y=-4x+3

8 C 12 10 D 16

C y=-Zx-2

Subtopic 5.4 15 Which of the following points does not lie on the straight line y = 3x - 5? A (-2, -1) C (0, -5) B (-1, -8) D (1, -2)

1x+2 D y=-Z

Subtopic 5.5 21 Which of the following pairs of straight lines are parallel?

16 The equation of a straight line

A y=5+1

which has a gradient of 2

A y= 2x-2

y=0.4x+2 B y=-2x+1 2y=4x+2 C 3y+9x=-3 3x-y=9

B y= Zx+3

D

and passes through point (0, -3) is

C 2y=x-6 D 2y=x-3 Find the x-intercept of the straight line PQ. A -12 C -4 3 B

-4

D

-

1 12

17 The equation of a straight line which passes through points (-3, -3) and (4, 11) is A y=-2x-3 B y=-2x+3 C y=2x-3 D y=2x+3

2+3-5 2y + 3x = 2

22 Given the straight line y = mx - 5 is parallel to the straight line 4x + 6y = 8. The value of m is A -3 C 2 2 3 B -2 D 3 3 2

20

I

i i

23 In the diagram , OKLM is a parallelogram . Given the gradient of the straight line OK is 3.

24 In the diagram , PQRS is a parallelogram and RST is a straight line.

y

25 Which of the following straight lines is parallel to the straight line 3y = x + 6 and passes through point (-6, -4)?

01 R(12, 3)

The value of t is A 5 C 7 B 6 D 8

The coordinates of point Tare A (-12, 0) C (0, -6) B (-6, 0) D (0, -12)

SECTION B Subjective Questions`y This section consists of 20 questions. Answer all the questions. You may use a non-programmable scientific calculator.

Subtopic 5.1

Subtopic 5.3 4

Based on the diagram , find the gradient of the straight line MN.

Based on the diagram, state (a) the x-intercept,

Answer:

(b) the y-intercept, of the straight line RS. Answer: (a)

Subtopic 5.2 (b)

2 Find the gradient of the straight line that passes through points (-4, 2) and (-8, 6). Answer:

5 A straight line PQ intersects the y-axis at point R. If the x-intercept of the straight line PQ is 4 and its gradient is -2, find the coordinates of point R. Answer:

3 Given points (1, -7), (4, k) and (6, 4) lie on a straight line. Find the value of k. Answer:

21

10 Find the equation of the straight line which is parallel to y = 4 - 6x and passes through point (-1, 1).

Subtopic 5.4 6 On the diagram in the answer space, draw the

Answer:

straight line y = 3 x + 1. Answer: Subtopics 5.1 - 5.5 11 Y A Mn x

0

7 Find the points of intersection of the following pairs of straight lines by solving the simultaneous linear equations. (b) 3x+2y=12 (a) y=x+5 y=2x+4

N(6, 8) 7 K

,

In the diagram, the straight line MN is parallel to the x-axis and the length of OK is 2 units.

Find (a) the y-intercept of the straight line MN, (b) the gradient of the straight line KN. Answer:

2x-y=1

(b)

(a) Answer:

12 The diagram shows a rectangle PQRS drawn on a Cartesian plane. Y

8 Find the equation of a straight line which passes through each of the following pairs of points. (a) (0, -7) and (3, 2) (b) (-2, 4) and (-8, 1) Answer: (a) Calculate the gradient of the straight line PR. (b) Find the y-intercept of the straight line QS. Answer:

(b)

(a)

In the diagram, the gradient of the straight

13

Subtopic 5.5 9 Determine whether each of the following pairs of straight lines are parallel. (a) y=x-3 (b) 2x-5y=1 3y=x-6 5y=2x+3

line KLM is - 2. Find

M

(a) the value of p, x (b) the x-intercept of the straight line MN.

Answer: Answer: (a)

22

(b)

y A

14

In the diagram, 0 is the origin. The gradient of

R

18

In the diagram, EF, FG and GH are straight lines. OE is parallel to FG and EF is parallel to GH. Given the equation of EF is 2x + y = 6. (a) State the equation of the straight line FG. (b) Find the equation of the straight line GH and hence , state its y-intercept.

G

the straight line ST is 2 *x

Find (a) the gradient of the S(4, -10) straight line ROS, (b) the y-intercept of the straight line ST.

0

F

H(10, -6)

Answer: (a)

(b) Answer:

(b)

(a) In the diagram, 0 is the origin. OPQR is a parallelogram. Find (a) the equation of the straight line PQ, (b) the coordinates of point Q.

(a)

16

19 In the diagram, 0 is the origin. Q lies on the x-axis and P lies on the y-axis. The straight line PT is parallel to the x-axis and the straight line PQ is parallel to the straight line RS. The equation of the straight PQ is x + 2y = 10. y

(b)

In the diagram, the straight line PQ is parallel to the straight line OR. Find (a) the gradient of the straight line OR, (b) the y-intercept of the straight line QR.

(a) State the equation of the straight line PT. (b) Find the equation of the straight line RS and hence, state its x-intercept. Answer:

Answer: (a)

(b)

(a)

(b) 20

17

M(2, 10)

In the diagram, OPQR is a parallelogram and 0 is the origin. Find (a) the equation of the straight line QR. (b) the y-intercept of the straight line PQ.

E(0, 6)

0 F(3, 0)

Answer: (a)

y

N

The diagram shows a straight line EF and a straight line MN drawn on a Cartesian plane. EF is parallel to MN. Find (a) the equation of the straight line MN, (b) the x-intercept of the straight line MN.

Answer:

(b)

(a)

23

(b)

6.4 Frequency Polygons 6.5 Cumulative Frequency 6.6 Measures of Dispersion

6.1 Class Intervals 6.2 Mode and Mean of Grouped Data 6.3 Histograms

SECTION A

Objective Questions

This section consists of 16 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 6.1 1.

Questions 4 and 5 are based on the following frequency table.

Age Group (years)

Score

Frequency

11-20

1-10

5

21-30

11 - 20

15

31 -40

21 - 30

41-50

31-40

Height (cm)

Frequency

10

101 - 110

2

8

111 - 120

5

121-130

6

131 - 140

9

141-150

4

151-160

3

161-170

1

Based on the frequency table, the lower limit of the class interval 31 - 40 is A 30.5 C 39.5 B 31 D 40

4 Calculate the size of the class interval in the table. C 9 A 7 B 8 D 10

Length of Rope (m)

5 State the lower boundary of the class interval 11 - 20. A 10 C 11 B 10.5 D 11.5

0.4-0.8 0.9 - 1.3 1.9-2.3 In the table, the missing class interval is A 1.3-1.8 B 1.3 - 1.9 C 1.4 - 1.8 D 1.4 - 1.9 3 The largest value in a data is 38 and the smallest value is 12. If the number of class intervals required is 6, then the suitable size of the class interval is A 4 C 6 B 5 D 7

7 The frequency table shows the heights of 30 students in a class.

The midpoint of the modal class is A 135 C 136 B 135.5 D 136.5

Subtopic 6.2 6 The frequency table shows the lengths of 30 ribbons. Length (cm)

Frequency

40-44

3

45 - 49

8

50 - 54

10

55 - 59

9

The modal class is A 45 - 49 B 49.5 - 54.5 C 50-54 D 50.5 - 54.5

8 The frequency table shows the marks obtained by 20 students in a game. Marks

Frequency

11-15

3

16-20

5

21-25

6

26 - 30

4

31-35

2

Calculate the mean mark. C 21.65 A 20.55 D 22.25 B 21.55

24

i

9 The frequency table shows the masses of 20 baskets of mangoes collected by a farmer. Mass of Frequency Mangoes ( kg) 9-11

3

12 - 14

6

15-17

5

18-20

4

21 - 23

2

Calculate the mean mass, in kg, of a baseket of mangoes. A 14.4 C 16.4 B 15.4 D 30.8

Subtopic 6.3 Questions 10 and 11 are based on the following histogram. The histogram shows the distribution of the ages of a group of participants in a competition.

Subtopic 6.4 Questions 12 and 13 are based on the following frequency polygon.

15 The table shows the distribution of the masses of sugar sold in a market on a certain day. Mass of

The frequency polygon shows the thickness of 100 books in a library.

Thickness of book (mm)

12 The modal class is A 10.5 - 15.5 B 11 - 15 C 12 - 15 D 12.5 - 15.5

6 12 10 18 2

4 5

Upper Boundary

Cumulative Frequency

0

0.5

0

1

1.5

6

2

2.5

18

3

3.5

x

4

4.5

46

5

5.5

48

The value of x is A 10 B 22 C 28 D 30

Subtopic 6.6 16 The ogive shows the total donation that is collected from 100 donors. Cumulative frequency

N M - tr l00

11 The percentage of the number of participants who are more than 40 years old is A 17 B 20 C 32 D 34

Frequency

3

Mass of Sugar (kg)

13 Of the total number of books with a thickness of between

them are written in Malay and the rest are in English. The number of English books with a thickness of between 5 mm and 20 mm is A 32 C 48 B 40 D 60

10 The mean age, in years, of the group is A 32.0 B 36.8 C 37.3 D 38.6

1 2

Based on the table above, a cumulative frequency table is constructed as follows:

5 mm and 20 mm each, 5 of

Age (years) .

Sugar (kg)

Subtopic 6.5 14 Which of the following is not a step to draw an ogive? A Add one class interval with a cumulative frequency of 0 before the first class interval. B Find the upper boundary of each class interval. C Find the cumulative frequency of each class interval. D Plot the graph of frequency against the upper boundary.

25

50-25-0

10 20 30 40 50 60 Donations (RM)

The first quartile is A 25 B 30 C 35 D 40

SECTION B Subjective Questions\ This section consists of 16 questions. Answer all the questions. You may use a non -programmable scientific calculator. Subtopic 6.1

Subtopic 6.2

1 The data shows the masses, in kg, of 40 boxes that are shipped by a transport company.

3 The data shows the circumferences, in cm, of 30 rubber tree trunks that are sent to a factory to be processed to produce furniture wood.

68 11 59 34 22

42 52 43 61 60

67 45 25 20 36

55 28 46 33 58

56 48 52 42 23

44 26 24 18 48

53 35 44 32 35

56 45 37 57 47

140 165 152 153 157 160 148 143 133 146 127 157 135 140 122 142 151 161 128. 147 137 142 163 131 139 149 141 145 162 150

Construct a frequency table for the data by using the class intervals, 11 - 20, 21 - 30, 31 - 40 and so on. State the size of the class interval.

(a) Construct a grouped frequency table for the data by using the class intervals, 120 - 129, 130 - 139, 140 - 149 and so on. (b) (i) State the size of the class interval. (ii) State the modal class. (iii) Calculate the mean circumference, in cm, of the trunks.

Answer:

Answer: (a)

2 The data shows the time, in minutes , required by 25 students to solve the mathematical problems in a set of questions. 8 24 15 17 28 7 12 8 11 14 16 12 16 7 21 11 10 13 14 8 26 27 18 30 20

4 The frequency table shows the distribution of the masses of -40 watermelons harvested by a farmer.

Construct a frequency table for the data by using the class intervals, 6 - 10, 11 - 15, 16 - 20 and so on.

Mass (kg)

Frequency

1.5- 1.9

6

Answer:

2.0-2.4

10

2.5 - 2.9

12

3.0-3.4

8

3.5 -3.9

4

(a) State the modal class. (b) Calculate the mean mass, in kg. Answer: (a)

(b)

26

8 The frequency table shows the masses of the baskets of prawns transported by a fisherman's boat.

Subtopic 6.3 5 The frequency table shows the distribution of the periods of complete oscillation of 55 pendulums.

Mass ( kg)

Frequency

12 - 15

5

16 - 19

7

Period of Oscillation (minutes)

Frequency

20-23

8

2.5 -2.9

6

24-27

12

3.0 - 3.4

5

28-31

4

3.5 - 3.9

18

32 - 35

3

4.0-4.4

11

36 - 39

6

4.5 - 4.9

10

5.0-5.4

5

Construct a frequency polygon based on the frequency table.

Based on the frequency table, draw a histogram.

Subtopic 6.5 6 The frequency table shows the heights of 100 students in a school.

9 Complete the cumulative frequency table below.

Height ( cm)

Frequency

120 - 124

8

125 - 129

10

3-5

4

130 - 134

22

6-8.

5

135 - 139

13

9-11

6

140 - 144

12

12 - 14

10

145 - 149

20

15 - 17

8

150-154

15

18-20

2

Distance Cumulative Upper Frequency Frequency Boundary (km)

Based on the frequency table, draw a histogram.

Subtopic 6.6 Subtopic 6.4

10 The frequency table shows the distribution of the masses of 45 watermelons in a stall.

7 The frequency table shows the distances travelled by a group of students to school. Distance (km)

Frequency

31-40

7

41 - 50

8

51 - 60

12

61-70

16

71 - 80

9

81-90

5

91-100

3

Mass (kg)

Frequency

1.6 -2.0

5

2.1 -2.5

8

2.6-3.0

9

3.1 - 3.5

12

3.6 -4.0

7

4.1 -4.5

4

(a) Draw an ogive based on the data given. (b) From the ogive, find (i) the median, (ii) the first quartile, (iii) the third quartile.

(a) Draw a histogram. (b) Construct a frequency polygon based on the histogram in (a).

27

Subtopics 6.1 - 6.6 13 The data shows the number of foreign workers employed by 40 factories in an industrial area. 24 21 50 33

11 The frequency table shows the lengths of 42 pieces of ribbon used to tie presents. Length (cm)

Frequency

61-63

2

64- 66

3

67-69

8

70-72

10

73 - 75

7

76 - 78

6

79-81

5

82-84

1

(a) Class Interval

Frequency Ntid- Cumulative Upper point Frequency Boundary

1 - 10 (ii) (iii) 12 The table shows the scores obtained by a group of shooters in a shooting competition. Frequency x Score

10

30

12

60

14

x

16

48

18

36

20

20

58 2 42 37 65 28 35 38 56 22 34 57

Answer:

(b) (i)

Score

43 29 16 68

(a) Based in the data and using a class interval of 10, complete the table in the answer space. (b) Based on the table in (a), (i) state the modal class, (ii) calculate the estimated mean number of foreign workers in each factory. (c) For this part of the question, use graph paper. Using a scale of 2 cm to 10 foreign workers on the horizontal axis and 2 cm to 5 factories on the vertical axis, draw an ogive for the data. From the ogive, find (i) the median, (ii) the third quartile.

(a) Draw an ogive based on the data given. (b) From the ogive, find (i) the median, (ii) the first quartile, (iii) the third quartile. Answer:

34 22 25 33 15 28 65 48 28 11 13 32 17 48 17 23 5 28 44 54

(b) (i)

If the total frequency is 20, find the value of x. Answer:

28

14 The data shows the volume, in mt, of water that is collected in each bottle by 50 participants in a telematch. 142 142 151 154 146

160 152 145 146 148 154 141 152 151 137 155 151 144 147 154 145 158 163 164 157

156 149 140 157 146

151 152 153 158 152

150 138 141 137 153

142 147 138 140 157

Answer: (a)

153 149 139 151 152

Marks

Midpoint

40 - 44

42

Frequency

45-49 50 - 54 55-59 60-64 65-69

(a) Construct a grouped frequency table for the data by using the class intervals, 130 - 134, 135 - 139 and so on. (b) For this part of the question, use graph paper. Using a scale of 2 cm to 5 mf on the horizontal axis and 2 cm to 5 participants on the vertical axis, draw an ogive for the data. (c) From the ogive, find (i) the median, (ii) the interquartile range.

16 The data shows the monthly savings, in RM, of 40 students. 46 45 52 47 50

60 56 54 45 64 66

68 63 40 58 69 56

59 55 60 46 61 65

61 44 57 67 50 58

44 54 34 40 58

60 32 45 48 51

42 46 52 45 36

38 56 35 42 48

41 40 50 53 56

55 60 36 44 32

(a) Based on the data and using a class interval of 5, complete the table in the answer space. (b) Based on the table in (a), calculate the estimated mean of the monthly savings of each student. (c) For this part of the question, use graph paper. Using a scale of 2 cm to RM5 on the horizontal axis and 2 cm to 1 student on the vertical axis, draw a frequency polygon to represent the data. (d) Based on the frequency polygon in (c), state one piece of information about the montly savings.

15 The data shows the marks scored by 36 students in a monthly mathematics test. 51 65 58 62 68 48

53 37 40 38 44

48 59 49 62 55 64

Answer:

(a) Using the data and a class interval of 5 marks, complete the table in the answer space. (b) Based on the table in (a), (i) state the modal class, (ii) calculate the mean score of the group and give the answer correct to 2 decimal places. (c) For this part of the question, use graph paper. Using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 1 student on the vertical axis, draw a histogram for the data.

(a)

Class Interval

Midpoint

Frequency

31 - 35

33

4

36-40

(b) (d)

29

7.1 Sample Spaces

7.2 Events

7.3 Probability of an Event

SECTION A Objective Questions `a This section consists of 25 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 7.1

Subtopic 7.2

Subtopic 7.3

1 A letter is selected at random from the word `MALAYSIA'. Which of the following outcomes is not possible? A A vowel is selected. B A consonant is selected. C Letter S is selected. D Letter T is selected.

5 A letter is selected at random from the word JASMANI'. The elements in the sample space excluding the letter A are A J, S, M, I B J, S, M, N C J, S, M, N, I D J, A, S, M, N, I

8 A factory produces 3 000 computers in a year. 60 of the computers are defective. If a computer is selected at random from the factory, find the probability that the computer is defective. A 1 60 B

2 A colour is selected at random from the colours of the traffic lights. All the possible outcomes are A yellow, red, blue B yellow, green, white C green, red , yellow D red, green, blue

3 A prime number less than 13 is selected at random. The sample space is A (3, 5, 7, 11) B (2, 3, 5, 7, 11) C {2, 3, 5, 7, 11, 13) D {2, 3, 5, 7, 9, 11, 13)

4 A coin is tossed twice. If H represents heads and T represents tails, the sample space is A {H,T} B (HH, TT, HT} C {HH, TT, HT, TH) D (H, T, HH, TT)

6 Two dice are rolled. M is the event of obtaining two numbers with a sum of 6. The elements of M are A {(2, 3), (3, 2)) B {(1, 6), (2 , 3), (3, 2)) C ((1, 5), (2, 4), (3, 3), (4, 2), (5, 1)) D {(3, 3), (5, 1), (2, 4), (0, 6), (4, 2))

7 A basket has a green apple and two red apples. Two apples are selected at random from the basket. Which of the following is a possible event? A Two green apples are selected. B An apple and an orange are selected. C A red apple is not selected. D A green apple and a red apple are selected.

30

1 50

C 1 40 D

1 30

9 A survey on the monthly expenses of 1 000 residents is carried out in a residential garden. The results are shown in the frequency table below. Monthly Expenses (RM)

Frequency

1 000

180

1200

420

1 400

210

1 600

190

Find the probability that a resident selected at random has expenses of more than RM1 200. A 3 8 B 2 5 C 3 5 D 3 4

10 The table shows the ages of 4 000 tourists who visited Tioman Island in a certain month. Age (years)

Frequency

25 - 31

160

32 - 38

800

39 - 45

1 250

46 - 52

1 790

If a tourist is selected at random, find the probability that the tourist's age is less than 39 years. A

6 C 3 25 10

B

3 D 2 20 5

11 A dice is tossed 2 400 times. The probability of obtaining a number 4 is 6. Find the number of times that the number 4 can be obtained. A 200 C 400 B 300 D 600 12 In a survey on the sizes of shoes worn by a group of women, it is found that 360 women wear shoes of size 5. If a woman is selected at random from the group, the probability that the. woman wears shoes of size 5 is 3. Find the total number of women in the group. A 300 C 480 B 360 D 540 13 There are 16 boys and some girls in a class. If a student is chosen at random from the class, the probability that a girl is chosen is 7 11' Find the number of girls in the class. A 24 C 32 B 28 D 36

14 A bag contains 6 yellow balls and x red balls. A ball is chosen at random from the bag and the probability of choosing a yellow ball is 1. The value of x is 3 A 12 C 16 B 14 D 18 15 A basket contains 8 mangoes and some mangosteens. If a fruit is selected at random from the basket, the probability of selecting a mangosteen is 3. Find the number of 5 mangosteens in the basket. A 12 C 14 B 13 D 15 16 A box contains 5 red pens and a number of green pens. If a pen is selected at random from the box, the probability of selecting a red pen is 3 . Three additional red pens are added into the box. If a pen is selected at random from the bag , find the probability of selecting a red pen.

18 A cupboard is filled with 35 science books and History books. If a book is selected at random from the cupboard, the probability of selecting a History book is 3 . Then 10 science books and 5 History books are added into the cupboard . A. book is selected at random from the cupboard . State the probability of selecting a Science book. A 1 7 B 2 7 C 2 5 D 3 5 19 A box contains nine cards as shown below. L A T 0 R [C] A L C A number of cards marked U are added into the box. If a card is selected at random from the box, the probability of selecting a card marked L is 8. How many cards

A 2 9

marked U are added into the box? A 4 B 5 C 6 D 7

B 1 4

C 4 9 D 3 4 17 There are 20 male workers and 25 female workers 'in a factory. 6 of the male workers have cars. If a worker is selected at random from the factory, the probability of selecting a worker who has a car is 5 . The number of female workers who have cars is A 8 B 12 C 16 D 18

31

20 A bag contains 20 pens which are either blue or red. If a pen is selected at random from the box, the probability of selecting a blue pen is 5. Then 8 blue pens are added into the bag. If a pen is selected at random from the box, the probability of selecting a red pen is A ? . C 4 5 7 B 2 D 5 7 7

21 The following number cards are put in a bag. 2

3

5

6

7

8

9 10

Then all the cards with numbers that are multiples of 3 are taken out. If a card is chosen at random from the bag, the probability that the number is a multiple of 2 is A 1 3 B 3 5

23 The table shows the results of a group of candidates in an examination. Grade

Number of Candi- 8 dates

A

D 4 5

B

A

3 C 8 20 15 B 1 D 13 5 20

B

C

D

E

16 11 10 5

Given that grade D is considered fail, if a candidate is selected at random from the group, the probability of selecting a candidate with a pass is

C 2 3

22 A box contains 40 sheets of paper. 24 of them are red and the rest are orange in colour. Then 10 sheets of orange coloured paper are used up. If a sheet is selected at random from the bag, the probability of selecting an orange sheet is

A

7 10 D 39 50

11 50 13 25

C

25 The incomplete table shows bank notes of four denominations in a bag. Value of RM1 RM2 RM5 RM10 Notes Number of Notes

10

6

12

If a bank note is taken out at random from the bag, the probability of selecting a RM2 note is 6 . The number of bank notes of more than RM2 value is A 8 B 20 C 24 D 36

24 A container has 12 blue beads, 20 green beads and some yellow beads. If a bead is selected at random from the container, the probability of selecting a green bead is 12. The number of yellow beads in the container is A 10 C 16 B 12 D 48

SECTION B Subjective Questions\ This section consists of 10 questions. Answer all the questions. You may use a non-programmable scientific calculator.

Subtopic 7.1

Subtopic 7.2

1 An even number is chosen at random from the numbers, 6, 7, 8, 9, 10, 11 and 12. Write all the outcomes of the experiment.

3 A letter is selected at random from the word 'ENGLISH' Write the following events. (a) A vowel is selected. (b) A consonant is selected.

Answer: Answer: (a) 2 Box P contains a red card and a yellow card. Box Q contains a red card and a blue card. A card is selected at random from each box. By using a suitable letter to represent each coloured card, write the sample space for the experiment.

(b)

Answer:

32

4 A bag is filled with six cards numbered 20, 22, 24, 26, 28 and 30. Two cards are selected at random. Determine whether each of the following events is possible. (a) Two multiples of 4 are selected. (b) Two prime numbers are selected. (c) At least one multiple of 5 is selected.

7 A box contains 24 green cards, 30 yellow cards and 26 white cards. If a card is selected at random from the bag, find the probability that the card is (a) a white card. (b) not a yellow card. Answer: (a)

Answer:

(b)

(a)

8 All the cards in the diagram are put into an empty box.

(b)

G

(c)

E

0 G

R

A

H

Y

If a card is selected at random from the box, find the probability that the card is marked with (a) the letter H, (b) a vowel.

Subtopic 7.3

Answer:

5 A school has 1 200 students. If a student is selected at random, the probability of selecting a prefect is 40 . Find the number of prefects 9 A box contains 24 fifty sen coins and a number of ten sen coins. If a coin is selected at random from the box, the probability of selecting a ten

in the school. Answer:

sen coin is 5 (a) Find the total number of coins in the box. (b) If 8 fifty sen coins are added into the box, find the probability a coin selected at random is a fifty sen coin.

6 The table shows the marks scored by 160 students in a mathematics test. Marks

Number of Students

51 - 55

16

56 - 60

50

61-65

72

66- 70

22

Answer:

10 There are 72 red chairs and blue chairs in a class. If a chair is selected at random from the class the probability of selecting a blue chair

If a student is selected at random from the group, find the probability that his score is (a) in the class interval 61 - 65, (b) less than 61 marks.

is 2 . 3 (a) Find the number of blue chairs in the class. (b) If 4 red chairs and 2 blue chairs are taken out from the class, find the probability that a chair selected at random is a red chair.

Answer: (a)

Answer:

(b)

33

8.1 Tangents to a Circle 8.2 Angles between Tangents and Chords

8.3 Common Tangents

Objective Questions,,,

SECTION A

This section consists of 30 questions . Answer all the questions . For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 8.1 1 The diagram shows a circle with centre O. FH and GH are tangents to the circle.

The value of y is A 10 C 20 B 15 D 35

Subtopic 8.2 6 In the diagram , PQR is a tangent to the circle QST at Q.

4 In the diagram, PQ is a tangent to the circle with centre O. PO is parallel to the straight line QR.

P

Which of the following is not true? A FH=GH B p° = q° C r°=s° D LOFH # 90° 2 In the diagram, PQ and PR are tangents to the circle with centre O.

Q

The value of x is

A B

The radius, in cm, of the circle is A 4.46 C 5.65 B 5.32 D 6.12

25 65

C D

72 82

7, In the diagram, ABC is a tangent to the circle BDEF at B.

5 In the diagram , XY and ZY are tangents to the circle with centre O. The value of x is A 48 C 56 B 54 D 59

R

The value of x is A 25 C 60 B 50 D 65 3 In the diagram, JL and KL are tangents to the circle with centre O.

8 In the diagram , PUV and PQR are tangents to the circle QSTU. The length of XY, in cm, correct to two decimal places is A 10.39 B 11.24 C 12.69 D 12.81

r

34

I

1

ZSQR is equal to 12 In the diagram, PQ and PS 16 In the diagram, the tangent A LPQU C ZQTU are tangents to the circle QRS MPN touches the circle PQRS B LQSU D ZQUS with centre O. with centre 0 at P. 9 In the diagram , JKL is a tangent to the circle KFGH at K. P

S

The value of y is A 45 C 60 B 50 D 65

The value of q is A 55 C 70 B 65 D 75

13 In the diagram, the tangents QR and SR touch the circle PQS at Q and S respectively. Q

10 In the diagram, JKN is a tangent to the circle KLM with centre O. JLOM is a straight line.

The value of x + y is A 50 C 70 B 60 D 80

17 The diagram shows a circle PQRS with diameter PTR. The tangent PU touches the circle at P. QTS is a straight line.

The value of x is A 25 C 35 B 30 D 40 14 In the diagram, PQS is a circle with centre O. The tangent RST touches the circle at S. POQR is a straight line. The value of x is A 29 B 32 C 34 D 35 11 In the diagram , ABF is a tangent to the circle BCDE with centre O. BOD and COEF are straight lines.

18 In the diagram, ABC and ADE are tangents to the circle BDF. E

The value of x is A 15 C 45 B 30 D 60 15 In the diagram , MPN is a tangent to the circle PQRS at P. PTR and QTS are straight lines..

Calculate the values of x and y. A x=25,y=40 B x=25,y=65 C x=25,y=75 D x=30,y=50

The value of y is A 70 C 90 B 80 D 100

A-

B.

The value of x is A 50 C 60 B 55 D 65 19 In the diagram , PQR and TSR are tangents to the circle QWS.

P The value of x is A 30 C 55 B 45 D 65

35

The value of x + y is A 124 C 132 B 128 D 144

20 In the diagram, QRS is a circle with centre O. PST is a tanget to the circle at S. PQOR is a straight line.

24 In the diagram , PQR is a tangent to the circle QST at Q. P

The length, in cm, of AB is A 2.47 C 3.17 B 2.67 D 3.47 28 In the diagram, MN is a common tangent to the two circles with centres 0 and C respectively.

R

The value of x is A 20 C 40 B 30 D 60 21 In the diagram , JKL is a tangent to the circle KMNP at K.

The length of arc QS is equal to the length of arc ST. Find the value of x.

A B

28 34

C D

56 68

25 In the diagram, SRT is a tangent to the circle with centre 0 at R. OQT, OUR and PUQ are straight lines.

If the length of OC is 15 cm, calculate the value Qf LMOC. C 84°10' A 81°40' D 85°20' B 82°20 ' 29 In the diagram, PQ is a common tangent to the two circles with centres 0 and C respectively.

I The value of y is A 55 C 95 B 85 D 125 22 In the diagram, QRS is a circle with centre O. PQT is a tangent to the circle at Q.

Find the value of x. A 15 C 35 B 20 D 55

Subtopic 8.3 26 In the diagram, HG is a common tangent to the two circles with centres E and F respectively.

P

The value of x is A 30 C 60 B 40 D 70 23 In the diagram , JKN is a tangent to the circle KLM at K and LMN is a straight line.

7 cm G

Calculate the length, in cm, of HG. A 14.96 C 15.67 B 15.45 D 15.87

Find the area, in cm2, of quadrilateral COPQ. A 104.4 C 110.2 B 108.6 D 120.4 30 In the diagram, PQR is a common tangent to the two circles with centres M and N respectively. LSR is a tangent to the circle with centre N. LMNQ is a straight line and MN = 4 cm.

27 The diagram shows two circles with centres 0 and C respectively. PQ is a common tangent to the two circles. OABC is a straight line. P Calculate the length, in cm, of QR. A 5.12 C 6.28 B 5.66 D 6.64

The value of y is A 20 C 40 B 30 D 50

36

SECTION B Subjective Questions This section consists of 10 questions. Answer all the questions. You may use a non-programmable scientific calculator. 4

Subtopic 8.1

In the diagram, ABC is a tangent to the circle BDEF at B. BGE and DGF are straight lines. Calculate the value of D (a) x

In the diagram, RS is a tangent to the circle with centre 0 and ROV is a diameter of the circle. STV is a straight line. Calculate R 10 cm'

C (b) y, (c) Z.

(a) ZTRS,

Answer:

(b) the length, in cm, of VT.

(a)

(c)

Answer:

(b)

(b)

(a)

5 2

In the diagram, KL and KM are tangents to the circle with centre O. Calculate (a) LKOL, (b) the length, in cm, of KO.

In the diagram, QRST is a circle with centre 0. The tangent PQ touches the circle at Q. Calculate the value of (a) x, (b) y, (c) Z. Answer: (a)

Answer: (a)

(c)

(b) (b)

6

In the diagram, the circle BCD with centre 0 has a radius of 5 cm. AB and AC are tangents to the circle. Calculate (a) the value of x, (b) the value of y, (c) the length, in cm, of AC.

Subtopic 8.2 3

In the diagram , PQR is a tangent to the circle QST. Calculate the value of

(a) x, (b) y. P Q

R

Answer:

Answer:

(a)

(a)

(b)

(b)

37

(c)

Subtopics 8.1 - 8.3

Subtopic 8.3

9 In the diagram, PQ is a common tangent to the two circles with centres 0 and C respectively.

7 In the diagram, PQ is a common tangent to the two circles with centres 0 and R respectively.

Given OP = 8 cm and RQ = 6 cm, calculate (a) the length , in cm, of PQ, (b) LPOR. Answer:

Given OP = 5 cm and CQ = 3 cm, calculate (a) the value of x, (b) the length, in cm, of PQ.

(a)

Answer: (a)

(b) (b)

8 The diagram shows, two circles with diameters OK and MK respectively. 0 is the centre of the big circle. KL is a common tangent to the circles.

10 In the diagram, ABD is a common tangent to the two circles with centres 0 and C respectively. OBC is a straight line.

M

Calculate (a) LB CD, (b) the radius, in cm, of the circle with centre C.

Given OK = 7 cm, calculate (a) the length, in cm, of KL, (b) the area, in cm2, of the shaded region. (Use it_ 7)

Answer: (a)

Answer: (a)

(b) (b)

38

9.1 The Values of Sin 9, Cos 9 and Tan 9

SECTION A

9.2 Graphs of Sine, Cosine and Tangent

Objective Questions I,,

This section consists of 35 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 9.1 1 In the diagram, 0 is the centre of the semicircle PQRS. y Q(-0.5, 0.866)

Which of the following is not true? A sin x° 0.866 B cos x° = 0.5 C tan 180° = 0 D sin 90° = 1 2 2 cos 600 - tan 45° = A -1 C 0 B -1 D 1 2 2 3 4 cos 180° + 2 sin 90° _ A -6 B -2 C 2 D 6 4 6 sin 30° - 3 tan 360° _ A -3 B 0 C 3 D 6 5 Given cos x° = -0.2079 and 0° , x° < 360°. The values of x are A 78 and 102. B 78 and 282. C 102 and 258. D 102 and 282.

6 Given tan 9 = 0.7265 and 180° , 0 , 360°, the value of 0 is A 216° C 306° B 234° D 324° 7 Given sin 9 = -0.9205 and 0° , 9 , 360°, the values of 9 are A 67° and 113°. B 113° and 247°. C 113° and 293°. D 247° and 293°. 8 Given tan p° _ -7.12 and 0° , p° , 360°, find the values of p. A 82 and 262 B 98 and 262 C 98 and 278 D 262 and 278 9 Given cos 9 = -0.8116 and 90° , 9 , 180°, find the value of 9. A 125°45' C 144°15' B 135°45' D 154°15' 10 In the diagram , QRS is a

11 In the diagram , cos ZBAC 5 13

B

The length, in cm, of BC is A 18 C 24 B 20 • D 26 12 In the diagram , ADC is a straight line. A

Given BD =15 cm, tan ZBAD 8 and tan LCBD = 3 calculate the length, in cm, of ADC. A 18 C 24 B 20 D 34 13 In the diagram, KLM is a straight line.

straight line and cos x° = 4

I

12 cm K 5 H

L

cm

M

Q The value of sin y° is

What is the value of cos 9?

A -4 C 3

A 12 C 5 T313 L D 12 B -13 13

5

5

B -3 D 4 5 5

39

14 In the diagram , KMN and MLP are straight lines. Given KM : MN = 2: 1 and

Find the value of cos LPSR.

A -4 5 B

cos ZLKM = 5

C 3 5

-3 5

D

22 In the diagram , QRST is a trapezium and PQR is a straight line.

4 5

18 In the diagram, DEF is a straight line.

T mmS

P rr "R Q 7 cm

The value of cos 0 is A -4 C 3 5 5 B F

Find the value of sin LMPN. A 1 C 9 3 5 B

5 9

D 9 4

19 In the diagram, PQR is a straight line. Given

15 In the diagram , PQST is a rectangle. Given QR : RS =1 : 4. Q

R

The value of tan LDEG is A -1.376 C -0.5878 B -0.8090 D 0.8090

D 4 5

23 In the diagram , PQRS is a straight line and PQ = QR.

20 cm

12 cm

cos LSPR = 5

P

R xo 10 cm

Q

S

U

S

Find the value of tan x°. A -5 C -4 5

5 cm P 16 cm Q P

15 cm

T

Find LQRT. A 67°23' C 157°23' B 112°37' D 161°34'

Find the length, in cm, of QR. A 8 C 18 B 9 D 25

P

A 12 B 18

M

N

D

C 24 30

21 In the diagram , PQRS is a rectangle . Given PT = 3TQ

3

3

-3 4

D 5 3

dan tan x° = 4 3

5 cm

Q

It is given that cos x° = 8 17 and tan y° = 2. Calculate the length, in cm, of EFG. A 19 C 38 B 31 D 46 25 In the diagram, R is the midpoint of the straight line QS. Q R 18 cm

17 In the diagram, PQRS is a rhombus. RST is a straight line. P

T

F

The length , in cm, of LMN is

A -4 C 4

24 In the diagram , EFG is a straight line.

K

L

The value of tan x° is

B D -3 3 4

20 In the diagram, LMN is a straight line. Given KM = 6 cm.

16 In the diagram , PTR and QTS are straight lines. Given ST = 3 cm.

B

-3 5

R

S

Find the value of sin y°.

C 4 5

A 3 5 B

3 4

D 5 3

40

S

The value of cos x° is A 5 C 3

4

B

4

5

4

D

3

5

26 In the diagram , KMN is a right-angled triangle.

30 In the diagram, PQS is a straight line. Given sin LPST = 5 and

M

tan LQSR = 5. 12

P 12 cm T K--

N

34 Which of the following represents the graph of y = cos x?

A y

It is given that LN = 10 cm, KM = 12 cm and L is the midpoint of KM. Find the value of tan 9.

1 S

A -5 C -3 4 4

The length, in cm, of PQ is A 7 C 10

B -4 D -4

B 8 D 13

3

The value of k is A 90° C 270 B 180° D 360°

0 -1

B

y

C

y

5

27 In the diagram, PQS and RST are straight lines. Given tan x° = 1 and cos y° 5

31 In the diagram, ABCD is a rectangle. BEC is a straight line and BE = IBC. 3 12 cm D

A

1 6 cm B E C The value of tan LAEC is R

The length, in cm, of RST is A 12 C 20 B 16 D 24 28 In the diagram, QRS is a straight line. Given tan LPSQ = 1. P

4 C 4 3 3 B -3 D 3 4 2 32 In the diagram , ABCD is a rectangle . ADF and BEF are straight lines. Given CE = ED and tan ZAFB = 3. 4

35 Which of the following represents the graph of y = sin x for 0° -- x -- 180°? A y

12 cm

The value of tan ZPRQ is A 1 C 4 3 4 B 1 D 4 29 In the diagram , PST and QRS are straight lines.

B C The value of tan ZBED is A -4 C 3

3

4 B -4 D 4 3

180°

C

Subtopic 9.2

15 cm J 1

33 The diagram shows the graph of y = cos x. y

D

Find the value of cos 9. A -4 C 5 5 4 B

-2 5

D 3 2

41

SECTION B Subjective Questions\ This section consists of 10 questions. Answer all the questions. You may use a non-programmable scientific calculator. 4 (a) Given sin 9 = 0.9397 and 00 9 = 360°,

Subtopic 9.1

find the values of 9. (b) Given cos a = 0.4352 and 00 a 3600,

1 In the diagram, 0 is the centre of the circle PQRST.

find the values of a. (c) Given tan f3 = -3.354 and 00 , f3 360°, find the values of P. Answer:

O >W1 '" Q(0.866, -0.5)

State the values of (a) sin w°, (b) tan 270 0, (c) cos 180 0.

In the diagram, EFG is a straight line. Find the values of (a) sin x°,

Answer:

(b) cos y°.

(b) Answer: (a) 2 Without using a scientific calculator, calculate the values of (a) sin 30° + cos 180°, (b) 4 tan 45° - 3 sin 270 °, (c) -5 cos 60° - sin 90 0.

(b)

Answer: 6

(a)

G

(b) (c) 3 Find the values of (a) sin 143°, (c) tan 310°, (b) cos 307°15', (d) tan 207.4°.

Answer: (a)

Answer:

(b)

42

In the diagram, DEF and DHG are straight lines. (a) State the values of sin x°. D (b) Calculate the length, cm, in of FG.

7 In the diagram, ACD is a straight line.

Subtopic 9.2 9 On the axes in the answer space, sketch the graph of each of the following functions. (a) y=sinxfor0°x360° (b) y = cos x for 00 x 360° (c) y = tan x for 0° x 360° Answer:

Given sin LACB = 3 find the values of

(a) Y

(a) cos x°, (b) y. Answer:

0

4- x

(a)

(b) Y (b)

0

(c) 8 In the diagram , PQST is a rectangle and 2QR = RS.

I- x

y

0

^x

10 The diagram shows the graphs of y = sin x and y = cos X.

12 cm

y

Find the values of (a) cos x°, (b) tan y°. Answer: (a) Find the coordinates of (a) point P, (b) point Q.

(b)

Answer: (a) (b)

43

Form 4

Angles of Elevation and Depression

10.1 Angles of Elevation and Depression

ective Questions

SECTION A 0

This section consists of 20 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 10.1 1 In the diagram, JKL and MN are two vertical poles on a horizontal plane. I r]

K

L

The height, in m, of the flag pole is A 3.56 C 3.72 B 3.68 D 3.82 4 In the diagram, K, L and M are three points on a horizontal plane. MN is a vertical tower. Given KLM is a straight line and L is the midpoint of KM.

N

The angle of elevation of point J from point M is

A LJMK C LKJM B LJML D LLMN 2 In the diagram, KL and MN are two vertical poles on a horizontal plane. P is a point on KL and MN = PL. K

P

it

3 In the diagram, EG is a vertical flag pole on a horizontal plane. The angle of elevation of G from F is 24°. G

7 In the diagram, PQ and RS are two vertical poles on a horizontal plane. The angle of elevation of S from Q is 35°. S

The angle of elevation of N from K is A 50°10' C 51°47' B 50024' D 53057' 5 In the diagram, X and Y are two points on a horizontal plane. YZ is a vertical pole.

L N The angle of depression of M from K is

A ZKML C LNKP B LMKP D LPMK

The angle of elevation of T from P is A 37°52' C 51°3' B 38°57' D 52°7'

Z 8m

Q km

4MI

P_

20 m

Calculate the value of x. .A 5.4 C 14.0 B 11.0 D 18.0 8 In the diagram, EF and GH are two vertical poles on a horizontal plane. E

12 m

The angle of depression of X from Z is A 26°24' C 32°24' B 28046' D 33°41' 6 In the diagram, QS and RT are two vertical poles on a horizontal plane. PQR and PST are two straight lines.

G

I

F 40 m H

The angle of depression of peak G from peak E is 25°. Calculate the height, in m, of the pole GH. A 9.33 C 18.65 B 11.35 D 25.34

44

i

9 The diagram shows two vertical poles, PQ and RS, on a horizontal plane. R

12 In the diagram, F, G and H are three points on a' horizontal plane, forming an equilateral triangle FGH. GK and HL are vertical poles. The angle of elevation of K from F is 65°.

15 In the diagram, PRS is a vertical pole on a horizontal plane. The angle of elevation of R from Q is 20°.

15 m

P

I Q, 10m ^S

The angle of depression of peak P from peak R is 32°. Calculate the angle of elevation of peak P from S. A 28°57' C 41°19' B 41011' D 61°3' 10 In the diagram, FG is a vertical flag pole on a horizontal plane EF. G

E'

25 m

Find the angle of elevation of L from G. A 41°16' C 43°12' B 42035' D 44°14' 13 In the diagram, EH and FG are two vertical poles on a horizontal plane. The angle of depression of G from H is 30°.

The height, in in, of the pole is A 14.46 C 23.10 B 16.28 D 50.21 16 In the diagram , P, Q and R are three points on a horizontal plane. RS is a vertical pole.

Q

-F 5m

The angle of elevation of G from E is 48°. The height, in in, of the flag pole is A 16.73 C 22.51 B 18.58 D 27.77 11 In the diagram, P and Q are two points on a horizontal plane. PS is a ladder which leans on a vertical wall QR.

E

8m

'F

The height, in in, of the pole EH is A 9.14 C 9.54 B 9.26 D 9.62 14 In the diagram, P, Q and R are three points on a horizontal plane. RS is a vertical pole.

Given the angle of elevation of S from Q is 40°. The height, in in, of the pole RS is A 4.06 C 4.20 B 4.12 D 4.28 17 In the diagram , K, L and M are three points on a horizontal plane. KP and LQ are two vertical poles. Given LKLM = 90° and the angle of elevation of Q from P is 25°.

S 4 10m

R

P

3m K

4 Q

Given the angle of depression of P from S is 60°. Find the length, in in, of RS. A 2.3 C 6.9 B 3.1 D 7.7

P r 13 m 12 m

Given LPQR = 90°, find the angle of elevation of S from P. A 26°34' C 28°12' B 27°14' D 29°31'

45

The height, in in, of the pole LQ is A 5.10 C 5.33 B 5.16 D 5.68

18 In the diagram, PU, QT and RS are three vertical poles on a horizontal plane. The angle of elevation of T from U is 15° and the angle of depression of S from T is 35°.

19 In the diagram, E, F and G are three points on a horizontal plane where EFG is a straight line. FH is a vertical lamp post. The angle of elevation of H from E is 42° and the angle of depression of G from H is 50°.

20 In the diagram , PS and RT are two vertical poles on a horizontal ground. The angle of elevation of S from Q is 60° and the angle of depression of Q from Tis 35°.

H my

Calculate the distance, in m, of QR. A 4.08 C 4.24 D 4.39 B 4.14

E 10m F G The distance, in m, of FG is A 6.45 C 10.73

B 7.56 D 13.24

The difference in distance, in m, between PQ and QR is A 1.61 C 6.19 B 3.34 D 18.65

SECTION B Subjective Questions This section consists of 8 questions. Answer all the questions. You may use a non-programmable scientific calculator. Answer:

Subtopic 10.1

(a)

Q

In the diagram, E, F and G are three points on a horizontal plane where 12 m EFG is a straight line. GT is a vertical pole. Given the angle of elevation of T from F is 65° and EF = FG.

Find (a) the angle of elevation of P from Q, (b) the distance of QR in m. Answer: (a)

2 0

(b)

In the diagram, Q and R are two points on horizontal ground. PR is m a vertical pole.

1

(b)

Calculate (a) the length, in m, of FG, (b) the angle of elevation of T from E.

In the diagram, P and Q are two points on a horizontal plane. PR is a vertical flag pole. The angle of depression of Q from R is 48°.

Answer: (a)

Find (a) the height, in m, of the flag pole, (b) the length, in m, of QR.

46

(b)

In the diagram, K, L and M are three points on a horizontal plane where KLM is a straight line. KN is a vertical tower. Given the angle of elevation of N from M is 58° and KL = LM.

Calculate (a) the angle of depression of T from U, (b) the height, in m, of the pole SV. Answer:

(b)

(a)

Calculate (a) the height, in m, of the tower, (b) the angle of elevation of N from L. Answer:

(b)

(a)

D q

C

In the diagram , A, B and are three points on a horizontal plane and LACB = 90°. BE and CD are two vertical poles. 5m

5

Calculate (a) the angle of elevation of D from A, (b) the angle of depression of E from D.

In the diagram, U and V are two points on a horizontal plane. UX and VW are two vertical flag poles. The angle of elevation of W from X is 24°.

Answer:

(b)

(a)

Calculate (a) the height, in m, of the flag pole UX, (b) the angle of depression of V from X. Answer:

8

(b)

(a)

8 m I \ 1 1 n° Q

In the diagram, E, F and G are three points on a horizontal plane where EFG is a straight line. EP and GQ are two vertical

E 6m F 5 m G poles. Calculate

(a) the angle of elevation of P from F, (b) the height, in m, of the pole GQ. Answer:

6 V n

7m

In the diagram, R, S and T are three points on a horizontal plane and LRTS = 90°. RU and SV are two vertical poles. Given the angle of elevation of U from V is 20°.

47

11.2 Angles between Two Planes

11.1 Angles between Lines and Planes

SECTION A

Objective Questions

This section consists of 20 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator.

Subtopic 11.1 1 The diagram shows a right prism with a horizontal rectangular base ABCD.

3 The diagram shows a right pyramid with a rectangular base PQRS. N

F

6 The diagram shows a right prism with a horizontal rectangular base PQRS. The isosceles triangle PQW is the uniform cross section of the prism . M is the midpoint of PQ. V

Q

Which of • the following is not true? A BCFE is an inclined plane. B ABE is a vertical plane. C Line AB is normal to the plane ADFE. D Line DF is the orthogonal projection of line CF on the plane ABCD.

What is the angle between line NQ and the base PQRS? A LNQR C LNSQ B LNQS D LQNS 4 The diagram shows a cuboid.

P M Q The angle between line SW and the base PQRS is

A LMSR C LMWS D LRSW B LMSW 7 The diagram shows a right prism with a horizontal rectangular base PQRS. W

2 The diagram shows a right prism with a horizontal rectangular base PQRS. The vertex V is vertically above point O.

The angle between line KR and the plane KNSP is A LNKR C LRKS B LNRK D LSKN 5 The diagram shows a cube.

P

Q

Name the angle between line RV and the plane RSW. A LPRV C LRVW B LQRV D ZVRW 8 The diagram shows a cuboid with a horizontal base JKLM.

F G

The angle between line SV and the plane PRV is A LOPS C LOSV B LOSR D LOVS

The angle between line FN and the plane KLMN is

A LFLN C LFNL B LFNK D LHFN

48

S

R

Name the angle between line JP and the plane JMQ. A LPJM C LPMQ B LPJQ D LPQ J 9 The diagram shows a cuboid with a horizontal rectangular base the KLMN.

12 The diagram shows a pyramid with a horizontal square base ABCD. The vertex E is vertically above point O. M is the midpoint of AB.

C

B

The angle between line KR and the base KLMN is A 26°34' C 63°26' B 53°8' D 68°12' 10 The diagram shows a right prism with an isosceles triangle PQR as its horizontal base. M and N are the midpoints of, QR and TU respectively.

The angle between the planes ABE and ABCD is A LEMO C LEAO B LEBO D LBAE 13 The diagram shows a right prism with a horizontal rectangular base ABCD. P and Q are the midpoints of BC and AD respectively.

15 The diagram shows a right pyramid. The vertex E is vertically above point D.

Name the angle between the plane BCE and the base ABCD. A LADE B LEAD C LEBC D LECD 16 The diagram shows a cuboid with a rectangular base EFGH.

5 cm

B

Q Calculate the. angle between line PN and the plane QRUT. A 26°34' C 63°26' B 32°24' D 68°12'

P

C

The angle between the planes BCE and BCF is A LEPF C LPEF B LEPQ D LPEQ 14 The diagram shows a cuboid. M is the midpoint of DH.

The angle between the plane EFM and the base EFGH is A LEFG C LFMG B LFEM D LGFM 17 The diagram shows a right prism with an isosceles triangle as its horizontal base. M and N are the midpoints of SU and PR respectively.

Subtopic 11.2 11 The diagram shows a cuboid. W

V

R

Name the angle between the planes PQVW and PQRS. A LVPQ C LVQR B LVPR D LWPR

Name the angle between the plane BCM and the base ABCD. A LBCD C LDBM B LBCM D LDCM

49

R

Name the angle between the planes PQR and QSU. A LMQN C LRQU B LNMQ D LSQN

18 The diagram shows a cuboid with a horizontal base PQRS. T

19 The diagram shows a cuboid with a horizontal base PQRS.

W

20 The diagram shows a right prism with a rectangular base ABCD. The right-angled triangle BCF is the uniform cross section of the prism.

P Q Name the angle between the planes PSWV and PSTU.

A ZRWS B LSWT C LSWU D ZTSW

P 12 cm Q

Calculate the angle between the planes SUV and TUVW. C 63°26' A 33°41' B 56°19' D 74°32'

Calculate the angle between the planes BCE and BCF. A 16°42 ' B 33°24 '

C 73°18' D 84°21'

SECTION B Subjective Questions This section consists of 20 questions. Answer all the questions. You may use a non -programmable scientific calculator. 2 The diagram shows a right prism with a horizontal rectangular base ABCD. M and N are the midpoints of the BC and AD respectively.

Subtopic 11.1 1 The diagram shows a right prism with a rectangular base KLMN.

Name (a) the angle between line BE and the base ABCD, (b) the angle between line EM and the base ABCD.

Name (a) the horizontal planes, (b) the vertical planes, (c) the inclined planes, (d) the normals to the plane KLMN, (e) the orthogonal projection of line KP on the base KLMN.

Answer:

Answer: 3 The diagram shows a pyramid with a horizontal square base PQRS. The vertex V is vertically above point S.

(a)

(b) (c)

(d) (e)

Name (a) the angle between line QV and the base PQRS,

50

(b) the angle between line RV and the base PQRS.

Identify and calculate the angle between line KR and the base KLMN.

Answer:

Answer:

(b)

(a)

7

4

The diagram shows a right prism with a rectangular base ABCD. Trapezium B CGF is the uniform cross section of the prism.

K

L 7

The diagram shows a right prism . The base KLMN is a horizontal rectangle . The right10 cm angled triangle LMQ is the uniform cross section of the prism.

Identify and calculate the angle between line KQ and the base KLMN. Name (a) the angle between line AG and the base ABCD, (b) the angle between line AG and the plane CDHG.

Answer:

Answer: The diagram shows a pyramid. The right-angled is a BCE triangle horizontal plane and the square ABCD is a vertical plane. Given CE = 12 cm.

8

5 The diagram shows a pyramid VEFGH. V

E

Identify and calculate the angle between line DE and the base BCE. E

Answer:

24 cm F

The base EFGH is a horizontal rectangle. N is the midpoint of EH. The apex V is 10 cm' vertically above point N. Calculate the angle between line FV and the base EFGH. Answer:

The diagram shows a pyramid with a rectangular base PQRS. The vertex E is vertically above point S.

9

8 6 The diagram shows a cuboid with a rectangular base KLMN.

Identify and calculate the angle between line QV and the base PQRS. Answer:

Q 7 cm N%----- - --- M 5 cm

51

13 The diagram shows a right prism. The rightangled triangle JKL is the uniform cross section of the prism.

Subtopic 11.2 The diagram shows a right pyramid with a triangular base ABC. M is the midpoint of AB. The vertex D is vertically above B point C.

10

Name (a) the angle between the planes ABD and ABC, (b) the angle between the planes BCD and ACD.

L

Identify and calculate the angle between the plane JPQ and the plane PQLK.

Answer:

Answer:

(b)

(a)

11 The diagram shows a cuboid. W

V

14 The diagram shows a right prism with the triangle PQU as its uniform cross section. M and N are the midpoints of PQ and RS respectively. Name (a) the angle between the plane RSTU and the base PQRS, (b) the angle between the plane PQV and the base PQRS, (c) the angle between the planes PTV and PSWT.

V

Identify and calculate the angle between the plane PQV and the base PQRS.

Answer: (a)

(c) Answer:

(b) 12 The diagram shows a right prism with a horizontal square base EFGH. The trapezium FGML is the uniform cross section of the prism. The rectangular surface GHNM is vertical while the rectangular surface EFLK is inclined. 15 The diagram shows a cuboid.

N

K

S

K F

R

8 cm L

Identify the angle between the plane KLS and the base KLMN.

12 cm G

Calculate the angle between the plane EFN and the base EFGH.

Answer:

Answer:

52

16 The diagram shows a right pyramid . with a horizontal square base ABCD. M is the midpoint of BC. E

Subtopics 11.1, 11.2 19 The diagram shows a cuboid.

Identify and calculate the angle between the plane BCE and the base ABCD.

Calculate (a) the length, in cm, of BH, (b) the angle between the line BH and the base ABCD, (c) the angle between the planes BHG and EFGH.

Answer:

Answer: (a) 17 The diagram shows a cuboid. M is the midpoint of AB.

(b)

(c)

20 The diagram ' shows a right prism with an equilateral triangle ABC as its uniform cross section. M, N and P are the midpoints of DF, AC and BC respectively.

Calculate the angle between the planes GHM and EFGH. Answer:

18 The diagram shows a right prism with a rectangular base PQRS.

P

8 cm

(a) Calculate the length, in cm, of MP. (b) Calculate the angle betweerf line MP and the base ABC. (c) Name the angle between the planes MNP and ACFD.

Q

Answer:

Identify and calculate the angle between the planes QSV and RSVW.

(a)

Answer: (b)

(c)

53

12.1 Numbers in Bases Two, Eight and Five

SECTION A Objective Questions This section consists of 35 questions. Answer all the questions. For each question, choose only one answer. You are may use a non-programmable scientific calculator.

Subtopic 12.1 1 State the value of digit 3 in base ten in the number 5368. A 8 C 24 B 11 D 192 2 What is the value of digit 2 in base ten in the number 20415? A 50 C 127 B 125 D 250

7 Given the value of digit 4 in a certain number is 100. The possible number is A 3425 C 14015 B 4178 D 240810 8 Express 4710 as a number in base, two. A 1010102 B 1011112 C 1101002 D 1110102

3 4768 = A 84+87+86 B 4x8°+7x81+6x82 C 4x82+7x81+6x8° D 4x83+7x82+6x81

9 Express 23810 as a number in base five. A 13435 B 14135 C 14235 D 14535

4 In which of the following does digit 1 have the highest value? A 1445 B 21910 C 71528 D 1000002 w

10 Express 41710 as a number in base eight. A 6418 B 6468 C 7128 D 7148

5 In which of the following does digit 3 have the value of 7510? A 3145 B 5308 C 3402* 43168 6 The value of digit 7 in the number 41718 is 7 x 8,,. The value of n is Al B 2 C 3 D 4

11 Express 11102 as a number in base ten. A 810 B 1010 C 1210 D 1410 12 Express 2435 as a number in base ten. A 6910 B 7310 C 7810 D 8110

54

13 Express 11418 as a number in base ten. A 59210 C 60910 B 59810 D 61410 14 Express 101010112 as a number in base eight. A 2538 C 2738 B 2718 D 3168 15 Convert 378 to a number in base two. A 11112 B 101112 C 111102 D 111112 16 Express 2318 as a number in base five. A 10235 C 11045 B 11035 D 11135 17 Express 11435 as a number in base eight. A 2558 C 2758 B 2658 D 3158 18 Convert 100112 to a number in base five. A 215 B 235 C 315 D 345 19 Convert 1235 to a number in base two. A 1001012 B 1001102 C 1010012 D 1011012

20 Express 23 + 2 as a number in base two. A 1012 B 10012 C 10102 D 100012

25 Express 2(84) + 8 as a number in base eight. A 10108 B 20108 C 100108 D 200108

21 Express 24 + 23 + 1 as a number in base two. A 11012 B 110002 C 110012 D 1100012

26 Express 82 + 6 as a number in base two. A 1001102 B 10001102 C 10011002 D 11001102

22 Express 54 + 4 as a number in base five. A 10045 B 40045 C 100045 D 400045

27 Given 2k48 is a three-digit number in base eight. Find the value of k if 2k48 = 101011002. A 4 C 6 B 5 D 7

23 Express 55 + 2(54) + 52 as a number in base five. A 1201005 B 1201105 C 1201205 D 1210105

28 1012 + 11112 = A 101002 B 101102 C 110002 D 111002

24 Express 83 + 6 as a number in base eight. A 20068 C 100068 B 10068 D 100168

29 1011012 + 1112= A 1100102 B 1101002 C 1101102 D 1110002

30 110112 + 11102= A 1010012 B 1011012 C 1100012 D 1110012 31 10112 - 1012= A 112 C 101 2 B 1002 D 1102 32 101012 - 10112 = A 1102 C 10102 B 10002 D 11002 33 1100102 - 11012 = A 101012 B 1001012 C 1001112 D 1011012 34 Given that 1112+P = 10110 21 find the value of P. A 10112 B 11002 C 11102 D 11112 35 Given that M -101112 =101121 find the value of M. A 11002 B 1000102 C 100100.2 D 1100102

UC N $ Subjective Questions This section consists of 15 questions. Answer all the questions. You may use a non-programmable scientific calculator. 2 State the value of the underlined digit in base ten in each of the following. (a) 578 (b) 1638 (c) 41228

Subtopic 12.1 1 State the value of the underlined digit in base ten in each of the following. (a) 11012 (c) 110010112 (b) 1010112

Answer: (a)

Answer: (a) (b)

(b) (c) (c)

55

9 Express 1008 as a number in (a) base two, (b) base five.

3 State the value of the underlined digit in base ten in each of the following. (a) 435 (b) 2105 (c) 11345

Answer:

Answer:

10 Express 1015 as a number in

(b)

(a) base two, (b) base eight. Answer:

4 Express 2910 as a number in (a) base two, (c) base five. (b) base eight, 11 (a) Express 7210 as a number in base five. (b) Express 1115 as a number in base eight.

Answer:

Answer:

(b)

12 (a) Express 4 x 83 + 3 x 8° as a number in base eight. (b) Express 628 as a number in base two.

5 Express 11011002 as a number in

(a) base ten, (b) base eight. Answer:

Answer:

6 Express 24 +2 2 + 2 + 1 as a number in (a) base two, (b) base eight.

13 Given lkl8 is a three-digit number in base eight. Find the value of k in each of the following. (a) 1k18 = 8910 (b) 1k18 = 11000012

Answer:

Answer: 7 Express 53 + 3 as a number in

(a) base five, (b) base eight.

14 Find the value of each of the following. (a) 100112 + 10112 (b) 111002 - 1102

Answer:

Answer: 8 (a) The value of digit 4 in the number 24325 is 4 x 5". State the value of n. (b) Express 50810 as a number in base five. 15 Solve each of the following. (a) 10012 + 101112 (b) 110002 - 112

Answer:

Answer:

56

13.1 Graphs of Functions 13.3 Region Representing Inequalities in 13.2 Solution of an Equation by the Graphical Method Two Variables

SECTION A

Objective Questions

This section consists of 20 questions. Answer all the questions. For each question, choose only one answer. You may use a non-programmable scientific calculator. 3 The diagram shows the graph of the function y = k - 2x".

Subtopic 13.1

6 The diagram shows the graph ofy=x2+2.

1 The diagram shows four straight lines drawn on a Cartesian plane.

Find the values of n and k. A n=-2andk=2 B n=-2andk=4 C n=2andk=2 D n=2andk=4

Which straight line is the graph of the function y = 2x - 5? A PQ C PS B PR D PT

4 In the diagram , the equation of the straight line PQR is y=-2x"+c. Y

From the graph, find the value of y when x = -2. A 2 C 6 B 5 D 8 7 The diagram shows the graph ofy=8- x3.

Q(1, 3) R

2 The diagram shows the graph of the function y = 2 - x". Y

x

0

The value of c is A 4 C 6 B 5 D 7 5 The diagram shows the graph of y = 4x". Y

(2, p)

The value of n is A -1 B 1 C 2 D 3

0I The valu e of p is A -2 C 2 B -1 D 4

57

From the graph, find the value of x when = 0. A 0 C 4 B 2 D 8

8 Which of the following graphs represents y = ax", where n = 3 and a < 0? A Y

Subtopic 13.2

Subtopic 13.3

10 The diagram shows the graph of the function y = x2 - 6.

13 Which of the following is not true? A Point (0, -6) satisfies the equation y = -3(x + 2). B Point (-2, 0) satisfies the equation y = -3(x + 2). C Point (-1, -4) satisfies the inequality y < -3(x + 2). D Point (-3, 2) satisfies the inequality y > -3(x + 2).

Y

C B

-x

Y x

C

.x

D

A suitable straight line is drawn to find the value of x which satisfies the equation x2 - x - 6 = 0. Which of the following is the line? A y=-x C y=2x B y=x D 2y=x

14 Which of the following shaded regions satisfies the inequalities y > x + 2, x+y,5and y-1 and 2+9-

D

B North Y

y+1 4y y+4 4y

C

A Y-1 Y y-4 B 4y

DIAGRAM 9 The angle of elevation of P from K is 25° and KL = 6 m. The angle of elevation of P from L is A 33°41' C 55°55' B 34°5' D 56°19'

y-x 4-x xy 4x

North

t

X 60°,

60°

18 The location of P is (75°N, 25°E) and PR is a diameter of the parallel of latitude 75°N. Find the longitude of R. A 25°W B 75°E C 155°W D 155°E

103

10. Find all the integer values of x which satisfy both inequalities. A -1, 0, 1, 2 C 0, 1 B -1, 0, 1 D 0, 1, 2 26 Table 1 shows the scores obtained by a group of participants in a competition. Score

1

2

3

4 5

Number of Participants

5

4

6

3 2

TABLE 1

Find the number of participants whose score is more than the mean score. A 5 C 11 B 9 D 15 27 Diagram 10 is a bar chart which shows the sales of four products, P, R, ' S and T, in a particular month. 10000

33 In Diagram 14, PR and SR are tangents to the circle with centre 0.

29

P

P

DIAGRAM 11

A

-3

C

8000

4

1 3

B -1 D 3 3

6 000 4 000 2 000 0

P

R S T Product

DIAGRAM 10 The percentage of the sales of product S in the month is A 15 C 30 B 25 D 35

30 Given the straight line 5x + 6y = 30, find the x-intercept of the straight line. A 6 C -5 B 5 D -6 31 Diagram 12 shows a Venn diagram with the universal setC=PURUS.

Calculate the perimeter, in cm, of the shaded region in the diagram. (Use it = 3.142) A 56.72 C 72.43 B 70.68 D 88.14 34 In a theatre, 18 of the patrons are children. If a patron is selected at random from all the patrons in the theatre, the probability of selecting a child is 9 . If another 3 children

A

B

DIAGRAM 12 Find n(S'). A 5 C B 6 D

7 8

32 Diagram 13 shows a Venn diagram with the universal set k=KULUM. K

1

4 3 4

C 7 9 D 7 27 35 There are 24 male workers in a factory. The probability of selecting a male worker from all the workers in the factory is 5 . The number of female workers in the factory is A 12 B 24 C 36 D 48

C

DIAGRAM 13 D

DIAGRAM 14

enter the theatre, the probability of selecting an adult is

P

28 Which of the following graphs represents y = -x3 + 8? A Y

B

S

The gradient of the straight line PR in Diagram 11 is

The shaded region is represented by A Kn(MUL) B (KUL)nM C (K'nL)nM D (KnM)U(KnL)

104

36 It is given that p varies directly as the cube of q and p = 108 when q = 3. Calculate the value of p when q = 1.5. A 13.5 B 22.5 C 45 D 162

37 It is given that h -

1 m

and

h = 2 when m = 25. Calculate the value of h when m = 36. A 3 5 B 5 3 C 15 D 60

38 Table 2 shows the values of the variables, x, y and z, which x2

satisfy z -

y

x

4

12

Y

8

p

z

24

96

TABLE 2 The value of p is A 12 C 24 B 18 D 28

PAPER 2

.

39 Given (2 p)I I = (12), then p = A 3 B 5

C D

6 7

40 (6 3)l 1 2 /

10 6

9

14 )

A ( 3 0 -6

C ( 33 30

B (1 6 12

D( 5

1/

Time : Two hours and thirty minutes

This question paper consists of two sections: Section A and Section B. Answer all the questions in Section A and four questions from Section B. Show your working. It may help you to get marks. You may use a non-programmable scientific calculator. Section A [52 marks] Answer all the questions in this section. 1 The Venn diagram in Diagram 1 shows the number of elements in sets F, G and H where i;=FUGUH. G

DIAGRAM 1 Given that n(E) = 41, find (a) the value of x,

(b) n(F U G). [3 marks]

2 Diagram 2 shows a solid consisting of a cylinder and a cone. 9cm

21 cm

DIAGRAM 2 Using it = 3.142, calculate the volume, in cm3, of the solid.

105

[4 marks]

3

Diagram 3 shows a right pyramid with a square base EFGH. The vertex A is 8 cm vertically above H. Identify and calculate the angle between the plane AFG and the base EFGH. [4 marks]

E 6 cm F

DIAGRAM 3

4 Solve the quadratic equation

k(2k2- 3) = k - 1. [4 marks]

5 Calculate the values of p and q that satisfy the following simultaneous linear equations: 4p - 3q=6 4p + q = 14 [4 marks]

6

In Diagram 4, 0 is the origin. ABCD is a parallelogram and the length of OC is 9 units. Find (a) the gradient of the straight line BC, (b) the equation of the straight line BC. [5 marks]

DIAGRAM 4

7 (a) State whether the following statement is true or false. -2(3) = 6 or -4 > -5. (b) Write down two implications based on the following statement: p3=8 if and onlyifp=2. (c) Complete the premise in the following argument: Premise 1 :............................................................................................................... ............................................. Premise 2: J x 0 3 Conclusion : x 0 9 [5 marks]

106

8 Five cards in Diagram 5 are put into a box. S

C

L

E

DIAGRAM 5 Two cards are selected at random from the box. The first card is returned to the box before the second

card is selected. Calculate the probability of selecting (a) the letter L on the first card or a vowel on the second card, (b) a consonant on the first card and the letter E on the second card. [5 marks] 9 Given matrix M = ( 1 5 ), find 2 (a) the inverse matrix of.M. (b) hence, using matrices, the values of u and v that satisfy the following simultaneous equations: u - 2v = 8 2u+5v=7 [6 marks] In Diagram 6, 0 is the centre of a semicircle with a diameter of 28 cm. OPM is a quadrant of a circle with centre O. Given M is the midpoint of OB.

10

Using it = i? , find (a) the area, in cm2, of the shaded region, (b) the perimeter, in cm, of the shaded region. [6 marks] 11

Speed (m s-') vt--a. 121 9

0

! I o Time (s) 4 10 24

Diagram 7 shows the speed-time graph of the movement of a particle for a period of 24 seconds. (a) State the uniform speed, in m s-', of the particle. (b) If the distance travelled in the first four seconds is 56 m, calculate (i) the value of v, (ii) the total distance, in m, travelled by the particle. [6 marks]

DIAGRAM 7 Section B [48 marks] Answer four questions from this section. 12 (a) Complete Table 1 with the values of y for the function y = 2x2 - 3x - 7. x

-2

y

7

-1.5

-1

0

1

-2

-7

-8

2

3

[3 marks]

4

2

TABLE 1 (b) For this part of the question, use graph paper. You may use a flexible curve rule. Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, draw the graph of [4 marks] y=2x2-3x-7for -2 3 (a) -11 > -12 (b) 0.25 < 3 (c) 3E{3,6,9} 4 (a) False (b) True (c) False 5 (a) False (b) True 6 (a) Some regular polygons have 8 sides of equal length. (b) Some workers in a factory wear spectacles. (c) Some triangles have right angles. (d) All trapeziums have two parallel sides. 7 (a) False (b) True (c) False (d) True 8 -8x(-3)=11 or 35 is a multiple of 7. 9 (a) , Antecedent: k = -4 Consequent: k3 = -64 (b) Antecedent: It rains today. Consequent: The football match will be cancelled. 10 (b) Antecedent: Ismail's father comes to school late. Consequent: Ismail will go home late. (b) Antecedent: j > 8 Consequent: m > 82 11 (a) Implication I: If x > y, then 3x > 3y. Implication 2: If 3x > 3y, then x>y. (b) Implication 1: If p is a negative number, then p3 is a negative number. Implication 2: If p3 is a negative number, then p is a negative number. 12 Azlina passed the SPM examination. 13 PQRSTis a regular pentagon. 14 5x # 20 15 6 is a factor of 18. 16 IfpOandq>0. Implication 2: If p > 0 and q > 0, then pq > 0.

If Juliana is a doctor, then Jamal is Juliana's brother. (i) 28 = 256 (ii) 72=49 22 (a) Triangle ABC has a sum of interior angles of 180°. (b) 2n2 + n, n =1, 2, 3, 4, ... 23 (a) True (b) Implication 1: If x3 = 64, then x = 4. Implication 2: If x = 4, then x3 = 64. (c) ABCDE is a pentagon. 24 (a) (i) False (ii) True (b) -2 is less than zero. (c) Implication 1: If 5p > 20, then p>4. Implication 2: If p > 4, then

19 (a) y=5 (b) y=-2 -3;-6 20

(a) y =-2x+14 (b) 7

TOPICAL ASSESSMENT 6 Section A : Objective Questions 1 B 2 C 3 B 4 D 5 B 6 C 7 B 8 D 9 B 10 C 11 D 12 B 13 C 14 D 15 C 16 B Section B : Subjective Questions 1

5p > 20. 25 (a) (i) Some (ii) All (b) If x > 4, then x > 7. False (c) PnQ#P

Section B : Subjective Questions 1 3 4 2 -1 3 -2 5 4 (a) -3 (b) -2 5 (0,8) 6

Tally

Frequency

11-20 21-30 31 - 40 41-50 51 - 60 61 - 70

III ff1 6t1T 11 4tT1W 1 +HIT ittf III

3 6 7 11 10 3

Size of the class interval =10 2

TOPICAL ASSESSMENT 5 Section A : Objective Questions 1 C 2 C 3 D 4- B 5 6 D 7 D 8 B 9 D 10 11 B 12 C .13 'B 14 C 15 16 C 17 D 18 C 19 B 20 21 D 22 B 23 C 24 C 25

Mass (kg)

Time (minutes)

Tally

Frequency

6-10 11-15 16-20 21-25 26 - 30

1W I mill OW 11 III[

6 8 5 2 4

D B A B C 3 (a)

Circumference (cm)

Tally

Frequency

120 -129 130 -139 140 -149 150 -159 160 -169

III 4Nt 4141m I 41st 1 441

3 5 11 6 5

(b) (i) 10 (ii) 140 - 149 (iii) 146.17 cm 4 (a) 2.5-2.9 (b) 2.625 kg 5 Frequency

0

7 (a) (-2, 3) 8 (a) y=3x-7 1 (b) y= 2 x+5

(b) (2, 3)

(b) Parallel 9 (a) Not parallel 10 y=-6x-5 11 (a) 8 (b) 2 12 (a) 2 (b) 12 13 (a) p=5 (b) 10

2.45 2.95 3.45 3.95 4.45 4.95 5.45 Period of oscillation (minutes) 6 Frequency 25

5 (b) -12 2 15 (a) y=2x-18 (b) (12,6) 16 (a) 2 (b) 5 17 (a) y=2x-18 (b) 12 18 (a) x=3 (b) y=-2x+14;14 14 (a)

119

20 15 l0{5k 0 119.5 124.5 129.5134.5 139.5 144.5 149.5 154.5 Height (cm)

11 (a)

7 (a), (b) Frequency

5 40.5 50.5 60.5 70.5 80.5 90.5 100.5 110.5 Distance (km)

Distance (km)

Frequency

3 -5 6-8 9 - 11 12 - 14 15 - 17 18 - 20

4 5 6 10 8 2

Mass (kg)

Frequency

1.1-1.5 1.6-2.0 2.1-2.5 2.6-3.0 ,3.1-3.5 3.6-4.0 4.1-4.5

0 5 8 9 12 7 4

Cumulative Upper Frequency Boundary 4 9 15 25 33 35

5.5 8.5 11.5 14.5 17.5 20.5

Cumulative Upper Frequency Boundary 0 5 13 22 34 41 45

1.55 2.05 2.55 3.05 3.55 4.05 4.55

14 (a)

Length (cm)

Frequency

58 - 60 61-63 64-66 67 - 69 70 - 72 73-75 76 - 78 79 - 81 82 - 84

0 2 3 8 10 7 6 5 1

Cumulative Upper Frequency Boundary 0 2 5 13 23 30 36 41 42

60.5 63.5 66.5 69.5 72.5 75.5 78.5 81.5 84.5

Frequency

Cumulative Frequency

Upper Boundary

130 - 134 135 - 139 140 - 144 145 - 149 150 - 154 155 - 159 160 - 164

0 5 8 10 17 7 3

0 5 13 23 40 47 50

134.5 139.5 144.5 149.5 154.5 159.5 164.5

60.5 63 .5 66.5 69.5 72.5 75.5 78 .5 81.5 84.5 Length (cm)

(b) (i) 72 cm (ii) 68.5 cm (iii) 76 cm 12 x=84 13 (a) Class Interval

Frequency

Midpoint

1- 10 11-20 21- 30 31-40 41-50 51 - 60 61 - 70

3 5 11 8 6 4 3

5.5 15.5 25.5 35.5 45.5 55.5 '65.5

i . It 11 1 H 134.5 139.5 144.5 149.5 154.5 159.5 164.5 Volume (m() Cumulative Upper Frequency Boundary

3 8 19 27 33 37 40

10.5 20.5 30.5 40.5 50.5 60.5 70.5

(c) (i) 150.25 me (ii) 9.75 mP 15 (a)

Marks

Midpoint

Frequency

40 - 44 45 - 49 50 - 54 55-59 60 - 64 65 - 69

42 47 52 57 62 67

2 5 3 10 9 7

(b) (i) 55 - 59 (ii) 57.56 marks

(b) (i) 21 - 30 (ii) 33.75

(c)

Cumulative frequency Cumulative frequency

Volume (me)

Frequency 4010+ 35 30 25 20 151 10

(b) (i) 3.1 kg (ii) 2.4 kg (iii) 3.5 kg

0.5 10 .5 20.5 30.5 40.5 50.5 60.5 70.5 Number of foreign workers

(c) (i) 31.5 (ii) 44.75

39.5 44.5 49.5 54.5 59.5 64.5 69.5 Marks

120

0

0

16 (a) Class Interval 31- 35 36 - 40 41-45 46 - 50 51 - 55 56-60

Midpoint Frequency 33 38 43 48 53 58

4 8 9 7 7 5

(b) RM45.50 (c) Frequency

Section B : Subjective Questions 1 (a) 25° (b) 19.43 cm 2 (a) 54° (b) 13.61 cm 3 (a) 70 (b) 66 (c) 58 4 (a) 28 (b) 28 (c) 90 5 (a) 60 (b) 60 (c) 9.40 cm 6 (a) 124 (b) 56 7 (a) 13.86 cm (b) 81°47' 8 (a) 11.75 cm (b) 63 cm2 9 (a) 35 (b) 7.75 cm 10 (a) 58° (b)

7.5 cm

TOPICAL ASSESSMENT 9 Section A: Objective Questions 3 B 1 B 2 C 4 C 6 A 8 C 9 C 7 D 11 C 14 B 12 D 13 B 18 A 19 B 17 B 16 A 21 A 22 B 23 D 24 C 26 B 27 C 28 D 29 A 32 A 33 B 34 B 31 B

28 33 38 43 48 53 58 63 Monthly savings (RM)

(.i) 19 students whose monthly savings is more then RM45. (Accept other possible answers.)

TOPICAL ASSESSMENT 7 Section A: Objective Questions 3 B 1 D 2 C 4 C 6 C 8 B 9 B 7 D 11 C 12 D 13 B 14 A 16 C 18 D 19 C 17 B 23 C 24 C 21 B 22 B

5 10 15 20 25

C A A B B

Section B : Subjective Questions 1 (6,8,10,12) 2 S = ((RP, RQ), (RP, BQ), (Ye, RQ), (Ye, BQ)) 3 (a) {E, I) (b) IN, G, L, S, H) (c) Possible 4 (a) Possible (b) Not possible 5 390 33 9 (b) 6 (a) 80 20 5 (b) 7 (a) 13 8 40 1 1 (b) 8 (a) 3 9 8 (b) 9 (a) 60 17 10 10 (a) 48 (b) 33

5C 10 C 15 C 20 B 25 B 30 A 35 A

Section B : Subjective Questions 1 (a) -0.5 (b) Undefined (c) -1 2 (a) 0.5 (b) 7 (c) -3.5 3 (a) 0.6018 (c) -1.1918 (b) 0.6053 (d) 0.5184 4 (a) 70° and 110° (b) 64°12' and 295°48' (c) 106°36' and 286°36' 5 (a) 0.7660 (b) -0.1736 6 (a) 7 (a) 8 (a) 9 (a)

(b) 128 ° 56 ' (b) 3 4

y

(b)

y=tanx,,

TOPICAL ASSESSMENT 8 Section A: Objective Questions 1 D 2 B 4 B 3 C 6 C 9 B 7 D 8 D 14 B 11 A 12 B 13 C 16 B 18 B 17 B 19 C 21 B 23 B 24 D 22 B 26 D 27 A 28 B 29 C

5A 10 A 15 C 20 B 25 B 30 B

x 90° 180° 270 360° -11

10 (a) (45 °, 0.7071) (b) (225°,-0.7071)

121

5D 10 D 15 A 20 B

Section B : Subjective Questions 1 (a) 36 (b) 5.51 m 2 (a) 33.32 m (b) 44.83 m 3 (a) 5.6 m (b) 46°58' 4 (a) 32 m (b) 72°39' 5 (a) 3.66 m (b) 16°58' 6 (a) 30°15' (b) 2.27 m 7 (a) 33°41' (b) 10°37' 8 (a) 53°8' (b) 1.52 m

TOPICAL ASSESSMENT 11 Section A: Objective Questions 3 B 1 D 4 C 2 D 8 B 9 C 6 B 7 D 11 C 12 A 13 A 14 D 18 D 19 A 16 D 17 A

5 (b) 9.6 cm 7 9 3 5

TOPICAL ASSESSMENT 10 Section A: Objective Questions 3 A 4 D 1 A 2 D 8 B 9 B 6 A 7 D 13 D 14 A 11 B 12 B 17 C 18 D 19 B 16 C

Section B : Subjective Questions 1 (a) KLMN (b) KNP, LMQ MNPQ (c) KLQP (d) MQ NP (e) KN 2 (a) LEBN (b) LEMN 3 (a) LSQV (b) LSRV 4 (a) LCAG (b) LAGD 5 21°48' 6 ZRKM= 28°18' 7 LQKM=21°48' 8 LDEC=22°37' 9 ZVQS=35° 10 (a) LDMC (b) LACB 11 (a) LPST or LQRU (b) ZVQR (c) LVTW 12 36°52' 13 ZJPK = 51°21' 14 LVMN = 21°48' 15 LSKN=33°41' 16 LEMO = 41°25' 17 33°41' 18 ZQSR = 36°52' 19 (a) 13 cm (b) 13021(c) 36°52' 20 (a) 5 cm (b) 36°52' (c) LCNP

5C 10 A 15 D 20 C

2

FORM 5 TOPICAL ASSESSMENT 12 Section A : Objective Questions 1 C 2 D 3 C 4 C 6 A 8 B 7 C 9 C 11 D 12 B 13 C 14 A 16 B 17 A 18 D 19 B 21 C 22 C 23 A 24 B 26 B 27 B 28 A 29 B 31 D 32 C 33 B 34 D

5 10 15 20 25 30 35

(a)

(c) (i) x=0,4 (ii) Draw the straight line y = -2; x=0.55,3.4

y

7 (a)

C A D C D A B

-2x

-2

1

3

9

0

14

(b)

(b) y=x'-3x

U 'H

-x

Section B : Subjective Questions 1 (a) 4 (b) 32 (c) 64 2 (a) 7 (b) 48 (c) 2048 3 (a) 20 (b) 50 (c) 125 4 (a) 111012 (b) 358 (c) 1045

tx

3 (a) n=-1 (b) k=6 4 (a) n= 3 (b) (-3, 0)

,Y ti: ,x .

iKi

5 (a)

5 (a) 108to

T.

^^

1.5

5

8 ;F C

(b) 1548 6 (a) 101112

6.7

'1.

1.3

ff"il

(b)

(b) 278 y

7 (a) 10035

F . l '.

(b) 2008

'IT

10

8 (a) n=2

9

(b) 40135 9 (a) 10000002

mffi (c) Draw the straight line y = x + 5; x=-2.65,2.55

8

(b) 224 10 (a) 110102

7

(b) 328

6

8 y> 2x,x'a5,y'a2x 'mm;:;.

i

11 (a) 2425 4

TU;

3 2

(b) 101102 15 (a) 1000002 (b) 101012

0

x

1 2 3 4

5 6

(c) (i) y=2-2 6 (a)

TOPICAL ASSESSMENT 13 Section A: Objective Questions 1 B 2 D 3 D 4 B 5 C 6 C 7 D 8 D 9 A 10 B 11 C 12 B 13 D 14 C 15 D 16 A 17 C 18 B 19 A 20 C

8

(ii) x =1.65

-0.5 2 3

x

12

y 2.3 -4 -3 (b) gf

t

t

it-.r

{. .r;

^1t

rt ;.

x

it

Section B : Subjective Questions 1 (a) y

1,114 t

x-2y=4

t1•

t ttY{

ti 11

t!J }

CI

77

13

x

'fr t

(b)

t

t

y=x'-8

s

c

't

i

i j

t

t

3r

r ,r

,k

}

t

HIM , MI

0

9 yx-3,4x+3y-- 12,xa'0 10 y--x+5,y+2x^0,x0

A"i UN

(b) 378 12 (a) 40038 (b) 1100102 13 (a) k=3 (b) k=4 14 (a) 111102

-x

H

3

$

J,- I

122

4

14 (a)

-2

1

2.5

-2

7

1.4

15 (a) (i) (5, -3) (ii) (a) (5, -1) (b) (2, -3) (b) (i) (a) R : A reflection in the line y = 4 (b) S : An enlargement of scale factor 2 with centre (1, 4) (ii) 41.1 cm2 16 (a) (i) (1,2) (ii) (0,4) (iii) (-4,7)

4

5

(b) (i)

(a) V : A reflection in the

line x = -2 (b) W An enlargement of scale factor 3 with centre (1, 7) ii) 192 m2 TOPICAL ASSESSMENT 15 Section A : Objective Questions 2 A 3 C 1 B 4 A 6 B 7 B 8 D 9 B 13 A 14 C 11 B 12 B 17 D 18 B 16 D 19 B 23 D 24 C 21 C 22 B 27 D 28 D 29 C 26 B

6

(c) (i) y = 5 (ii) x=-2 .3,-0.35,2.6 (d) Draw the straight line y = x + 1; x = -2.15 , -0.2, 2.3 15 (a) -1 1 1.5 9

1

(b), (d)

(c) Draw the straight line y = x + 5; x=-2.35,0,2.4 TOPICAL ASSESSMENT 14 Section A: Objective Questions 1 D 2 C 3 B 4 A 6 C 7 D 8 A 9 C Section B : Subjective Questions 1 (a) ACBE (b) ABCE 2 (a) AVRK (b) AVRK

3

y

(b) (3, -2) (b) (1, 2) (b) (5, 6)

7 (a) (1, 4) 8 (a) (4, 0) 9 (a) (1, 2)

0.9

5 B 10 B

123

A A B B A C

Section B : Subjective Questions 1 (a) 3 (b) 2 (c) 3x2 2 (a) -3 (b) 9 (c) 8 (b) q=2 3 (a) p=1 4 (a) x=-3 (b) y=1 (c) z=4 5 (a)

10 (a) V A translation ( 4) 0 W A rotation of 180 about the centre (5, 3) (b) A rotation of 180° about the centre (3, 3) 11 (a) P A reflection in the line EHM (y = 2) Q : An enlargement of scale factor 3 with centre E(1, 2) (b) 72 unite 12 (a) (i) (4, 0) (ii) (7, 1) (iii) (10, 0) (b) (i) (a) U : An anticlockwise rotation of 90° about the centre A(2, 3) V An enlargement of scale factor 3 with centre A (2, 3) (ii) 9 cm2 13 (a) (i) (-6, 5) (ii) (-6, 9) (b) (i) A reflection in the line AD (ii) A clockwise rotation of 90° about the centre (-6, 6) (c) (i) (-6,3) (ii) 45.8 unite (ii) (0, -1) 14 (a) (i) (2,-1) (b) (i) T A clockwise rotation of 90° about the centre (0,5) V An enlargement of scale factor 2 with centre E(-3, 1) (ii) 60 m2

5 10 15 20 25 30

8 \ -4

3/

3 13 / 6 (a) p = -2

(c)

(10)

(b)

7

(a)

1 1 4

(b) q=3 6J

(b)

-6

7

(b) m=3,n=-5

8 (a) 0/ 9 (a)

(

(b) 1 10 •(a)

4)

-1

28 1

2

3

2 (b) 9 ^- 2

1 5 2

(c)

11

-1

(a)

2 3 -1 2 - 23 2

(b)

-2 5 2 -3 7 3 3

-1 (c) -2

-11 2 3 2

(c)

\ -1 3

TOPICAL ASSESSMENT 17 Section A : Objective Questions 1 D 2 C 3 B 4 C 5 B 6 B 7 A 8 C 9 C 10 D

\3/ 1-4/

5 14 (a) 4 2 -3 2 (b) m3,n=-1 15 (a) p = -5,q = -3 (b) x=3,y=-1 16 (a) e=-15 (b)

(-2 -3 (c) h=-2,k=2 17 (a) r=- 2 1

(b) 2 _52 (c) v=-1,w=-3 18 (a) p= 2 (b) v = 2, w = -1 TOPICAL ASSESSMENT 16 Section A : Objective Questions 1 A 2 C 3 A 4 D 5 6 C 7 B 8 C 9 C 10 11 B 12 B 13 B 14 B 15 16 A 17 D 18 C 19 D 20 21 A 22 D 23 D 24 B 25 26 B 27 C 28 B 29 D 30

Section B : Subjective Questions 1 (a) E _' (b) 48 (b) h=4

2 (a)

D A C A C C

Section B : Subjective Questions 1 (a) 60 km (b) 45 minutes (c) 80 km h-' 2 (a) 45 m (c) 4.5 ms' (b) 90m 3 (a) 80m (b) 3 seconds (c) 2ms' 4 (a) 105 km (c) 35 km (b) 0800 hours (d) 42 km h-' 5 (a) d=90 (c) 3.6 m s-' (b) 4.5 m s-' 6 (a) 0.4 hour (b) 70 km h-' (c) (i) 60 km (ii) 1.2 hours 7 (a) 30 seconds (c) 150 m (b) lO m s-2 8 (a) 20 km h-2 (b) 600 km (c) 50 km h-' 9 (a) v = 14 (b) 580 m (c) 14.5ms' 10 (a) 8 m s-2 (b) u=8 11 (a) T,=8 (b) 3.75 m s-2 (c) T2 = 15 12 (a) 2 3 m s-2 (b) 2 loom (c) T=42.5 13 (a) v=23 (b) v=30 14 (a)' lms2 (b) 144 m (c) T=25 15 (a) 20 m s-' (b) (i) t = 32 (ii) 20.75 m s-1

3 (a) G= (b) (i) r=3

(ii) s = 1 4

4 (a) r 40 s2

(b) (i) 2-1 (ii) s= 2 2 3 5 (a) A 60 (b) C=9 B,4

TOPICAL ASSESSMENT 18 Section A : Objective Questions 1 B 2 D 3 C 4 D 5 B 6 C 7 D 8 B 9 D 10 C 11 C 12 B 13 D 14 C 15 B 16 B 17 C 18 C 19 B 20 A Section B : Subjective Questions

6 (a) a=Z,b=-3 6,2 (b) s=7 (a) y = 32x2 (b) k=2 2 8 (a) h=2

(b) M=75

9 (a) y=4, ( b) r=1 3 10 (a) (i) n = 1 (ii) n = --L (b)

5 6

9 (a) 10 (a)

3 -1 13 (a) p=3,q=1 (b) m=2,n=-2 (c) x=-1,y=-5

1

8 (a)

7 5

124

11 (a) 12 (a) 13 (a) 14 (a)

(b)

15 (a)

(b)

TOPICAL ASSESSMENT 19 Section A : Objective Questions 1 C 2 C 3 C 4 A 5 D 6 C 7 B 8 C 9 C 10 D 11 B 12 C 13 C 14 A 15 D 16 D 17 C 18 D 19 B 20 D Section B : Subjective Questions 1 (a) 340° (b) 310° (c) 2 (a) 290° (b) 170° (c) 3 (a) 000° (b) 210° (c) 4 (a) 090° (b) 215° (c) 5 (a) 005 ° (b) 030° (c) 6 (a) 290° (b) 050° 7 (a) 185° (b) 330° (c) 020° 8 (a) 040° (b) 2209 (a) 085° (b) 24010 (a) 105° (b) 322.5°

160° 230° 105° 305° 185°

TOPICAL ASSESSMENT 20 Section A : Objective Questions 1 B 2 D 3 A 4 C 5 D 6 C 7 C 8 D 9 B 10 D 11 C 12 A 13 A 14 A 15 A 16 D 17 C 18 C 19 D 20 A Section B : Subjective Questions 1 (a) 60°W (b) 5°W 2 (a) 38°W (b) 7°E 3 (a) 18°S (b) 40°S 4 (a) 60°N (b) 4°N 5 (a) 84°W (b) 4°E (c) (44°N, 40°W) 6 (a) x=52 (b) (52°N, 93°W) (c) (0°, 130°W) 7 (a) 3 000 n.m. (b) 927.05 n.m. (c) 4 320 n.m. 8 (a) 180° (b) 8 400 n.m. 9 . (a) 8 025.96 n.m. (b) 5 760 n.m.

10 (a) 3 300 n.m. (b) 1 650 n.m. (c) 1800 n.m. 11 (a) 8=66 (b) 4 392.76 n.m. 12 (a) WE (b) (i) (38°S, 36°E) (ii) 9 hours 36 minutes 13 (a) 120°W (b) (i) 5°N (ii) 5 196.15 n.m. (iii) 810.7 knots 14 (a) 60°S (b)

5 (a) J/K/E

G/F

LID 12 cm 4 cm

H/A

14 cm

C

I/B 3cm

4cm

(b) 4 900 cm' 8 (a)

(b)

U/P

4cm

T/N

I/J

H/G

4 cm K 5 cm M

Q

3 cm

3 cm A/F

(c) 1 800 n.m. (d) (i) 3 600 n.m. (ii) 100°E 15 (a) 140°E (b) 3 600 n.m. (c) 2 760 n.m. (d) 7.2 hours

B/E

4cm

3cm

C/D R/K

(c) 1/H

4cm

S/L

J/G

(b) R

S

2 cm L/K

3 cm

5 cm

2 cm C/B/A

DIE/F K/Q/P

6 (a) Section B : Subjective Questions 1 TIS W

T

U

3 cm

TOPICAL ASSESSMENT 21 Section A: Objective Questions 1 D 2 B 3 B 4 B 5 C 6D

G/A

FIE

6 cm

4 cm

L/M/N

(c) SIR

R

3 cm 5 cm

6 cm V

U/P 3cm

2

E/D

4 cm

Q

I/C

J

L/K H/B

C

3 cm

3 cm

3 cm

M/Q

4 cm

N/P

I

4 cm

9 (a)

(b)

U/T H/G

K/S

I/F

6 cm

F/A 2cm G 3cm H/B L/R

4 cm

3

V

U/T

4 cm

2 cm V/P C

B/A 3cm

3 cm

E

2 cm P/S

4

3cm W/Q

N/W

M

4 cm

(b) V/U

Q/R

(c) I/H

F/G

V 2 cm

6 cm 4 cm 4cm

L/T

K/U

2 cm C/B Q/P

5cm

6cm

R/S

125

E/A

P/T 3 cm Q/S

(c)

4 cm

V

(b)

U M

V/U

WIT

N

2 cm

2 cm L

W

K

KIN

3 cm

3 cm HID

4 cm

GIC P/S

2 cm Q/P

K

SIT

R

Q/R

6 cm

L T

V 2.12 cm u

2 cm

10 (a) T/S

M/W

2 cm

R 4 cm

E/A

M

FIB

2.12 cm

N

3 cm 4 cm

12 (a) E

F P 4.24 cm Q/S 4.24 cm 2 cm

U/P

N/V

3 cm

3 cm

Q AID

(b)

B/C

14 (a) FIE

GIH

NIM 4 cm

5 cm

P/S

Q/R

4 cm P/S

Q/R

6 cm

EIS

FIR 2 cm

N

(c) M

D

C

3 cm

T

2 cm A/P

U 1cm r ------------- I V 1 cm

SIR

BIQ 2 cm 5 cm

P/Q

4 cm

11 (a)

HIE

GIF

FIE

LIK

2 cm

2 cm

K 1 cm N

L

6 cm

4 cm 3 cm

M/B/A

4 cm 4 cm

Q/P

CID

5 cm

RIS

P

(b) (i) K

Q

15 (a) R/K

13 (a)

L

T/S

4 cm

Q 2 cm PIN

U/R

2 cm FIG

E/H

3 cm

6 cm

6cm 6cm

V/N

3 em 3 cm A/D/M

4cm

B/C/N

W/M/P

6cm

126

K/Q

SIL

T

U/M

R

(b) (i) DIE

4 cm

T/Q/F 2 cm U/P

2 cm SIR

16 B 21 B 26 C 31 B 36 A

17 22 27 32 37

D D C B B

18 23 28 33 38

C D B B B

19 24 29 34 39

D B C B D

20 25 30 35 40

B D A C C

5 cm 3 cm

HIG MIN

L/K/I

Paper 2 1 (a) x= 7 (b) 31 2 1021.15 cm3 3 LAGH=53°8' 4 k= 2,2

U/T P/QID 2 cm

FIE

2 cm

(b)

R

S

5 cm 3 cm

M/L

6 cm

N/H/K G/I

16 (a)

5 p=2,q=6 3 (b) 4y=-3x+27 6 (a) 4 7 (a) True Implication 1 : If p3 = 8, then p = 2. Implication 2: If p = 2, then p3=8. (c) If x = 9, then f = 3. 13 8 (a) 25 (b) 3 25 5 2 9 9 9 (a) 12 1 9 9

N/K

(b) (i) (a) V : A translation ( 6 1 (b) W: An enlargement of scale factor 3 with centre P(2,4) (ii) 112 cm2 14 (a) Lower Upper Marks Frequency Boundary Boundary 21- 30

11

20.5

30.5

31- 40

8

30.5

40.5

41 - 50

13

40.5

50.5

51 - 60

15

50.5

60.5

61 - 70

10

60.5

70.5

71- 80

3

70.5

80.5

(b) 47.83 marks (c)

1

7 cm

(b) u=6,v=-1 10 (a) 269 2 cm2 (b) 83 cm 2

11 (a) 9ms 1 (b) (i) v =16 (ii) 257 m 6 cm

FIE

G/H

12 (a)

-1.5

0 10.5 20.5 30.5

2

4

(b) (i) 4 cm

- K/H

2

P/U 2 cm TIG

15 (a)

F/E

70.5

G

-5 13

(b)

4 cm 6 cm H

6cm

2cm AID 3 cm B/C

LIE

Q/R

(b) (1)

S/F

E/D 3 cm G/K/C

4 cm

LIM

(ii) K

P

F/A

H/B

B/A

5 cm

2 cm E/H

FIG

SPM MODEL TEST 1 Paper l 1 C 2 A 3 C 4 B 5 D 6 A 7 D 8 B 9 C 10 B 11 D 12 D 13 D 14 B 15 C

(c) (i) y = 0.2 (ii) x=-1.3, 2.7 (d) Draw the straight line y = x - 2; x=-0.9,2.9 13 (a) (i) (-1, 3) (iii) (-1, -1) (ii) (5,3)

127

M/C/D

16 (a) (i) 35°N (ii) 113°E

(b)

(d) Frequency

11l

(b) (i) 13442.67 n.m. (ii) 16 hours 48 minutes

l0f

SPM MODEL TEST 2 Paper 1 1 D 2 B 3 C 6 D 7 A 8 A 11 B 12 B 13 B 16 D 17 B 18 B 21 B 22 A 23 A 26 A 27 C 28 A 31 D 32 B 33 A 36 C 37 D 38 A

4 9 14 19 24 29 34 39

C C D C C D C C

5B 10 C 15 B. 20 A 25 A 30 A 35 C 40 B

Paper 2 1 (a) 0` 4 49.5 59 .5 69.5 79.5 89.5 99 .5 109.5 Age (years)

(c) (i) y = -9.2 (ii) x = 0.65

15 (a) M/N

(d) Draw the straight line y = -2x + 4; x=-2.4,-0.4,2.85

(b) 4

L/K

2 452.16 cmz

4 cm

13 (a) (i) (5,2) (ii) (1,6) (iii) (2, 3)

3 t=- 1 3 2 4 p=-1,4=2 5 31°36'

6 (a) (i) Some (ii) All (b) Ify