Maths T STPM 2014 Sem 1 Trial Sekolah Tinggi Segamat

SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT 954/1TINGGI SEGAMAT SEKOLAH SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT UJIAN PENGESANAN SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT PROFISIENSI PENGGAL 1 TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT STPM 2014 SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT T) SEKOLAH TINGGIMATHEMATICS SEGAMAT SEKOLAH T(MATEMATIK TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT PAPER 1(KERTAS 1) SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT One and a half hours SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT SEKOLAH TINGGI SEGAMAT jam TINGGI setengah) SEKOLAH TINGGI SEGAMAT(Satu SEKOLAH SEGAMAT SEKOLAH TINGGI SEGAMAT

SEKOLAH TINGGI SEGAMAT Instructions to candidates: DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO. Answer all questions in section A and any one question n section B. Answers may be written in either English or Bahasa Melayu. All necessary working should be shown clearly. Non-exact numerical answers may be given correct to three significant figures, or one decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.

Mathematical tables, a list of mathematical formulae and graph paper are provided. Arahan kepada calon: JANGAN BUKA KERTAS SOALAN INI SEHINGGA ANDA DIBENARKAN BERBUAT DEMIKIAN. Jawab semua soalan dalam Bahagian A dan mana-mana satusoalan dalam Bahagian B.. Jawapan boleh ditulis dalam bahasa Inggeris atau Bahasa Malaysia. Semua kerja yang perlu hendaklah ditunjukkan dengan jelas. Jawapan berangka tak tepat boleh diberikan betul hingga tiga angka bererti, atau satu tempat perpuluhan dalam kes sudut dalam darjah, kecuali aras kejituan yang lain ditentukan dalam soalan.

This question paper consists of 3 printed pages . (Kertas soalan ini terdiri daripada 3 halaman bercetak) 954/1 Section A [ 45 marks] *This question paper is CONFIDENTIAL the examination is over. CONFIDENTIAL* Answer all until questions in this section *Kertas soalan ini SULIT sehingga peperiksaan kertas ini tamat SULIT*

Section A [ 45 marks] Answer all questions in this section 1.

Find the sum of all the integers between 1 and 1000 which are divisible by 7.

[3]

142

Hence, or otherwise, evaluate

∑ ( 7 r + 2) .

[2]

r =1

2. Use De Moivre’s Theorem to evaluate

(1 + i )11 (1 − i ) 9

3. The polynomial f (x) is defined by f(x) = 27x3 – 9x + 2 a) Find the remainder when f(x) is divided by 3x + 1  

2 3

b) i) Show that f  −  =0.

[6]

[2] [1]

ii)

Express f(x) as a product of three linear factors. 27 x 3 − 9 x + 2 iii) Simplify 9 x 2 + 3x − 2

[4] [2]

4. a) Find the equation of a parabola with vertex at (0,0) if its axis of symmetry is the x-axis and its graph contains the point (-1/2, 2) Find its focus and directrix, and graph the equation. [9]

1

5. a) i) Obtain the binomial expansion of (1 − x ) 4 up to and including the term in x2 .

[2]

4 8 xx 2 for small values of x. [3] 27 729 b) Use the result from part a) ii) to find an approximation for 4 80 , giving your answer 1

ii) Hence show that ( 81 − 16 x ) 4

≈3-

to seven decimal places.

[2]

6. The equation of a straight line l is r = 4i + 2j – 5k + λ ( i – 3k ) and the point A has coordinates (7, 3, 6 ). Find i) the foot of the perpendicular from A to l,

[7]

ii) the perpendicular distance from A to l.

[2]

Section B [ 15 marks ] Answer any one question in this section .

7.

If

and

Hence, find

find

and

.

[6]

During the school holidays, a supermarket offers three sale packages A, B, and C for shirts, long pants and shoes with brand name Tampan . The number of each item and the offer price for each package are shown in the following table.

4

Number of long pants (pairs) 2

Number of shoes (pairs) 2

Offer price (RM) 190

B

3

4

3

295

C

2

4

2

250

Sales package

Number of shirts

A

By representing the prices of a shirt, a pair of long pants, and a pair of shoes as x, y, and z respectively, obtain a matrix equation representing the information above. [3] Solve the matrix equation you have obtained to determine the price of each item. [6]

8. The function f and g are defined by f : x  x+1,x ≥0 g : x  ln x , x > 0 (i) Show that the function fg does not exist. Find the maximal domain of positive real numbers such that the composite function fg exists. [7] (ii) Determine if the function gf exests. If it does, give its rule and state its range.

[5]

(iii) Determine the exact value of x for which gg(x) = 2.

[3]

Suggested solution( sts/ PT 1/MT 1 ( 954/1) / L6, 2013) 1. (a)

1×7+2×7+…

a = 7, d = 7, n = 142

n = 142

n(n + 1) Sn = 12 n(a + b) or 12 n(2a + (n – 1)d) or 7 × 2 142 142 142 ×143 = (7 + 994) or (14 + 141 × 7) or 7 × = 71 2 2 2

B1 M1 (use of correct formula)

A1

(3)

071 (b)

142

∑ (7r + 2) = r =1

142

∑7r + r =1

142

∑2 r =1

M1

split 142

∑2 = 2 × 142

∴

2.

r =1 142

∑ (7r + 2) r =1

= 71 071 + 2 × 142 = 71 355

A1

(2)

3.

4. Given Vertex=(0,0) , point (-1/2, 2) is on the parabola , and axis of symmetry is x-axis, so the form of the equation is y2 = -4ax …………………(1) [1] Substitute x = -1/2 , y=2 into (1), 4 = -4a(-1/2)

⇒ a=2

y2 = -4(2)x = -8x

[1] [1]

Hence the equation of the parabola is y2 = -8x

[1]

Hence,

[2]

Focus is at (-2,0) and the directrix is x=2

When x=2, y2 = 16 ⇒ y = ± 4

5.

6.

7.

If

and

[1]

[1]

[1]

[1]

[1] [2]

[2]

[1]

[1]

[1]

The prices of a shirt, a pair of long pants, and a pair of shoes are RM 10, RM 40 and RM 35 respectively. [3] 8.

(iii) gg (x) = 2

⇒ g( g( x ) = 2

⇒ g( ln x) = 2 ⇒ ln ( ln x) =2 [1] ⇒ ln x = e2 [1]

∴x = e e

2

[1]