CSEC Math May-June 2013 p1

TESTCODE

01234010

FORM TP 2013091 MAY/JUNE 2013

CARIBBEAN SECONDARY EDUCATION CERTIFICATE® SECONDARY EDUCATION CERTI.FICATE - EXAMINATION MATHEMATICS Paper 01 - General Proficiency 1 hour 30 minutes (22 MAY 2013 (p.m.)) READ THE FOLLOWING INSTRUCTIONS CAREFULLY. 1.

This test consists of60 items. You will have 1 hour and 30 minutes to answer them.

2.

In addition to this test booklet, you should have an answer sheet.

3.

A list of formulae is provided on page 2 of this booklet.

4.

Each item in this test has four suggested answers, lettered (A), (B), (C), (D). Read each item you are about to answer, and decide which choice is best.

5.

On your answer sheet, find the number which corresponds to your item and shade the space having the same letter as the answer you have chosen. Look at the sample item below. Sample Item

2a + 6a (A) (B) (C) (D)

=

Sample Answer

8a 8a2 12a 12a2

The best answer to this item is "8a", so answer space (A) has been shaded.

---;;;; ----

6.

If you want to change your answer, erase it completely before you fill in your new choice.

7.

When you are told to begin, turn the page and work as quickly and as carefully as you can. If you cannot answer an item, go on to the next one. You may return to this item later. Your score will be the total number of correct answers.

8.

You may do any rough work in the booklet.

9.

Calculators and mathematical tables are NOT allowed for this paper.

i iiiii

-

!!!!!!!

DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO.

!!!!!!!

Copyright© 2011 Caribbean Examinations Council All rights reserved. 01234010/F 2013

-2LIST OF FORMULAE Volume of a prism

V

=

Volume of cylinder

V

=

Ah where A is the area of a cross-section and h is the perpendicular length.

Volume of a right pyramid

nrh where r is the radius of the base and his the perpendicular height. 1 V = 3 Ah where A is the area of the base and h is the perpendicular height.

Circumference of a circle

C = 2nr where r is the radius of the circle.

Arc length

S = _!l_ x 2nr where eo is the angle subtended by the arc. 360

Area of a circle

A = nr where r is the radius of the circ)e.

Area of a sector of a circle

A = 360

Area of trapezium

A=

()

1

2

X

nr where eo is the angle in the sector.

(a+ b) h where a and bare the lengths of the parallel sides and his

the perpendicular distance between the parallel sides. Roots of quadratic equations

If ax2 + bx + c

=

0,

then x = -b ± --/b 2 - 4ac 2a Trigonometric ratios

sine

opposite side hypotenuse

cos e

adjacent side hypotenuse

e

opposite side adjacent side

Opposite

Adjacent

tan

Area of triangle

Area of MBC = _!_ bh where b is the length of the 2

base and h is the perpendicular height Area of MBC = _!_ab sin C 2

Area of MBC = ~s(s - a) (s - b)(s - c) B

where s

a

Sine rule

=

a+b+c 2

b

sinA sinE Cosine rule

a2

=

b2 + c2

c sinC · -

/Jh

C (

b

A

2bc cos A

GO ON TO THE NEXT PAGE 01234010/F 2013

-3-

1.

(%Y is equal to

6.

4

(A)

-

6 4

(A) (B)

3

(C)

-

(B)

In a school, the ratio of the number of pupils to the number of teachers is 20 : 1. If the number of pupils is 840, how many teachers are there?

(D)

2

(C)

-

(D)

-

9 7.

4

9

The LARGEST prime number that is less than 100 is, (A) (B)

2.

(C)

What percentage of 340 is 425?

(D)

(A) (B)

(C) (D) 3.

80% 85% 125% 152%

8.

(C)

(D)

(D) 9.

$72 $ 80 $180 $300

(A) (B)

(C)

If 12 .!_% of a sum of money is $40, what 2 is the TOTAL sum of money? (A) (B) (C)

(D)

$ $ $ $4

10.

(C) (D) 11.

5.

The value of29.94 (A) (B) (C) (D)

0.15 1.5 15 150

x

0.5 is approximately

52+ 66 52 X 66 49 +20 49 X 20

The value of the digit 5 in the number 537 is (A) (B)

45 320 500 500

1 3 12 60

By the distributive law 49 x 17 + 49 x 3=

(D) 4.

91 93 97 99

The H.C.F. of 12, 15 and 60 is (A) (B)

Ann and Betty shared a sum of money in the ratio 2:3. Ann received $120. What was Betty's share? (A) (B) (C)

40 42 800 840

5 100 500 5 000

Which of the following sets is equivalent to {a, b, c, d}? (A) (B)

(C) (D)

{ 4} {a, b, c} {p, q, r, s} {1, 2, 3, 4, 5}

GO ON TO THE NEXT PAGE 01234010/F 2013

-4Item 12 refers to the Venn diagram below.

15.

IfTT$6 .00 is equivalent to US$1.00, then TT$15.00 in U.S. dollars is (A) (B) (C) (D)

16. 12.

In the Venn diagram, the shaded area represents

$0.25 $0.40 $2.50 $4.00

A man's taxable income is $15 200. He pays tax at the rate of 25%. The amount of income tax he pays is '

(A)

(B) (C) (D)

13.

P' (P u Q)' Q uP' Q n P'

(A) (B) (C) (D)

If X and Yare two finite sets such that n(X) = 7, n(Y) = 5 and n(X n Y) = 3, then n(X u Y) is (A) (B) (C) (D)

17.

6 9 15 18

$3 $3 $3 $3

775 800 825 875

At the end of any year a car is worth 5% less than what it was worth at the beginning of the year. If a car was worth $1 0 000 in January 2011, then its value in December 2011 was (A) (B) (C) (D)

$9 $9 $9 $9

995 500 025 000

Item 14 refers to the Venn diagram below.

u

18.

Tom bought a pen for $60 and sold it to gain 20% on his cost price. How much money did he gain? (A) (B) (C) (D)

14.

$12 $40 $72 $80

IfP = {Factorsof6} andQ={Factorsof4} , then the shaded region represents

19. (A) (B) (C) (D)

{} {1, 2} {4, 6, 8 ... } {12, 24, 36 ... }

Mr. Duncan bought a table at a discount of 30% thus saving $42. What was the marked price of the table? (A)

$ 98

(B) (C) (D)

$110 $140 $182

GO ON TO THE NEXT PAGE 01234010/F 2013

-5-

20.

If the simple interest on $800 for 3 years is $54, what is the rate of interest per annum?

25.

If 5(2x- 1) = 35, then x (A)

(A)

(B) (C) (D)

~%

=

-4

9

(B)

2_!__% 4 5%

(C)

3

(D)

4

4

44% 26.

3x2 x 2x3

= ;

21.

(A)

(B) (C) (D)

22.

$20.00 $21.50 $24.50 $26.00

(B) (C) (D)

27.

(B) (C) (D)

$ $ $ $1

If x = 4 andy = 2, what is the value of

105 210 370 050

(A)

1~

(B)

2_!__ 2

(C)

22 8

(D)

2~

Seven times the product of two numbers, a and b, may be written as (A)

(B) (C) (D)

7ab 49ab 7a+ b 7(a+ b)

28.

If xis an integer that satisfies the inequality 4 < 2x ::; 6, then (A) (B)

(C) (D)

4

4

The sum of two positive numbers (p and q) is 32. Their difference is 12. What is the SMALLER number? (A)

(B) 24.

6x 5 6x6 5x6 72x5

x 2 +3y xy

If $7 000 is borrowed at the rate of 5% per annum for 3 years, the simple interest is (A)

23.

(A)

At a sale, each book was marked $3.00 off the original price. Daniel paid $46.00 for two books that had the same sale price. What was the original cost of ONE of his books?

(C) (D)

10 12 20 22

2 y x + y> 2x x + y < 2x

X =

i

2 4

6 8

Item 57 refers to triangle ABC below. Item 54 refers to the triangle below.

54.

B

In the triangle, the value of x is 57. (A) (B) (C) (D)

55.

30° 60° 120° 150°

The image of the point P (-3, 2) under the translation [ (A) (B) (C) (D)

In the triangle, not drawn to scale, angle BA C = 30° and AB = 40 m. The length BC, in metres, is (A) (B) (C) (D)

40 40 40 40

sin 30° tan 30° sin 60° tan 60°

~ Jis

(- 5, 3) (-2, 4) (- 1, 1) (-1, 3)

GO ON TO THE NEXT PAGE 01234010/F 2013

- 11 -

Item 58 refers to the triangle LMN below.

59.

M

L~N 58.

(A) (B) (C) (D)

Triangle LMN is rotated in a clockwise direction about L through an angle of 90°. What is its image? (A)

A plane is flying in a direction of 045° and changes course in a clockwise direction to 135°. The angle through which the plane turns is

L ~N'

Item 60 refers to the following graph.

M' (B)

L

M' N' (C)

N'~L M'

(D)

60.

L

A' B' C' is the image of ABC under an enlargement of scale factor 2. The area of A' B' C', in square units, is (A) (B) (C) (D)

M'

2 4 8 12

N'

ENDOFTEST

IF YOU FINISH BEFORE TIME IS CALLED, CHECK YOUR WORK ON THIS TEST.

01234010/F 2013