Kuen Cheng High School

Third Examination 2014

Mathematics
Name : _____________________( ) Date : October 2014
Class : JR2A - 2P Time : 2 hours
Total no of pages : 6_

Section A : Objective Questions [30%]

2x 2y
1. Simplify + 2
x −y
2 2
y − x2
2 2 x+ y x− y
A. 2( x + y ) B. C. D. E.
x+ y x− y 2 2

( −2x y )  (3 y )
3
=
2 2
2.

A. −72x 6 y 5 B. −6x 6 y 5 C. −6x 5 y 6 D. −72x 5 y 5 E. −72x 6 y 6

y −1
3. Given that = x , express y as the subject of the formula.
y +1
1+ x 1− x x +1 x −1 x −1
A. B. C. D. E.
1− x 1+ x x −1 x +1 1− x

4. Convert 11011012 to octal number.

A. 1828 B. 1558 C. 1188 D. 1098 E. 1088

5. Solve the inequality 17 – 4x > 2x – 1.

A. x < 3 B. x < 4 C. x < 5 D. x > 4 E. x > 5

6. Find the length of AB in Figure 1. D

20 cm
A. 5 cm A
B. 7 cm 15 cm
C. 8 cm Figure 1
D. 12 cm
E. 25 cm B 24 cm C

1
7. Figure 2 shows a regular pentagon. Find the value of y– x.

A. 36º

B. 72º x
C. 108º y

D. 126º
Figure 2
E. 540º

2x + 3y = 45
8. Solve the simultaneous equations: 
3x - 4 y = 8

A. x = 3, B. x = 13, C. x = 8, D. x = 6, E. x = 12,
y = 13 y=2 y=4 y=5 y=7

9. Given that B = {2, 4, 8, 16, 32, 64}, which of the following set builder notation is correct?

A. B = { x | x  N, 2 ≤ x ≤ 64}

B. B = { x | x  Z, x is even number, 2 ≤ x ≤ 64}

C. B = { x | x = 2n, n  N, 2 ≤ x ≤ 64}

D. B = { x | x = 2n, n  Z, n ≤ 64 }

E. B = { x | x = 2n, n  N, n ≥ 2 }

10. Given n() = 14, n(A’) = 7, n(B) = 6, n(AB)’ = 2, find n(AB).

A. 1 B. 3 C. 5 D. 7 E. 9

11. Find the midpoint for A (4, -9) and B (-12, 7).

11 21
A. ( ,− ) B. (8, -8) C. (-4, -8) D. (4, -8) E. (-4, -1)
2 2

12. Which of the below is the intersection point for line x = 3 and y = 12?

A. (12, 3) B. (4, 1) C. (1, 4) D. (3, 12) E. (-12, -3)

2
13. Find the gradient and y intercept from Figure 3.
3 Y
A. Gradient = − , y - intercept = 6
4
3
B. Gradient = , y - intercept = 6 6
4
3
C. Gradient = , y - intercept = 8
4
3 Figure 3 X
D. Gradient = − , y - intercept = 8 0 8
4
3 3
E. Gradient = − , y - intercept =
4 4

14. Figure 4 is a cuboid. Find the length of PC and the area of the ACP.
S R
A. PC = 6 cm, area = 24 cm2
P Q
B. PC = 10 cm, area = 40 cm2

C. PC = 12 cm, area = 48 cm2

8 cm C
D
D. PC = 15 cm, area = 60 cm2 Figure 4 9 cm
A 12 cm B
E. PC = 17 cm, area = 60 cm2

15. Base on the data in Figure 5, find a.

A. 4 cm a cm

B. 5 cm 9 cm
C. 6 cm 8 cm
6 cm
D. 7 cm Figure 5

E. 8 cm

Section B: Subjective questions [70%]

Answer any 7 questions

1. a) Find the value in binary for 112× 10012 – 12 ÷ 112 (2%)

b) Convert 12348 to binary numbers. (2%)

c) If 5.23 = 2.286 , 52.3 = 7.232 , find the value of 0.000523 . (1%)

d) A job can be done by 15 men in 30 days. How long would it take if 10 men to do the same job?
(2%)

c) Expand 4 ( a + 2 ) (a + 2) − 2(a − 4)(3 − a) (3%)

3
2. a) Factorize completely each of the following:

i) 2y² – 72 (2%)

ii) a2 – b2 + 5a – 5b (3%)

b) Solve (5y – 2)² = 16 (2%)

 5x 1  9 x 2 − 16
c) Simplify  +   (3%)
 3x − 4 4 − 3x  5 x + 4 x − 1
2

3. a) Find the quotient and remainder of ( 3 x 2 + 10 )  ( 3 x + 6 ) (2%)

p + q2
b) Given = 2 , express q in terms of p. (2%)
4

c) Given that x2 + y 2 = 41 and xy = 9, find the value of ( x + y ) .

2
(3%)

2 ( 7 − x )  2

d) Solve the simultaneous inequalities  x + 5 1 (3%)
 
 8 2

P Q A 15 cm B
P o
50 x◦
5 cm
17 cm y◦ 128o
8 cm R
S D C

Q R F
S 6 cm
T E
Figure 6 Figure 7 Figure 8

4. a) In Figure 6, QSR is a straight line. Calculate

i) the length of PR. (2%)

ii) the perimeter of triangle PQR. (2%)

b) In Figure 7, PQ is parallel to RS, find the value of x + y. (3%)

c) In Figure 8, ABCD is a rectangle and CDE is a right angle triangle.

Given F is the mid -point of CE and CE=12cm, find the area of the shaded region. (3%)

4
 R A
Q S
50˚

U
a
30˚ 4 cm D
70˚ P T
6 cm B C
Figure 9 Figure 10 Figure 11
5. a) In Figure 9, find the value of a. (3%)

b) In Figure 10, PQRST is a square and PUT is an isosceles triangle. R is a midpoint of QS.

Find the area, in cm2, of the shaded region. (3%)

c) In Figure 11, ABC is an isosceles triangle where AB = AC = 30 cm, BDA = 90 ,

BAC = 30 , find

i) the length of BD.

ii) the area of ABC (4%)

6. a) Let  = {x  Z | - 4 < x < 10},

A = {x  Z | x is even number; x > 0},

B = {x  Z | x can be divided by 3}

C = {x  Z | x is neither positive number nor negative number}

i) List down all the elements in B. (1%)

ii) Find (AB)’\C iii) Find n (B’A) (4%)

b) There are 50 students in Class A. Base on the height, 40% of the students are in the range 161 –
180 cm, 60% of the students are in range 151 – 170 cm tall. There are 20% of the students consider
short, their height are less than 150cm.

i) How many students consider short? (2 %)

ii) How many students in range 161 – 170 cm? (3%)

5
 A O P
120
3 cm
B C

9 cm

30
D E Q
S R
Figure 12
Figure 13

7. a) Base on the Figure 12 answer the following question.

i) Show that ABC ~ ADE (2%)

ii) Find BC: DE (2%)

iii) Given AE = 16 cm, find the length of CE. (2%)

b) Figure 13 is a combination of 2 polygons. PQS is a right angle triangle; OPRS is a parallelogram

with area 50cm2. R is the midpoint of SQ straight line. Base on Figure 13, answer the following
question.

i) Find the area of PRQ. (2%)

ii) If SR = 8cm, find the length of PQ. (2%)

8. a) Find the equation of the line which passing through (-5, 4) and (10, 10). (2%)

b) Given that y = 7 + 2x – 3x2, copy and complete the following table: (4%)

x -5 -4 -3 -2 -1 0 1 2 3

y -78 -49 -26 2 7 6 -1

i) Taking 2cm to represent 1 unit on the x-axis and 2cm to represent 10 units on y-axis, draw
the graph of y = 7 + 2x – 3x2 for -5 ≤ x ≤ 3. (3%)

ii) Use your graph to find the value of x when y = - 40 (1%)

~END OF QUESTION PAPER~