MOCK 16(I)

MATH
COMPULSORY
PART
PAPER 2

OXFORD UNIVERSITY PRESS

MOCK 16(I)

MATHEMATICS Compulsory Part

PAPER 2

(1 1 / 4 hours)

INSTRUCTIONS

1. Read carefully the instructions on the Answer Sheet and insert the information required in the
spaces provided.

2. When told to open this book, you should check that all the questions are there. Look for the words
‘END OF PAPER’ after the last question.

3. All questions carry equal marks.

4. ANSWER ALL QUESTIONS. You are advised to use an HB pencil to mark all the answers on the
Answer Sheet, so that wrong marks can be completely erased with a clean rubber.

5. You should mark only ONE answer for each question. If you mark more than one answer, you will
receive NO MARKS for that question.

6. No marks will be deducted for wrong answers.

© Oxford University Press 2016

MOCK 16(I) MATH COMPULSORY PART PAPER 2 1

There are 30 questions in Section A and 15 questions in Section B.

The diagrams in this paper are not necessarily drawn to scale.

Choose the best answer for each question.

Section A

6 648
1. =
16162
A. 3 486 .
B. 3 648 .
486
 3
C.   .
8
648
 3
D.   .
8

a b3
2. If  = 2, then b =
c b
c
A. .
ac
2c
B. .
a  3c
3c
C. .
ac
3c
D. .
a  3c

3. a 2 + 8ab + 16b 2  9a 2 b 2 =

A. (a + 3ab + 4b)(a  3ab + 4b).

B. (a + 3ab  4b)(a  3ab  4b).

C. (a + 3ab + 4b)(a + 3ab  4b).

D. (a  3ab + 4b)(a  3ab + 4b).

MOCK 16(I) MATH COMPULSORY PART PAPER 2 2

4. 0.033 746 71 =

A. 0.034 (correct to 2 decimal places).

B. 0.033 7 (correct to 4 significant figures).

C. 0.033 74 (correct to 5 decimal places).

D. 0.033 747 (correct to 5 significant figures).

5. If 3r  5s + 22 = 4r + 3s = 1, then s =

A.  2.
B. 1.

C. 3.

D. 5.

6. If a < 0 and b < 0, which of the following may represent the graph of y = ax 2 + 2x + b?

A. y B. y

x
O
x
O

C. y D. y

x
O x
O

7. The solutions of 2x  5  5x + 1 < 16 are

A.  3 < x  2.

B.  3  x < 2.

C.  2  x < 3.

D.  2 < x  3.

MOCK 16(I) MATH COMPULSORY PART PAPER 2 3 Go on to the next page
8. Let f(x) = (x 2 + k)(x + 1), where k is a non-zero constant. If f(x) is divisible by x  k, find
the remainder when f(x) is divided by x + 2.

A. 4

B. 3
C. 5
D. 9

9. 65% of all the students in a class pass a Mathematics test. It is known that 75% of the boys
and 50% of the girls in the class pass the test. Find the ratio of the number of boys to the
number of girls in the class.

A. 2:1
B. 1:2

C. 3:2

D. 2:3

10. The marked price of a box of apples is $70. If the box of apples is sold at a discount of
40% on the marked price, then the loss is $8. If the box of apples is sold at the marked
price, then the profit is

A. $20.

B. $28.
C. $36.

D. $42.

11. Let a, b and c be non-zero constants. If a : b = 3 : 1, b : c = 2 : 3 and a + 2b  3c = 3, then

a=

A. 3.
B. 6.

C. 9.

D. 18.

MOCK 16(I) MATH COMPULSORY PART PAPER 2 4

12. It is given that f(x) partly varies directly as x and partly varies inversely as x 2 . If f(2) =  5
and f(3) = 2, then f(1) =

A.  34.

B.  16.
C. 20.
D. 38.

13. If the radius of a solid sphere is measured as 5 cm correct to the nearest cm, then the least
possible volume of the sphere is
243
A.  cm 3 .
2
500
B.  cm 3 .
3
1 331
C.  cm 3 .
6
729
D.  cm 3 .
2

14. In the figure, the 1st pattern consists of 11 dots. For any positive integer n, the (n + 1)th
pattern is formed by adding 6 dots to the nth pattern. Find the number of dots in the 8th
pattern.

A. 35

B. 41

C. 47
D. 53

15. In the figure, BCD is a straight line and ACEF is a rectangle. △ ABC and △ CDE are
right-angled triangles. If AB = 16 cm, BC = 30 cm and CD = 12 cm, find the perimeter of
ACEF.
F
A. 59.5 cm
B. 119 cm
E
C. 140 cm
A
D. 199.5 cm
16 cm

B 30 cm C 12 cm D
MOCK 16(I) MATH COMPULSORY PART PAPER 2 5 Go on to the next page
16. In the figure, ABCD is a rectangle with AB = 10 cm and AD = 20 cm. An arc with radius AD
and centre A is drawn to cut BC at E. Find the area of the shaded region in the figure,
correct to 3 significant figures.

A. 8.68 cm 2 B E C
B. 11.0 cm 2
C. 34.9 cm 2 10 cm

D. 95.3 cm 2
A D
20 cm

17. In the figure, ABCD is a trapezium with AB // DC and AB : DC = 4 : 3. F is the mid-point of

AB. AC and DF intersect at E. If the area of △ ADE is 24 cm 2 , then the area of ABCD is
340
A. cm 2 . D C
3
B. 140 cm 2 . E

C. 160 cm 2 .
A F B
D. 180 cm 2 .

18. In the figure, the solid consists of a right circular cylinder and a hemisphere with a
common base. The radius of the hemisphere and the height of the solid are 2 cm and 10 cm
respectively. Find the total surface area of the solid.
A. 40  cm 2
B. 44  cm 2

C. 52  cm 2
D. 56  cm 2

  
19.

In the figure, A, B and C are three points on the circle. AB : BC : AC = 13 : 11 : 12 and D
is a point on AB . Two lines are drawn from D to meet AB at E and F respectively such that
DE // BC and DF // AC . Find  EDF .
A. 55  C

B. 60 

C. 63 
D. 65 
E F
A B

D
MOCK 16(I) MATH COMPULSORY PART PAPER 2 6
20. If the sum of the interior angles of a regular n -sided polygon is 2 520  , which of the
following is/are true?
I. The number of diagonals of the polygon is 14.

II. Each exterior angle of the polygon is 22.5  .

III. Each interior angle of the polygon is 140  .

A. I only
B. II only
C. I and III only
D. II and III only

AE
21. In the figure, AEB is a straight line. If  AED =  ABC = 90  , then =
BE
AD C
A. .
CD

AD tan 
B. . D
CD
AD
C. .
CD cos

D.
AD
. 
CD tan  A E B

22. The figure below consists of 26 identical equilateral triangles and 2 identical rhombuses.
The two rhombuses are shaded. Which of the following is true?

A. The number of axes of reflectional symmetry of the figure is 2.

B. The number of folds of rotational symmetry of the figure is 2.

C. The number of folds of rotational symmetry of the figure is 3.

D. The number of folds of rotational symmetry of the figure is 6.

MOCK 16(I) MATH COMPULSORY PART PAPER 2 7 Go on to the next page
23. The rectangular coordinates of the point P are ( 3 , 5). If P is reflected with respect to
the line y = 2, then the polar coordinates of its image are

A. (2 , 300  ).

B. (2 , 330  ).
C. (4 , 300  ).

D. (4 , 330  ).

24. The coordinates of two points A and B are (  1 , 4) and (  5 , 2) respectively. P is a moving
point in the rectangular coordinate plane such that P is equidistant from A and B . Which of
the following must be true?

I. The equation of the locus of P is 2 x + y  3 = 0.

II. The locus of P is the perpendicular bisector of the line segment AB .
III. △ PAB is an equilateral triangle.

A. II only

B. III only

C. I and II only
D. II and III only

25. The straight lines L 1 : ax + 4 y  12 = 0 and L 2 : 2 x + by  6 = 0 intersect at a point on the

y -axis. If L 1  L 2 , then a =

A.  4.

B.  2.
C. 2.

D. 4.

26. A chord L of the circle x 2 + y 2 + kx  12 y  12 = 0 cuts the two axes at (8 , 0) and (0 , 12).
If L divides the circle into two equal parts, then k =

A.  4.
B.  6.

C.  8.

D.  12.

MOCK 16(I) MATH COMPULSORY PART PAPER 2 8

27. A bag contains eight balls which are marked with the numbers 1, 2, 3, 4, 5, 6, 7 and 8
respectively. Two balls are randomly drawn from the bag at the same time. Find the
probability that the sum of the numbers drawn is not more than 5.
1
A.
8
1
B.
7
5
C.
12
5
D.
28

28. The bar chart below shows the numbers of different banknotes in a cash box. A banknote is
randomly drawn from the cash box. Find the expected face value of the banknote drawn.
A. $12.5

Number of banknotes
B. $20 20

C. $31 15

D. $45 10
5
0
$10 $20 $50 $100
Face value of the banknote

29. The stem-and-leaf diagram below shows the distribution of the ages of all employees in an
office. If the median and the inter-quartile range of the distribution are 27 and 14
respectively, find the values of a and b .

A. a = 6 and b = 3 Stem (tens) Leaf ( units )

B. a = 7 and b = 3 1 8 9
2 1 3 a 8
C. a = 6 and b = 5 3 2 b
D. a = 7 and b = 5 4 0 2

30. If the mean and the mode of the data 3, 5, 8, x , x , x , y are 7 and 8 respectively, where x and
y are distinct numbers, find the standard deviation of the data.
A. 1

B. 2

C. 4
D. 8

MOCK 16(I) MATH COMPULSORY PART PAPER 2 9 Go on to the next page
Section B

1 x
31. 2
 3 =
x  2x  3 x  27
2x  9
A. .
( x  1)( x  3)( x 2  3x  9)
3 x  10
B. .
( x  1)( x  3)( x 2  3 x  9)

5x  9
C. .
( x  1)( x  3)( x 2  3 x  9)

2x2  4x  9
D. .
( x  1)( x  3)( x 2  3 x  9)

32. The graph in the figure shows the linear relation between x and log 5 y . If log 5 y = a + bx ,
which of the following may be a relation between x and y ?

1
x
log 5 y
A. y = 3 
5 log 5 y = a + bx

B. y = 3(5) x
x
5x O
C. y=
3
x
11
D. y=  
35

33. 250  16 10 + 192  16 5 + 29 =

A. FA00C00001D 16 .
B. FB00D00001E 16 .

C. FA000C00001D 16 .

D. FB000D00001E 16 .

MOCK 16(I) MATH COMPULSORY PART PAPER 2  10 

34. In the figure, the equation of PQ is x + y = 9. If ( x , y ) is a point lying in the shaded region
PQRS (including the boundary lines), then the minimum value of 18 + x  4 y is
A.  13. y

B.  3. P
6
C.  1. 5
S
D. 22.
R Q
x
0 4 6 8

1
35. Let z = a + i + , where a is a real number. Which of the following must be true?
a i
I. z is a real number.
II. If z is a purely imaginary number, then z = 2 i .
Real part of z
III. is an irrational number.
Imaginary part of z

A. I only
B. II only

C. I and III only

D. II and III only

36. Let b n be the n th term of a sequence, where b n = 3 n  8. Let a n be the n th term of another
a  a 2  a3    a n
sequence, where 1 = b n . Which of the following are true?
n
I. a 1 , a 2 , a 3 , … , a n is an arithmetic sequence.

II. 79 is a term of the sequence b 1 , b 2 , b 3 , … .

3n 2  13n
III. The sum of the first n terms of the sequence b 1 , b 2 , b 3 , … is .
2
A. I and II only

B. I and III only

C. II and III only

D. I, II and III

MOCK 16(I) MATH COMPULSORY PART PAPER 2  11  Go on to the next page

37. For 0   < 360, how many roots does the equation sin 2  = sin  cos  have?
A. 2
B. 3

C. 4

D. 5

38. In the figure, ABCDEFGH is a cuboid, where AB = 6 cm and BC = 3 cm. M is the mid-point
1
of CH. If cos AMF = , find the volume of the cuboid.
9
A. 144 cm 3 E

B. 216 cm 3 F H
G
C. 240 cm 3
M
D. 108 3 cm 3 D
A C
6 cm 3 cm
B

39. The figure shows the graph of y = h  sin kx, where h and k are constants, and 0  x  45.
Find the values of h and k.
1 y
A. h = 1 and k =
2
1
B. h = 1 and k = 2
y = h  sin kx
1
C. h = 1 and k =
2
x
D. h = 1 and k = 2 0 45

MOCK 16(I) MATH COMPULSORY PART PAPER 2  12 

40. In the figure, PQ is the tangent to the circle at C and BD // PQ. AC and BD intersect at E.
F is a point on AC such that FB bisects ABD. Which of the following must be true?
I. CA bisects BAD. A
II. BC = FC

III. BF // CD F
A. I and II only
B E D
B. I and III only
P Q
C. II and III only C

D. I, II and III

41. Let k be a constant. If the straight line x + 2y  k = 0 and the circle x2 + y2  8x + 12y  48 = 0
intersect at A and B, then the y-coordinate of the mid-point of AB is

k 2  8k  48
A. .
10

 k 2  8k  48
B. .
10
14  2k
C. .
5

2k  14
D. .
5

42. The coordinates of two vertices of a triangle are (7 , 0) and (5 , 4). If the x-coordinate of
the circumcentre of the triangle is 2, then the y-coordinate of the circumcentre is

A. 10.
B. 4.
C. 0.
D. 6.

MOCK 16(I) MATH COMPULSORY PART PAPER 2  13  Go on to the next page

43. There are 4 cans of different dog food and 5 cans of different cat food in a box. If 4 cans
are randomly selected from the box at the same time, find the probability that 1 can of dog
food and 3 cans of cat food are selected.
5
A.
63
10
B.
63
20
C.
63
40
D.
63

44. 6 different Mathematics books, 2 different Economics books and 3 different Geography
books are arranged in a row on a bookshelf. If books of the same subject are put together,
how many different ways of arranging the books are there?
A. 216
B. 8 640
C. 25 920
D. 51 840

45. Let P be a group of numbers {x + a, x + b, x + c, x + d, x + e} and Q be another group of

numbers {y + a, y + b, y + c, y + d, y + e}, where a < b < c < d < e and x > y. Which of the
following are true?
I. Mean of P > mean of Q
II. Range of P = range of Q
III. Variance of P > variance of Q
A. I and II only
B. I and III only
C. II and III only
D. I, II and III

END OF PAPER

MOCK 16(I) MATH COMPULSORY PART PAPER 2  14 