MOCK 17(I)

MATH
COMPULSORY
PART
PAPER 2

OXFORD UNIVERSITY PRESS

MOCK 17(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 2017

MOCK 17(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

1. 8 2n + 222  9 3n + 333 =
A. 5 5n + 555 .

B. 5 6n + 666 .
C. 6 5n + 555 .

D. 6 6n + 666 .

2. 4x 2  12xy + 9y 2  2x + 3y =
A. (2x  3y)(2x  3y + 1).

B. (2x  3y)(2x  3y  1).

C. (2x + 3y)(2x  3y + 1).
D. (2x + 3y)(2x  3y  1).

b 2c
3. If  = 5, then c =
ac ca
A. 5a  b.

B. b  5a.
3
C. .
5a  b
5a  b
D. .
3

4. If 3p + q = 1  2p = p  q  6, then q =

A. 4.
7
B.  .
2
C. 1.
D. 4.

MOCK 17(I) MATH COMPULSORY PART PAPER 2 2

 x2  x  p
5. Let f(x) = , where p and q are non-zero constants. If f (3)  f (  3) =  3, then q =
q

A.  7.

B.  2.
C. 2.

D. 7.

6. If the length of a side of a square is measured as 10 cm correct to the nearest 2 cm, then the
least possible area of the square is

A. 64 cm 2 .
B. 81 cm 2 .

C. 98 cm 2 .

D. 99 cm 2 .

7. The solutions of  4 x < 6  x and 5( x + 1) > 17 + x are

A. x > 3.

B. x >  2.

C.  2 < x < 3.

D. x <  2 or x > 3.

8. If m is a constant such that the quadratic equation mx 2  4 x + m = 3 has equal roots, then
m=
A. 3.

B.  2 or 2.

C. 4 or  1.
D.  4 or 1.

9. If a book is sold at a 20% discount on its marked price, then the percentage loss is 50%. If
the marked price of the book is r % below the cost, then the value of r is

A. 37.5.

B. 40.
C. 60.

D. 62.5.

MOCK 17(I) MATH COMPULSORY PART PAPER 2 3 Go on to the next page
10. The figure shows the graph of y = a ( x + 2) 2  b , where a and b are constants. Which of the
following is true?
y
A. a < 0 and b > 4 a 2
y = a ( x + 2)  b
B. a < 0 and b < 4 a

C. a > 0 and b > 4 a

x
D. a > 0 and b < 4 a O

11. If m and n are non-zero constants such that m : n = 8 : 3, then (2 m + 3 n ) : (4 m + n ) =

A. 3 : 2.

B. 5 : 2.
C. 5 : 7.

D. 19 : 15.

12. In the figure, the 1st pattern consists of 3 dots. For any positive integer n , the ( n + 1)th
pattern is formed by adding 2 n dots to the n th pattern. Find the number of dots in the 7th
pattern.

A. 17
B. 23
C. 33
D. 45

13. If w varies directly as x 2 and inversely as y , which of the following must be constant?

x2
A.
wy

w2 x 4
B.
y
x4
C.
w2 y

D. y wx 2

MOCK 17(I) MATH COMPULSORY PART PAPER 2 4

14. In the figure, ABCD is a trapezium, where AB // DC . The area of ABCD is 156 cm 2 . E is a
point lying on AB . If BC = 13 cm, BE = 5 cm, DC = 6 cm and CE = 12 cm, then AD =
A. 13 cm. A E 5 cm B
B. 15 cm.

C. 17 cm. 12 cm 13 cm

D. 20 cm.
D 6 cm C

15. In the figure, ABCDEFGH is a regular octagon. Find p + q + r .

A. 67.5  B A

B. 90  r
C H
C. 112.5  p q
D. 135  D G

E F

16. Find the percentage change in the volume of a solid right circular cone if the base radius of
the cone is increased by 10% and the height of the cone is decreased by 15%.
A. Increased by 2.85%.

B. Decreased by 2.85%.

C. Increased by 5%.
D. Decreased by 5%.

17. In the figure, QR = UR and PQ // UR . PR and QU meet at S . T is a point lying on PQ such

that RT is the angle bisector of  PRQ . If  QUR = 30  and  PSQ = 80  , then  PTR =

A. 70  . P
U
B. 75  .
30 
C. 80  .
T 80  S

D. 85  .
Q R

MOCK 17(I) MATH COMPULSORY PART PAPER 2 5 Go on to the next page
18. In the figure, ABCD is a trapezium with AB // DC and AB : DC = 1 : 2. F is a point lying on
AB such that AF : FB = 1 : 3. E is the point of intersection of DF and AC . If the area of
△ CED is 64 cm 2 , then the area of ABCD is
A F B
A. 96 cm 2 .

B. 105 cm 2 . E

C. 108 cm 2 .

D. 128 cm 2 . D C

19. ABCD is a parallelogram. The diagonal BD is an axis of symmetry of ABCD and AC = BD .

AC and BD meet at E . If M is the mid-point of AB and N is the mid-point of CD , which of
the following are true?
I. AB = BC = CD = AD

II. AC  BD
III. △ BEM  △ CEN

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

20. In the figure, ABCD is a square. P and Q are points lying on AB and AD respectively such
that PQ is perpendicular to CQ and AQ = 2 DQ . Find  PCQ , correct to the nearest degree.

A. 27  A P B
B. 34 
C. 56 
Q
D. 63 

D C

MOCK 17(I) MATH COMPULSORY PART PAPER 2 6

 tan (90   ) cos (360   ) sin (180   )
21.  =
sin 210 cos120
2
A. .
sin 
1
B. .
2 sin 
2  2 sin 2 
C. .
sin 
1  sin 2 
D. .
2 sin 

22.
 
In the figure, ABCD is a semi-circle. If BC : CD = 4 : 3 and  BCD = 103, then  ABC =
A. 44. C
B. 46. 103 
D
C. 57.
D. 77.
A B

23. The polar coordinates and the rectangular coordinates of a point P are ( r , 150) and ( x , 1)
respectively. Find the value of x .

A. 2

B.  3

C. 3
D. 2

24. The figure shows the straight lines L 1 : y + ax = b and L 2 : y + cx = d . Which of the following
is/are true?
y
I. a>c>0
L1
II. c<d

III. bd>ac
L2
A. I only
x
0 1
B. II only

C. I and III only

D. II and III only

MOCK 17(I) MATH COMPULSORY PART PAPER 2 7 Go on to the next page
25. The straight lines L 1 and L 2 : 6 x + ky – 16 = 0 are perpendicular to each other, where k is a
constant. If L 1 and L 2 intersect at (1 ,  2), then the equation of L 1 is
A. 5 x + 6 y – 3 = 0.

B. 5 x + 6 y + 7 = 0.

C. 6 x – 5 y – 3 = 0.
D. 6 x – 5 y – 16 = 0.

26. The coordinates of M and N are (1 , a ) and (7 , 2) respectively, where a is a constant. Let P
be a moving point in the rectangular coordinate plane such that MP 2 + NP 2 = MN 2 . If the
equation of the locus of P is x 2 + y 2  8 x + 4 y  5 = 0, find the value of a .

A. 8
B. 6
C. 6

D. 8

27. The equation of circle C is given by 4 x 2 + 4 y 2  4 kx  4 ky + k 2 = 0, where k > 0. Which of

the following is/are true?
I. The coordinates of the centre of C are (2 k , 2 k ).

πk 2
II. The area of C is .
4
III. The origin lies inside C .
A. II only

B. III only

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

MOCK 17(I) MATH COMPULSORY PART PAPER 2 8

28. A box contains some cards and there is a number on each card. The stem-and-leaf diagram
below shows the distribution of the numbers on the cards.

Stem (tens) Leaf ( units )

0 1 1 3 5 6 6 7 8 8
1 0 0 1 2 2 3 4 4 7 8 9
2 1 2 4 7 9
3 3 7 8
4 2 5

Peter draws a card at random from the box. If the number on the card drawn is less than 15,
he gets 0 tokens. If the number on the card drawn is between 15 and 30, he gets 60 tokens.
Otherwise, he gets 120 tokens. Find the expected number of tokens got by Peter.

A. 30
B. 36

C. 42

D. 60

29. There are 5 balls of different colours in a bag. Susan draws a ball at random from the bag.
Then she puts the ball drawn back into the bag and draws a ball at random from the bag
again. Find the probability that the two balls drawn are of different colours.
4
A.
25
1
B.
5
1
C.
4
4
D.
5

30. Consider the data set {3, x , x , 4, 5}, where x is a positive integer. Which of the following
statements must be true?
I. The mean of the data is an integer.

II. The median of the data is not less than 3.

III. The mode and the upper quartile of the data are equal.
A. II only

B. III only

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

MOCK 17(I) MATH COMPULSORY PART PAPER 2 9 Go on to the next page
Section B

31. If the figure shows the graph of y = f ( x ) and the graph of y = g ( x ) on the same rectangular
coordinate plane, then
y
A. g ( x ) = 2 f (2 x ).
y = g(x)
 x
B. g(x) = 2 f   . 8
2
C. g(x) = f(2x) + 4.
y = f(x) 4
 x
D. g(x) = f   + 4.
2 x
6 3 0
1 2

32. Let x = log 3 y. If x 3  log 3 y 2 = 2x, then y =

A. 1 or 9.
9
B. 1 or 9.

C. 1 or 1 or 9.
3

D. 1 or 1 or 9.
9

33. 5  45 + 83 =
A. 101100000000 2 .

B. 111000000000 2 .

C. 1011000000000 2 .
D. 1110000000000 2 .

34. i + 2i 2 + 4i 3 + 8i 4 + 16i 5 + … + 65 536i 17 =

A. 52 494  26 214i.
B. 52 494 + 26 214i.
C. 26 214  52 429i.
D. 26 214 + 52 429i.

MOCK 17(I) MATH COMPULSORY PART PAPER 2  10 

35. Let x n be the nth term of an arithmetic sequence. If x 18 + x 20 = 92 and x 200 + 300 = x 100 , which
of the following are true?
I. The first term of the sequence is 100.
II x 1 + x 2 + x 3 + … + x 2 018 < 5.9  10 6

III. x 33 is the smallest positive term of the sequence.

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

36. If y = 4x 2 + 24x + 36, which of the following graphs may represent the linear relation
between x and y?

A. y B. y

6 3

x x
0 0

C. y D. y

6 3
x x
0 0

MOCK 17(I) MATH COMPULSORY PART PAPER 2  11  Go on to the next page

37. Consider the following system of inequalities:
x  y  4  0

x  3 y  6  0
x  0

Let R be the region which represents the solution of the above system of inequalities. If ( x , y )
is a point lying in R and m is a non-zero real number such that mx + y + 1 attains its
maximum value at (3 , 1) only, then
1
A. < m < 1.
3
B. m > 1.
1
C. 1 < m <  .
3
D. m <  1.

38. In the figure, ABCD is a rhombus. E is a point lying on BC such that AE = BE . Find CDE ,
correct to the nearest degree.
A
A. 8 D

B. 9

C. 10 
35 
D. 11  B E C

39. In the figure, ABCDEFGH is a cube. EG and FH intersect at P . Q is the mid-point of AB . If

the angle between PQ and the plane EFGH is  , then tan  =
1 B C
A. .
2 Q
2 A D
B. .
2
C. 2.
D. 2. H
G
P
F E

MOCK 17(I) MATH COMPULSORY PART PAPER 2  12 

40. In the figure, AD is a diameter of the circle. BC is the tangent to the circle at T such that
AB  BC and ADC is a straight line. If TC = 8 cm and CD = 4 cm, find the length of BT .
A. 4 cm

B. 4.8 cm 4 cm C
D
C. 6 cm
8 cm
D. 7.2 cm
A
T

41. A (1 , 2), B (73 , 98) and C (145 , 2) are three points on the rectangular coordinate plane. Let H
and Q be the orthocentre and the circumcentre of △ ABC respectively. Find the length of HQ .

A. 11

B. 21
C. 22

D. 33

42. In a school, there are 7 boys and 5 girls in a music club. On a stage, there are 2 rows of
chairs and there are 3 chairs in each row. 3 boys and 3 girls are randomly selected from the
music club to sit on the stage. If the girls selected must sit in the front row, find the number
of ways of arranging boys and girls to sit on the stage.

A. 350

B. 720
C. 12 600

D. 25 200

43. In a military special task team of 18 soldiers, 6 soldiers are female and the rest are male. If
8 soldiers are randomly selected from the team, find the probability that not more than
4 female soldiers are selected.

A. 7
221
B. 89
442
C. 353
442
D. 214
221

MOCK 17(I) MATH COMPULSORY PART PAPER 2  13  Go on to the next page

44.

50 55 60 65 70 75 80 85
Score (marks)
The box-and-whisker diagram above shows the distribution of the scores (in marks) of the
students of a class in an examination. In the examination, Leon gets the lowest score and
the score of Mary is equal to the lower quartile of the distribution. If the standard score of
Leon in the examination is  1.5 and the standard deviation of the distribution is 8 marks,
then the standard score of Mary in the examination is

A.  0.75.

B.  0.5.
C. 1.
D. 1.25.

45. Let m 1 , r 1 and v 1 be the mean, the range and the variance of a group of numbers
{ a , b , c , d , e , f } respectively while m 2 , r 2 and v 2 be the mean, the range and the variance of
a group of numbers {7 a , 7 b , 7 c , 7 d , 7 e , 7 f , 7 m 1 } respectively. Which of the following must
be true?
I. m2 = 7m1

II. r2 = 7r1

III. v 2 > 49 v 1
A. I and II only

B. I and III only

C. II and III only

D. I, II and III

END OF PAPER

MOCK 17(I) MATH COMPULSORY PART PAPER 2  14 