MOCK10

PAPER 2

MATHEMATICS Compulsory Part

PAPER 2

Time allowed: 1 hour 15 minutes

INSTRUCTIONS

1. Read carefully the instructions on the Answer Sheet. After the announcement of the start of
the examination, you should first write 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. You must mark the answers clearly; otherwise you will lose marks if the answers
cannot be captured.

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 deduced for wrong answers.

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

x 3
1. 
( 2 x 2 ) 3
x3
A. .
8
1
B. .
8x 3
x3
C. .
6
1
D. .
6x 3

q
2. If p  q   2 , then q =
p
p ( p  2)
A. .
p 1
p ( p  2)
B. .
1 p

p2  2
C. .
p 1
p2  2
D. .
1 p

3. If A and B are constants such that 3x( x  1)  A( x  1)  3x 2  3x  B , then B =

A. –6.
B. –3.
C. 0.
D. 6.
4. It is given that x – k is a factor of f ( x)  x 3  kx 2  2 x  4 , where k is a constant.
When f (x) is divided by x + k, the remainder is
A. 24.
B. 8.
C. 2.
D. 0.

5. In a bakery, the price of 3 donuts and 2 egg tarts is $69 while the price of 4 donuts
and 5 egg tarts is $120. If Wendy wants to buy 1 donut and 8 egg tarts, how much does
she need to pay?
A. $78
B. $96
C. $111
D. $132

6. The figure shows the graph of y  ax 2  b , where a and b are constants. It is given that
the graph passes through (2, 0). Which of the following are true?

I. a<0
II. b < 0
III. The solutions of the inequality y > 0 are 2 < x < 2.

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

67 1
7. The solutions of  3 x  and x – 1 > 0 are
2 2
A. x 1.
B. x  11 .
C. 1  x  11 .
D. x  1 or x  11 .
8. John sold a watch which cost $600 to Peter. John set the selling price 30% higher
than the cost, but then gave a 30% discount to Peter. At the end, John
A. lost $366.
B. lost $54.
C. gained $114.
D. had no gain and no loss.

9. If the base of a triangle is increased by 60% and its height is decreased by k% such that
its area remains unchanged, then k =
A. 37.5.
B. 50.
C. 60.
D. 62.5.

3y 2
10. If x and y are non-zero distinct constants such that  , then ( x  y ) : x 
x y 3
A. 2 : 11 .
B. 11 : 2 .
C. 11 : 13 .
D. 13 : 11 .

11. It is given that z varies directly as x2 and inversely as y.When x =  and y = –6, z = –2.
When y = 9 and z = 3, x =
A. 2.
B. 3.
C. 2 or 2.
D. 3 or 3.
12. Sam and Philip went hiking at the MacLehose Trail. They started from location A at the
same time. Sam travelled 75 m in 45 seconds, while Philip travelled 2 km in 15 minutes.
How far apart were they after travelling for 1.5 hours?
A. Philip leads Sam 3 km.
B. Sam leads Philip 3 km.
C. Philip leads Sam 2000 m.
D. Sam leads Philip 2000 m.

13. In a 110 m hurdle race, the first hurdle is set at a distance of 13.7 m from the starting
line. Each of the next nine hurdles is set at a distance of 9.1 m from the previous one. If
the maximum absolute error for setting each hurdle is 0.05 m, find the maximum
distance between the last hurdle and the finish line.
A. 13.9 m
B. 14.4 m
C. 14.65 m
D. 14.9 m

14. In the figure, AB = BC = 1 cm, CD = 2 cm and DE = 2 cm. Find the area of ABCDE.
A. 3 cm2
7 2
B. cm
2
C. 6 cm2
D. 7 cm2
15.

The figure above shows a sphere and a cylinder with the dimensions as shown. It is
given that their total surface areas are equal. Find the volume of the sphere.
A. 108 cm3
B. 324 cm3
C. 486 cm3
D. 972 cm3

16. In the figure, △ABC is a right-angled triangle. D is a point on AC such that DB bisects
∠ABC. If BC = 12 cm and ACB  50 , find the length of AD correct to 3 significant
figures.
A. 2.81 cm
B. 3.35 cm
C. 5.70 cm
D. 6.79 cm

2
17. For 0    180 , the greatest value of is
3  cos  3 cos(180   )
A. 2.
2
B. .
5
2
C. .
3
D. 2.
18. In the figure, AE and BD intersect at C. △ABC and △CDE are both equilateral
triangles. It is given that CBE  35 . Which of the following are true?

I. BEC  25
II. AB // DE
III. AD = BE

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


19. In the figure, AD is a diameter of the circle ABCD, where BC  CD . If ADC  68 ,

then ADB 
A. 22 .
B. 34 .
C. 46 .
D. 52 .

20. In the figure, O is the centre of the circle ABCD. Let ADB  x and OCB  y ,
then AOC 
A. 2x  y .
B. 90  x  y .
C. 180  2 x  2 y .
D. 360  2 x  2 y .
21. Which of the following triangles has/have reflectional symmetry but no rotational
symmetry?
I. II. III.

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

22. The polar coordinates of the point A are (4, 60°). If A is reflected about the polar axis,
then the rectangular coordinates of its image are
A. (1, 3 ) .
B. (1,  3 ) .
C. (2, 2 3 ) .
D. (2,  2 3 ) .

23. X(2, 8) and Y(6, 4) are two points in the coordinate plane, and Z is the point of
intersection between the line segment XY and the y-axis. Find the coordinates of Z.
 10 
A.   , 0
 3 
B. (2, 0)
C. (0,  5)
D. (0,  4)

24. The figure shows the graph of the straight line x  ay  b  0 . Which of the following is
true?
A. a > 0 and b > 0
B. a > 0 and b < 0
C. a < 0 and b > 0
D. a < 0 and b < 0
25. P is a moving point in the coordinate plane such that the distance between P and the
x-axis is equal to the distance between P and the line y = 4. Which of the following
about the locus of P is/are true?

I. It is a pair of straight lines.

II. It is a straight line.
III. It passes through (4, 2).

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

26. In the figure, the equation of the circle is

A. x 2  y 2  4ax  3ay  0 .
B. x 2  y 2  4ax  3ay  0 .
C. x 2  y 2  8ax  6ay  0 .
D. x 2  y 2  8ax  6ay  0 .

27. In a class of 30 students, 60% of them are boys. Now, two more girls join the class. Find
the probability that a randomly selected student from the class is a girl.
3
A.
8
5
B.
8
7
C.
16
9
D.
16
28. The box-and-whisker diagram below shows the distribution of the weights (in kg) of the
cats in a pet shop.

If the standard weight of a cat is within 3 kg and 6 kg, find the percentage of cats in the
pet shop which weigh out of this range.
A. 33.3%
B. 50%
C. 66.7%
D. 75%

29. It is given that the mode of ten numbers 1, 2, 5, 12, 8, 9, 2, 3, m and n is 5, where m and
n are integers. Which of the following are true?

I. The median of the ten numbers is 5.

II. The mean of the ten numbers is 5.2.
III. The range of the ten numbers is 11.

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

30.

The figures above show the cumulative frequency curves/polygons of three

distributions. Arrange the three distributions in descending order of their standard
deviations.
A. X, Y, Z
B. X, Z, Y
C. Y, X, Z
D. Z, Y, X
Section B

31. The H.C.F. of 3x( x  2)( x 2  x  6) , 6 x 2 ( x  2)( x 2  9) and 12( x  3)( x 3  8) is

A. 3.
B. ( x  2) .
C. 3( x  3)( x  2) .
D. 12 x 2 ( x  2)( x 2  9)( x 3  8) .

32. It is given that y  4 x 2 . Which of the following graphs represents the linear relation
between log 2 x and log 2 y ?
A. B.

C. D.

33. 110010000100012 
A. 213  29  4113 .
B. 213  2 9  8226 .
C. 214  210  4113 .
D. 214  210  8226 .
 1 i 4i
34.  
i 1 i
A.  5  5i .
B.  3  3i .
C. 1  3i .
D. 3  3i .

35. Which of the following systems of inequalities has solutions represented by the shaded
region in the figure?

x  1  0

A. y  2  0
x  y  4  0


x  1  0

B. y  2  0
x  y  4  0


x  1  0

C. y  2  0
x  y  4  0


x  2  0

D. y 1 0
x  y  4  0


36. If a, 3, b are the first three terms of an arithmetic sequence and b, 2, a are the first
three terms of a geometric sequence, then (a  b) 2 
A. 4.
B. 14.
C. 20.
D. 36.
37. Which of the following statements about the graph of y   x 2  4 x  6 is false?
A. The x-intercepts of the graph are irrational numbers.
B. The coordinates of the vertex of the graph are (2, 10).
C. If the graph is translated 3 units leftwards, then the equation of the new graph
will be y   x 2  2 x  9 .
D. The graph intersects the line y = 8 at two points.

38. Let a and b be constants. If the figure shows the graph of y  a sin 2 x  b , where
0  x  180 , then
A. a = 3 and b = 2.
B. a = 2 and b = 1.
C. a = 2 and b = 1.
D. a = 3 and b = 2.

39. The figure shows a triangular prism ABCDEF, where AC  6 cm , CD  5 cm ,

EF  7 cm and ACB  50 . It is given that M and N are the mid-points of AB and
ED respectively. Find the angle between the line MN and the plane DEF, correct to the
nearest degree.
A. 33
B. 44
C. 48
D. 54
40. In the figure, EF, FG and GE are the tangents to
the circle ABCD at A, B and D respectively. AC
and BD intersect at H. If AED  70 and
CBG  40 , then CHD 
A. 80 .
B. 85 .
C. 95 .
D. 110 .

41. Find the range of values of k such that the circle x 2  y 2  kx  6 y  10  0 and the
line 2 x  y  5  0 do not intersect.
A.  62  k  2
B. 2  k  62
C. k  62 or k  2
D. k  2 or k  62

42. In a rectangular coordinate plane, O(0, 0), A(8, 6) and B(16, 0) are the vertices of
△OAB respectively. Which of the following are true?

I. The coordinates of the centroid of △OAB are (8, 2).

II. The orthocentre of △OAB lies outside the triangle.
III. The circumcentre of △OAB lies outside the triangle.

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

43. How many 4-digit even numbers can be formed by choosing ‘2’, ‘3’, ‘4’, ‘6’, ‘7’ and ‘8’
as the digits without repetition?
A. 40
B. 240
C. 360
D. 480
44. Mathematics examination consists of two papers, paper I and paper II. The probabilities
4 1
that Edison obtains grade 5 or above in paper I and paper II are and respectively.
5 3
Given that he obtains grade 5 or above in only one of the papers, find the probability
that he obtains grade 5 or above in paper I.
4
A.
15
1
B.
2
8
C.
15
8
D.
9

45.

The graph above shows the curves of two normal distributions M and N. Which of the
following are true?

I. The mean of M = the mean of N

II. The mode of M < the mode of N
III. The standard score of a datum a in M < the standard score of a datum a in N

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

END OF PAPER