HKDSE

MATH CP

PAPER 2
HONG KONG EDUCATIONAL PUBLISHING COMPANY LTD.

HONG KONG DIPLOMA OF

SECONDARY EDUCATION EXAMINATION

MATHEMATICS Compulsory Part

S6 MOCK EXAM 11 (2021)
PAPER 2
Time allowed: 1¼ hours

INSTRUCTIONS

1. Read carefully the instructions on the Answer Sheet. After the announcement of the start of the
examination, you should first stick a barcode label and insert the information required in the spaces
provided. No extra time will be given for sticking on the barcode label after the ‘Time is up’
announcement.

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 deducted for wrong answers.

© 香港教育圖書有限公司 保留版權
Not to be taken away before the
Hong Kong Educational Publishing Company Ltd.
end of the examination session
All Rights Reserved 2021

CP S6 MOCK 11 PAPER 2-1 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. 9333 8222 =
A. 6555.
B. 6666.
C. 72555.
D. 72666.

b − (n + 1)c
2. If a = , then n =
n −1
b+c+a
A. .
a−c
b−c+a
B. .
a−c
b+c+a
C. .
a+c
b−c+a
D. .
a+c

7 3
3. − =
5 + 2x 5 − 2x
20 − 8 x
A. .
25 − 4x 2
20 − 20x
B. .
25 − 4x 2
50 − 8 x
C. .
25 − 4x 2
50 − 20x
D. .
25 − 4x 2

CP S6 MOCK 11 PAPER 2-2 2 © Hong Kong Educational Publishing Company Ltd.

4. (5x − 3y)(2x + 3y) + y(8x + 12y) =
A. (2x − 3y)(5x + 7y).
B. (2x − 3y)(5x − 7y).
C. (2x + 3y)(5x + y).
D. (2x + 3y)(5x − y).

5. Let h(x) = 2x2 + x − 7. If a is a constant, then h(a − 1) + h(−a − 1) =

A. 4a2 − 12.
B. −6a.
C. 4a2.
D. −12.

6. Let f(x) = −kx3 − kx2 − 18, where k is a constant. If x + 3 is a factor of f(x), then f(3) =
A. 18.
B. 1.
C. 0.
D. −54.

CP S6 MOCK 11 PAPER 2-3 3 © Hong Kong Educational Publishing Company Ltd.

7. If a and b are constants such that (y − 8)(y + a) (3 − y)2 + b, then b =
A. −25.
B. −16.
C. 2.
D. 7.

8. In the figure, the equations of the straight lines L1 and L2 are px + y + r = 0 and
qx + py + s = 0 respectively. Which of the following is/are true?
I. pq 0 y
L2
II. r 0
L1
III. pr s
A. I only
B. II only
x
C. I and III only O

D. II and III only

9. If the cost of a dress is a% lower than its selling price, then the percentage profit of selling the
dress is
100a
A. %.
100 − a
B. a%.
10 000
C. %.
100 − a
100(100 − a )
D. %.
a

CP S6 MOCK 11 PAPER 2-4 4 © Hong Kong Educational Publishing Company Ltd.

10. The actual area of a park is 0.24 km2. If the area of the park on a map is 150 cm2, then the scale
of the map is
A. 1 : 16 000 000.
B. 1 : 25 600.
C. 1 : 4000.
D. 1 : 400.

11. It is given that y varies as the square root of m and the cube of n. When m = 25 and n = 4,
y = −800. When m = 4 and n = 9, y =
A. 3645.
B. −480.
C. −233.28.
D. −3645.

12. In the figure, the 1st pattern consists of 2 dots. For any positive integer n, the (n + 1)th pattern
is formed by adding (2n + 2) dots to the nth pattern. Find the number of dots in the 6th pattern.

A. 30
B. 42
C. 46
D. 56

CP S6 MOCK 11 PAPER 2-5 5 © Hong Kong Educational Publishing Company Ltd.

 7 − 3a
13. The solution of a + 3 and 11 − 7a 4 is
5
A. a −1.
B. a −1.
C. a 1.
D. a 1.

14. In the figure, PQRST is a pentagon, where all the measurements are correct to the nearest cm.
Let k cm2 be the actual area of the pentagon. Find the range of values of k.
A. 68.75 k 87.75
8 cm
B. 68.75 k 87.75 T S

C. 70.375 k 85.875
P
D. 70.375 k 85.875 7 cm
4 cm

Q 12 cm R

15. The angle of a sector is increased by 25% but its radius is decreased by a%. If the arc length of
the sector remains unchanged, find the value of a.
A. 20
B. 25
1
C. 33
3
D. 80

CP S6 MOCK 11 PAPER 2-6 6 © Hong Kong Educational Publishing Company Ltd.

16. If the volume of a right circular cone of base radius 3x cm and height 8y cm is 168 cm3, then
the volume of a right circular cylinder of base radius 8x cm and height 3y cm is
A. 1344 cm3.
B. 504 cm3.
C. 448 cm3.
D. 168 cm3.

17. In the figure, P and Q are points lying on OR while U and T are points lying on OS such that
OP : PQ : QR = 1 : 2 : 3 and PU // QT // RS. The ratio of the area of the trapezium PQTU to the
area of the trapezium QRST is
O
A. 2 : 3.
B. 4 : 9. P U

C. 8 : 27.
D. 16 : 81. Q T

R S

18. In the figure, ABCD is a parallelogram. Let E be a point lying on BC such that BE : EC = 3 : 2.
BC is produced to the point F such that CF = BE. Denote the point of intersection of AF and
CD by G. It is given that BD and AG intersect at the point H. If the area of CEG is 78 cm2,
then the area of ABH is
A. 200 cm2. D A
2
B. 320 cm .
H
C. 325 cm2.
D. 520 cm2. G

F B
C E

CP S6 MOCK 11 PAPER 2-7 7 © Hong Kong Educational Publishing Company Ltd.

19. According to the figure, which of the following must be true?
I. x + y − z = 0
II. y + z − x = 180
x
III. x + y + z = 360
A. I only y

B. II only z

C. I and III only

D. II and III only

20. In the figure, ABC is an isosceles triangle with AC = BC and CDE is an equilateral triangle. If
ACB = 72 and ADC = CAD = 55 , then CBE =
A. 11 . A
D
B. 16 .
C. 22 .
D. 32 .
C

B E

21. In the figure, ABCD is a parallelogram. Let E be a point lying on AD such that CE = 12 cm and
BE = 16 cm. If BC = 20 cm, find the area of the parallelogram ABCD.
A. 96 cm2 D E A
B. 120 cm2
C. 192 cm2
D. 240 cm2

C B

CP S6 MOCK 11 PAPER 2-8 8 © Hong Kong Educational Publishing Company Ltd.

22. In the figure, PQRS is a circle. If PQ = 8 cm, QR = 13 cm, PQR = 90 and PQS = 70 , find
PS correct to the nearest cm.
Q
A. 13 cm
B. 14 cm
C. 15 cm
D. 16 cm P
R

23. A ship is 60 km due south of a port. If the ship moves in the direction of 330 , find the shortest
distance between the ship and the port.
A. 30 km
B. 35 km
C. 52 km
D. 104 km

24. The point P is translated upwards by 4 units to the point Q. If Q is rotated clockwise about the
origin through 270 to the point (−6, −2), then the polar coordinates of P are
A. (2, 45 ).
B. (2, 135 ).
C. ( 8 , 45 ).
D. ( 8 , 135 ).

CP S6 MOCK 11 PAPER 2-9 9 © Hong Kong Educational Publishing Company Ltd.

25. The straight line 3x − 4y + 12 = 0 cuts the x-axis and the y-axis at the points A and B
respectively. If P is a moving point on the rectangular coordinate plane such that P is
equidistant from A and B, then the locus of P is a
A. straight line.
B. pair of straight lines.
C. parabola.
D. circle.

26. The equation of the straight line L is kx − 9y − 3k = 0, where k is a constant. If L is parallel to

the straight line 4x − 6y + 5 = 0, find the y-intercept of L.
A. −3
B. −2
C. 2
D. 3

27. The equation of the circles C1 and C2 are 3x2 + 3y2 + 54x − 6y − 638 = 0 and
x2 + y2 + 6x − 18y − 10 = 0 respectively. Which of the following is/are true?
I. The centre of C1 lies on C2.
II. The radii of C1 and C2 are equal.
III. C1 and C2 intersect at only one point.
A. I only
B. II only
C. I and II only
D. I and III only

CP S6 MOCK 11 PAPER 2-10 10 © Hong Kong Educational Publishing Company Ltd.

28. Two numbers are randomly drawn at the same time from four cards numbered 2, 4, 6 and 8
respectively. Find the probability that the result of subtracting the smaller number from the
larger number is less than 4.
1
A.
6
1
B.
2
5
C.
8
5
D.
6

29. The bar chart below shows the distribution of the ages of the members of the basketball team in
a school. Find the inter-quartile range of the distribution.
A. 2
Number of members
8
B. 2.5
6
C. 3
4
D. 4
2

0
13 14 15 16 17
Age

30. Consider the following integers:

2 3 4 5 5 5 12 x y
Let a, b and c be the median, the mean and the mode of the above integers respectively. If the
range of the above integers is 10 and x y, which of the following must be true?
I. a = 5
II. b = 5
III. c = 5
A. I only
B. III only
C. I and II only
D. II and III only

CP S6 MOCK 11 PAPER 2-11 11 © Hong Kong Educational Publishing Company Ltd.

Section B

31. C0000000000002016 =
A. 12 256 + 32.
B. 13 256 + 32.
C. 12 260 + 512.
D. 13 260 + 512.

32. If and are the roots of the equation (log3 x)2 − 9log3 x + 18 = 2log3 x, then =
A. 39.
B. 311.
C. log3 9.
D. log3 11.

33. In the figure, the graph of y = ax is reflected with respect to the y-axis to obtain the graph of
y = bx, where a and b are positive constants. Which of the following are true?
I. a 1
y = bx y y = ax
II. b 1
III. ab = 1
A. I and II only
B. I and III only
C. II and III only
D. I, II and III
x
O

CP S6 MOCK 11 PAPER 2-12 12 © Hong Kong Educational Publishing Company Ltd.

34. The graph in the figure shows the linear relation between x and y. If y = −2, then x =
A. 0. y
B. 2.
2
C. 4.
D. 64.
O 1

35. If a 0, which of the following are arithmetic sequences?

I. log a7, log a3, log a−1
II. 4a − 7, 5a − 11, 6a − 15
III. sin (90 + a) , sin 180 , sin (270 − a)
A. I and II only
B. I and III only
C. II and III only
D. I, II and III

36. Consider the following system of inequalities:

0 y 3
3x − 2 y − 6 0
x − y +1 0
Let D be the region which represents the solution of the above system of inequalities. Find the
constant k such that the greatest value of 5x + 2y + k is 35, where (x, y) is a point lying in D.
A. −23
B. 9
C. 26
D. 40

CP S6 MOCK 11 PAPER 2-13 13 © Hong Kong Educational Publishing Company Ltd.

 10 − ki k + 10i
37. Define z1 = and z2 = , where k is a real number. If the sum of the real part of z1
3−i 2+i
and the real part of z2 is 10, find the imaginary part of z1 + z2.
A. −4
B. 0
C. 4
D. 10

38. In the figure, ABCDEFGH is a cuboid. If AB = 20 cm, AD = 8 cm, BG = 15 cm and

EG = 2k cm, find the area of AEG.
A. (k 2 − 16)(441 − k 2 ) cm 2 A B

B. (k 2 − 16)(k 2 − 441) cm 2
D C
C. (k + 16)(441 − k ) cm
2 2 2

D. (k 2 + 16)(441 + k 2 ) cm 2
F
G

E H

39. In the figure, ABC and CDEF are circles such that ACD and BCF are straight lines. PQ is the
common tangent to the two circles at C. If DE = EF, BAC = 26 and CDE = 70 , find
ABC.
P
A. 66
F E
B. 70
A
C. 88 C
D. 92
D
B

CP S6 MOCK 11 PAPER 2-14 14 © Hong Kong Educational Publishing Company Ltd.

40. The equations of the three sides of a triangle are 12x + 5y = 60, 12x − 5y = 60 and x = c, where
c is a constant. If the x-coordinate of the in-centre of the triangle is 18, then c =
A. 18.
B. 30.
C. 31.
D. 36.

41. Find the range of values of a such that the circle x2 + y2 + ax + 4y + 27 = 0 and the straight line
x − y − 5 = 0 do not intersect.
A. −22 a 10
B. −10 a 22
C. a −22 or a 10
D. a −10 or a 22

42. 5 boys and 4 girls sit in a row. If no girls are next to each other, how many different rows can
be formed?
A. 2880
B. 5760
C. 43 200
D. 362 880

CP S6 MOCK 11 PAPER 2-15 15 © Hong Kong Educational Publishing Company Ltd.

43. There are 9 blue balls and 6 yellow balls in a bag. If 4 balls are randomly chosen from the bag
at the same time, find the probability that at least 3 blue balls are chosen.
1
A.
7
6
B.
7
6
C.
13
7
D.
13

44. In a test, the difference of the test scores and the difference of the standard scores of two
students are 24 marks and 3 respectively. In the test, the standard deviation of the test scores is
A. 8 marks.
B. 16 marks.
C. 21 marks.
D. 27 marks.

45. The variance of seven numbers 9c + 2, 9c + 5, 9c + 8, 9c + 11, 9c + 14, 9c + 17 and 9c + 20 is

A. 6.
B. 12.
C. 36.
D. 9c + 36.

END OF PAPER

CP S6 MOCK 11 PAPER 2-16 16 © Hong Kong Educational Publishing Company Ltd.