2020-POST MOCK-MATH-CP 2–1 1

2020-DSE MATH CP PAPER 2

P.O.C.A. WONG SIU CHING SECONDARY SCHOOL

HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2020

MATHEMATICS Compulsory Part PAPER 2

11:15 am – 12.30 pm (1¼ hours)

INSTRUCTIONS

1. Read carefully the instruction on the Answer Sheet. After the announcement of the start of the examination,

you should first insert the information required in the space 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 answer 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.

Not to be taken away before the end of the examination session

2020-POST MOCK-MATH-CP 2–2 2

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

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

Choose the best answer for each question.

Section A

1. 2( 1)( 2 1)y y y− + + =

A. 3 1y − .

B. 3 1y + .

C. 3 2 1y y y+ − − .

D. 3 2 1y y y− + − .

2.

333

334 18

2

− =

A. 6692− .

B. 669

1

2− .

C. 6692 .

D. 669

1

2.

3. Consider ( ) ( 1)( 2)f x x x ax b= + − − + . If ( 1) 9f − = and (2) 3f = , then

A. 2a = , 7b = .

B. 2a = , 7b = − .

C. 2a = − , 7b = − .

D. 2a = − , 7b = .

2020-POST MOCK-MATH-CP 2–3 3

4. If a and b are non-zero constants such that 2 2( ) ( )x x b x a x a x+ − + + − , find :a b .

A. 1:1

B. 1: 2

C. 2 :1

D. 4 :1

5. If 2q

p qp

+ = + , then q =

A. ( 2)

1

p p

p

−

−.

B. 2 2

1

p

p

−

−.

C. 2 2

1

p

p

−

−.

D. ( 2)

1

p p

p

−

−.

6. If 0.7549 0.7551a , which of the following must be true?

A. 0.7a = (correct to 1 significant figure)

B. 0.75a = (correct to 2 significant figures)

C. 0.755a = (correct to 3 significant figures)

D. 0.7550a = (correct to 4 significant figures)

7. The solution of 4 3 13x− or 3(4 ) 2 3x x− − is

A. 4x .

B. 3x .

C. 3x − .

D. 3 4x .

Go on to the next page

2020-POST MOCK-MATH-CP 2–4 4

8. If 2

( )1

f xx

=+

, then 1

( )f x fx

=

A. 1 .

B. 2

4

( 1)x +.

C. 2

4

( 1)

x

x +.

D. 2

2

4

( 1)

x

x +.

9. The figure shows the graph of a quadratic function ( )y f x= . If 8p q+ = − and ( 3) 24f − = , find ( )f x .

A. 2( ) ( 4) 73f x x= − − +

B. 2( ) ( 4) 25f x x= − − +

C. 2( ) ( 4) 73f x x= − + +

D. 2( ) ( 4) 25f x x= − + +

10. When 2 22x bx b− + is divided by x b+ , the remainder is 100 . Find the remainder when it is divided by

x b− .

A. 50

B. 25

C. 25−

D. 50−

2020-POST MOCK-MATH-CP 2–5 5

11. A sum of $10000 is deposited at an interest rate 1.6% p.a. for 4 years, compounded quarterly. Find the

interest correct to the nearest dollar.

A. $10161

B. $10660

C. $161

D. $660

12. If : : 1: 2 : 3a b c = and 2 3 70a b c+ + = , then 2 2 22 3a b c+ + =

A. 900 .

B. 1296 .

C. 2450 .

D. 3600 .

13. z partly varies directly as 2x and partly varies directly as y . If x is decreased by 20% and y is

decreased by 36% , then z is

A. decreased by 20% .

B. decreased by 36% .

C. increased by 10% .

D. increased by 20% .

14. Let na be the thn term of a sequence. If 8 12a = , 10 24a = and 2 1n n na a a+ += + for any positive integer

n , then 11a =

A. 12 .

B. 30 .

C. 36 .

D. 48 .

Go on to the next page

2020-POST MOCK-MATH-CP 2–6 6

15. The figure shows a frustum of a right circular cone. The height of the frustum is 3 cm . If the areas of the upper

and the lower bases of the frustum are 216 cm and 236 cm respectively, find the volume of the frustum.

A. 332 cm

B. 376 cm

C. 392 cm

D. 3276 cm

16. In the figure, ABCD is a parallelogram. E and F are points lying on AD such that

: : 4 :3: 2AE EF FD = . G is a point lying on BC such that : 1: 2BG GC = . AG and BE intersect at

H . If the area of ABH is 212 cm , then the area of the quadrilateral EFGH is

A. 224 cm .

B. 227 cm .

C. 230 cm .

D. 233 cm .

17. In the figure, ABCD is a square with sides 7 cm . It is given that AEF BFG = and 90EFG = . If

4 cmBG = and 5 cmFG = , find CED correct to the nearest 0.1 .

A. 51.3

B. 54.5

C. 56.8

D. 60.3

2020-POST MOCK-MATH-CP 2–7 7

18. In the figure, ABEF and ABCG are parallelograms. AGF and BCDE are straight lines. Find CAG .

A. 42

B. 45

C. 66

D. 78

19. In the figure, the bearing of B from A is 035 . If ABCDE is a regular pentagon, then the true bearing of

E from D is

A. 209 .

B. 215 .

C. 251 .

D. 253 .

20. In the figure, ABCD is a rhombus. M and N are points lying on the diagonal BD such that

CMB CND BAD = = . If 5 3AB BD= and the perimeter of ABD is 22 cm , find MN .

A. 2.8 cm

B. 3.4 cm

C. 3.6 cm

D. 6.4 cm

21. In the figure, O is the centre of the circle ABCDE . If 10ABE = and 80CDE = , then AOC =

A. 130 .

B. 140 .

C. 150 .

D. 160 .

Go on to the next page

2020-POST MOCK-MATH-CP 2–8 8

22. If 180 270x y , which of the following statements is/are true?

I. cos cosx y

II. sin sinx y

III. sin cosx y

A. I only

B. I and II only

C. II and III only

D. I, II and III

23. In the figure, ABCD is a rectangle. Let CBF = . The shortest distance from D to EF is

A. ( )sinAB AD + .

B. ( ) cosAB AD + .

C. sin cosAB AD + .

D. cos sinAB AD + .

24. The straight line 9 6 0hx y− + = and 18 54 0x ky+ + = are perpendicular to each other. If they have the same

x − intercept, then k =

A. 2 .

B. 4 .

C. 5 .

D. 9 .

2020-POST MOCK-MATH-CP 2–9 9

25. In the figure, the equations of the straight lines 1L and 2L are 5x py q+ = and 2rx y s+ = respectively.

Which of the following is/are true?

I. 10pr

II. 5s qr

III. 0p q+

A. I only

B. II only

C. I and III only

D. II and III only

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 2 2 2MP NP MN+ = . If the equation of the locus of

P is 2 2 8 4 5 0x y x y+ − + − = , find the value of a .

A. 8−

B. 6−

C. 6

D. 8

27. The equation of a circle C is 2 22 2 8 6 3 0x y x y+ + − − = . Let A be the centre of the circle. If the

coordinates of a point B are (1 , 2) , which of the following is/are true?

I. The coordinates of A are ( 4 , 3)− .

II. B lies outside C .

III. If O is the origin, then AOB is an acute angle.

A. I only

B. III only

C. I and II only

D. II and III only

Go on to the next page

2020-POST MOCK-MATH-CP 2–10 10

28. There are four cards which are numbered 1 , 2 , 3 and 4 respectively. If two cards are drawn randomly

without replacement, find the probability that the sum of the two numbers is an odd number.

A. 1

3

B. 1

2

C. 2

3

D. 5

6

29. The box-and-whisker diagram below shows the distribution of the heights (in cm) of some students.

Which of the following statements must be true?

I. The mean of the distribution is 175 cm .

II. Less than half of the students are shorter than 170 cm .

III. The range of the distribution is twice the interquartile range of the distribution.

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

30. Consider the following data:

12 10 11 17 18 19 16 13 18 14 a b

It is given that a and b are positive integers such that a b . If both mean and the median of the above data

are 15 , which of the following are true?

I. 32a b+ =

II. 18a

III. 14b

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

2020-POST MOCK-MATH-CP 2–11 11

Section B

31. The H.C.F. and the L.C.M. of three expressions are 24ab c and 5 4 672a b c respectively. If the first expression

and the second expression are 2 3 48a b c and 5 236a b c respectively, then the third expression is

A. 3 42ab c .

B. 4 62ab c .

C. 3 44ab c .

D. 4 64ab c .

32. The figure shows the graph of logay x= and the graph of 1logb

y x= on the same rectangular coordinate

system, where a and b are positive constants. If a vertical line cuts the graph of logay x= , the x − axis

and the graph of 1logb

y x= at the points A , C and B respectively, which of the following is/are true?

I. 1b

II. 1ab

III. loga

ABab

BC=

A. I only

B. II only

C. I and III only

D. II and III only

33. Convert the decimal number 916 28+ into a hexadecimal number.

A. 16100000001C

B. 16100000001D

C. 161000000001C

D. 161000000001D

Go on to the next page

2020-POST MOCK-MATH-CP 2–12 12

34. If a is a real number, then the real part of 2 5i

i a

−

+ is

A. 2

5 2

1

a

a

+

+.

B. 2

2 5

1

a

a

−

+.

C. 2

2 5

1

a

a

+

−.

D. 2

2 5

1

a

a

+

−.

35. Consider the following system of inequalities:

0

5

4 12 0

3 14 0

x

y

x y

x y

+ − + −

Let D be the region which represents the solution of the above system of inequalities. If ( , )x y is a point

lying on D , then the greatest value of 3 2 4x y+ − is

A. 2 .

B. 10 .

C. 12 .

D. 15 .

36. The product of the 1st term and the 2nd term of a geometric sequence is 48 , while the product of the 2nd term

and the 4th term of the sequence is 1296 . The product of the 3rd term and the 5th term of the sequence is

A. 3888 .

B. 5184 .

C. 11664 .

D. 34992 .

2020-POST MOCK-MATH-CP 2–13 13

37. The straight line 3 0kx y− + = and the circle 2 2 2 6 1 0x y x y+ − + − = intersect at A and B . Find the

y − coordinate of the mid-point of AB in terms of k .

A. 2

2

3 3

1

k k

k

− + +

+

B. 2

2

3 3

1

k k

k

− −

+

C. 2

1 6

1

k

k

−

+

D. 2

1 6

1

k

k

− +

+

38. For 0 360 , how many roots does the equation 32sin sin = have?

A. 2

B. 4

C. 5

D. 7

39. 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 8 cmTC = and 4 cmCD = , find the length of BT .

A. 4 cm

B. 4.8 cm

C. 6 cm

D. 7.2 cm

Go on to the next page

2020-POST MOCK-MATH-CP 2–14 14

40. The figure shows a right triangular prism ABCDEF with an equilateral triangular base ABC of side 5 cm

and 15 cmCD = . Find the angle between the line FC and the plane BCDE , correct to the nearest 0.1 .

A. 9.3

B. 15.9

C. 16.3

D. 18.4

41. Consider the point (0 , 2)P and the straight line 8 5x y k+ = , where k is a positive constant. The straight

line cuts the x − axis and y − axis at the points Q and R respectively. If the y − coordinate of the

circumcentre of PQR is 5 , then the x − coordinate of the circumcentre is

A. 41

10.

B. 9

2.

C. 5 .

D. 16

5− .

42. At a studio, 3 men and 5 women sit in a row to take a photo. If all the men must sit next to each other, in how

many ways can the people be arranged?

A. 39600

B. 14400

C. 4320

D. 720

2020-POST MOCK-MATH-CP 2–15 15

43. Box A contains 4 white balls, 3 black balls and 2 blue balls while box B contains 6 white balls, 1 black ball and

3 blue balls. If two balls are randomly drawn from each box at the same time, find the probability that at least 1

white ball is drawn.

A. 1

18

B. 26

27

C. 7

54

D. 169

270

44. An examination consists of paper 1 and paper 2. The probability that Tony passes paper 1 is 3

4 and the

probability that Tony passes paper 2 is 3

5. Given that Tony passes at least one paper in the examination, find the

probability that he passes paper 1.

A. 1

6

B. 1

3

C. 3

5

D. 5

6

45. Consider an arithmetic sequence 1x , 2x , … , 100x with common difference d . Let 1m , 1r and 1v be the

mean, the range and the variance of the first 10 terms respectively while 2m , 2r and 2v be the mean, the range

and the variance of the last 10 terms respectively. Which of the following must be true?

I. 2 1 90m m d= +

II. 2 1r r=

III. 2 1 90v v d= +

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

END OF PAPER