mathematics compulsory part practice paper set 5

PP5-DSE-MATH-CP-2-1 1

© Canotta Publishing Co., Ltd.

CANOTTA PUBLISHING CO., LTD.

HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION

MATHEMATICS Compulsory Part

Practice Paper Set 5

Paper 2

(1 1/4 hours)

1. Read carefully the instructions on the Answer Sheet. Stick a barcode label 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.

2020 HKDSE Math CP Paper 2

PAPER 1

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

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.


Section A

1. (32•42n + 1)2

A. 216n + 14.

B. 216n + 12.

C. 28n + 14.

D. 28n + 12.

2. If 4+=m

nxy , then x =

A. n

ym )4 ( −.

B. n

my 4 −.

C. n

my 4 −.

D. m

yn )4 ( −.

3. mn + mp – m2 – np =

A. (m – n) (p – m).

B. (m – n) (p + m).

C. (m – p) (n + p).

D. (m + n) (p – m).

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.

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.

© Can otta Publishing Co., Ltd.

PP5-DSE-MATH-CP-2-3 3 Go on to the next page

4. 0.0706747 =

A. 0.070 (correct to 2 significant figures).

B. 0.0707 (correct to 3 decimal places).

C. 0.0707 (correct to 3 significant figures).

D. 0.07067 (correct to 4 decimal places).

5. The solution of 3 3

2 +

−x

x or 6 > x – 2 is

A. x < 0.5.

B. x < 5.5.

C. x < 8.

D. x < 11.

6. If is a root of the equation 3x2 + 2x − 1 = 0, then 5 − 4 − 62 =

A. 3.

B. 5.

C. 7.

D. 9.

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



7. The diagram shows the graph of nmxxy 2 ++= , where m and n are constants. The equation of the axis of

symmetry of the graph is

A. x = –2.

B. x = –3.

C. x = –4.

D. x = –6.

8. If A, B and C are non-zero constants such that A(4x + 5) + Bx2 ≡ 4x(3x + 4) + C, then A: B: C =

A. 1: 3 : 5.

B. 1: 5 : 3.

C. 3: 1 : 5.

D. 3: 5 : 1.

9. In the figure, the 1st pattern consists of 4 dots. For any positive integer n, the (n + 1)th pattern is formed by

adding 3 dots to the nth pattern. Find the number of dots in the 7th pattern.

A. 19

B. 22

C. 25

D. 28

…

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



10. If a small electrical appliance is sold at the marked price, there will be a profit of 30%. If it is sold at a 30%

discount on the marked price, there will be a loss of $45. Find the cost of the electrical appliance.

A. $400

B. $425

C. $450

D. $500

11. A sum of $80 000 is deposited at an interest rate of 6% per annum for 2 years, compounded half-yearly. Find

the interest correct to the nearest dollar.

A. $9 600

B. $10 000

C. $10 040

D. $10 041

12. The actual area of a square plot of land is 1 600 m2. If the area of this plot of land is 4 cm2 on a map, then the

scale of the map is

A. 1 : 250.

B. 1 : 400.

C. 1 : 500.

D. 1 : 2 000.

13. It is given that z varies directly as x and inversely as y2. If y is increased by 25% and z is decreased by 64%,

then x

A. is increased by 40%.

B. is increased by 80%.

C. is decreased by 43.75%.

D. is decreased by 55%.The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



14. There is a bag of tea. The weight of tea in the bag is measured as 10 kg correct to the nearest kg. If the bag

of tea is packed into n packets such that the weight of tea in each packet is measured as 30 g correct to the

nearest g, find the greatest possible value of n.

A. 333

B. 344

C. 350

D. 355

15. In the figure, D is a point lying on BC and E is a point lying on DF. The area of ABC is

A. 96 cm2.

B. 120 cm2.

C. 144 cm2.

D. 240 cm2.

16. In the figure, the diameter of the semicircle ABC is 3 cm. If BAC = 48°, find the area of the shaded region

correct to the nearest 0.01 cm2.

A. 0.23 cm2

B. 0.53 cm2

C. 0.64 cm2

D. 1.07 cm2

26 cm

10 cm

20 cm

6 cm

6 cm

A

B C D

E

D

F

D

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



17. The solid in the figure consists of a right circular cone and a hemisphere whose bases are of the same area

9π cm2. The height of the solid is 7 cm. Find the total surface area of the solid.

A. 30π cm2

B. 33π cm2

C. 48π cm2

D. 51π cm2

18. In the figure, ABCD is a trapezium in which AD // BC and AD : BC = 2 : 3. E is the mid-point of BC. AC and

DE intersect at F. If the area of △ADF is 80 cm2, then the area of the trapezium ABCD is

A. 270 cm2.

B. 330 cm2.

C. 350 cm2.

D. 400 cm2.

19. In the figure, O is the centre of the circle ABC, AB // OC and ∠ABC = 105°. Find AB : BC .

A. 4 : 1

B. 5 : 1

C. 9 : 2

D. 13 : 3

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



20. In the figure, the bearing of P from O is S58°E and the bearing of Q from O is N32°E. If OP = 2OQ, find the

bearing of P from Q correct to the nearest degree.

A. N27°W

B. N63°W

C. S27°E

D. S31°E

21. If an interior angle of a regular n-sided polygon is 5 times an exterior angle, then which of the following

is/are true?

I. The value of n is 12.

II. The number of diagonals of the polygon is 12.

III. The number of folds of rotational symmetry of the polygon is 12.

A. I only

B. II only

C. I and III only

D. II and III only

22. The polar coordinates of the points P, Q and R are (40, 20), (5, 110) and (30, 290) respectively. The

perpendicular distance from Q to PR is

A. 27.

B. 28.

C. 40.

D. 5 65 .

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



23. If A + B = 90°, then which of the following are true?

I. tan A tan B = 1

II. sin A = cos B

III. cos A + cos B > 0

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

24. The coordinates of the points P and Q are (0, 2) and (2, 0) respectively. If M is a moving point in the

rectangular coordinate plane such that MP = PQ, then the locus of M is

A. the perpendicular bisector of PQ.

B. the circle with PQ as a diameter.

C. the circle with centre P and radius PQ.

D. the straight line passing through P and Q.

25. The equation of the circle C is 3x2 + 3y2 − 6x + 18y − 80 = 0. Which of the following is/are true?

I. The centre of C lies on the line 2x + 3y + 7 = 0.

II. The point (−6, −8) lies outside C.

III. C cuts the line y = 8.

A. I only

B. III only

C. I and II only

D. I , II and III

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



26. In the figure, the equations of the straight line L1 and L2 are ay = 1 and bx + cy = 1 respectively. Which of the

following are true?

I. a > 0

II. b > 0

III. a > c

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

27. Three fair coins are tossed in a game. If three heads are obtained, $100 will be gained; otherwise, $20 will be

gained. Find the expected gain of the game.

A. $30

B. $40

C. $60

D. $240

28. Consider the following integers:

2 3 4 4 4 4 4 5 5 6 7 7 7 8 x

Let a, b and c be the mean, the median and the mode of the above integers respectively.

If 2 x 5, which of the following must be true?

I. a > b

II. a > c

III. b > c

A. I only

B. II only

C. I and III only

D. II and III only

x

y

L1

L2

O

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



29. The box-and-whisker diagram below shows the distribution of the marks of a class of 40 students in a test. It

is known that the passing mark is 30 and that no students obtained this mark. If a student is randomly

selected from the class, then the probability that the student passes the test is

A. 40

9.

B. 4

1.

C. 2

1.

D. 4

3.

30. The pie chart below shows Mr. Chan’s expenses in a certain month. Which of the following is/are true?

I. Rents make up 30% of the total expenses.

II. Entertainment expenses do not exceed travel expenses.

III. = 30°

A. I only

B. I and II only

C. I and III only

D. I, II and III

Food

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



Section B

31. The L.C.M. of 4x2 − 4xy + y2, 4x2 − y2 and 8x3 − y3 is

A. 2x – y.

B. (2x + y) (2x − y)2 (4x2 + 2xy + y2).

C. (2x − y) (2x + y)2 (4x2 + 2xy + y2).

D. (2x + y) (2x − y)2 (4x2 − 2xy + y2).

32. BA00000C002116 =

A. 11 × 1612 + 10 × 1611 + 12 × 165 + 257.

B. 11 × 1612 + 10 × 1611 + 13 × 165 + 257.

C. 11 × 1611 + 10 × 1610 + 12 × 164 + 33.

D. 11 × 1611 + 10 × 1610 + 13 × 164 + 33.

33. The graph in the figure shows the linear relation between x and y. Which of the following

must be true?

A. 36244 2 ++= yyx

B. 962 +−= yyx

C. 934

1 2 +−= yyx

D. 43

4

9

1 2 +−= yyx

O−3

6

y

x

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



34. If log y – x = x2 – log y2 – 17 = –3, then y =

A. 10.

B. 1 or –5.

C. 000 100or 10

1.

D. 10or 000 100

1.

35. If α ≠ β and

−=

−=

2

2

2 7 3

2 7 3

, then (α − β)2 =

A. 4

23.

B. 4

37.

C. 4

58.

D. 4

65.

36. Let z = a(i3 − i5) + (a + 1)(i + i2), where a is a real number. If z is a real number, then a =

A. −1.

B. 3

1− .

C. 1.

D. 3.

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



37. Consider the following system of inequalities:

−+

+−

03035

0932

0

yx

yx

y

Let D be the solution region representing the above system. If (x, y) is a point in D, then the least value of

x − 3y + 1 is

A. –9.

B. –11.

C. –3.5.

D. 7.

38. It is given that {Tn} is an infinite sequence, where13

2+

=n

n

nT . Which of the following is/are true?

I. {Tn} is a geometric sequence.

II. The greatest term in the sequence is

3

2.

III. The sequence cannot be summed to infinity.

A. I only

B. III only

C. I and II only

D. I and III only

39. Let k be a positive constant and − 90 < < 90. If the figure shows the graph of y = 2 cos (kx + ), then

A. k =1

2 and = 30.

B. k =1

2 and = 60.

C. k = 2 and = 30.

D. k = 2 and = 60.120

O x

y

480

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



40. If the height of a regular tetrahedron is 6 cm, then the volume of the tetrahedron is

A. 327 cm3.

B. 69 cm3.

C. 39 cm3.

D. 18 cm3.

41. In the figure, O is the centre of the circle ABC and DE is the tangent to the circle at A. If AB is the angle

bisector of CAE, then ABO =

A. 24°.

B. 26°.

C. 32°.

D. 38°.

42. Find the value(s) of k for which the circle x2 + y2 − 6x + 4y + 3 = 0 touches the line 3x − y − k = 0.

A. 1

B. −21

C. −21 or −1

D. 1 or 21

E

D

A

C

O

B

128

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.



43. Let O be the origin. If the coordinates of the points A and B are respectively (0, 12) and (15, 12), then the

x-coordinate of the centroid of OAB is

A. 5.

B. 7.5.

C. 9.

D. 15.

44. A code is made up of 8 different characters, the first three being English letters from A to F inclusive, and the

last five being digits from 0 to 9 inclusive. How many different codes can be formed?

A. 5 040

B. 30 360

C. 3 628 800

D. 7 257 600

45. It is given that X = { p, q, r, s, t1, t2, … , tn}, where t1 = t2 = … = tn = t. If the mean of X is t, which of the

following is/are true?

I. After adding

4

srqp +++to X, the new mean is t.

II. After removing p + q + r + s – 3t from X, the new mean is t.

III. After removing n t’s from X, the new mean is t.

A. I only

B. I and II only

C. II and III only

D. I, II and III

END OF PAPER

The

exer

cise

is li

cens

ed to

sch

ool f

or fr

ee u

ntil

the

exam

inat

ion

date

of m

athe

mat

ice

HK

DS

E 2

020.


mathematics compulsory part practice paper set 5

Documents