Analysis on the HKCEE/HKDSE questions2006 2007 2008 2009 2010

1. Percentages 10, 11 10, 11 12 10, 11 13, 14

2. Numbers and Estimation 12 16, 17 15 11, 17

3. Polynomials 3, 4, 6, 40 2, 3, 40 3, 4, 5 3, 4, 5, 41 3, 4, 5, 41

4. Formulas 2 2 2 1

5. Equations 8, 9 4, 7, 42 8, 41 8 7, 8

6. Functions and Graphs 5, 7 5, 8, 38 6, 9, 10, 37 6, 37 6, 9, 37

7. Rate, Ratio and Variations 13, 14, 15 13, 14 13, 14, 15 13, 14 15, 16

8. Exponential and Logarithmic Functions

1, 37, 38, 39 1, 37, 39, 41 1, 38, 39, 40 1, 38, 39, 40 2, 38, 39, 40

9. Geometry (1) – Straight Lines and Rectilinear Figures

26, 48, 49 19, 27, 28, 50 21, 27, 28, 52 26, 27, 28, 51 25, 26, 27

10. Geometry (2) – Circles 19, 46, 47 48, 49 50, 51 48, 49, 50 49, 50

11. Transformation and Symmetry 25 25, 26 25, 26 29 23, 24

12. Coordinate Geometry (1) 27, 31 29, 30 29, 30, 32 30, 33, 52 30

13. Coordinate Geometry (2) 28, 29, 30, 50, 51 31, 32, 51, 52 31, 53 31, 32, 53 29, 31, 32, 51, 52

14. Sequence 12, 42, 43 9, 44, 45 11, 43, 44 12, 42, 43 12, 43, 44

15. Mensuration 17, 18, 20 16, 17, 18 7, 18, 19, 20 7, 17, 18, 19, 20 18, 19, 20

16. Trigonometry 21, 22, 44 20, 21, 22, 46 23, 24, 45, 46, 47 21, 24, 25, 45, 46 22, 45, 46

17. Applications of Trigonometry 16, 23, 24, 45 15, 23, 24, 47 22, 48, 49 16, 22, 23, 47 21, 28, 47, 48

18. Inequalities and Linear Programming

41 6, 43 42 9, 44 10, 42

19. Permutation and Combination

20. Probability 32, 33, 52, 53 33, 53, 54 33 34 33, 53

21. Statistics 34, 35, 36, 54 34, 35, 36 34, 35, 36, 54 35, 36, 54 34, 35, 36, 54

Note: 1. The numbers listed above refer to the question numbers in the HKCEE/HKDSE mathematics Paper II that year. 2. ‘Permutation and Combination’ is a new topic in the HKDSE syllabus.

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Paper II of the HKDSE mathematics examination consists of two sections: Sections A and B. There are 30 questions in Section A and 15 questions in Section B. As the time allowed is 75 minutes, students are required to answer one question in about 1.5 minutes on average. In order to spend time in the most effective way, it is essential for candidates to learn some useful strategies in answering multiple-choice questions.

Strategy 1 Direct computationIn questions such as finding interest, area of plane figures or solving equations with quadratic formulas, candidates can apply the related formulas and calculate the answers directly. However, as not all the formulas are provided in the examination paper, candidates should be familiar with some useful formulas.

Example 1A sum of $30 000 is deposited for 1 year at 6% p.a., compounded monthly. Find the interest correct to the nearest dollar.A. $1750B. $1800C. $1850D. $1900

Solution:

Interest = $30 000 × 112

+6%12

– $30 000

= $1850 (cor. to the nearest dollar)The answer is C.

Compound interest I = P(1 + r%)n – P

Example 2In the figure, the solid consists of a hemisphere and a cylinder. If the base radius and the height of the cylinder are 6 cm and 5 cm respectively, find the volume of the solid.A. 204πB. 324πC. 396πD. 468π

12 cm

Reference: HKDSE 15 Q10

Reference: HKDSE 13 Q17

Multiple-choice question tackling strategy

6 cm

sample

l x + 2x + 1x – x

x + 3x – 1

3x + 13x – 3

4

2

2

sample

sample

sample

HKDSE Exam Series – Mathematics Multiple-choice Questions (Compulsory Part) (4th Edition)

32

E. Greatest Common Divisor and Least Common Multiple

44. Find the G.C.D. of x2y5z3 and x2yz2. A. xyz B. x2yz3

C. x2y5z3

D. x2yz2

45. The G.C.D. of 20ab2, 40a2bc and 80a3c2 is A. 20ac. B. 20a. C. 40ab. D. 80a3b2c.

46. Find the G.C.D. of x2(x – 4)(x + 3)2 and x3(x – 4)4. A. x2(x – 4) B. x3(x – 4)4

C. x(x – 4)(x + 3) D. x3(x – 4)4(x + 3)2

47. The G.C.D. of x2 – 4y2 and (x – 2y)(x + 2y)2 is A. x – 2y. B. x + 2y. C. (x – 2y)(x + 2y). D. (x – 2y)2.

48. The G.C.D. of x5 – x4, x3 – 2x2 + x and x4 – x is A. x(x – 1). B. x(x – 1)(x – 2). C. x3(x – 1)2. D. x3(x – 1)2(x + 1).

49. Find the L.C.M. of xy5z and x2y3z4. A. xyz B. xy3z C. x2y3z4

D. x2y5z4

NF

Reference:HKDSE 14Q31

50. The L.C.M. of 15a2b, 30b3c and 90a3c2 is A. 30a2b3c2. B. 60a2b3c. C. 90a3b3c2. D. 120a2b2c.

51. Find the L.C.M. of 2x4 + 4x3 + 2x2 and 5x4 + 10x2. A. 10x2(x2 + 2)(x + 1)2

B. 10x2(x2 + 2)(x + 1) C. x(x2 + 2)(x + 1) D. x2

52. Find the L.C.M. of 2x – 1, 4x2 – 1 and 8x3 – 1. A. (2x – 1)(2x + 1)(4x2 – 2x + 1) B. (2x – 1)(2x + 1)(4x2 + 2x + 1) C. (2x – 1)(2x + 1)(4x2 – 4x + 1) D. (2x – 1)(2x + 1)(4x2 + 4x + 1)

53. The G.C.D. and L.C.M. of two polynomials f(x) and g(x) are 2xyz3 and 8x2y3z4 respectively. If f(x) = 8x2yz3, find g(x).

A. 2x2y3z3

B. 4x2y3z4

C. 6xy3z4

D. 2xy3z4

F. Rational Functions

54. x1

1-

+ x x

22 -

=

A. x x

x22 -

+

B. x

x

x

2 22 -

+

C. x x

x22 -

-

D. x x

x2 12 -

+

Reference:HKDSE 16Q31

Reference:HKDSE 13Q31

Reference:HKDSE 12Q31

NF

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HKDSE Exam Series – Mathematics Multiple-choice Questions (Compulsory Part) (4th Edition)

34

Revision TestLevel 1

1. Find the coefficient of x2 for (6x4 – 5x3 + x2 + 1) – (2x4 + 3x3 – 5x2 – 2).A. –4B. 0C. 4D. 6

2. Expand (2x + 3)(4x2 – x – 7).A. 8x3 + 10x2 – 17x – 21B. 8x3 + 10x2 + 11x + 21C. 8x3 + 14x2 + 11x – 21D. 8x3 + 14x2 – 17x – 21

3. Find the quotient when 3x3 – 8x2 + 2x + 4 is divided by x – 2.

A. 3x2 – 7x – 12 B. 3x2 – 7x – 2 C. 3x2 – 2x – 2 D. 3x2 – 2x + 6

4. If a(2x2 – 1) + b(2x2 + 1) � 2x2 + 3, then b = A. –2. B. –1. C. 1. D. 2.

5. If 2x3 + 12x2 + ax + 4 � 2x(x + b)2 + 4(x2 + c), find the values of a, b and c.

A. a = 8, b = 4, c = 4 B. a = 18, b = 3, c = 1 C. a = 8, b = 2, c = 1 D. a = 8, b = 8, c = 4

Reference:HKCEE 09Q4

Reference:HKDSE 14Q3

6. Factorize x4 – 16. A. (x2 – 4)2

B. (x + 2)(x – 2)(x2 – 2x + 4) C. (x + 2)(x – 2)(x2 + 4) D. Cannot be factorized.

7. Factorize x2 + y2 – 2xy – 1. A. (x + y – 1)(x – y – 1) B. (x + y + 1)(x – y + 1) C. (x – y – 1)(x + y – 1) D. (x – y – 1)(x – y + 1)

8. Factorize 4x2 – y2 + 4y – 4. A. (x – y – 2)(x + y – 2) B. (2x – y + 2)(2x + y – 2) C. (2x – y – 1)(2x + y – 1) D. (x – 2y + 1)(x + 2y – 1)

9. Factorize 3(x – y)2 – 2(x – y) – 1. A. (x – y + 1)(3x – 3y – 1) B. (x – y – 1)(3x – 3y + 1) C. (x – y – 1)(3x – 3y – 1) D. (x – y + 1)(3x – 3y + 1)

10. Find the remainder when ax3 – bx2 + cx + d is divided by x.

A. a B. b C. c D. d

11. When 3x3 – 7x2 – kx + 3 is divided by x – 2, the remainder is –5. Find the value of k.

A. –22 B. –2 C. 2 D. 22

Reference:HKDSE 14Q2

Reference:HKDSE 12Q4

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© 樂思教育出版有限公司 保留版權Pan Lloyds Publishers LtdAll Rights Reserved 2017

Not to be taken away before theend of the examination session

Pan Lloyds Publishers Ltd

MATHEMATICS Compulsory PartMOCK TEST 1

PAPER 2

(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.

MC

sample

HKDSE Exam Series – Mathematics Multiple-choice Questions (Compulsory Part) (4th Edition)

100

5. If p + 23 – p

= 2q + 3q + 4

, then q =

A. 7p – 13p – 4

.

B. 17 – p4 – 3p

.

C. 1 + 7p3p – 4

.

D. 1 – 7p3p – 4

.

6. –p2 + q2 – p – q =A. (p + q)(–p + q – 1)B. (p + q)(–p – q – 1)C. (p – q)(–p + q – 1)D. (p – q)(–p – q – 1)

7. If (x + a)(x + 2) – a(x + b) ≡ x2 + ax + 12, then b =A. –4.B. –2.C. 2.D. 4.

8. 0.00849795 =A. 0.008 (correct to 3 significant figures)B. 0.0085 (correct to 4 decimal places)C. 0.0085 (correct to 4 significant figures)

D. 0.0084980 (correct to 5 decimal places)

9. Solve the equation (3x – 5)(2x + 4) = (x + 2)2.

A. x = 72

B. x = –2 or 125

C. x = –2 or 72

D. x = –2 or 85

Section A

1. (–3)2016 × 1

32017 =

A. 3B. –3

C. 13

D. – 13

2. 42n × 9n =A. 122n

B. 12n

C. 36n

D. 362n

3. If (x – 2a)2 = 9a2 + 6a + 1, then x =A. 5a + 1.B. 5a + 1 or 5a – 1.C. 5a + 1 or –5a – 1.D. 5a + 1 or –a – 1.

4. If m(2a – 5) = a3

– m, then a =

A. 6m – 114m

.

B. 14m

6m – 1.

C. 6m – 112m

.

D. 12m

6m – 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.

sample

Mock Test 1

103

26. Suppose z varies directly as x2 and inversely as y, which of the following is a constant?A. x2yz

B. x2

yz

C. x2yz

D. 1

x2yz

27. Suppose z varies directly as x3 and inversely as y .

When x = 12

and y = 16, z = 38

. Find the value of

x when y = 36 and z = 16.

A. 14

B. 12

C. 2D. 4

28. Suppose z varies directly as x2 and inversely as y. If x is increased by 50% and y is increased by 20%, find the percentage change of z.A. Increased by 125%B. Increased by 87.5%C. Increased by 80%

D. Increased by 30%

29. John is finding the weight of one paper clip by first weighing 200 paper clips. He finds that the weight of 200 paper clips is 285 g, correct to the nearest g. What is the upper limit of the weight of 1 paper clip?A. 1.425 gB. 1.4255 gC. 1.4275 gD. 1.43 g

30. A

B C

E

H D3.0 cm

2.4 cm

2.6 cm

Referring to the figure, all the measurements are correct to the nearest 0.1 cm. If the actual area of the pentagon ABCDE is x cm2, thenA. 10.69375 ≤ x < 11.51375.B. 11.05 ≤ x < 11.15.C. 10.69375 ≤ x ≤ 11.51375.D. 11.05 ≤ x ≤ 11.15.

Section B

31. The L.C.M. of 9a2 – 4, 9a2 – 12a + 4 and 6a2 – 5a – 6 isA. 1.B. (3a + 2)(3a – 2).C. (3a + 2)(3a – 2)(2a – 3).D. (3a + 2)(3a – 2)2(2a – 3).

32. Let f be a polynomial in p, q and r. If the H.C.F. of 16p3q2r4, 12p4q3r3 and f is 4p2q2r2, which of the following is a possible expression of f?A. 8p2q2r2

B. 8p3q3r3

C. 8p4q3r2

D. 8p4q3r4

33. x

x3 + 27 –

1x2 – 9

=

A . –9x – 9

(x + 3)3(x – 3)

B . –6x – 9

(x + 3)(x – 3)(x2 + 3x + 9)

C . –6x – 9

(x + 3)(x – 3)(x2 – 3x + 9)

D . –9

(x + 3)(x – 3)(x2 – 3x + 9)

sample

(40 50) kg50 kg−

0 935. lw lwlw

−

$ 12 000 10 000$10 000

( )−

sample

x x+ +13 4

x x+ − +32

25

2 35

− x

x + 25

x + 43

42

15x x−

+−

sample

( )14 24

14 53

− − −k

14 53

k −

14 53

k −

sample