MATH CP The Association of Directors and

PAPER 2 Former Directors of Pok Oi Hospital Limited

Leung Sing Tak College
S.6 1st Mock Examination 2020-2021

Date: 30 – 10 – 2020
Time: 11: 15 – 12:30 (1¼ hour)
Full marks: 45

MATHEMATICS Compulsory Part

PAPER 2

INSTRUCTIONS

1. After the announcement of the start of the examination, you should first insert the information
required in the spaces provided on Answer Sheet.

2. When told to open this book, you should check that all 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.

2020-2021-LSTC-MATH-MOCK1-CP 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. ( x − y)( x 2 − xy + y 2 ) =

A. (x – y)3 .

B. x3 – y3 .

C. x3 – 2x2y + 2xy2 – y3.

D. x3 + 2x2y – 2xy2 – y3.

(−3a3n ) 2
2. =
3a 6

A. −a n .
B. 3a n .
C. −3a n .
D. 3a 6( n −1) .

3. If 3x − 2 y = −11 = 2 x − y − 2 , then y =

A. −7 .
B. −5 .
C. 5 .
D. 7 .

2020-2021-LSTC-MATH-MOCK1-CP 2-2 2
4. If  and  are constants such that ( x − 10)( x −  ) − 12 = ( x − 8)2 +  , then  =

A. 16 .
B. 6 .
C. −6 .
D. −16 .

r + 4s 2s
5. If = 3 + , then r =
3r r

s
A. − .
2
s
B. − .
4
2s
C. − .
3
3s
D. − .
2

6. If 0.002468  x  0.002486 , which of the following must be true?

A. x = 0.0025 (correct to 2 significant figures)

B. x = 0.0025 (correct to 3 decimal places)
C. x = 0.00246 (correct to 4 significant figures)
D. x = 0.00247 (correct to 5 decimal places)

2x + 3
7. The least odd integer satisfying the compound inequality −3( x − 2) + 7  16 and 2
−3
is
A. −5 .
B. −4 .
C. −3 .
D. −1.

2020-2021-LSTC-MATH-MOCK1-CP 2-3 3
8. Let f ( x) = kx3 + kx2 + k 3 x + k . f (k 2 ) − f (−k 2 ) =

A. 0 .
B. 2k .
C. 2k 7 + 2k 5 .
D. 2k 7 + 4k 5 + 2k .

9. Let f ( x) = 6 x4 − 2kx3 + 9 x − 12 . f (x) is divisible by 3x − k . Find k.

A. −2
B. 2
C. 4
D. 8

10. Which of the following statements about the graph of y = (6 − x)( x + 3) + 10 is/are not true?

I. The graph opens upwards.

II. The graph passes through the point (5, 18) .
III. The y-intercept of the graph is 10 .

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

11. A sum of $60 000 is deposited at an interest rate of 30% per annum for 5 years, compounded
quarterly. Find the interest correct to the nearest dollar.

A. $181 340
B. $194 871
C. $241 340
D. $254 871

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12. The cost of tea of brand A and brand B are $22/kg and $36/kg respectively. If x kg tea A and
y kg tea B are mixed so that the cost of the mixture is $30/kg, then x : y =

A. 3:4.
B. 4:3.
C. 9 :16 .
D. 16 : 9 .

13. If z varies directly as 3

x and inversely as y 2 , which of the following must be constant?

xz 3
A.
y2
xz 3
B.
y6
x
C. 3
z y4

23 x
D.
zy 2

14. In the figure, the 1st pattern consists of 1 dot. For any positive integer n, the (n + 1)th pattern is
formed by adding (2n + 1) dots to the nth pattern. Find the number of dots in the 9th pattern.

A. 36
B. 64
C. 81
D. 100

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15. If a solid right circular cone of height 36 cm is melted and recast into 3 identical spheres with
radii same as the base radius of the cone, then the total surface area of 3 spheres is

A. 36 cm 2 .
B. 72 cm 2 .
C. 108 cm 2 .
D. 216 cm 2 .

16. In the figure, ABC is a triangle and ADEF is a square such that D lies on AC and E lies on BC.
G is the point of intersection between AB and EF. It is given that FG : GE = AD : DC = 2 : 1
and the area of the square ADEF is 4 cm2, find the area of ABC .

3 F G
A. cm 2 E
11
27
B. cm 2
7
C. 4 cm 2
9
D. cm 2 A D C
2

sin(− ) 1 + cos(180 +  )
17. + =
1 + cos(180 −  ) sin(360 −  )

2
A. .
sin 
2
B. .
cos 
2
C. − .
sin 
2
D. − .
cos 

2020-2021-LSTC-MATH-MOCK1-CP 2-6 6
18. In the figure, ABCD is a rectangle. If E is a point lying on BC such that DE = 3 cm ,
AD = 4 cm and CED = 65 , find EAB correct to the nearest degree.

A D
A. 35
B. 45
C. 55
D. 65 B E C

19. The rectangular coordinates of Q are (−1, 3) . If Q is rotated clockwise about the origin

through 180 , then the polar coordinates of the image of Q are

A. (2,150) .
B. (2,300) .
C. (4,150) .
D. (4,300) .

20. In the figure, the equations of the straight lines L1 and L2 are x − ay − b = 0 and
x − cy − d = 0 respectively. Which of the following are true?
I. ac
II. b  d y L1
III. a = b

A. I and II only
x
B. I and III only
L2
C. II and III only
D. I, II and III −1

2020-2021-LSTC-MATH-MOCK1-CP 2-7 7
21. If the sum of the interior angles of a regular n-sided polygon is three times of the sum of
exterior angles, which of the following must be true?

I. The value of n is 6.
II. Each interior angle is 135 .
III. The number of axes of reflectional symmetry is 10.

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

22. In the figure, AC is the diameter of circle ABCD, If ECD = 27 , then CBD =

AA
DD
A. 27 .
EE
B. 54 .
C. 60 . BB
D. 63 .
27∘

CC

23. Suppose A(−8, 6) is a fixed point. Find the equation of the locus of a moving point P such
that P is always 10 units from A.

A. 10 x − y + 86 = 0
B. x2 + y 2 − 16 x + 12 y = 0
C. x2 + y 2 + 16 x − 12 y = 0
D. x2 + y 2 + 16 x − 12 y − 200 = 0

2020-2021-LSTC-MATH-MOCK1-CP 2-8 8
24. If P is a moving point in the rectangular coordinate plane such that the distances between P
and the two points (3, 6) and (2020, 2021) are always equal, then the locus of P is

A. a straight line.
B. a circle.
C. a pair of straight lines.
D. a parabola.

25. In the figure, ACD and BCE are straight lines and ACE = 90 . If AC = m and DE = n
then tan CBD =

E D
m
A. . θ
n sin  tan 
n sin  tan 
B. .
m C
m
C. .
n cos  B
n cos  θ
D. .
m A

26. Two fair dice are thrown. Find the probability that numbers shown on the two dice are not the
same.

1
A.
2
1
B.
6
4
C.
5
5
D.
6

2020-2021-LSTC-MATH-MOCK1-CP 2-9 9
27. Denote the circle 2 x 2 + 2 y 2 − 10 x + 16 y = 0 by C. Which of the following is/are true?

I. The area of C is 89 .

II. The point (0, 0) lies on C.
III. The centre of C lies in the second quadrant.

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

28. In the figure, ABCD is a rhombus. E is a point on AD such that EC bisects ACD . If
BE = BC , find CED .
D E A

A. 36
B. 54
C. 60
D. 72

C B

29. Which of the following cannot be obtained from any box-and-whisker diagram?

I. Variance
II. Mean
III. Range

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

2020-2021-LSTC-MATH-MOCK1-CP 2-10 10
30. The table below shows the distribution of number of mobile phones each student in LSTC
owns this year.

Number of mobile phones each 0 1 2 3

student in LSTC owns
Number of students 120 460 240 80

Which of the following is true?

A. The mode of the distribution is 460.

B. The median of the distribution is 1.5.
C. The lower quartile of the distribution is 1.
D. The range of the distribution is 2.

2020-2021-LSTC-MATH-MOCK1-CP 2-11 11
Section B

31. It is given that log8 y is a linear function of log 2 x . The intercepts on the vertical axis and
on the horizontal axis of the graph of the linear function are 7 and 9 respectively. Which of the
following must be true?

A. x7 y3 = 263
B. x3 y 7 = 263
C. x7 y9 = 263
D. x9 y 7 = 263

1 6 1
32. If + = 1 , then log =
log x − 3 log x + 1 x

1 1
A. or .
2 7
B. 2 or 7 .
C. −2 or −7 .
1 1
D. − or − .
2 7

3 − i9
33. If k is a real number, then the real part of − 2i10 is
k −i

2k 2 + 3k + 3
A. .
k 2 −1
3− k
B. .
k 2 −1
3− k
C. .
k 2 +1
2k 2 + 3k + 3
D. .
k 2 +1

34. 101100000101012 =

A. 11 210 + 21 .
B. 11 210 + 42 .
C. 11 211 + 21 .
D. 11 211 + 42 .

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35. Consider the following system of inequalities :

 x + 4 y  19

7 x − 2 y  −2
 x − 2 y  −2


Let R be the region which represents the solution of the above system of inequalities. If (x, y)
is a point lying in R, then the least value of 3x + 4 y + 5 is

A. 9 .
B. 18 .
C. 30 .
D. 34 .

36. The sum of the 2nd term and the 5th term of a geometric sequence is 14 while the sum of the
7th term and the 10th term of sequence is −448 . Find the 16th term.

A. −131072
B. −32768
C. 16384
D. 65536

37. Let k be a constant and k  0 . The straight line 4 x + ky + 8 = 0 and the circle
x2 + y 2 + x − 4 y − 2 = 0 intersect at points A and B . If the y-coordinate of the mid-point of
AB is −2 , find k.

A. 3
B. 4
C. 5
D. 6

2020-2021-LSTC-MATH-MOCK1-CP 2-13 13
38. In the figure, O is the centre of the semi-circle. It is given that OCD and OAB are two
equilateral triangles. AE and OB intersects at the point F . DE and OC intersect at point G . If
OA = 10 cm and OE⊥AD, find the area of shaded region correct to the nearest cm2 .
E
2 C B
A. 8 cm
B. 16 cm2
G F
C. 26 cm2
D. 52 cm2
D O A

39. In the figure, ABCDEFGH is a cuboid with square bases ABCD and EFGH. M is the mid-point
of AB. If AB = 10 cm and DE = 16 cm, find the angle between the plane HBM and the plane
ABCD correct to the nearest degree.

AA BB
A. 55∘
B. 58∘ DD
C. 60∘ CC
D. 61∘ 16 cm
HH GG
EE FF
MM

40. In ABC , ABC = 35 . Which of the following must be true?

I. The orthocentre of ABC lies outside ABC .
II. The centroid of ABC lies on AC.
III. The in-centre of ABC lies inside ABC .

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

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41. In the figure, BD and CE are two tangents to the circle at A and C respectively. If
BCE = 28 and ABC = 48 , find CAD . D

A. 100∘ A
B. 102∘
C. 104∘
D. 106∘ B

F C E

42. There are 24 boys and 16 girls in a class. If 5 students are selected to form a committee and
there must be at least 1 boy in the committee, how many different committees can be formed?

A. 43 680
B. 218 400
C. 611 136
D. 653 640

43. There are three questions in a mathematics competition. The probabilities that Susan answers
the first question correctly, the second question correctly and the third question correctly are
1 1 1
, and respectively. The probability that Susan answer at least one question
2 4 8
correctly in the competition is

1
A. .
8
7
B. .
8
1
C. .
64
43
D. .
64

2020-2021-LSTC-MATH-MOCK1-CP 2-15 15
44. In an examination, the standard deviation of the examination scores is 6 marks. The
examination score of David is 92 marks and his standard score is 2. If the standard score of
James in examination is −2.5 , then his examination score is

A. 80 marks.
B. 72 marks.
C. 65 marks.
D. 62 marks.

45. The mean, the range and the variance of a set of numbers are m, r and v respectively. Each
number of the set is multiplied by 2020 and then 2021 is added to each resulting number to
form a new set of numbers. Which of the following is/are true?

I. The mean of the new set of number is 2020m .

II. The range of the new set of number is 2020r .
III. The variance of the new set of number is 2020v + 2021 .

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

END OF PAPER

2020-2021-LSTC-MATH-MOCK1-CP 2-16 16