Elegantia College (Sponsored by Education Convergence and
Patronized by H.K.Yee’s Five Tong Assn.)
2019-2020 Mock Examination
Form 6 Mathematics Paper 2
Time Limit：11:15 – 12:30
Name：_____________________
Class：______ Class No.：_____
(1¼ hours)
Marks：__________________
Date：
2020 – 02 – 25
__________________________________________________________________________________
2020-DSE
MATH CP
PAPER 2
MATHEMATICS Compulsory Part
PAPER 2
INSTRUCTIONS
1.
Read carefully the instructions on the Answer Sheet. Insert your Candidate information required in
the spaces provided.
2.
When told to open this Question 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.
Subject: Mathematics Paper II
Setter : KSW, FCY
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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.
2.
x2 – 4y2 – 4y + 2x =
A.
(x + 2y)(x – 2y + 2) .
B.
(x + 2y)(x – 2y – 2) .
C.
(x – 2y)(x + 2y + 2) .
D.
(x – 2y)(x + 2y – 2) .
(3)
2019
A.
B.
3.
4.
1
 
3
2020

1
.
3
1
 .
3
C.
3.
D.
 3.
1
1


a b a b
2a
A.
2
a  b2
2a
B.
2
b  a2
2b
C.
2
a  b2
2b
D.
2
b  a2
.
.
.
.
If A and B are constants such that 3x2 + 36x + B  A(x + 6)2  96 , then B =
A.
– 81 .
B.
– 63 .
C.
3.
D.
12 .
Subject: Mathematics Paper II
Setter : KSW, FCY
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5.
6.
7.
8.
9.
If 0.764 7 < y < 0.765 3 , which of the following must be true?
A.
y = 0.7 (correct to 1 significant figure)
B.
y = 0.76 (correct to 2 significant figures)
C.
y = 0.765 (correct to 3 significant figures)
D.
y = 0.765 0 (correct to 4 significant figures)
The solution of 8 – 3x  17  2x – 1 is
A.
x  9.
B.
x   9.
C.
 3  x  9.
D.
x  3
or
x  9.
If x and y are non-zero constants such that (x + y) : (4x – 3y) = 2 : 5 , then x : y =
A.
3 : 11 .
B.
11 : 3 .
C.
17 : 18 .
D.
18 : 17 .
If the figure shows the graph of quadratic function y = f(x) , then f(x) =
y
2
A.
x + 9x + 12 .
B.
3x – 9x + 12 .
C.
– x2 + 9x + 12 .
D.
– 3x2 – 9x + 12 .
y = f(x)
2
O
If f(x) = x2 – 3x + 2 , then f(x + 1) – f(x) =
A.
2x – 2 .
B.
–2 .
C.
– 4x + 5 .
D.
– 6x + 2 .
Subject: Mathematics Paper II
Setter : KSW, FCY
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x
10. Given that f(x) = 4x3 + kx2 – 25x + 6 is divisible by x + 3 .
divided by 4x – 1 .
A.
99
8
B.

C.

D.
 12
Find the remainder when f(x) is
11. John deposits $200 000 at 5% p.a. compounded monthly. Find the interest he will get after one
year, correct to the nearest dollar.
A.
$10 000
B.
$10 125
C.
$10 232
D.
$10 300
12. Given that z varies directly as x and inversely as
y . If x is decreased by 13% and y
is increased by 44% , then z is
A.
decreased by 27.5% .
B.
decreased by 72.5% .
C.
increased by 27.5% .
D.
increased by 72.5% .
13. In the figure, all the measurements are correct to the nearest cm .
the polygon ABCDE . Find the range of values of x .
A
A. 391.375 < x < 434.375
B.
391.375 < x < 442.875
C.
399.875 < x < 434.375
D.
399.875 < x < 442.875
Subject: Mathematics Paper II
Setter : KSW, FCY
Let x cm2 be the actual area of
E
11 cm
6 cm
D
18 cm
B
-4-
25 cm
C
14. Let an be the nth term of a sequence.
positive integer n > 1 , then a2 =
A.
0.
B.
8.
C.
16 .
D.
24 .
If a5 = 16 ,
a7 = 40 and an = an – 1 + an – 2 for any
15. The radii of the upper face and the base of a frustum of a right circular cone are 2 cm and 4 cm
respectively. The height of the frustum is 3 cm. Find its volume.
A.
16 cm3
B.
24 cm3
C.
28 cm3
D.
32 cm3
16. In the figure,
ABCD
is a parallelogram.
M
and
N
are two points on
respectively such that AM : MB = 3 : 1 and BN : NC = 4 : 1 .
find the area of MNCD .
AB and
BC
If the area of ADM is 60 cm2 ,
A
M
2
A.
48 cm
B.
52 cm2
C.
60 cm2
D.
84 cm2
N
D
17. Given that ABCD is a rhombus. E is a point on AD such that BE  AD .
ADC = 120 . Find the area of ABCD .
A.
18 3 cm2
B.
20 3 cm2
C.
26 3 cm2
D.
36 3 cm2
Subject: Mathematics Paper II
Setter : KSW, FCY
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C
AE = 3 cm and
B
18. In the figure, OAB and OCD are sectors with centre O .
OA = 1 cm , COD = 120 and the
perimeter of the sector OCD is ( + 3) cm . Which of the following must be true?
I. The length of AC is 0.5 cm .
C
II. The perimeter of the sector OAB is ( + 2) cm .
A
III. The area of the shaded region is  cm2 .
120
A. I only
O
B. II only
C.
I and III only
D.
II and III only
B
D
19. In the figure, 32 identical squares form a figure like a chess board. Half of the squares are
shaded. Which of the following is correct?
No. of axes of
reflectional symmetry
No. of folds of
rotational symmetry
A.
4
2
B.
4
4
C.
2
2
D.
2
4
20. In the figure, O is the centre of the circle and also the orthocenter of ABC .
find AOC .
A.
160
B.
130
C.
120
D.
100
B
If ABC = 80 ,
A
O
C
Subject: Mathematics Paper II
Setter : KSW, FCY
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21. In the figure, two circles intersect at A and D .
FD intersect at G such that AGD = 92 .
BCD =
A.
76 .
B.
82 .
C.
98 .
D.
104 .
C.
D.
AE and
If ABC = 104 and AED = 43 , then
A
F
B
G
C
D
E
22. In the figure, AB is perpendicular to AC .
BD = k , then BC =
k sin 
A.
.
cos 
B.
FAB and EDC are straight lines.
ABD =  and DBC =  .
If BD = DC and
A
k sin 
.
sin 
k sin   k
.
cos 
k cos   k
.
sin 
D
B
C
23. Which of the following about a regular 12-sided polygon is correct?
A.
The polygon has no rotational symmetry.
B.
The number of diagonals of the polygon is 12 .
C.
Each interior angle of the polygon is 120 .
D.
Each exterior angle of the polygon is 30 .
24. The polar coordinates of the point A and B are (4, 80) and (2, 110) respectively.
rotated 180 anti-clockwise about the origin to the point A’ . Find the area of ABA’ .
A.
4
B.
4 3
C.
2
D.
2 3
Subject: Mathematics Paper II
Setter : KSW, FCY
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A is
25. In the figure, the equation of the straight line is 3x – ay + b = 0 . Which of the following must be
true?
y
I. a < 3
II. b < 9
III. ab > 0
A.
I only
B.
III only
C.
I and II only
D.
II and III only
3x – ay + b = 0
3
26. A and B are two fixed points.
locus of P is
3
O
x
If P is a moving point such that PAB = PBA , then the
A.
a circle that passes through A and B .
B.
a line that is parallel to AB .
C.
a line that passes through A .
D.
the perpendicular bisector of AB .
27. C1 : x2 + y2 + 6x – 2y – 7 = 0 and C2 : x2 + y2 – 4x – 12y – 8 = 0 are two circles with centres A
and B respectively. Denote the origin by O . Which of the following must be true?
I. AOB is a right angle.
II. Radius of C1 < Radius of C2
III. OA = OB
A.
I only
B.
I and II only
C.
II and III only
D.
I, II and III
Subject: Mathematics Paper II
Setter : KSW, FCY
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28. There are 4 cards numbered 2 , 3 , 5 and 8 respectively. In a game, a player draws two
cards at the same time randomly. If the product of the numbers in the cards is a multiple of 3 , the
player will get $20 . If the product of the numbers in the cards is a multiple of 10 , the player will
get $30 . Find the expected gain of the game.
A.
$0
B.
$10
C.
$15
D.
$20
29. Consider the following positive integers :
1
1
5
6
8 8
p
q
Given that there is no mode. Let a and b be the mean and the interquartile range of the above
positive integers. Which of the following must be true?
I. p = q
II. a = 5
III. b = 4
A.
I only
B.
II only
C.
II and III only
D.
I, II and III
30. The table below shows the distribution of the numbers of books borrowed by a group of students in
an academic year.
number of books borrowed
0
1
2
3
4
number of students
6
10
32
40
12
Which of the following must be true?
I. The median of the distribution is 2 .
II. The range of the distribution is 6 .
III. The upper quartile of the distribution is 3 .
A.
I only
B.
III only
C.
I and II only
D.
I, II and III
Subject: Mathematics Paper II
Setter : KSW, FCY
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Section B
31. Let f ( x) be a quadratic function. The figure below may represent the graph of y  f ( x) and
y
A. the graph of y   f (2 x) .
(4, 16)
B.
the graph of y  f (2 x) .
C.
the graph of y   f ( x  4) .
D.
the graph of y  f ( x  8) .
x
0
4
(2, –16)
7
12
17
32. 4 + 4 + 4 =
33. If
34. If
A.
2010020016.
B.
4010040016.
C.
10100100016.
D.
40100400016.
k is a real number, then the real part of
A.
4k .
B.
4k .
C.
k2 – 16 .
D.
k2 + 16 .
k 3  64i
is
k  4i
1
6
1
1 
, then log 
2 log x  3
log x  2
x
A.
5
– 3 or  .
2
B.
3
– 1 or  .
2
C.
3 or
D.
1
2
or .
3
5
5
.
2
Subject: Mathematics Paper II
Setter : KSW, FCY
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8
35. Consider the following system of inequalities.
x  0
7x  8 y  40  0


8 x  3 y  70  0
2 x  5 y  60  0
Let D be the region which represents the solution of the above system of inequalities.
If (x, y)
is a point lying in D , then the greatest value of 2x – 3y is
A.
36.
B.
40.
C.
47.
D.
70.
36. If the 5th term and the 9th term in an arithmetic sequence are 10 and – 6 respectively, then the sum
of the first n terms of the sequence is
A.
24n – 2n2 .
B.
28n + 2n2 .
C.
28n – 2n2 .
D.
56n – 4n2 .
37. Let k be a constant.
intersect at the points
A.
– 22
B.
– 37
C.
– 47
D.
– 77
Subject: Mathematics Paper II
The straight line x + y + 2 = 0 and the circle 3x2 + 3y2 + kx – 5y – 12 = 0
A and B .
If the x-coordinate of the mid-point of AB
Setter : KSW, FCY
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is 5 , find k .
38. In the figure, ABCD is a square. It is given that E is a point lying on BC such that BE : CE  3 :1
and F is a point lying on AE such that AF : EF  3 :1 . If AB = 16 cm, find DF correct to 1 decimal
place.
A
D
A.
13.6 cm
B.
13.9 cm
C.
15.0 cm
D.
16.5 cm
F
B
39. In the figure, AB is a diameter of the circle ABC.
straight line.
CD is the tangent to the circle at C.
C
ABD is a
E is a point on AC such that DE bisects ADC. Find CED.
A.
45
B.
52.5
C.
60
D.
E
C
E
A
B
D
75
40. There is a right pyramid with a square base of side 10 cm.
If the slant edge of the pyramid is 8 cm,
find the angle between two adjacent lateral faces correct to the nearest degree.
A.
53
B.
106
C.
124
D.
130
Subject: Mathematics Paper II
Setter : KSW, FCY
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41. Let O be the origin.
The coordinates of the points A and B are (10, 5) and (– 3, – 20) respectively.
Which of the following must be true?
I.
The centroid of OAB lies inside OAB.
II.
The circumcentre of OAB lies on AB.
III. The orthocentre of OAB lies outside OAB.
A.
I only
B.
II only
C.
I and III only
D.
II and III only
42. Mary, John and 5 people are arranged to sit in a row. Find the number of arrangements in which
Mary will not sit at the end of the left side and John will not sit at the end of the right side.
A.
240
B.
1440
C.
2520
D.
3720
43. A bag contains 1 yellow ball, 2 blue balls, 3 green balls and 4 red balls. 4 balls are drawn one by
one at random from the bag without replacement.
Given that at least 1 red ball is drawn, find the
probability that the colour of the 4 balls drawn are all different.
A.
4
35
B.
8
65
C.
1
2
D.
13
14
Subject: Mathematics Paper II
Setter : KSW, FCY
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44. In a quiz, the standard deviation of the score is 8 marks. John gets 54 marks in the quiz and his
standard score is – 0.25. If Mary gets 60 marks in the quiz, then her standard score is
A.
0.5 .
B.
1.
C.
– 0.5 .
D.
–1.
45. The variance of a set of numbers is 18. Each number of the set is multiplied by – 2 and then 80 is
added to each resulting number to form a new set of numbers. Find the variance of the new set of
numbers.
A.
36
B.
72
C.
98
D.
152
END OF PAPER
Subject: Mathematics Paper II
Setter : KSW, FCY
- 14 -