HKUGA College
MOCK EXAMINATION (2023/2024)
TOTAL MARKS: 45
Mathematics (Compulsory Part)
Paper 2
Time allowed:
1 hour 15 minutes
Form:
Name:
Teacher:
Class ( No.):
AY /
EUL /
HC / JKL /
JY
6
(
)
/ WC
INSTRUCTIONS
1. This paper consists of 16 pages including this cover page. The words “END OF PAPER”
should appear on the last page.
2. Do not open this test paper until instructed to do so.
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 MC 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.
7. The use of an HKEAA-approved calculator is permitted.
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.
3.
3k + 2 92k  1 =
If
If
p
A.
33k  1 .
B.
35k .
C.
9k + 1 .
D.
93k + 1 .
and
q
A.
2.
B.
3.
C.
4.
D.
5.
are constants such that px  3  qx  px2  9x  2 , then p =
2
a(3a  b) = 5(a + b) , then b =
A.
3a 2  a
.
5a
B.
3a 2  5a
.
5 a
C.
3a 2  5a
.
5a
D.
3a 2  a
.
5a
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4.
5.
6.
m2  2mn  3n2  2m + 6n =
A.
(m  n  2)(m  3n) .
B.
(m  n  2)(m + 3n) .
C.
(m + n  2)(m  3n) .
D.
(m + n  2)(m + 3n) .
4
3

=
7a  2 7a  2
A.
7a  2
.
49 a 2  4
B.
7a  2
.
49 a 2  4
C.
7a  14
.
49 a 2  4
D.
7 a  14
.
49 a 2  4
If y = 410 (correct to 2 significant figures), find the range of values of y .
A.
405 < y  415
B.
405  y < 415
C.
409.5 < y  410.5
D.
409.5  y < 410.5
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7.
Let f ( x)  ( x  a)( x  5)  b , where a and b are non-zero constants. If f  x   f   x  for
any real values of x , then a 
8.
A.
5 .
B.
0.
C.
2.
D.
5.
Let g(x) = ax2 + 3x + b , where a and b are constants. When g(x) is divided by x + 2 , the
remainder is 5. Find the remainder when g(x) is divided by x  2 .
9.
A.
7
B.
4
C.
5
D.
17
The marked price of a video game is x% higher than its cost. If the video game is sold at a
discount of 20% , the percentage profit is 20% . Find x .
10.
A.
0
B.
36
C.
40
D.
50
Let a, b and c be non-zero numbers. If a : b = 5 : 2 and 3a = 7b + c, then b : c =
A.
1:2.
B.
1:4.
C.
2:1.
D.
4:1.
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11.
12.
The solution of 13 > x  7 or
x3
 5 is
2
A.
x>7.
B.
x < 20 .
C.
7 < x < 20 .
D.
all real numbers .
If the actual area of a piece of land is 78.75 km2 and the area of this land on a map is
1 260 cm2 , find the scale of the map.
A.
B.
C.
D.
13.
1:4
1 : 2 500
1 : 4 000
1 : 25 000
If x varies inversely as the square root of y and directly as z , which of the following are
true?
I.
II.
x 2 varies inversely as y and directly as the square of z .
y varies inversely as the square of x and directly as the square of z .
Ill.
z2 x2
is a constant .
y
A.
B.
C.
D.
I and II only
I and III only
II and III only
I , II and III
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14.
The figure shows the graph of y = (ax  h)2 , where a and h are constants. Which of the
following must be true?
y
I.
II.
a>0
h<0
Ill.
c = h2
A.
B.
C.
D.
15.
O
x
c
I only
III only
I and III only
I , II and III
y = (ax  h)2
The base of a solid right pyramid is an equilateral triangle. If the perimeter of the base is
30 cm and the length of each slant edge of the pyramid is 13 cm, find the total surface area
of the pyramid.
A.
B.
C.
D.
16.
60  50 3  cm
180  25 3 cm
195  25 3 cm
180  50 3 cm
2
2
2
2
The radii of a sphere and the base radius of a right circular cone are both equal to r. If the
surface area of the sphere equals the curved surface area of the cone, find the volume of the
cone in terms of r.
A.
15 3
r
3
B.
4 3
r
3
C.
17 3
r
3
D.
5r 3
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17.
In the figure, PTQ is semi-circle. PQRS is a rectangle while PQ = 80 cm and PS = 40 cm .
Find the area of the shaded region correct to the nearest cm2 .
A.
116 cm2
B.
218 cm2
C.
884 cm2
D.
1 587 cm2
T
S
R
P
18.
Q
In the figure, ABCD is a trapezium with AD // BC. Let M and N be points on AD such that
AM : MN : ND  3 : 2 : 1 . BN and CM intersect at point P. If the area of the quadrilateral
ABPM and area of the quadrilateral CDNP are 39 cm2 and 21 cm2 respectively, find the area
of trapezium ABCD.
B
A.
79.5 cm2
B.
86.7 cm2
C.
90 cm2
D.
103.5 cm2
A
19.
C
M
N
D
According to the figure, which of the following must be true?
I.
II.
Ill.
a
a + b + c = 720
a + b > 360
a + b  c = 90
A.
I and II only
B.
C.
D.
I and III only
II and III only
I, II and III
2324_S6_MA_MOCK_EXAM_P2
b
c
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20.
The figure shows the equilateral triangle ABC , the square ACDE and the regular 10-sided
polygon AEFGHIJKLM . Find BML .
A.
150
B.
156
C.
159
D.
165
B
C
M
A
D
L
E
K
F
J
G
I
H
21.
It is given that ABCD is a parallelogram. Denote the point of intersection of AC and BD by
E . Which of the following must be true?
22.
I.
ECD = EAD
II.
Ill.
AC 2  BD 2  4AD2
Area of ∆BCE = area of ∆ABE
A.
II only
B.
C.
D.
III only
I and II only
I, II and III
In the figure, P , Q , R and S are concyclic. O is the mid-point of PQ . PR and QS intersect
at T . If QR // OS, QRP = 90° and QPR = 24° , then QTR =
S
A.
48° .
B.
C.
D.
R
55° .
57° .
66° .
T
P
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O
Q
23.
What is the domain of the function f( x) 
A.
B.
C.
D.
24.
x3
?
4 x
The domain is all real numbers x , where x  3 .
The domain is all real numbers x , where x  4 .
The domain is all real numbers x , where  3  x  4 .
The domain is all real numbers x , where x  3 or x  4 .
The equations of the straight lines L1 and L2 are 2x – 5y + 20 = 0 and 4x – 10y – 85 = 0
respectively. L1 cuts the y-axis at the point H while L2 cuts the x-axis at the point K . Let P
be a moving point in the rectangular coordinate plane such that the perpendicular distances
from P to L1 and L2 are equal. Denote the locus of P by  . Which of the following are true?
I.
II.
Ill.
25.
The inclination of  is less than 25 .
9
The y-intercept of  is
.
4
 85 
The coordinates of the point of intersection of  and HK are  , 2  .
 8

A.
B.
II only
III only
C.
D.
I and II only
I, II and III
In the figure, the equations of the straight lines L1 and L2 are x  ay  b  0 and
x  my  n  0 respectively. Which of the following are true?
I.
II.
Ill.
y
nb0
L1
ab  0
ma
1
A.
I and II only
B.
I and III only
C.
II and III only
D.
I, II and III
2324_S6_MA_MOCK_EXAM_P2
x
O
L2
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26.
27.
Denote the circle 4x2 + 4y2 – 12x + 60y + 217 = 0 by C . Which of the following is true?
A.
The coordinates of the centre of C are (3 , –15) .
B.
C lies in the first quadrant.
C.
The origin lies inside C .
D.
The area of C is greater than 12 .
In the figure, ABCD is a square. E is a point lying on BA produced. If ECD = α, then
AE 
E
28.
A.
CDtan   1 .
B.
CD1 tan   .
C.
 1  tan  
CD
 .
 tan  
D.
 tan   1 
CD
 .
 tan  
A
D
B
C
There are five balls numbered ‘2’, ‘4’, ‘5’, ‘7’ and ‘9’ in a box. In a game, two balls are
randomly drawn from the box at the same time. If the sum of the two numbers drawn is odd,
15 tokens will be obtained; otherwise, 25 tokens will be obtained. Find the expected number
of tokens obtained in the game.
A.
B.
19
19.8
C.
D.
20
21
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29.
The bar chart below shows the distribution of the numbers of smartphones sold by an
Number of days
electric appliance store in September. Find the inter-quartile range of the distribution.
8
6
4
2
3
5
7
9
11
Number of smartphones sold
30.
A.
2
B.
4
C.
6
D.
8
If the mean of the eight numbers {3 , 5 , 10 , a , b , c , d , e} is equal to the mean of the five
numbers {a , b , c , d , e} , find the mean of the eight numbers {3 , 5 , 10 , a , b , c , d , e } .
A.
6
B.
9
C.
12
D.
18
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Section B
31.
111001110011102 =
7  211 + 7  26 + 7  21 .
7  212 + 7  27 + 7  22 .
7  213 + 7  28 + 7  23 .
7  214 + 7  29 + 7  24 .
A.
B.
C.
D.
n
32.
n
1
1
Solve    3   4 .
4
2
n2
A.
B.
C.
D.
33.
2n0
n  2
n  2
Consider the following system of inequalities:
11x  4 y  71

 x  4 y  11
3x  4 y  1

Let D be the region which represents the solution of the above inequalities. Find the
positive constant k such that the greatest value of 2 x  ky is 2, where (x, y) is a point
lying in D.
A.
B.
C.
2
2
3
D.
20
7
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34.
The graph in the figure shows the linear relation between log 4 x and log 8 y . Which of
the following must be true?
A.
B.
log 8 y
x 9 y 4  218
x 9 y 4  418
3
4
C.
D.
y
 218
x9
x9
 418
4
y
O
35.
36.
If k is a real number, then the imaginary part of
A.
4k  2
.
k2  4
B.
4k  2
.
k2  4
C.

k 8
.
k2  4
D.

k 8
.
k2  4
2
log 4 x
4
i

is
k  2i k  2i
Let a , b , c be an arithmetic sequence and b , c , d be a geometric sequence. If
a + b + c = 24 and bcd = 1 728 , then ad =
A.
B.
C.
D.
18 .
64 .
72 .
96 .
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37.
Let f ( x)  5( x  8k ) 2  2k 2  6 , where k is a non-zero real constant. Denote the vertex of
the graph of y  f ( x) and the vertex of the graph of y  f (2 x) by P and Q respectively.
Let R be a point lying on PQ such that the area of OPR is the triple of the area of
OQR , where O is the origin. Express the coordinates of R in terms of k .
A.
B.
C.
D.
38.
(13 k , k 2  3)
(7 k , k 2  3)
(7 k ,  k 2  3)
(5k ,  k 2  3)
In the figure, ABCD is a circle. EF is the tangent to the circle at C. BDE is a straight line. If
BCF = 58 and BEF = 37, then BAD =
A.
B.
C.
D.
39.
74 .
79 .
85 .
95 .
ABCD is a regular tetrahedron. Let  be the angle between ∆ABC and ∆ACD . Find
cos  .
A.
1
3
B.
1
2
C.
D.
3
3
2
3
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40.
The straight line mx + 3y + 24 = 0 and the circle x2 + y2  20x  ny = 0 intersect at the points
H and K , where m and n are constants. If the coordinates of the mid-point of HK are
(3 , 1) , find n .
41.
A.
B.
50
4
C.
D.
8
14
The equation of the straight line L is 4 x  3 y  3k  0 , where k is a positive constant. L cuts
the x-axis and the y-axis at the points P and Q respectively. Let R be a point lying on the
x-axis such that the y-coordinate of the orthocentre of PQR is 9. Find the x-coordinate of
R.
42.
A.
12 .
B.
3.
C.
D.
3 .
12 .
There are 16 S4 students and 12 S5 students in the Cheese Club. If 5 students are selected
from the club to form a team consisting of not more than 2 S5 students, how many different
teams can be formed?
A.
B.
C.
D.
43.
63 168
36 960
35 112
26 208
The table below shows the scores and the corresponding standard scores of three students in
a test.
Score
54
70
74
Standard score
y
1.5
y
Find the value of y .
A.
B.
C.
D.
5
2.5
2.5
5
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44.
Wing and Horace take turns to throw a fair die. The player who first gets a number ‘6’ wins.
They play until one of them wins. Wing throws the die first. Find the probability that Wing
wins.
45.
A.
6
11
B.
1
2
C.
1
5
D.
1
6
It is given that S(n) is the nth term of an arithmetic sequence with non-zero common
difference. Let m1 , r1 and v1 be the mean, the range and the variance of the group of
numbers  S(1) , S(2) , S(3) , S(4) , S(5)  respectively while m2 , r2 and v2 be the mean,
the range and the variance of the group of numbers
respectively. Which of the following must be true?
I.
II.
III.
m1  m2
r1  r2
v1  v2
A.
B.
C.
D.
I only
II only
II and III only
I, II and III
END OF PAPER
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 S(21) , S(22) , S(24) , S(25) 