HKFYG Lee Shau Kee College
1st Term Test (2022 – 2023)
S.2 Mathematics
Time allowed: 45 minutes
Name: ________________________
Full marks: 60
S.2 __ (Set: M __ ) Class No.: _____
This paper consists of 11 pages.
Marks obtained:
Inappropriate headers:
Inappropriate units:
Instructions:
Total:
1. This paper consists of 3 sections, Sections A and B, and Challengers’ Section. Answer
ALL questions in Section A (42 marks) and Section B (18 marks) in the space provided.
Challengers’ Section is optional. Students should attempt this section after answering all
the questions in Sections A and B.
2. Only calculators pad-printed with “H.K.E.A.A. approved” or “H.K.E.A. approved” label
are allowed.
3. Unless otherwise stated on the question paper, blue or black pen should be used to write
down the answers, while pencil should be used to draw diagrams or plot graphs.
4. Rough worksheet would not be marked.
5. Unless otherwise stated, numerical answers should be either exact or correct to 3 significant
figures.
6. Diagrams in this paper are not necessarily drawn to scale.
7. A maximum of 1 mark will be deducted for inappropriate units.
8. Each question should be answered starting with a header. A maximum of 2 marks will be
deducted for inappropriate headers.
9. Any answers given without following the instructions may risk mark penalty.
Section (A) Conventional Questions
1.
Complete the following table.
Number
2.
(42 marks)
(a)
910.048
(b)
0.008
(c)
8.00
(3 marks)
The 1st significant
figure
The 2nd significant
figure
Number of
significant figures
The weight of a pack of standard salt is measured as 95 g, correct to the nearest g.
(a) Find the minimum possible weight of a pack of standard salt.
(b) Bernice puts 80 packs of standard salt in a bag. Is it possible that the actual weight of the bag of
salt is 7.5 kg? Explain your answer.
(4 marks)
3.
In an experiment, the speed of sound is measured as 320 m/s at 20 ℃ and its percentage error is 3.75%.
If the actual speed of sound at 20 ℃ is y m/s, find the range of the values of y.
Page 2 of 11
(3 marks)
HKFYG Lee Shau Kee College
S.2 Mathematics 1st Term Test 22-23
4.
Name: _________________________ Class: _____ (
Complete the following table.
(3 marks)
Number of
Polynomial
 x2
terms
)
Coefficient of
x3
x2
Constant
Degree of
Term
polynomial
x
x3
5
5.
Determine whether the equation  3( x  2)  3(3  x)  3 is an identity.
(3 marks)
6.
( xy 2 ) 6
Simplify
and express the answer with positive indices.
x7 y
(2 marks)
Page 3 of 11
7.
Expand and simplify (2a  a 2 )  (a  2)(3a  1) .
8.
Simplify the following expressions.
(a)
2a  5b 4a  b

3a  2b 3a  2b
(b)
2
8m

1  4m 4m  1
(3 marks)
(5 marks)
Page 4 of 11
HKFYG Lee Shau Kee College
S.2 Mathematics 1st Term Test 22-23
9.
Name: _________________________ Class: _____ (
)
The dimensions of a cuboid are ( x  3) cm, (1  2 x) cm and x 2 cm respectively, where x  3 .
(a)
Express the volume of the cuboid in terms of x and arrange the terms in descending powers of x.
(b)
If x = 50, find the volume of the cuboid in m3.
(4 marks)
10. Factorize the following expressions.
(a)
qs  pr  qr  ps
(b) 6(2a  b)  (a 2  1)(2a  b)
(4 marks)
Page 5 of 11
11. (a)
(b)
Expand (m  5)( m  5) .
Hence, or otherwise, find the value of 765432152 – 76543220 × 76543210.
(4 marks)
Page 6 of 11
HKFYG Lee Shau Kee College
S.2 Mathematics 1st Term Test 22-23
Name: _________________________ Class: _____ (
)
1
12. (a) Expand (k  ) 2 .
k
(b) Hence, or otherwise, find the value of k 2 
1
1
when k   8 .
2
k
k
(4 marks)
Page 7 of 11
Section (B) Multiple Choice Questions
(18 marks)
Choose the best answer for each question by writing down the letter A, B, C or D in the table on P.10.
13. 0.0522515 =
A.
0.052 (correct to 3 significant figures).
B.
0.0522 (correct to 4 decimal places).
C.
0.05225 (correct to 5 significant figures).
D.
0.052252 (correct to 6 decimal places).
14. ax  bx  ay  by  az  bz 
A.
(a  b)( x  y  z ) .
B.
(a  b)( x  y  z ) .
C.
(a  b)( x  y  z ) .
D.
(a  b)( x  y  z ) .
15. ( x  1)( x 2  x  1) 
A.
x3  2x 1.
B.
x3  x 2 1 .
C.
x3  2x 2 1 .
D.
x3  x 2  2x 1 .
16. Which of the following are NOT identities?
I.
1
1 x
1 
x
x
II.
( x  1) 2  x 2  1
III. (ax  b)( x  b)  ax 2  b 2
A.
I and II only
B.
I and III only
C.
II and III only
D.
I, II and III
Page 8 of 11
HKFYG Lee Shau Kee College
S.2 Mathematics 1st Term Test 22-23
Name: _________________________ Class: _____ (
)
17. If ( x  3) 2  ( x  1)( x  4)  P( x  1)  Q , find P and Q.
A.
P  3, Q  4
B.
P  4, Q  3
C.
P  4, Q 9
D.
P  9, Q  4
18. There is a bag of coffee sugar. The weight of coffee sugar in the bag is measured as 1.876 kg correct to
the nearest 0.001 kg. If the bag of coffee sugar is packed into k packets such that the weight of coffee
sugar in each packet is measured as 15 g correct to the nearest 1 g, find the least possible value of k.
A.
121
B.
122
C.
123
D.
124
19. If x 2  y 2  m and x  y  n , then xy 
A.
1 2
( n  m) .
2
B.
n2  m .
C.
n2 
D.
n2
m.
2
m
.
2
Page 9 of 11
20.
1
1
1



x 1 1  x x  1
2
2x 1
.
x2 1
A.

B.
2x 1
.
x2 1
C.

D.
3
.
x 1
3
.
x 1
2
2
1
21. ( ) 555 (9) 333 
3
A.
3111 .
B.
3 222 .
C.
1
.
3111
D.
1
3 222
.
Question No.
13
14
15
16
Answer

Page 10 of 11
17
18
19
20
21
HKFYG Lee Shau Kee College
S.2 Mathematics 1st Term Test 22-23
Name: _________________________ Class: _____ (
Challengers’ Section (OPTIONAL)
)
(3 marks)
22. (a) Factorize x 4  x 2  1 as a product of two other polynomials of smaller degrees.
(b) It is given that x( x  1)  5 and x( x  1)  4 . Hence, or otherwise, evaluate x 4  x 2  1 .
END OF PAPER
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