F.2 Mathematics Trial Common Test 1B
200x – 200y First Term
Marymount Secondary School
First Term Trial Common Test 1B
Mathematics
Form 2
Date of Exam. : --Time Allowed : 1 hour
Total Marks
: 65 marks
Instructions to Candidates
1.
This paper consists of Section A and Section B.
2.
ANSWER ALL QUESTIONS. Write all the answers on the single lined papers.
3.
In Section A, each question carries 2 marks. No mark will be deducted for wrong answers.
No step is required.
4.
In Section B, necessary steps must be shown. Unless otherwise specified, numeric
answers should either be exact or correct to 2 decimal places.
Section A Multiple Choice Questions (20 marks)
1.
2.
Expand [–(1 – 2x)]2.
A.
–1 + 4x – 4x2
B.
–1 + 4x + 4x2
C.
1 – 4x + 4x2
D.
1 + 4x – 4x2
4.
2
Factorize 36x – 104x + 64
A.
(6x + 8)2
B.
(6x – 8)2
C.
(9x – 8)(4x – 8)
D.
(3x – 16)(12x – 4)
5.
In which of the followings is x the
subject of the formula?
A.
y = 2x + 3
4
B.
x = +9
y
C.
1 1
= +2
x y
D.
2x + 3y – 4 = 0
A.
3.
If (ax + b)(bx + a) ≡ 16x + 68x + 16,
find (a + b).
A.
10
B.
–10
C.
10 or –10
D.
Cannot be determined
2
B.
6.
5y
5y2
÷
6ax 2 2ax
3xy
1
3 xy
Simplify
C.
1
6 xy
D.
25 y 3
12a 2 x 3
Find the L.C.M. of 3b(b + 1)(b – 1)2
and 6b2(b + 1)2(b – 1)
A.
3b (b + 1)(b – 1)
B.
6b(b + 1) 2(b – 1)2
C.
6b2(b + 1)(b – 1)
D.
6b2(b + 1)2(b – 1)2
Page 1 of 5
F.2 Mathematics Trial Common Test 1B
200x – 200y First Term
For questions 7 to 9, please refer to the following graph.
The cumulative frequency polygon above shows the mathematics test results of a group of
students.
7.
How many students are there in total?
A.
40
B.
90
C.
193
D.
Cannot be determined
8.
What is the percentage of students are getting 40 – 60 marks?
A.
21.1%
B.
37.5%
C.
47.5%
D.
9.
85.0%
What is the lowest possible mark of the “Top 5” students?
A.
60
B.
64
C.
70
D.
Cannot be determined
Page 2 of 5
F.2 Mathematics Trial Common Test 1B
200x – 200y First Term
10.
Which of the following graphs can be a frequency polygon?
I.
Freq.
0
II.
Freq.
0
III.
Freq.
0
A.
B.
C.
D.
I and II only
II and III only
I and III only
I, II and III
- End of Section A -
Page 3 of 5
F.2 Mathematics Trial Common Test 1B
200x – 200y First Term
Section B Long Questions (45 marks)
Show all necessary steps clearly.
1.
2.
3.
⎛ 2x 2 2
⎞⎛ 2 x 2 2
⎞
+ − x ⎟⎟⎜⎜
− + x ⎟⎟
Expand ⎜⎜
5
5
⎝ 3
⎠⎝ 3
⎠
(4 marks)
Simplify the following expressions.
1
1
1
a.
+
+
.
(a − b )(b − c ) (a − c )(b − c ) (b − a )(c − a )
b.
a 2 − bc + ab − ac
a 2 + bc + ab + ac
a.
Make y the subject of the formula
b.
If x = –2 and u = 5, find the value of y.
(3 marks)
(4 marks)
1
2
+
= x.
x y −u
(4 marks)
(2 marks)
4.
If 3(Ax + B)2 ≡ 12x2 + Cx + 75, in which A, B and C are positive numbers, find the
values of A, Band C.
(6 marks)
5.
a.
b.
Show that a3 + b3 = (a + b)(a2 – ab + b2) is an identity.
Using the result of part (a) or otherwise, factorize 8x3 + (2x – 3y)3
(3 marks)
(4 marks)
Page 4 of 5
F.2 Mathematics Trial Common Test 1B
200x – 200y First Term
6.
The price of pork per catty (斤) is fluctuated (波動) recently. The prices in the past 45
days are recorded below.
Price of pork per catty less than ($)
31.5
33.5
35.5
37.5
39.5
41.5
43.5
45.5
Cumulative frequency
0
2
6
9
15
24
35
45
a.
Copy and complete the following table on your single-line paper.
Class mark ($)
Frequency
(7 marks)
b.
Using the table in part (a), draw a frequency polygon on a graph paper. (4 marks)
c.
Find the percentage of days where the price is between $37.5 and $41.5. (2 marks)
d.
The spokesman of the wholesalers’ association predicted that the price of the pork
will still be high in the coming future. Is he making a right comment? (2 marks)
- End of Section B -
- End of Paper -
Page 5 of 5