Sacred Heart Canossian College
Mathematics Common Test 2 (2012-2013 )
Time allowed : 1 h Name:______No. : __
Group _____ S1 ___
Full Marks : 80 Score :_____
This paper consists of three sections, A, B and C . Answer all questions in each section .
Section A (24 marks)
Answer all 8 questions in this section . In the following table , put a “√ “ in the box
corresponding to the right answer . Each question carries 3 marks .
1 / 2 / 3 / 4 / 5 / 6 / 7 / 8A
B
C
D
1. If a and b are positive numbers and c is a negative number, which of the following expressions must be positive?
A. a – b + c B. a + b – c C. a – b – c
D. a + b + c
2. The price of a table and 4 chairs is $c . If the price of a table is $d , find the
price of each chair.
A. $(c – 4d) B. $(c – C. $(
D. $(
3. Given the formula S = (p – 4)(q). If p = –3 and q = –2, find the value of S.
A. – 28 B. – 4 C. 4
D 196
4. If E = T(2A – B), which of the following is/are true?
(I) If A = 3 , B = 6 and T = 7, then E = 0.
(II) If A =10 , B = 5 and T = 2, then E = 0.
(III) If A =8 , B = 4 and T = 0, then E = 0.
A. (II) only
B. (III) only
C. (I) and (II) only
D. (I) and (III) only
5. What should be added to (3p – 4q) to make (2p – 6q)?
A. – p – 2q B. – p + 2q C. 5p – 10q
D. 5p + 10q
6. Which of the following is correct ?
A. (–3a) + (–3a) = 0
B. –b – (–b) = –2b
C. (–2a)( –b) = 2ab
D. (–a) (–b) = –
7. If –8 < x < y < 3, then it is possible that
A. x = – 9 , y = 0.
B. x = –9, y = – 5.
C. x = 0 , y = –1.
D. x = –2 , y = 1.
8. Which of the following is/are true ?
(I) (– m) = – m
(II) (–2a) = – 6a
(III) –3 = 9
A. (I) only
B. (III) only
C. (I) and (III) only
D. (I) , (II) and (III)
Section B (34 marks)
Answer all eight questions in this section and show your working steps clearly in the space provided.
1. Peter and Jane shared $2200. Peter has $x and Jane has $500 less than twice
that of Peter .
(a) Set up an equation in x and find the value of x . ( 3 marks)
(b) Find the amount of money Jane received. ( 2 marks)
Name______No. :___ Group _____ S1 ___
2.
(a) The above figures show the first three patterns of a sequence formed by matchsticks. Complete the following table. ( 2 marks)
Patterns / Number of matchsticks1st pattern / 6
2nd pattern / 11
3rd pattern / 16
4th pattern
5th pattern
(b) Write down an algebraic expression for the number of matchsticks
in the n pattern of the sequence. ( 2 marks)
Number of matchsticks in the n pattern = ______
(c) Find the number of matchsticks in the 20th pattern of the sequence .
There are ______matchsticks in the 20th pattern of the sequence. ( 1 mark)
(d) If there are 51 matchsticks in the k pattern of the sequence , find the value of k . ( 2 marks)
3. During the week, the temperatures of town A at midnight were as follows :
and .
(a) Find the difference between the highest and the lowest temperature in the
week. ( 2 marks)
(b) Find the average midnight temperature of the week. (2 marks)
4. A fruit grower has n small boxes and (p – 2) large boxes. Fruits are packed in the boxes. The average weight of each small box with fruits is 18 kg and that of each large box is 40 kg. The total weight of the boxes with fruits is T kg.
Write a formula for T. ( 3 marks)
5. If p = – 2 and q = – 3 , find the value of
(3 marks)
6. Simplify :
(a) (2 marks)
(b) (2 marks)
(c) (2 marks)
Name______No. :___ Group _____ S.1 ___
7(a) Tom, Susan and Emily have a total of 92 story books. If Tom has w story books and Susan has twice that of Tom, express the number of story books that Emily has in terms of w. (2 marks)
Emily has ______story books.
(b) Fiona has r story books more than one-third of Emily’s number of story books. Express the number of story books that Fiona has in terms of r and w.
Fiona has ______story books. ( 1 mark)
8. Martin’s present age is x years. Sam is twice as old as Martin. Four years ago ,
Sam was 4 times as old as Martin. Find the value of x by setting up an equation. ( 3 marks)
Section C ( 22 marks)
Answer both questions in this section and show your working steps clearly in the space provided.
1. Solve the following equations:
(a) x + 2 = 5 – 2x – 9 (3 marks)
(b) (3 marks)
(c) 2( c + 7) – 4(c – 3) = 10 ( 3 marks)
(d) (3 marks)
2(a) Peter drove from his house to his working place for half an hour at an average speed of (8x -12) km /h . The distance between Peter’s house and his working
place was (3x + 2) km.
(i) Set up an equation in x and find the value of x . ( 3 marks)
(ii) Find Peter’s average driving speed. ( 2 marks)
Name______No. : ___ Group _____ S.1 ___
(b) On Saturday, Peter drove for 3 hours to visit a farm. For the first hour, he
drove at a speed of (3p – 16) km/h and for the last two hours, the average speed was (2p – 3) km/h. The total distance was 202 km.
(i) Set up an equation in p and find the value of p. (4 marks)
(ii) Find the distance travelled by Peter during the last two hours. (1 mark)
Distance travelled by Peter during the last two hours =
End Of Paper
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