QUEEN’S COLLEGEHalf-Yearly Examination, 2011 – 2012

MATHEMATICS

PAPER 1

Question-Answer Book

Secondary 2 Date: 12– 1 – 2012Time: 8:30 am – 9:45 am

1. Write your class, class number in the spaces provided on this cover.

2. This paper consists of TWO sections, A and B. Section A and Section B carry 80 marks and 40 marks respectively.

3. Attempts ALL questions in this paper. Write your

answer in the spaces provided in this Question-Answer Book.

4. Unless otherwise specified, all working must be

clearly shown.

5.

Unless otherwise specified, numerical answers should either be exact or correct to 3 significant figures.

6. The diagrams in this paper are not necessarily drawn to scale.

Teacher’s Use Only

Question No. Max. Marks Marks

Section A: Short Questions

1 8

2 7

3 9

4 7

5 8

6 8

7 10

8 11

9 12

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Class

Class Number

Section B: Long Questions

10 20

11 20

Total: 120

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Section A: Short Questions. (80 marks)

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1. Find the rates of the following. Express your answers in the units stated in the

bracket. (8 marks)

(a) Kenny finished the 100 m race in 12.5 seconds. [m/s]

(b) The annual salary of Kate is $174 000. [$/month]

(c) The selling price for 400 g of beef is $11.2. [$/kg]

(d) 0.5 L of water weighs 6.8 kg. (Given:1 L = 1000 ) [g/ ]

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2.

If , find the values of P, Q,, R and S. (7 marks)

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3.Let S be the surface area of a cuboid. Its length, width and height are p cm,

2q cm and 3r cm respectively.

(a) Express S in terms of p, q and r. (4 marks)

(b) Make r the subject of the formula in (a). (3 marks)

(c) Hence find the value of r if S = 94, p = 5, q = 2. (2 marks)

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4.Find the quotient and remainder of . Express the

answer in descending powers of x.(7 marks)

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5.

The above frequency polygon shows the lengths (in cm) of a group of metal bars produced

by a machine.

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(a) Complete the table below.

(3 marks)

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Length(cm) 5-9 10-14 15-19 30-34 35-39 40-44 45-49

Frequency 3 13 8

(b) How many metal bars are there in the group ? (2 marks)

(c)If metal bars of lengths less than 24.5 cm are rejected, how many bars in the group are

accepted ?(3 marks)

6. Simplify the following expressions:

(a) (4 marks)

(b) (4 marks)

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7. The thickness of 500 sheets of paper of the same quality is 46.2 mm and

given that the relative error is .

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(a)

(b)

(c)

Find the percentage error of the thickness of all papers. (Correct your

answer to 3 sig.fig.)

Find the actual range of thickness of all papers.

Find the actual range of thickness of each sheet of paper.(Correct your

answer to 3 sig.fig.)

(2 marks)

(6 marks)

(2 marks)

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8. Simplify the following expressions and express the answers with positive

indices.

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(a) (5 marks)

(b) (6 marks)

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9.

(a)

Given that 2a = 3b. Find a : b. (2 marks)

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(b) Given that . Find a : b : c. (7 marks)

(c) Given that . Find x : y. (3 marks)

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Section B: Long Questions. (40 marks)

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10. (a) Simplify . (6 marks)

(b) If a + b = 4 and ab = 3, find the value of . (4 marks)

(c) Factorize . (7 marks)

(d) Using the result of (b) and (c), find the value of . (3 marks)

11. x and y are the units digit and the tens digit of a 2-digit number P respectively.

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(a) Express P in terms x and y. (2 marks )

(b) Q is another 2-digit number which is formed by reversing the digits of P. Express Q in

terms of x and y.

(2 marks)

(c) P is three times the sum of its digits. Find the equation involving x and y. (4 marks)

(d) 45 added to P is equal to Q. Find another equation involving x and y. (4 marks)

(e) By solving the equations in (c) and (d) simultaneously, find the number Q. (8 marks)

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