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Transcript of 1qc.edu.hk/math/Links/Past Papers/S2 11-12 Half yearly... · Web viewClass Class Number Teacher’s...
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
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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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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Page total
5.
The above frequency polygon shows the lengths (in cm) of a group of metal bars produced
by a machine.
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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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Page total
(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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Page total
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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Page total
(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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