QUEEN’S COLLEGE

Half-Yearly Examination, 2010 – 2011

MATHEMATICS PAPER 1

Question-Answer Book

Secondary 2Date:7 – 1 – 2011

Time: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.

Class
Class Number
Teacher’s Use Only
Question No. / Max. Marks / Marks
Section A: Short Questions
1 / 4
2 / 8
3 / 13
4 / 7
5 / 5
6 / 12
7 / 7
8 / 8
9 / 6
10 / 10
Section B: Long Questions
11 / 20
12 / 20
Total: / 120

- P.1 -

Section A: Short Questions. (80 marks)
1. / State whether each of the following is true (T) or false (F):
(a) / 0.00340 has 3 significant figures. / (1 mark)
(b) / In the number 6.0008, there are only 2 significant figures. / (1 mark)
(c) / If 231.698 is rounded off the nearest hundredth, the result is 231.70. / (1 mark)
(d) / If the height of a bus is 3.0 m, then the maximum error is 0.5 m. / (1 mark)
(a) ____T______(b) ____F______(c) _____T______(d) ____F_______
2. / A basketball court is measured to be 30.4 m long, and 18.0 m wide to the nearest 0.2 m.
(a)
(b) / Find the accumulated error of its perimeter.
Find the range of the true value of its perimeter. / (3 marks)
(5 marks)
(a) / / 1M:max error
1M: ()
(1A)
(b) / / 1M:upper limit
1A
1M:lower limit
1A
1A
3. / Simplify the following expressions and express your answers in positive indices.
(a) / where n is a positive integer / (3 marks)
(b) / / (5 marks)
(c) / / (5 marks)
(a) / / 1M:
1M:
1A
Or / 1M:
1M:
1A
(b) / / 1M:-ve
1M:multiplication rule
1A
1M:addition rule
1A
(c) / / 1M, 1A
1M:factorization
1A
1A
4. / (a) Make t the subject of the formula. / (5 marks)
(b) Hence, find the value of t if x= –2. / (2 marks)
(a) / / 1M
1A
1M
1M
1A
(b) / When x = -2
/ 1M:substitution
1A
5. / (a) Expand. / (3 marks)
(b) / What is the coefficient of the term with the highest degree in the expansion in (a)? / (1 mark)
(c) / What is the constant term in the expansion in (a)? / (1 mark)
(a) / / 1A
1M
1A
(b) / The coefficient = / 1A
(c) / The constant = / 1A
6. / (a) If , find a : b. (3 marks)
(b) Using (a), find a : b : c if . (5 marks)
(c) / Hence, find a and c if b = 45. / (4 marks)
(a) / / 1M: fraction
1M
1A
(b) / / 1M
1A
1M: by (a)
1M
1A
(c) / / 1M
1A
1M
1A
7. / Find the quotient and remainder of .
Express the answer in descending powers of x. / (7 marks)
/ 1: descending
power of x
/ 1M: place holder
2M
1A
The quotient =
The remainder = / 1A
1A
8. / Simplify the following expressions:
(a)
(b) / (3 marks)
(5 marks)
(a) / / 1M
1A
1A
(b) / / 1M:factorization
1A:
1M:denominator
1A
1A
  1. A teacher asks 70 students to solve an IQ problem and records the time (in
seconds) that each student spent. The results obtained are presented in the
following table.
Time(s) / 11–20 / 21–30 / 31–40 / 41–50 / 51–60 / 61–70
Frequency / 7 / 10 / 13 / 14 / 15 / 11
(a) / For the class interval 31 s – 40 s,
(i) What are the class limits ? / (1 mark)
(ii) What are the class boundaries ?
(iii) What is the class mark ? / (1 mark)
(1 mark)
(1 mark)
(2 marks)
(b)
(c) / Which class interval has the highest frequency ?
How many students can solve the problem within 40.5 s ?
(a) / (i) upper class limit = 40 s
lower class limit = 31 s / 1
(ii) upper class boundary = 40.5 s
Lower class boundary = 30.5 s / 1
(iii) class mark = 35.5 / 1
(b) / 51 s – 60 s / 1
(c) / No of students = 7+10+13
= 30 / 1M
1
10. (a) Expand . (2 marks)
(b) / Using (a), expand. / (3 marks)
(c) / Hence, simplify . / (5 marks)
(a) / / 1M
1
(b) / / 1M: Difference
of 2 squares
1A
1A
(c) / / 1M:factorization
1A
1M
1A
1A
11. / A factory produces wooden tables and chairs. To produce a table, it takes 4 hours on machine A ,and afterwards 2 hours on machine B. To produce a chair, it takes 3 hours on machine A, and afterwards 5 hours on machine B.(Fig 1)
Supposex tables and y chairs are produced each week.
(a) / Find the number of hours per week neededto work on
(i) machine A,
(ii) machine B.
Express your answers in terms of x and y. (4 marks)
(b) / Machine A is used for 108 hours per week.
Write down an equation involving x and y. (2 marks)
(c) / Machine B is used for 96 hours per week.
Write down an equation involving x and y. (2 marks)
(d) / By solving the equations in (b) and (c) simultaneously,
find the number of tables and chairs that are produced
each week. (8 marks)
(e) / Using (d), solve . (4 marks)
(a) / (i) no. of hours worked by machine A = 4x +3y / 1A+1A
(ii) no. of hours worked by machine B = 2x +5y / 1A+1A
(b) / 4x +3y = 108 / 1M, 1A
(c) / 2x +5y = 96 / 1M, 1A
(d) / / 2M: correct
method
1A
1A
1M:substitution
1A
1A
1
(e) / / 1M
1A
1A+1A
12. (a) Determine whether the equation is an identity. (7 marks)
(b) Using (a), factorize . / (3 marks)
(c) Factorize . / (2 marks)
(d) Hence, factorize . / (8 marks)
(a) / / 1M
2A
2A
1
1
(b) / / 1M
2A
(c) / / 1A+1A
(d) / / 1A
1M:gouping, 1A
1M: by (b)(c),1A
1M:factorization,1A
1A

------End of Paper ------

- P.1 -