Half-Yearly Examination, 2010 2011

QUEEN’S COLLEGE 5. Unless otherwise specified, Half-Yearly Examination, 2010 – 2011 Class Class Number numerical answers should either be MATHEMATICS exact or correct to 3 significant figures.

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

PAPER 1

Question-Answer Book

Teacher’s Use Secondary 2 Date: 7 – 1 – 2011 Only Time: 8:30 am – 9:45 am Question Max. Marks No. Marks Section A: Short Questions 1 4

1. Write your class, class number in the spaces 4 7 provided on this cover. 5 5 2. This paper consists of TWO sections, A and B. Section A and Section B carry 80 marks and 40 6 12 marks respectively.

3. Attempts ALL questions in this paper. Write your 7 7 answer in the spaces provided in this Question- Answer Book. 8 8

4. Unless otherwise specified, all working must be 9 6 clearly shown.

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Section B: Long Questions 11 20

Total: 120

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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 to 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)______(b)______(c)______(d)______

2. A basketball court is measured to be 30.4 m long, and 18.0 m wide to the nearest 0.2 m. (a) Find the accumulated error of its perimeter. (3 marks) (b) Find the range of the true value of its perimeter. (5 marks)

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3. Simplify the following expressions and express your answers in positive indices. (a) 4n  22n where n is a positive integer (3 marks) (b) (5 marks) (a3b2 )3 (ab)3 (2a)5

(c) 3n  3n1  3n2 (5 marks) 3n  3n1  3n2

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4. 1 2  (5 marks) t (a) Make t the subject of the formula x  . 1 2  t (b) Hence, find the value of t if x = –2. (2 marks)

5.  1 1  (3 marks) (a) Expand (3x 1)(x 1) x   .  6 3  (b) What is the coefficient of the term with the highest degree in the (1 mark) expansion in (a)? (c) What is the constant term in the expansion in (a)? (1 mark)

- P.5 - Page total 6. 1 1 (a) If :  3 : 2 , find a : b. (3 marks) a b 2 (b) Using (a), find a : b : c if c  a . (5 marks) 3 (c) Hence, find a and c if b = 45. (4 marks)

7. Find the quotient and remainder of (5x4 1 4x)  (x 1) . Express the answer

in descending powers of x. (7 marks)

- P.6 - Page total 8. Simplify the following expressions: 1 2 (a)  2y  x x  4y (3 marks) 3a  b b (b)  a  b 3b  3a (5 marks)

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9. 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 ? (1 mark) (iii) What is the class mark ? (1 mark)

(b) Which class interval has the highest frequency ? (1 mark) (c) How many students can solve the problem within 40.5 s ? (2 marks)

10. (a) Expand (a  b)2 . (2 marks)

(b) Using (a), expand (a  b 1)(a  b 1) . (3 marks)

(c) (5 marks) Hence, simplify (a  b)(a  b)2  (a  b)(a  b 1)(a  b 1) .

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Section B: Long Questions. (40 marks)

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) Wood Suppose x tables and y chairs are produced each week. 4 hours 3 hours

(a) Find the number of hours per week needed to work on Machine A Machine A (i) machine A, (ii) machine B. 2 hours 5 hours Express your answers in terms of x and y. (4 marks) (b) Machine A is used for 108 hours per week. Machine B Machine B 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, Table Chair find the number of tables and chairs that are produced each week. (8 marks) Fig 1

(e) 4 3    108 Using (d), solve a b . (4 marks)  2 5    96  a b

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3 12. (a) Determine whether the equation (3x  5)2  6x( x)  5(5  6x) is an identity. (7 marks) 2 (b) Using (a), factorize 9x2  30x  25 . (3 marks) (c) Factorize 6x2 10x . (2 marks) (d) Hence, factorize 27x 2  90x  75 18x 2  30x . (8 marks)

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