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MATHEMATICS

PAPER 02: 2hrs 45 minutes

INSTRUCTIONS TO CANDIDATES

1. Answer ALL questions.

2. Begin the answer for each question on a new page.

3 . All working MUST BE clearly shown.

4. Silent electronic NON PROGRAMMABLE calculators may be used for this paper.

5. A list of formulae is provided on page 1 of this booklet.

Examination Materials Electronic scientific calculator (non-programmable) Geometry sets Mathematics tables Graph paper

DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO

Copyright© 2011 Department of Mathematics Bethel High School

Aptitude exam

All rights reserved

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1) (a) Determine the EXACT value of

411

523

52

431

(3 marks)

(b) 1575.17.1 2 giving your answer correct to 2 significant figures. (3 marks)

(c) 0225.025.025.4 giving your answer correct to 2 decimal places. (3 marks)

(d) 22.56.0

07.2 (3 marks)

TOTAL 12 MARKS

2) (a) A sum of money is to be shared between Chris and Rhianna in the ratio 3:5.

Chris received $120. How much money was shared altogether? (3 marks) (b) The cash price of a television set is $1200. It can be bought on hire purchase by making a deposit of 15% and 10 monthly installments of $120 EACH.

(i) Calculate the amount deposit to be made on the television set. (1 mark)

(ii) What is the TOTAL hire purchase price? (2 marks)

(iii) Calculate the difference between the TOTAL hire purchase price and the cash price. (1 mark)

(iv) Express your answer in (iii) above as a percentage of the cash price writing your answer to 2 significant figures. (2 marks)

(c) Calculate the TOTAL amount of money a man would receive if he invested

$2000 in a credit union for 2 years at an interest rate of 5% per annum. (3 marks) TOTAL 12 MARKS

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3) (a) EC $1.00 = US $0.37 Jillian converted $500 EC to US to take with her to the Virgin Islands.

(i) How much US did Jillian receive if the exchange rate stated above was used? (2 marks)

(ii) She spent US $100 and converted the remainder back to EC $. How much EC $ did she receive (to the nearest cent) assuming that the buying and selling rates are the same? (3 marks)

(b) The basic rate per hour earned by a mason for a 40-hour week is $50. If he worked for 52 hours in one week and his overtime rate is time and a half, calculate his basic wage for that week. (4 marks) (c) A vehicle which was purchased 2 years ago for $20 000 depreciates by 5%

yearly. What is the present value of the vehicle? (3 marks) TOTAL 12 MARKS

4) (a) Use algebraic statements to express each statement below.

i. Three apples and two oranges cost $15.25

ii. Four times the sum of x and 5

iii. I think of a number, doubled it then add five to it. (3 marks)

(b) Simplify the expressions

(i) )3(7)(5 yxyx (2 marks)

(ii) 3

42

634

xxx (3 marks)

(iii) yx

yx 24

53

(2 marks)

(c) Simplify

5

23

3

xx

(3 marks)

TOTAL 13 MARKS

5) (a) Factorize completely i. 263 nmn (1 mark) ii. yxxy 23 (2 marks) iii. 254 2 x (2 marks) iv. tytxsysx 2233 (2 marks)

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(b) Given that 2a , 3b and 4c , calculate

a

acb2

42

(3 marks)

(c) Given that baaba 2*

Evaluate 4*8 in its simplest form (2 marks) (d) Solve for x

(i) 1452 xx

(3 marks)

(ii) 1032

xx

(3 marks)

TOTAL 18 MARKS

6) (a) A survey was conducted among 40 students. 30 students like reading the Searchlight newspaper. 20 students like reading the News newspaper and 5 like reading neither.

i. Copy and complete the Venn diagram above to represent the given information. (2 marks)

ii. Calculate how many students like reading both papers. (3 marks)

iii. How many students like reading the News newspaper only?(1 mark)

(b) The figure below is a Venn diagram showing a Universal set. and two subsets, G and H . The numerals in the diagram represent members of the sets.

i. List the members of the set a. HG

b. HG

c. )( HG

ii. Determine the value of HGn (

(4 marks) TOTAL 10 MARKS

N

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7) (a) The diagram to the right, not drawn to scale, shows a vertical pole AC, which is supported by a straight wire AB 10 metres long and pinned to to horizontal ground some 6 metres away from the foot of the pole.

(i) Calculate in metres, AC the length of the pole. (2 marks)

(ii) Calculate the size of the angle formed at B, which is angle ABC. (3 marks)

(b) The diagram below, not drawn to scale, shows PQR , which represents the cross section of a roof. QS Is perpendicular to PSR

Using the dimensions shown on the diagram, calculate, correct to 3 significant figures.

i. the length QS (2 marks) ii. the measure of RQS

(3 marks) iii. the area of triangle PQR (3 marks)

TOTAL 13 MARKS

8) The diagram below, not drawn to scale, shows a triangular prism with right-angled isosceles triangles at both ends. Angle 90ABC and AB = BC = 4cm

i. Calculate the area of triangle ABC. (2 marks)

The volume of the prism is 72 cm2

ii. Calculate the length of the edge CD (3 marks)

iii. Calculate, to one decimal place, the length of the edge AC (2 marks)

iv. State the number of faces, edges and vertices of the prism (3 marks) TOTAL 10 MARKS

6 m

10 m

B C

A

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9) (a) Find the surface area of the cuboid below with the given dimensions. (4 marks)

(b) In this question, use 722

i. A piece of wire is bent to form a square of area 121 cm2. Calculate

a. The length of each side of the square

b. The perimeter of the square (3 marks)

ii. The same piece of wire is bent to form a circle

a. The radius of the circle

b. The area of the circle (4 marks) TOTAL 11 MARKS

10) Given that f(x) = x – 2 and g (x) = 3x + 4 (a) f (2) (1 mark) (b) g (-3) (2 marks) (c) f -¹ (x) (2 marks) (d) g-¹ (x) (3 marks) (e) fg (x)

(4 marks) TOTAL 12 MARKS END OF TEST!

5 cm

5 cm