Name: _______________________________________
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Room: ____________________
O C S 4 M AT H / 2 0 2 3
Name: _______________________________________
Room: ____________________
Answer ALL the questions in this section.
All working must be clearly shown.
Time: 1 ½ Hours
1. (a) (i) (Using a calculator, or otherwise, determine the exact value of
(3.7)2 – (6.24 ÷ 1.3).
(3 marks)
(ii) Express as a single fraction
1
4
22 −5
3
4
(b) Mrs. Jack bought 150 T-shirts for $1 920 from a factory.
(i) Calculate the cost of ONE T-shirt.
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(3 marks)
(1 mark)
O C S 4 M AT H / 2 0 2 3
Name: _______________________________________
Room: ____________________
The T-shirts are sold at $19.99 each.
Calculate
(ii) the amount of money Mrs. Jack received after selling ALL of the T-shirts. (1 mark)
(iii) the TOTAL profit made
(1 mark)
(iv) the profit made as a percentage of the cost price, giving your answer correct to
the nearest whole number.
(2 marks)
TOTAL 11 MARKS
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O C S 4 M AT H / 2 0 2 3
Name: _______________________________________
Room: ____________________
𝑏
2. (a) Given that a * b = ab - 𝑎
Evaluate
(i)
4*8
(2 marks)
(ii)
(3 marks)
2 * (4 * 8)
(b) Find the value of EACH of the following when a = 2, b = -1, c = 3
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(i) a(b + c)
(2 marks)
(ii) 4b2 – 2ac
a+b+c
(3 marks)
O C S 4 M AT H / 2 0 2 3
Name: _______________________________________
Room: ____________________
(c) Change the following statements into algebraic expressions:
(i) Four times the sum of x and 5.
(ii) The square of the sum of a and b.
(d) Solve the equation
15 – 4x = 2(3x + 1)
(1 mark)
(1 marks)
(3 marks)
TOTAL 15 MARKS
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O C S 4 M AT H / 2 0 2 3
Name: _______________________________________
Room: ____________________
3. The diagram below, not drawn to scale, represents the plan of a floor. The broken line
RS, divides the floor into two rectangles, A and B.
(a) (i) Calculate the length of RS
(1 mark)
(ii) Hence state the value of x
(1 mark)
(b) Calculate the perimeter of the entire floor.
(3 marks)
(c) Calculate the area of the entire floor.
(3 marks)
TOTAL 8 MARKS
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O C S 4 M AT H / 2 0 2 3
Name: _______________________________________
Room: ____________________
4. The diagram below, not drawn to scale, shows two straight wires, LJ and NK, supporting
a vertical pole, MJ. LMN is a straight line on the horizontal plane. Angle JML = 90°,
angle KNM = 30°, LJ = 13 m, LM = 5 m and KN = 10 m.
Calculate, in metres, the length of
(i) MK
(ii) JK
(3 marks)
(3 marks)
TOTAL 6 MARKS
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O C S 4 M AT H / 2 0 2 3
Name: _______________________________________
Room: ____________________
5. The line graph below shows the monthly sales, in thousands of dollars, at a car
dealership for the period July to November 2014.
(a) Complete the table below to show the sales for EACH month.
Month
July
Sales in $
Thousands
13
August
September
October
November
36
(2 marks)
(b) Which month saw the highest increase in sales?
(1 mark)
(c) Which month saw the lowest increase in sales?
(1 mark)
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O C S 4 M AT H / 2 0 2 3
Name: _______________________________________
Room: ____________________
(d) The TOTAL sales for the period July to December was $130, 000.
(i) Calculate the sales, in dollars, for the month of December.
(1 mark)
(ii) Complete the line graph to show the sales for December.
(2 marks)
TOTAL 7 MARKS
TOTAL 47 MARKS
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