Time allowed: 60 minutesTotal marks: 60Questions: 28
Instructions
• Answer ALL questions.
• Show your working where required — marks may be awarded for method.
• Write your answers clearly in the spaces provided.
• You may NOT use a calculator unless stated otherwise.
• Check your work if you finish early.
1. Q1: Work out the value of 5/7 of 63.
[2 marks]
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2. Q2: Simplify 5x - 6y - x + 3y.
[2 marks]
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3. Q3(a): Simplify w^8 ÷ w^2.
[1 mark]
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4. Q3(b): Simplify 5c^2d × 3c.
[2 marks]
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5. Q4: By rounding each number to 2 significant figures, estimate the answer to (24.3 × 14.93) / 123.
[2 marks]
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6. Q5(a): Expand and simplify 4c(d - 5).
[2 marks]
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7. Q5(b): Expand and simplify 3x - (2x - 3).
[2 marks]
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8. Q6(a): A function diagram shows: 4 → [+6] → [×8] → ? Complete the missing output number.
[1 mark]
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9. Q6(b): A function diagram shows: 14 → [÷ ?] → [+4] → 11. Find the missing number in the ÷ operation.
[1 mark]
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10. Q6(c): A function diagram shows: ? → [×3] → [-5] → 13. Find the missing input number.
[1 mark]
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11. Q7(a): Given that a - b = 5, work out the value of 3(a - b).
[1 mark]
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12. Q7(b): Given that a - b = 5, work out the value of b - a.
[1 mark]
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13. Q8: A 3×3 grid must be completed so that the product of the three numbers in every row, column and diagonal equals 1. The given numbers are: Row 1: 10, ?, 1/2. Row 2: 1/20, ?, 20. Row 3: 2, 5, ?. Find the three missing numbers. Give your answer as three values separated by commas in reading order (Row 1 middle, Row 2 middle, Row 3 right). (Refer to original PDF for figure.)
[3 marks]
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14. Q9: There are 24 boys, 45 girls and 281 adults in a badminton club. 50 more children join the club. The number of girls is now 18% of the total number of members. How many of the 50 children were boys?
[4 marks]
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15. Q10(a): A football team has P points. P = 3W + D, where W is the number of wins and D is the number of draws. A team gets 0 points for losing. A team has won 5 games, drawn 3 games and lost 1 game. How many points does the team have?
[1 mark]
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16. Q10(b): A football team has P points where P = 3W + D (W = wins, D = draws, 0 points for a loss). After 33 games a different team has 53 points. 11 games were draws. How many games has this team lost?
[3 marks]
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17. Q11: BCD is a straight line. Triangle ABC is equilateral. CE = DE. Angle DEC = 28°. Work out the size of angle x, where x is angle ACE. (Refer to original PDF for figure.)
[4 marks]
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18. Q12: AB is parallel to CD. A transversal crosses both lines. At line AB the angle between the transversal and AB is 2x°. At line CD the angles between the transversal and CD are 5x° and x°. Calculate the value of x. (Refer to original PDF for figure.)
[3 marks]
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19. Q13: Nicola thinks of a number. She doubles it, adds 4 to the answer, and then divides the result by 7. The number she now has is 2. Find the number she first thought of.
[3 marks]
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20. Q14(a): A rectangle has width x cm and length (3x - 2) cm. Form a simplified expression for the perimeter of this rectangle. (Refer to original PDF for figure.)
[2 marks]
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21. Q14(b): The perimeter of the rectangle (with width x cm and length (3x - 2) cm) is 124 cm. Calculate the value of x.
[3 marks]
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22. Q15: Here are five cards: 1, 5, 7, 9, 11. One of the cards is removed. The mean of the remaining four cards is 6. Which card was removed? You must show your working.
[2 marks]
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23. Q16: The range of a set of numbers is 15 1/4. The smallest number is -2 7/8. Work out the largest number. Give your answer as a mixed fraction.
[3 marks]
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24. Q17(a): A sequence has term-to-term rule 'multiply by 8 and then add 11'. The first term is -1. Work out the third term.
[2 marks]
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25. Q17(b): The sequence from part (a) is -1, 3, 35. The order of the three terms is reversed to make a new sequence: 35, 3, -1. Work out the term-to-term rule for this new sequence.
[1 mark]
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26. Q18: Find the value of x given that 1/2 : 2/3 = x : 1.
[2 marks]
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27. Q19: A solid has a uniform cross section. The cross section is a rectangle and a semicircle joined together. The rectangle has width x cm and height 2x cm, with the semicircle sitting on top (diameter = x cm). The depth of the solid is x cm. Work out an expression, in cm^3, for the total volume of the solid. Give your answer in terms of pi. (Refer to original PDF for figure.)
[3 marks]
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28. Q20: The minute hand of a clock is missing. The angle between the hour hand and twelve o'clock is 137°. How many minutes have passed since the last full hour? (Refer to original PDF for figure.)