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 3/8 of 24.
[1 mark]
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2. Q2: Simplify 8x − 4x² − 5x − 4x².
[2 marks]
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3. Q3(a): Simplify a⁶ ÷ a³.
[1 mark]
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4. Q3(b): Simplify 2x⁴y² × 5y³.
[2 marks]
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5. Q4(a): Expand and simplify 9mn − n(3 − 7m).
[3 marks]
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6. Q5(a): By rounding each number to 2 significant figures, estimate the answer to 200 / (16.3 × 25.2).
[2 marks]
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7. Q5(b): Is your estimate in part (a) larger or smaller than the actual answer? You must justify your decision.
[1 mark]
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8. Q6(a): Complete the missing number in the function diagram: 8 → [−5] → [×7] → ?
[1 mark]
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9. Q6(b): Complete the missing number in the function diagram: 12 → [÷ ?] → [×9] → 27. What is the missing number in the ÷ box?
[1 mark]
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10. Q6(c): Complete the missing number in the function diagram: ? → [÷2] → [+2] → 16. What is the missing input number?
[1 mark]
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11. Q7: Given that p = −2 and q = 25, find the value of p²q − (5p)².
[2 marks]
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12. Q8(a): The cost of petrol is £1.20 per litre. Alice buys £48 worth of petrol. How many litres of petrol does she buy?
[2 marks]
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13. Q8(b): Alice can drive 8.5km for every litre of petrol. How many km can she drive using the petrol she bought?
[1 mark]
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14. Q9: A jar contains 60 jelly beans. If 35% of the jelly beans are removed, how many remain in the jar?
[2 marks]
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15. Q10: In a mathematics competition, the winner won £100 more than twice the amount won by the runner-up. The total winnings were £2350. Let the amount won by the runner-up be r. Form an equation in r and solve it to find how much the winner received.
[5 marks]
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16. Q11: A 3×3 grid contains numbers where all rows, columns and diagonals have the same product. Some cells are given: Row 1 has 8, [?], 2/5. Row 2 has [?], 2, [?]. Row 3 has [?], 8/5, 1/2. Complete the grid by finding the four missing numbers. Give your answer as four values in order: Row 1 middle, Row 2 left, Row 2 right, Row 3 left. (Refer to original PDF for figure.)
[3 marks]
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17. Q12: A sports club has 65 men and 35 women as members. A new activity has just begun and 50 new members have joined. Given that the number of men is now 60% of the total members, how many of the 50 new members were women?
[3 marks]
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18. Q13(a): A rectangle is 50cm long and 40cm wide. Its length is extended by 12% and its width is reduced by 15%. Does the perimeter of the rectangle change? Justify your answer.
[3 marks]
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19. Q13(b): A rectangle is 50cm long and 40cm wide. Its length is extended by 12% and its width is reduced by 15%. Does the area of the rectangle change? Justify your answer.
[2 marks]
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20. Q14: Tasha scored an average of 78% across three of her five exams this year. She wants to score 85% minimum this year. What is the lowest score she can gain in her fourth exam to achieve her desired goal?
[3 marks]
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21. Q15: In a star (pentagram) formed by five intersecting lines with vertices A (top), B (upper-left), C (lower-left), D (lower-right), E (upper-right), the angles at B, C, D, and E are 30°, 35°, 36°, and 31° respectively. The angle at vertex A is split into x and y. T and S are intersection points on line BE near vertex A. Find the value of x, where x is the angle at intersection point T in triangle ATS. (Refer to original PDF for figure.)
[2 marks]
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22. Q15: In the same star diagram, find the value of y, which is the angle at vertex A (the star tip angle at A). (Refer to original PDF for figure.)
[2 marks]
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23. Q16: Nadia visits a restaurant every five days. She visited the restaurant on Sunday 1 January 2017. What is the date of her next Sunday visit?
[3 marks]
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24. Q17(a): A sequence is formed by 1 × 2², 2 × 3², 3 × 4², ... Find the next two terms of the sequence.
[2 marks]
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25. Q17(b): For the sequence 1 × 2², 2 × 3², 3 × 4², ... work out the 10th term of the sequence.
[1 mark]
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26. Q18: The prices of two items P and Q in a shop are in the ratio 4:5. When the price of P is increased by £12 and the price of Q is reduced by £6, then the items have the same price. Find the original price of P.
[3 marks]
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27. Q19: A measuring cylinder with diameter 5cm is partially filled with water. When a stone is placed in the cylinder, the water level rises by 3cm. Find the volume of the stone in terms of π. (Refer to original PDF for figure.)
[3 marks]
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28. Q20: Given the values w = 2^129 × 3^81 × 5^128, x = 2^127 × 3^81 × 5^128, y = 2^126 × 3^82 × 5^128, z = 2^125 × 3^82 × 5^129, write these numbers in ascending order.