Time allowed: 60 minutesTotal marks: 60Questions: 35
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(a): A gold prospector finds three gold nuggets weighing 1.54g, 0.87g, and 1.704g. What is the total weight of the three nuggets?
[1 mark]
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2. Q1(b): A gold prospector finds three gold nuggets weighing 1.54g, 0.87g, and 1.704g. What is the difference in weight between the biggest and smallest nuggets?
[1 mark]
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3. Q1(c): If gold sells for £43 per gram, how much is the smallest nugget (0.87g) worth?
[2 marks]
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4. Q1(d): An ounce is approximately 28 grams. Convert the weight of the 1.54g nugget into ounces.
[2 marks]
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5. Q2(a): Work out the following, obeying the correct order of operations: 3 + 5 × 8 − 6
[1 mark]
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6. Q2(b): Work out the following, obeying the correct order of operations: 10 − (20 − 8) ÷ 2
[1 mark]
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7. Q2(c): Work out the following, obeying the correct order of operations: 24 ÷ (16 − 4 × 2)
[1 mark]
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8. Q2(d): Work out the following, obeying the correct order of operations: 100 − 80 − (60 − 40)
[1 mark]
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9. Q3(a): Calculate the following. Your answer should be fully simplified and written as a mixed number where appropriate: 2 1/5 + 1 3/4
[2 marks]
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10. Q3(b): Calculate the following. Your answer should be fully simplified and written as a mixed number where appropriate: 4 2/7 − 2 5/14
[2 marks]
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11. Q3(c): Calculate the following. Your answer should be fully simplified and written as a mixed number where appropriate: 2 2/9 × 4 1/5
[2 marks]
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12. Q3(d): Calculate the following. Your answer should be fully simplified and written as a mixed number where appropriate: 1 3/8 ÷ 4 2/5
[2 marks]
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13. Q4(a): Write down the prime factorisation of 60.
[2 marks]
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14. Q4(b): List all of the factors of 60, in ascending order.
[2 marks]
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15. Q5(a): Hotdogs come in packs of 10 and buns come in packs of 6; each bun holds one hotdog. What is the smallest number of packs of each you would need to buy if you didn't want any left-over hotdogs or buns? Give packs of hotdogs and packs of buns.
[2 marks]
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16. Q5(b): A group of 20 boys and 24 girls are going to be split into even teams. Each team must contain the same number of boys and girls. What is the maximum number of teams which can be made in this way?
[3 marks]
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17. Q6(a): If a = 4, b = 3 and c = −5, find the value of: a + bc
[1 mark]
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18. Q6(b): If a = 4, b = 3 and c = −5, find the value of: ab²
[1 mark]
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19. Q6(c): If a = 4, b = 3 and c = −5, find the value of: 2(a + b) − 2c
[2 marks]
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20. Q7(a): Fully simplify the following algebraic expression: 4a + 2b − a + 6b
[1 mark]
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21. Q7(b): Fully simplify the following algebraic expression: 2x + 4x + 6 − x − 12
[1 mark]
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22. Q7(c): Fully simplify the following algebraic expression: 3x² + 2x + y − 4x
[1 mark]
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23. Q7(d): Fully simplify the following algebraic expression: 7x × 2xy
[1 mark]
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24. Q8(a): Solve the following equation, leaving your answer as an improper fraction where necessary: 5x − 8 = 27
[1 mark]
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25. Q8(b): Solve the following equation, leaving your answer as an improper fraction where necessary: 3x/5 + 4 = 6
[2 marks]
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26. Q8(c): Solve the following equation, leaving your answer as an improper fraction where necessary: 4(3x − 5) = 10
[2 marks]
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27. Q8(d): Solve the following equation, leaving your answer as an improper fraction where necessary: 8 − 2x = 10x − 4
[2 marks]
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28. Q8(e): Solve the following equation, leaving your answer as an improper fraction where necessary: 15 − 4x = 1
[1 mark]
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29. Q8(f): Solve the following equation, leaving your answer as an improper fraction where necessary: 3x + 1/5 = (1/2)x − 3
[2 marks]
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30. Q9(a): I think of a number, subtract seven, then treble the result; I now have 27. What was the number I thought of? You must form and solve an equation.
[3 marks]
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31. Q9(b): John has twice as many marbles as Kelly. Beth has five fewer marbles than Kelly. Between the three of them they have a total of 27 marbles. How many marbles does John have? You must form and solve an equation.
[3 marks]
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32. Q10(a): A square, two equilateral triangles, and one other regular polygon are placed together as shown in an incomplete diagram (refer to original PDF for figure). What is the interior angle of an equilateral triangle?
[1 mark]
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33. Q10(b): A square, two equilateral triangles, and one other regular polygon are placed together at a point (refer to original PDF for figure). Calculate the interior angle of the incomplete regular polygon. You should give an angle reason to justify your answer.
[2 marks]
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34. Q10(c): Calculate the number of sides that the incomplete regular polygon has. (Its interior angle is the value found in part (b).)
[2 marks]
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35. Q11: Godfrey has a four-digit combination lock which uses the digits 1-9. He writes down some clues: the mean of the digits is 4.75; the range of the digits is 8; two of the digits are prime numbers; if the digits are put in ascending order, a < b < c < d, then the correct order is a, c, b, d. Find Godfrey's combination.