Time allowed: 60 minutesTotal marks: 72Questions: 38
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): Peter bought three presents for his friends which cost £12.97, £9.85 and £17.23. Quentin bought two presents costing £25.64 and £13.59. Who spent the most in total, and by how much?
[3 marks]
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2. Q1(b): A box contains 37 chocolates. How many chocolates are there in 23 of these boxes?
[2 marks]
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3. Q1(c): Apples are sold at a price of £4.27 per kilogram. Some apples are selected and weighed and put in a bag. If the bag of apples weighs 0.35 kilograms, how much will it cost?
[3 marks]
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4. Q1(d): Thirty seven identical coins weigh 20.35 grams. What does one coin weigh?
[2 marks]
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5. Q2(a): Work out the following, obeying the correct order of operations: 1 - 0 + (-1)
[1 mark]
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6. Q2(b): Work out the following, obeying the correct order of operations: 0 x (-7)
[1 mark]
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7. Q2(c): Work out the following, obeying the correct order of operations: 9 + 1 x 0
[1 mark]
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8. Q2(d): Work out the following, obeying the correct order of operations: 5 + 0 / 1
[1 mark]
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9. Q2(e): Work out the following, obeying the correct order of operations: -1 x 3 + 5 x (-3)
[1 mark]
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10. Q2(f): Work out the following, obeying the correct order of operations: 5 - 5 - 5 / 5
[1 mark]
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11. Q2(g): Work out the following, obeying the correct order of operations: 3 - (3 / 3 + 3)
[1 mark]
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12. Q2(h): Work out the following, obeying the correct order of operations: 56 / 2 / 4 x 3
[1 mark]
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13. Q2(i): Work out the following, obeying the correct order of operations: 2 / 5 - 4 / 10
[1 mark]
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14. Q3(a): Where possible, fully simplify the following algebraic expression: 3x - 2x
[1 mark]
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15. Q3(b): Where possible, fully simplify the following algebraic expression: x + x
[1 mark]
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16. Q3(c): Where possible, fully simplify the following algebraic expression: x + 5x - 7 - 3x - 9
[1 mark]
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17. Q3(d): Where possible, fully simplify the following algebraic expression: 7x * x * 4x
[1 mark]
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18. Q4(a): Write down, in ascending order, all factors of 36.
[2 marks]
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19. Q4(b): Write down, in ascending order, all factors of 54.
[2 marks]
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20. Q5(a): Write down the prime factorisation of 72.
[2 marks]
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21. Q5(b): Write down the prime factorisation of 360.
[2 marks]
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22. Q6(a): Calculate the following: 1/4 x 3/5
[2 marks]
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23. Q6(b): Calculate the following: 5/6 - 5/4
[2 marks]
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24. Q6(c): Calculate the following: (5/6) / (5/4)
[2 marks]
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25. Q6(d): Calculate the following: (40/21) x (35/8)
[2 marks]
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26. Q7: A solid wooden cube is painted blue on the outside. The cube is then cut into eight smaller cubes of equal size. What fraction of the total surface area of these new cubes is blue?
[4 marks]
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27. Q8(a): Solve the following equation, leaving your answer as an improper fraction where necessary: 5x - 13 = 32
[2 marks]
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28. Q8(b): Solve the following equation, leaving your answer as an improper fraction where necessary: x/2 - 3 = 1/2
[2 marks]
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29. Q8(c): Solve the following equation, leaving your answer as an improper fraction where necessary: 2 + (2x - 3)/4 = 7
[3 marks]
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30. Q8(d): Solve the following equation, leaving your answer as an improper fraction where necessary: 3x - 6 = 12 - 9x
[2 marks]
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31. Q8(e): Solve the following equation, leaving your answer as an improper fraction where necessary: 6(13x - 5) = 48
[2 marks]
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32. Q8(f): Solve the following equation, leaving your answer as an improper fraction where necessary: 4x - 3/4 = (1/3)x + 5
[3 marks]
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33. Q9(a): If a = 4, b = -1 and c = -2, find the value of: abc
[1 mark]
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34. Q9(b): If a = 4, b = -1 and c = -2, find the value of: bc^2
[1 mark]
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35. Q9(c): If a = 4, b = -1 and c = -2, find the value of: 3a - 2b - 4c
[2 marks]
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36. Q10(a): Six times a number is ten less than eight times the number. Find the number. (Define an unknown, form an equation and solve it algebraically.)
[3 marks]
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37. Q10(b): John thought of a number. He added twenty-four and then divided by three. The result was the same as when multiplying the original number by three and then adding four. What number did John think of?
[3 marks]
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38. Q11: In a 7-digit numerical code each group of four adjacent digits adds to 16 and each group of five adjacent digits adds to 19. What is the sum of all seven digits?