Oundle School — 13+ Maths Exam Paper 2022

Questions in this paper

1. Question 1short answer · 1 mark

   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?

2. Question 2short answer · 1 mark

   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?

3. Question 3short answer · 2 marks

   Q1(c): If gold sells for £43 per gram, how much is the smallest nugget (0.87g) worth?

4. Question 4short answer · 2 marks

   Q1(d): An ounce is approximately 28 grams. Convert the weight of the 1.54g nugget into ounces.

5. Question 5short answer · 1 mark

   Q2(a): Work out the following, obeying the correct order of operations: 3 + 5 × 8 − 6

6. Question 6short answer · 1 mark

   Q2(b): Work out the following, obeying the correct order of operations: 10 − (20 − 8) ÷ 2

7. Question 7short answer · 1 mark

   Q2(c): Work out the following, obeying the correct order of operations: 24 ÷ (16 − 4 × 2)

8. Question 8short answer · 1 mark

   Q2(d): Work out the following, obeying the correct order of operations: 100 − 80 − (60 − 40)

9. Question 9short answer · 2 marks

   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

10. Question 10short answer · 2 marks

    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

11. Question 11short answer · 2 marks

    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

12. Question 12short answer · 2 marks

    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

13. Question 13short answer · 2 marks

    Q4(a): Write down the prime factorisation of 60.

14. Question 14short answer · 2 marks

    Q4(b): List all of the factors of 60, in ascending order.

15. Question 15short answer · 2 marks

    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.

16. Question 16short answer · 3 marks

    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?

17. Question 17short answer · 1 mark

    Q6(a): If a = 4, b = 3 and c = −5, find the value of: a + bc

18. Question 18short answer · 1 mark

    Q6(b): If a = 4, b = 3 and c = −5, find the value of: ab²

19. Question 19short answer · 2 marks

    Q6(c): If a = 4, b = 3 and c = −5, find the value of: 2(a + b) − 2c

20. Question 20short answer · 1 mark

    Q7(a): Fully simplify the following algebraic expression: 4a + 2b − a + 6b

21. Question 21short answer · 1 mark

    Q7(b): Fully simplify the following algebraic expression: 2x + 4x + 6 − x − 12

22. Question 22short answer · 1 mark

    Q7(c): Fully simplify the following algebraic expression: 3x² + 2x + y − 4x

23. Question 23short answer · 1 mark

    Q7(d): Fully simplify the following algebraic expression: 7x × 2xy

24. Question 24short answer · 1 mark

    Q8(a): Solve the following equation, leaving your answer as an improper fraction where necessary: 5x − 8 = 27

25. Question 25short answer · 2 marks

    Q8(b): Solve the following equation, leaving your answer as an improper fraction where necessary: 3x/5 + 4 = 6

26. Question 26short answer · 2 marks

    Q8(c): Solve the following equation, leaving your answer as an improper fraction where necessary: 4(3x − 5) = 10

27. Question 27short answer · 2 marks

    Q8(d): Solve the following equation, leaving your answer as an improper fraction where necessary: 8 − 2x = 10x − 4

28. Question 28short answer · 1 mark

    Q8(e): Solve the following equation, leaving your answer as an improper fraction where necessary: 15 − 4x = 1

29. Question 29short answer · 2 marks

    Q8(f): Solve the following equation, leaving your answer as an improper fraction where necessary: 3x + 1/5 = (1/2)x − 3

30. Question 30short answer · 3 marks

    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.

31. Question 31short answer · 3 marks

    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.

32. Question 32short answer · 1 mark

    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?

33. Question 33short answer · 2 marks

    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.

34. Question 34short answer · 2 marks

    Q10(c): Calculate the number of sides that the incomplete regular polygon has. (Its interior angle is the value found in part (b).)

35. Question 35short answer · 4 marks

    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.

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