Sevenoaks School — 13+ Maths Exam Paper 2022

Questions in this paper

1. Question 1short answer · 1 mark

   Q1(a)(i): Find the next three terms: 8, 11, 14, 17, 20, ...

2. Question 2short answer · 1 mark

   Q2(a)(ii): Find the next three terms: 4, 7, 12, 19, 28, ...

3. Question 3short answer · 2 marks

   Q3(b): A sequence starts 1, 4, 9, 16, 25, .... Find the 20th number in this sequence.

4. Question 4short answer · 2 marks

   Q4(c): Find a formula for the nth term of the sequence which starts 7, 9, 11, 13, 15, ....

5. Question 5short answer · 1 mark

   Q5(d)(i): A sequence where each term is the sum of the two terms before it. The 4th to 8th numbers are 4, 7, 11, 18, 29. Find the 10th number.

6. Question 6short answer · 1 mark

   Q6(d)(ii): Using the same sequence (each term = sum of two before it, 4th to 8th terms are 4, 7, 11, 18, 29), find the first number.

7. Question 7short answer · 1 mark

   Q7(2a)(i): Simplify: 5x + 2x − 3x

8. Question 8short answer · 2 marks

   Q8(2a)(ii): Simplify: 3ab + 2a² + 4ba − 2a²

9. Question 9short answer · 2 marks

   Q9(2a)(iii): Simplify: 5x − (2x + 1)

10. Question 10short answer · 1 mark

    Q10(2b)(i): If p = 5, q = 2 and r = −3, find: 2p + q

11. Question 11short answer · 1 mark

    Q11(2b)(ii): If p = 5, q = 2 and r = −3, find: pq − r

12. Question 12short answer · 2 marks

    Q12(2b)(iii): If p = 5, q = 2 and r = −3, find: (r² + p) ÷ q

13. Question 13short answer · 1 mark

    Q13(2c): If a − b = 5, find the value of 3a − 3b.

14. Question 14short answer · 1 mark

    Q14(2d)(i): Freddie has five times as many sweets as Marcus. If Marcus has x sweets, write down an expression for how many sweets Freddie has.

15. Question 15short answer · 1 mark

    Q15(2d)(ii): Freddie (who has 5x sweets) gives six sweets to Marcus (who has x sweets). How many sweets does Freddie have now? (Write an expression in terms of x)

16. Question 16short answer · 2 marks

    Q16(2d)(iii): After Freddie gives 6 sweets to Marcus, Freddie has 5x − 6 sweets and Marcus has x + 6 sweets. Freddie now has three times as many as Marcus. How many sweets did Marcus start with?

17. Question 17short answer · 2 marks

    Q17(3a)(i): For the list of numbers: 8, 5, 6, 8, 9, 6, 4, 8, find the mean.

18. Question 18short answer · 1 mark

    Q18(3a)(ii): For the list of numbers: 8, 5, 6, 8, 9, 6, 4, 8, find the range.

19. Question 19short answer · 2 marks

    Q19(3b): Six boys and four girls take a test. The boys get a mean score of 71 and the girls get a mean score of 74. Find the mean of all ten children.

20. Question 20short answer · 2 marks

    Q20(3c): I think of four whole numbers. The mode is 12. The median is 10. The range is 5. Find the four numbers.

21. Question 21short answer · 1 mark

    Q21(4a)(i): Simplify: m² × m⁵

22. Question 22short answer · 1 mark

    Q22(4a)(ii): Simplify: q⁷ ÷ q⁴

23. Question 23short answer · 1 mark

    Q23(4a)(iii): Simplify: (x⁴)³

24. Question 24short answer · 2 marks

    Q24(4b): 16³ = 4096. Use this fact to find the 12th root of 4096 (i.e. ¹²√4096).

25. Question 25multiple choice · 2 marks

    Q25(4c): Which of these numbers are multiples of 12? (12 = 2² × 3) A) 2⁴ × 3 × 7⁴ × 11 B) 2 × 3⁵ × 5² × 7⁴ × 11² C) 2⁶ × 5³ × 7⁵ × 11³ D) 2 × 3² × 5⁴ × 7⁶ × 11³

26. Question 26short answer · 2 marks

    Q26(5a)(i): Calculate: 3/4 − 1/5

27. Question 27short answer · 2 marks

    Q27(5a)(ii): Calculate: 2/3 × 9/10

28. Question 28short answer · 2 marks

    Q28(5a)(iii): Calculate: 2¾ + 1⅔

29. Question 29short answer · 2 marks

    Q29(5b): Show that 1¼ × 4/5 = 1. What is the value of 1¼ × 4/5?

30. Question 30short answer · 1 mark

    Q30(5c): The price of a diamond ring is increased by 25%. The following week it is reduced back to its previous price. By what percentage was it reduced?

31. Question 31short answer · 1 mark

    Q31(5d): Write down the value of: 7/8 × 6/7 × 5/6 × 4/5 × 3/4 × 2/3 × 1/2

32. Question 32short answer · 2 marks

    Q32(5e): Tim and Alanna have to mark some exam papers. Tim alone would take 12 hours. Alanna alone would take 6 hours. How long will it take them working together?

33. Question 33short answer · 1 mark

    Q33(6a)(i): In a triangle, the two base angles are 70° and 50°. Find angle a at the apex.

34. Question 34short answer · 1 mark

    Q34(6a)(ii): Three lines meet at a point. On one side of a straight line, the consecutive angles are b, 80°, and c. On the other side, the angle opposite to b is 30°. Using vertically opposite angles, find b.

35. Question 35short answer · 1 mark

    Q35(6a)(ii cont.): Using the same diagram, angles b, 80° and c are on one side of a straight line (so they sum to 180°). Given b = 30°, find c.

36. Question 36short answer · 1 mark

    Q36(6a)(iii): Two parallel lines are cut by a transversal. The angle between the transversal and the lower parallel line is 36°. Find angle d (the alternate angle at the upper parallel line).

37. Question 37short answer · 2 marks

    Q37(6b): Find the area of a trapezium with parallel sides 8 cm (top) and 12 cm (bottom) and height 6 cm.

38. Question 38short answer · 2 marks

    Q38(6c perimeter): An L-shaped figure has outer dimensions: bottom = 12 cm, right side = 10 cm, top section = 5 cm wide. The step creates a lower-left section 4 cm tall, with a 3 cm horizontal step. Find the perimeter.

39. Question 39short answer · 2 marks

    Q39(6c area): For the same L-shaped figure (bottom 12 cm, right side 10 cm, top section 5 cm wide, lower portion 4 cm tall), find the area.

40. Question 40short answer · 2 marks

    Q40(6d): A square and an equilateral triangle have the same perimeter. They are joined along one side to form an irregular pentagon. Find the ratio of the perimeter of the pentagon to the perimeter of the square.

Frequently asked questions