Winchester College — 13+ Maths Exam Paper 2022

Questions in this paper

1. Question 1short answer · 2 marks

   Q1(a): Find 3/7 of 42.

2. Question 2short answer · 2 marks

   Q1(b): Find 30% of 150.

3. Question 3short answer · 1 mark

   Q2(a): 24, written as the product of its prime factors, is 2^3 x 3. Write 18 as the product of its prime factors.

4. Question 4short answer · 1 mark

   Q2(b): What is the highest common factor of 18 and 24?

5. Question 5short answer · 1 mark

   Q2(c): 60 = 2^2 x 3 x 5 and 75 = 3 x 5^2. What is the lowest common multiple of 60 and 75?

6. Question 6short answer · 1 mark

   Q3(a): Calculate 11 x 121.

7. Question 7short answer · 1 mark

   Q3(b): Calculate 5432 - 433.

8. Question 8short answer · 1 mark

   Q3(c): Calculate 5432 - (5432 - 19).

9. Question 9short answer · 1 mark

   Q3(d): Calculate (sqrt(169))^2.

10. Question 10short answer · 1 mark

    Q3(e): Calculate (133 + 134 + 135) / 3.

11. Question 11short answer · 1 mark

    Q3(f): Calculate 2 x 678 x 5 + 9.

12. Question 12short answer · 2 marks

    Q3(g): Calculate sqrt(640000).

13. Question 13short answer · 2 marks

    Q3(h): Calculate 6 / 0.4.

14. Question 14short answer · 1 mark

    Q4(a): Find in the simplest form: 1 1/13 - 4/13.

15. Question 15short answer · 2 marks

    Q4(b): Find in the simplest form: (39/7) x (14/33) x (11/13).

16. Question 16short answer · 3 marks

    Q4(c): Find in the simplest form: (9/17) / (45/51).

17. Question 17short answer · 3 marks

    Q4(d): Find in the simplest form: (1/2 + 1/4) / (1/3 + 1/6).

18. Question 18short answer · 2 marks

    Q5(a): Find 48% of 50% of 400.

19. Question 19short answer · 2 marks

    Q5(b): Evaluate the cube root of (9 x 33 x 121).

20. Question 20short answer · 2 marks

    Q5(c): Evaluate sqrt(27/48).

21. Question 21short answer · 3 marks

    Q5(d): Evaluate (-2)^17 / ((-2)^4 x (-2)^8).

22. Question 22short answer · 1 mark

    Q6(a): Solve 3x + 7 = 40.

23. Question 23short answer · 2 marks

    Q6(b): Solve 56 / (2x + 1) = -8.

24. Question 24short answer · 3 marks

    Q6(c): Solve sqrt((3 + 2x/5)^3) = 8.

25. Question 25short answer · 2 marks

    Q6(d): a and b are integers. b is 80% more than a. Find and simplify the ratio a : b.

26. Question 26short answer · 1 mark

    Q7(a): Given a = 5, b = -3 and c = 17, find the value of 14a / (b + c).

27. Question 27short answer · 1 mark

    Q7(b): Given a = 5, b = -3 and c = 17, find the value of a^3 / 25.

28. Question 28short answer · 1 mark

    Q7(c): Given a = 5, b = -3 and c = 17, find the value of (100a + 100b + 100c) / (a + b + c).

29. Question 29short answer · 2 marks

    Q7(d): Given a = 5, b = -3 and c = 17, find the value of sqrt(2a - 3b + 6c).

30. Question 30short answer · 2 marks

    Q7(e): Given a = 5, b = -3 and c = 17, find the value of (c^2 - a^2) / (c - a).

31. Question 31short answer · 2 marks

    Q7(f): Given a = 5, b = -3 and c = 17, find the value of (a^2 + ab + b^2)(a - b).

32. Question 32short answer · 3 marks

    Q8(a): In the diagram, a triangle has angle 36 degrees at the top-left vertex. Three lengths in the triangle are marked as equal (with tick marks), creating two sub-triangles. Find the angle a at the right vertex. (Refer to original PDF for figure.)

33. Question 33short answer · 3 marks

    Q8(b): The diagram shows four lines, two of which are parallel (marked with arrows). Angles of 29 degrees and 97 degrees are shown at intersections. Find the angle b at the lower-left intersection. (Refer to original PDF for figure.)

34. Question 34short answer · 3 marks

    Q9(a): Order from smallest to largest: 4sqrt(3), sqrt(50), 7, 3sqrt(5), 2sqrt(13). (Hint: try squaring the numbers.)

35. Question 35short answer · 2 marks

    Q9(b): Order from smallest to largest: 295 x 305, 290 x 310, 299 x 301.

36. Question 36short answer · 3 marks

    Q9(c): Order from smallest to largest: 1/2, 4/9, 6/13, 10/21, 5/11, 8/17.

37. Question 37short answer · 2 marks

    Q10(a): Each of the small circles has radius 2. The innermost circle is just touching the six which surround it, and each of those circles are just touching each of their neighbours and the large circle. Determine the circumference of the large circle. Leave pi in your answer. (Refer to original PDF for figure.)

38. Question 38short answer · 3 marks

    Q10(b): Each of the small circles has radius 2. The innermost circle is just touching the six which surround it, and each of those circles are just touching each of their neighbours and the large circle. Determine the shaded area. Leave pi in your answer. (Refer to original PDF for figure.)

39. Question 39short answer · 1 mark

    Q11(a): Find the median of the square numbers from 1 to 169 (inclusive).

40. Question 40short answer · 2 marks

    Q11(b): Four friends are aged 12, 12, 15 and 17. They are by themselves in a room. Four more people, all the same age, enter the room and the mean age increases by 3. How old are the newcomers?

41. Question 41short answer · 3 marks

    Q11(c): Three sisters are aged 8, 9 and 14. When their friend Kelly is with them the mean of their ages is equal to the median. How old could Kelly be? (There is more than one answer.) Give all possible answers.

42. Question 42short answer · 1 mark

    Q12(a): Harry is training for a running race. A training session consists of a 1 minute sprint followed by a 30 second jog repeated 10 times. He sprints twice as fast as he jogs. How long is the entire training session?

43. Question 43short answer · 2 marks

    Q12(b): In the training session Harry travels exactly 6 km. For what fraction of the distance was he sprinting?

44. Question 44short answer · 3 marks

    Q12(c): Exactly how long has Harry been travelling for when he has travelled 2 km?

45. Question 45short answer · 2 marks

    Q13(a): Chloe writes a list, in order, of all whole numbers that are written using no digits other than 1s and 5s. The list begins: 1, 5, 11, 15, 51, ... How many numbers in the list are less than 1000?

46. Question 46short answer · 1 mark

    Q13(b): Chloe writes a list, in order, of all whole numbers that use no digits other than 1s and 5s. Which number in this list comes directly before 115511?

47. Question 47short answer · 2 marks

    Q13(c): Chloe writes a list, in order, of all whole numbers that use no digits other than 1s and 5s. What is the 32nd number in the list?

48. Question 48short answer · 3 marks

    Q13(d): Chloe writes a list, in order, of all whole numbers that use no digits other than 1s and 5s. What is the average of all the numbers in the list that are more than 100,000 but less than 1,000,000?

49. Question 49short answer · 2 marks

    Q14(a): The diagram shows two right-angled triangles. One has a right angle at the bottom-right with base 10 and vertical side 5. The other has a right angle at the top, with a vertical side of 2. The two triangles share a common hypotenuse. Find the value of x, where x is a side of the upper triangle. (Refer to original PDF for figure.)

50. Question 50short answer · 2 marks

    Q14(b): The diagram shows two right-angled triangles. One has a right angle at the bottom-right with base 19 and vertical side 12 (split into 4 at top and 8 at bottom). The sloped line y connects two vertices. Find the value of y. (Refer to original PDF for figure.)

51. Question 51short answer · 5 marks

    Q14(c): ABCDEFGH is a box in the shape of a cuboid. A thin rod of length 21 cm just fits inside the box with one end at A and the other at G (the space diagonal). If the same rod has one end at A and passes through C, exactly 1 cm sticks out of the box. If the rod passes through H, exactly 2 cm sticks out. If the rod passes through F, exactly z cm sticks out. Find z. (Refer to original PDF for …

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