Oundle School — 13+ Maths Scholarship 2020

Questions in this paper

1. Question 1short answer · 1 mark

   Q1(a): Work out 74 + 19

2. Question 2short answer · 1 mark

   Q1(b): Work out -13 - (-17)

3. Question 3short answer · 1 mark

   Q1(c): Work out 8 × 2/3

4. Question 4short answer · 1 mark

   Q1(d): Work out 8 ÷ 2/3

5. Question 5short answer · 1 mark

   Q1(e): Work out 2000 × 0.0005

6. Question 6short answer · 1 mark

   Q1(f): Work out 0.4 ÷ 0.08

7. Question 7short answer · 2 marks

   Q1(g): Work out 1 3/4 + 1 1/3

8. Question 8short answer · 2 marks

   Q1(h): Work out 12 - 4 ÷ 1/2 + 6 ÷ (1 - 4)

9. Question 9short answer · 1 mark

   Q1(i): Work out 10% of 30% of 3000

10. Question 10short answer · 1 mark

    Q1(j): Work out the cube root of 8, i.e. ∛8

11. Question 11short answer · 2 marks

    Q1(k): Work out ∛8000000 (the cube root of 8,000,000)

12. Question 12short answer · 1 mark

    Q1(l): Work out √(6² + 8²)

13. Question 13short answer · 1 mark

    Q1(m): Work out 3 × 2⁰

14. Question 14short answer · 1 mark

    Q1(n): Work out (3 × 2)⁰

15. Question 15short answer · 2 marks

    Q2(a): If d = 2, e = -3 and f = -1/4, find the value of d - e + f

16. Question 16short answer · 2 marks

    Q2(b): If d = 2, e = -3 and f = -1/4, find the value of (d × e) / f

17. Question 17short answer · 2 marks

    Q2(c): If d = 2, e = -3 and f = -1/4, find the value of 2def

18. Question 18short answer · 2 marks

    Q2(d): If d = 2, e = -3 and f = -1/4, find the value of d² / f²

19. Question 19short answer · 2 marks

    Q2(e): If d = 2, e = -3 and f = -1/4, find the value of (ef)^d

20. Question 20short answer · 1 mark

    Q3(a): Insert the correct sign (+, -, × or ÷) to make the statement true: 2/3 ☐ 1.5 = 4/9

21. Question 21short answer · 1 mark

    Q3(b): Insert the correct sign (+, -, × or ÷) to make the statement true: 3/4 ☐ 3 = 2 1/4

22. Question 22short answer · 2 marks

    Q3(c): Insert the correct signs (+, -, × or ÷) in the three boxes to make the statement true: 3/8 ☐ 3/4 ☐ (1/12 ☐ 1/4) = 1/6

23. Question 23short answer · 1 mark

    Q4(a): Find the next two terms in the sequence: 8, 2, -4, -10, ...

24. Question 24short answer · 1 mark

    Q4(b): Find the next two terms in the sequence: 20, 10, 5, 2.5, ...

25. Question 25short answer · 2 marks

    Q4(c): Find the next two terms in the sequence: 1, 4, 9, 16, ...

26. Question 26short answer · 2 marks

    Q4(d): Find the next two terms in the sequence: -1, 2, 1, 3, 4, 7, ...

27. Question 27short answer · 2 marks

    Q4(e): Find the next two terms in the sequence: 2/7, 3/14, 5/21, 7/28, ...

28. Question 28short answer · 2 marks

    Q5(a): Find the fraction that is halfway between 1/5 and 1/6. The numerator and denominator of your answer must both be whole numbers.

29. Question 29short answer · 2 marks

    Q5(b): Find the fraction that is halfway between 1/a and 1/b. Give your answer as a single fraction in terms of a and b.

30. Question 30short answer · 1 mark

    Q6(a): Remove brackets and simplify: 2(5 - x)

31. Question 31short answer · 2 marks

    Q6(b): Remove brackets and simplify: 3x(x + 3) - (1 - x)

32. Question 32short answer · 2 marks

    Q6(c): Remove brackets and simplify: (4x + 1)²

33. Question 33short answer · 1 mark

    Q7(a): Factorise fully: 8y - 16

34. Question 34short answer · 1 mark

    Q7(b): Factorise fully: xy² - 2xy

35. Question 35short answer · 2 marks

    Q7(c): Factorise fully: 8y - 16 + xy² - 2xy

36. Question 36short answer · 2 marks

    Q8(a): Solve for x: 6x + 1 = -2

37. Question 37short answer · 2 marks

    Q8(b): Solve for x: 5 - 2(x + 3) = 4 - x

38. Question 38short answer · 2 marks

    Q8(c): Solve for x: 4 - x/3 = 7/2

39. Question 39short answer · 2 marks

    Q8(d): Solve for x: (9x + 2)/(9x - 2) = 2

40. Question 40short answer · 3 marks

    Q9: John takes 40 minutes to walk to school and then to run home. When he runs both ways, it takes him 24 minutes. He has one constant speed whenever he walks, and another constant speed whenever he runs. How long would it take him to walk both ways?

41. Question 41short answer · 1 mark

    Q10(a): You are told that x² - y² = (x + y)(x - y). Use this result (and NOT long multiplication) to find the value of 45² - 15²

42. Question 42short answer · 1 mark

    Q10(b): You are told that x² - y² = (x + y)(x - y). Use this result (and NOT long multiplication) to find the value of 736² - 264²

43. Question 43short answer · 1 mark

    Q10(c): You are told that x² - y² = (x + y)(x - y). Use this result (and NOT long multiplication) to find the value of 1007 × 993

44. Question 44short answer · 3 marks

    Q11: Asif is shopping for a new outfit for a special occasion. He needs a shirt, a pair of trousers and a pair of shoes. If he doesn't buy the shirt, he can get the other items for £115. If he doesn't buy the trousers, he can get the other items for £100. If he doesn't buy the shoes, he can get the other items for £75. How much will he have to pay for all of them?

45. Question 45short answer · 4 marks

    Q12: In a bag, there are 180 marbles, of which n are red and the others green. A marble is to be drawn randomly from the bag. If 10 more red marbles were added to the bag, the probability of drawing a red would be doubled. Write down and solve an equation in n to work out how many red marbles were originally in the bag.

46. Question 46short answer · 3 marks

    Q13: A solid cuboid has dimensions 3 cm by 5 cm by 6 cm. A spider at point S (bottom corner of the 6 cm edge on the front face) needs to crawl on the outside of the cuboid to reach a fly at point F (top corner diagonally opposite, at the back of the top face). What is the shortest distance the spider can travel to reach the fly? (Refer to original PDF for figure.)

47. Question 47short answer · 4 marks

    Q14: A rectangle ABCD has a diagonal line from a point on the top edge (1 cm from corner A along the top) to corner C. The length along the bottom from D is split as 1 cm and 4 cm, making DC = 5 cm. The shaded region consists of a vertical strip on the left of width 1 cm (full height) and the triangle below the diagonal in the remaining portion. Express the shaded area as a fraction of the whol…

48. Question 48short answer · 5 marks

    Q15: A rectangular piece of card ABCD has AB = 12 cm and AD = 16 cm, where A is the bottom-left corner, B is top-left, C is top-right, and D is bottom-right. If the card is folded so that C is on top of A, how long is the crease? (Refer to original PDF for figure.)

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