Benenden School — 13+ Maths Scholarship 2020

Questions in this paper

1. Question 1short answer · 1 mark

   Q1(a): Becky and Jo deliver advertising leaflets for a firm. They are given leaflets in the ratio 7 : 5 and are paid accordingly. One week, Jo earns £35. How much does Becky earn?

2. Question 2short answer · 1 mark

   Q1(b): Becky and Jo deliver advertising leaflets for a firm. They are given leaflets in the ratio 7 : 5 and are paid accordingly. The next week, Becky earns £126. How much does Jo earn?

3. Question 3short answer · 3 marks

   Q1(c): Becky and Jo deliver advertising leaflets for a firm. They are given leaflets in the ratio 7 : 5 and are paid accordingly. The third week, their total earnings are £312. How much does each earn? Give your answer as 'Becky £___, Jo £___'.

4. Question 4short answer · 1 mark

   Q2(Vanilla): Maria asked her class which flavour of ice cream each liked best. The responses were: Vanilla 12, Strawberry 6, Chocolate 5, Other 7. Maria decided to represent these results in a pie chart. What angle would she need to draw for the Vanilla sector?

5. Question 5short answer · 1 mark

   Q2(Strawberry): Maria asked her class which flavour of ice cream each liked best. The responses were: Vanilla 12, Strawberry 6, Chocolate 5, Other 7. Maria decided to represent these results in a pie chart. What angle would she need to draw for the Strawberry sector?

6. Question 6short answer · 1 mark

   Q2(Chocolate): Maria asked her class which flavour of ice cream each liked best. The responses were: Vanilla 12, Strawberry 6, Chocolate 5, Other 7. Maria decided to represent these results in a pie chart. What angle would she need to draw for the Chocolate sector?

7. Question 7short answer · 1 mark

   Q2(Other): Maria asked her class which flavour of ice cream each liked best. The responses were: Vanilla 12, Strawberry 6, Chocolate 5, Other 7. Maria decided to represent these results in a pie chart. What angle would she need to draw for the Other sector?

8. Question 8short answer · 2 marks

   Q3: The mean of six numbers is 5. The numbers are: 2, 3, 7, 8, 6, ?. What is the missing number?

9. Question 9short answer · 4 marks

   Q4(a): Calculate 6 4/7 − 2 1/3. Give your answer as a mixed number in simplest form.

10. Question 10short answer · 3 marks

    Q4(b): Calculate 4 ÷ 7/9. Give your answer as a fraction or mixed number in simplest form.

11. Question 11short answer · 3 marks

    Q5(a): Solve the equation 4(p − 13) = 37 − 6p.

12. Question 12short answer · 3 marks

    Q5(b): Solve the equation (9q − 11)/4 = 2q.

13. Question 13short answer · 1 mark

    Q6(a): Find the value of 8² − √25.

14. Question 14short answer · 2 marks

    Q6(b): Find the perimeter of a square whose area is 121 cm². Give your answer in cm.

15. Question 15short answer · 2 marks

    Q6(c): Find the square root of 90, to the nearest whole number.

16. Question 16short answer · 1 mark

    Q7(a): In the diagram, two pairs of parallel lines intersect. The angle of 142° is marked at one intersection. Find angle a. The diagram shows a parallelogram formed by two pairs of parallel lines (indicated by arrows and tick marks). Angle a and 142° are at the same vertex on a straight line. (Refer to original PDF for figure.)

17. Question 17short answer · 1 mark

    Q7(b): In the diagram, two pairs of parallel lines intersect. The angle of 142° is marked at one intersection. Find angle b. The diagram shows a parallelogram formed by two pairs of parallel lines (indicated by arrows and tick marks). Angle b is at the lower intersection. (Refer to original PDF for figure.)

18. Question 18short answer · 1 mark

    Q7(c): In the diagram, two pairs of parallel lines intersect. The angle of 142° is marked at one intersection. Find angle c. The diagram shows a parallelogram formed by two pairs of parallel lines (indicated by arrows and tick marks). Angle c is at the right intersection of the parallelogram. (Refer to original PDF for figure.)

19. Question 19short answer · 1 mark

    Q7(d): In the diagram, two pairs of parallel lines intersect. The angle of 142° is marked at one intersection. Find angle d. The diagram shows a parallelogram formed by two pairs of parallel lines (indicated by arrows and tick marks). Angle d is at the lower intersection, adjacent to angle b. (Refer to original PDF for figure.)

20. Question 20short answer · 2 marks

    Q8(a): Add signs (+, −, ×, ÷) and brackets to the following statement to make it true: 3 ☐ 4 ☐ 5 = −17. Write the complete expression.

21. Question 21short answer · 2 marks

    Q8(b): Add signs (+, −, ×, ÷) and brackets to the following statement to make it true: 9 ☐ 2 ☐ 7 ☐ 4² = 2. Write the complete expression.

22. Question 22short answer · 2 marks

    Q9(a): Expand and simplify a(pq − a).

23. Question 23short answer · 3 marks

    Q9(b): Expand and simplify 8(6s − 5t) − (2s + t).

24. Question 24short answer · 3 marks

    Q9(c): Expand and simplify (9 − 2v)(7v + 5).

25. Question 25short answer · 2 marks

    Q10(a): List all the factors of 60.

26. Question 26short answer · 2 marks

    Q10(b): Find the Highest Common Factor (HCF) of 96 and 60.

27. Question 27short answer · 2 marks

    Q11(a): Look at the following pattern sequence of connected diamond/bow-tie shapes made from triangles, crosses (intersection points), and short lines. Pattern 1 has 1 shape, Pattern 2 has 2 connected shapes, and so on. (Refer to original PDF for figure.) Describe the 5th pattern in the sequence. How many triangles are in the 5th pattern?

28. Question 28short answer · 2 marks

    Q11(b): Look at the pattern sequence of connected diamond/bow-tie shapes. (Refer to original PDF for figure.) How many triangles are there in the 10th pattern?

29. Question 29short answer · 2 marks

    Q11(c): Look at the pattern sequence of connected diamond/bow-tie shapes. (Refer to original PDF for figure.) How many short lines connecting two crosses will there be in the 10th pattern?

30. Question 30short answer · 2 marks

    Q11(d): Look at the pattern sequence of connected diamond/bow-tie shapes. (Refer to original PDF for figure.) How many crosses will there be in the 10th pattern?

31. Question 31short answer · 3 marks

    Q12(a): If x = 1.2, y = 7 and z = −4, find the value of xy − z.

32. Question 32short answer · 3 marks

    Q12(b): If x = 1.2, y = 7 and z = −4, find the value of z² + 6x.

33. Question 33short answer · 2 marks

    Q13(a): 48% of the members of a swimming club are male. What fraction of the club are female? Write this fraction in its lowest terms.

34. Question 34short answer · 2 marks

    Q13(b): Bella scored 56 out of 80 in a Maths test. What was her score as a percentage?

35. Question 35short answer · 4 marks

    Q13(c): A bookshop owner took a box of 24 books from the delivery van to the storeroom. On the way he tripped, dropping the box. 6 books fell out and were damaged. He had to sell these 6 at a 15% loss. He had been intending to sell the whole box of 24 for a total of £288. How much did he lose?

36. Question 36short answer · 2 marks

    Q14(a): The equation y = x − 2 can be written in different ways. Which of the following are correct? (i) y − x = 2, (ii) x = 2 + y, (iii) y + 2 = −x, (iv) x = y − 2, (v) x − y − 2 = 0. List all the correct options by their Roman numerals.

37. Question 37short answer · 3 marks

    Q14(b): On a coordinate grid, the line y = x − 2 passes through several points. What are the coordinates where this line crosses the x-axis and y-axis? Give your answer as '(x-intercept), (y-intercept)'.

38. Question 38short answer · 3 marks

    Q15: The table shows the times Hannah was at work during a particular week. Monday: 09:00–17:05, Tuesday: 08:55–16:10, Wednesday: 08:15–16:00, Thursday: 09:10–17:00, Friday: 09:15–16:30. Which day did Hannah work for the longest time?

39. Question 39short answer · 5 marks

    Q16: Solve the simultaneous equations: 3x + 2y = 5 and 7x + 3y = 5. Give your answer as 'x = ___, y = ___'.

40. Question 40short answer · 4 marks

    Q17: In 2005, Sarah was three times as old as her daughter Louise. In 2000, their ages totalled 50. How old was Louise in 2005?

41. Question 41short answer · 2 marks

    Q18(a): In a school there were 100 children in Year 8. A survey found: Boys left-handed 9, Boys right-handed 40, Girls left-handed 7, Girls right-handed 44. A teacher randomly picked a child for a task. What was the probability that the child was a girl? Give your answer as a fraction.

42. Question 42short answer · 2 marks

    Q18(b): In a school there were 100 children in Year 8. A survey found: Boys left-handed 9, Boys right-handed 40, Girls left-handed 7, Girls right-handed 44. A teacher randomly picked a child for a task. What was the probability that the child was a left-handed boy? Give your answer as a fraction.

43. Question 43short answer · 2 marks

    Q18(c): In a school there were 100 children in Year 8. A survey found: Boys left-handed 9, Boys right-handed 40, Girls left-handed 7, Girls right-handed 44. A teacher randomly picked a child for a task. What was the probability that the child was not a right-handed girl? Give your answer as a fraction in its lowest terms.

44. Question 44short answer · 3 marks

    Q19(a): Howgood Primary School has two swimming pools. The pool area forms an L-shape: Pool A is in the upper section (the left column is 11m tall and 5m wide), and Pool B is in the lower-right section (3m tall and 5m wide). A cement path 2m wide surrounds both pools at all points. Calculate the outer perimeter of the whole pool complex (including the path). Give your answer in metres. (Refer t…

45. Question 45short answer · 3 marks

    Q19(b): Howgood Primary School has two swimming pools. The pool area forms an L-shape: Pool A is in the upper section (the left column is 11m tall and 5m wide), and Pool B is in the lower-right section (3m tall and 5m wide). A cement path 2m wide surrounds both pools at all points. Calculate the total area of the path, all around the pool. Give your answer in m². (Refer to original PDF for figu…

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