Benenden School — 13+ Maths Scholarship 2022

Questions in this paper

1. Question 1short answer · 2 marks

   Q1(a): Given a = 9, b = -14 and c = 20, find the value of a - b.

2. Question 2short answer · 3 marks

   Q1(b): Given a = 9, b = -14 and c = 20, find the value of (2a + b) × c.

3. Question 3short answer · 3 marks

   Q1(c): Given a = 9, b = -14 and c = 20, find the value of 6c - (ab + 6).

4. Question 4short answer · 6 marks

   Q2: Write each of the following in standard form and then place them in order of size, smallest to largest: 0.0705, 7.08, 79.3, 0.007008, 560900. Give your answer as the numbers in order separated by commas.

5. Question 5short answer · 3 marks

   Q3(a): Work out 9/11 - 2/5 × 3/4. Give your answer as a fraction.

6. Question 6short answer · 4 marks

   Q3(b): Work out 3 1/4 ÷ 2 3/5. Give your answer as a fraction or mixed number.

7. Question 7short answer · 3 marks

   Q4(a): Simplify 8 - 3(2 + 5x).

8. Question 8short answer · 4 marks

   Q4(b): Simplify t × tu⁴v³ ÷ uv.

9. Question 9short answer · 3 marks

   Q5(a): Mrs Smith has been allocated 250 seats to take the 6th Form at her school to a show. Because she has bought so many tickets she has been given a 15% discount. The normal price of each ticket is £15. How much did she pay in total for the tickets?

10. Question 10short answer · 2 marks

    Q5(b): 8% of the 250 tickets are given to the staff members accompanying the 6th Form. How many staff members get tickets?

11. Question 11short answer · 3 marks

    Q5(c): 7/10 of the students who go are girls. How many girls go to the show?

12. Question 12short answer · 2 marks

    Q6: Rob hammers seven nails into a piece of wood. The nails are 1.5 cm apart and are in a straight line. How many centimetres apart are the first and last nails?

13. Question 13short answer · 2 marks

    Q7(a): Two parallel lines are cut by two transversals forming a trapezium shape. The angle above the top-left intersection is 115° and the angle to the right of the top-right intersection is 83°. Four angles a, b, c, d are marked: c at the top-left (below the line), b at the top-right (left of the transversal), d at the bottom-left, and a at the bottom-right (refer to original PDF for figure). …

14. Question 14short answer · 2 marks

    Q7(b): In the same diagram with two parallel lines cut by two transversals, what is the value of angle b (in degrees)? (refer to original PDF for figure)

15. Question 15short answer · 2 marks

    Q7(c): In the same diagram with two parallel lines cut by two transversals, what is the value of angle c (in degrees)? (refer to original PDF for figure)

16. Question 16short answer · 2 marks

    Q7(d): In the same diagram with two parallel lines cut by two transversals, what is the value of angle d (in degrees)? (refer to original PDF for figure)

17. Question 17short answer · 3 marks

    Q8(a): Write down the first four terms of the sequence whose nth term is 5n - 2. Give your answer as four numbers separated by commas.

18. Question 18short answer · 3 marks

    Q8(b): Write down the first four terms of the sequence whose nth term is 2/n. Give your answer as four numbers separated by commas.

19. Question 19short answer · 2 marks

    Q9(a): Kelly has a bag of sweets containing 15 raspberry creams, 18 chocolates, 22 mints and 25 pear drops. She takes a sweet at random. What is the probability that she takes a mint? Give your answer as a fraction.

20. Question 20short answer · 1 mark

    Q9(b): Kelly has a bag of sweets containing 15 raspberry creams, 18 chocolates, 22 mints and 25 pear drops. She takes a sweet at random. What is the probability that she takes a fruity sweet? Give your answer as a fraction.

21. Question 21short answer · 1 mark

    Q9(c): Kelly has a bag of sweets containing 15 raspberry creams, 18 chocolates, 22 mints and 25 pear drops. She takes a sweet at random. What is the probability that she takes a toffee? Give your answer as a number.

22. Question 22short answer · 2 marks

    Q9(d): Last year, Kelly had 120 days of school. If the probability that Kelly is late to school is 0.6, how many days would you expect her to have been late last year?

23. Question 23short answer · 2 marks

    Q10(a): Grandfather is 63 years and 8 months old. Father is 38 years and 4 months old. Mother is 35 years and 10 months old. Tilly is 12 years and 6 months old. How old was Father when Tilly was born? Give your answer in years and months.

24. Question 24short answer · 3 marks

    Q10(b): Grandfather is 63 years and 8 months old. Father is 38 years and 4 months old. How old was Grandfather when Father turned 10? Give your answer in years and months.

25. Question 25short answer · 3 marks

    Q10(c): Mother is 35 years and 10 months old. Tilly is 12 years and 6 months old. How old will Mother be when Tilly turns 21? Give your answer in years and months.

26. Question 26short answer · 5 marks

    Q11: The diagram shows a regular octagon with two of its sides extended to complete an arrow-head shape. What is angle x at the point of the arrow-head? (refer to original PDF for figure). Give your answer in degrees.

27. Question 27short answer · 3 marks

    Q12(a): Solve for y: 6y - 2 - 3(y - 4) = 13.

28. Question 28short answer · 3 marks

    Q12(b): Meg has w pounds and Faz has 6 pounds less than Meg. Together they have £30. How much money does Meg have?

29. Question 29short answer · 1 mark

    Q13(a): A square is divided into six triangular regions A, B, C, D, E, F by its diagonals and an additional line (refer to original PDF for figure). Write down the ratio B : A in its simplest form.

30. Question 30short answer · 1 mark

    Q13(b): Using the same square divided into regions A-F (refer to original PDF for figure), write down the ratio C : B in its simplest form.

31. Question 31short answer · 1 mark

    Q13(c): Using the same square divided into regions A-F (refer to original PDF for figure), write down the ratio E : A + B in its simplest form.

32. Question 32short answer · 1 mark

    Q13(d): Using the same square divided into regions A-F (refer to original PDF for figure), write down the ratio E : C + D in its simplest form.

33. Question 33short answer · 1 mark

    Q13(e): Using the same square divided into regions A-F (refer to original PDF for figure), write down the ratio C : whole square in its simplest form.

34. Question 34short answer · 5 marks

    Q14: The lateness of 12 buses is recorded (in minutes): 5, 6, 7, 8, 8, 10, 10, 10, 11, 12, 13, 14. The lateness of 12 trains is also recorded. The range in lateness of the trains is 14 minutes and the mean lateness is 5 minutes. Work out the mean and range for the buses and decide whether the buses or the trains are more reliable, giving your reasons. Give your answer as: mean, range, and which…

35. Question 35short answer · 2 marks

    Q15(a): The diagram shows a sketch of the straight line with equation y = 2x + 6. Point A is where the line crosses the y-axis (refer to original PDF for figure). Give the coordinates of point A.

36. Question 36short answer · 2 marks

    Q15(b): The diagram shows a sketch of the straight line with equation y = 2x + 6. Point B is where the line crosses the x-axis (refer to original PDF for figure). Give the coordinates of point B.

37. Question 37short answer · 1 mark

    Q15(c): The equation of the line is y = 2x + 6. What is the gradient of AB?

38. Question 38short answer · 4 marks

    Q16: A square is divided into five congruent (equal) rectangles stacked horizontally (refer to original PDF for figure). The perimeter of each rectangle is 72 cm. What is the perimeter of the square?

39. Question 39short answer · 4 marks

    Q17: Find the values of p and q if 2p + 3q = 12 and 5p + 4q = 23. Give your answer as p, q.

Frequently asked questions