Benenden School — 13+ Maths Scholarship Paper 2020 (Interactive)

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?

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?

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 £___'.

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?

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?

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?

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?

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

Q4(a): Calculate 6 47 − 2 13. Give your answer as a mixed number in simplest form.

Q4(b): Calculate 4 ÷ 79. Give your answer as a fraction or mixed number in simplest form.

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

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

Q6(a): Find the value of 8² − √25.

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

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

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.)

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.)

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.)

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.)

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

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

Q9(a): Expand and simplify a(pq − a).

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

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

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

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

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?

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?

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?

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?

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

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

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.

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

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?

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.

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)'.

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?

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

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?

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.

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.

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.

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 to original PDF for figure.)

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 figure.)