Benenden School — 13+ Maths Scholarship Paper 2022 (Interactive)

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

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

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

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.

Q3(a): Work out 911 - 25 × 34. Give your answer as a fraction.

Q3(b): Work out 3 14 ÷ 2 35. Give your answer as a fraction or mixed number.

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

Q4(b): Simplify t × tu⁴v³ ÷ uv.

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?

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

Q5(c): 710 of the students who go are girls. How many girls go to the show?

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?

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). What is the value of angle a (in degrees)?

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)

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)

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)

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.

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.

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.

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.

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.

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?

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.

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.

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.

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.

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

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

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.

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.

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.

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.

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.

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 is more reliable.

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.

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.

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

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?

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