Sevenoaks School — 13+ Maths Entrance Exam 2022 (Interactive)

Q1(a)(i): Find the next three terms: 8, 11, 14, 17, 20, ...

Q2(a)(ii): Find the next three terms: 4, 7, 12, 19, 28, ...

Q3(b): A sequence starts 1, 4, 9, 16, 25, .... Find the 20th number in this sequence.

Q4(c): Find a formula for the nth term of the sequence which starts 7, 9, 11, 13, 15, ....

Q5(d)(i): A sequence where each term is the sum of the two terms before it. The 4th to 8th numbers are 4, 7, 11, 18, 29. Find the 10th number.

Q6(d)(ii): Using the same sequence (each term = sum of two before it, 4th to 8th terms are 4, 7, 11, 18, 29), find the first number.

Q7(2a)(i): Simplify: 5x + 2x − 3x

Q8(2a)(ii): Simplify: 3ab + 2a² + 4ba − 2a²

Q9(2a)(iii): Simplify: 5x − (2x + 1)

Q10(2b)(i): If p = 5, q = 2 and r = −3, find: 2p + q

Q11(2b)(ii): If p = 5, q = 2 and r = −3, find: pq − r

Q12(2b)(iii): If p = 5, q = 2 and r = −3, find: (r² + p) ÷ q

Q13(2c): If a − b = 5, find the value of 3a − 3b.

Q14(2d)(i): Freddie has five times as many sweets as Marcus. If Marcus has x sweets, write down an expression for how many sweets Freddie has.

Q15(2d)(ii): Freddie (who has 5x sweets) gives six sweets to Marcus (who has x sweets). How many sweets does Freddie have now? (Write an expression in terms of x)

Q16(2d)(iii): After Freddie gives 6 sweets to Marcus, Freddie has 5x − 6 sweets and Marcus has x + 6 sweets. Freddie now has three times as many as Marcus. How many sweets did Marcus start with?

Q17(3a)(i): For the list of numbers: 8, 5, 6, 8, 9, 6, 4, 8, find the mean.

Q18(3a)(ii): For the list of numbers: 8, 5, 6, 8, 9, 6, 4, 8, find the range.

Q19(3b): Six boys and four girls take a test. The boys get a mean score of 71 and the girls get a mean score of 74. Find the mean of all ten children.

Q20(3c): I think of four whole numbers. The mode is 12. The median is 10. The range is 5. Find the four numbers.

Q21(4a)(i): Simplify: m² × m⁵

Q22(4a)(ii): Simplify: q⁷ ÷ q⁴

Q23(4a)(iii): Simplify: (x⁴)³

Q24(4b): 16³ = 4096. Use this fact to find the 12th root of 4096 (i.e. ¹²√4096).

Q25(4c): Which of these numbers are multiples of 12? (12 = 2² × 3) A) 2⁴ × 3 × 7⁴ × 11 B) 2 × 3⁵ × 5² × 7⁴ × 11² C) 2⁶ × 5³ × 7⁵ × 11³ D) 2 × 3² × 5⁴ × 7⁶ × 11³

Q26(5a)(i): Calculate: 34 − 15

Q27(5a)(ii): Calculate: 23 × 910

Q28(5a)(iii): Calculate: 2¾ + 1⅔

Q29(5b): Show that 1¼ × 45 = 1. What is the value of 1¼ × 45?

Q30(5c): The price of a diamond ring is increased by 25%. The following week it is reduced back to its previous price. By what percentage was it reduced?

Q31(5d): Write down the value of: 78 × 67 × 56 × 45 × 34 × 23 × 12

Q32(5e): Tim and Alanna have to mark some exam papers. Tim alone would take 12 hours. Alanna alone would take 6 hours. How long will it take them working together?

Q33(6a)(i): In a triangle, the two base angles are 70° and 50°. Find angle a at the apex.

Q34(6a)(ii): Three lines meet at a point. On one side of a straight line, the consecutive angles are b, 80°, and c. On the other side, the angle opposite to b is 30°. Using vertically opposite angles, find b.

Q35(6a)(ii cont.): Using the same diagram, angles b, 80° and c are on one side of a straight line (so they sum to 180°). Given b = 30°, find c.

Q36(6a)(iii): Two parallel lines are cut by a transversal. The angle between the transversal and the lower parallel line is 36°. Find angle d (the alternate angle at the upper parallel line).

Q37(6b): Find the area of a trapezium with parallel sides 8 cm (top) and 12 cm (bottom) and height 6 cm.

Q38(6c perimeter): An L-shaped figure has outer dimensions: bottom = 12 cm, right side = 10 cm, top section = 5 cm wide. The step creates a lower-left section 4 cm tall, with a 3 cm horizontal step. Find the perimeter.

Q39(6c area): For the same L-shaped figure (bottom 12 cm, right side 10 cm, top section 5 cm wide, lower portion 4 cm tall), find the area.

Q40(6d): A square and an equilateral triangle have the same perimeter. They are joined along one side to form an irregular pentagon. Find the ratio of the perimeter of the pentagon to the perimeter of the square.