Sevenoaks School — 13+ Maths Entrance Exam 2021 (Interactive)

Q1: Work out the value of 38 of 24.

Q2: Simplify 8x − 4x² − 5x − 4x².

Q3(a): Simplify a⁶ ÷ a³.

Q3(b): Simplify 2x⁴y² × 5y³.

Q4(a): Expand and simplify 9mn − n(3 − 7m).

Q5(a): By rounding each number to 2 significant figures, estimate the answer to 200 / (16.3 × 25.2).

Q5(b): Is your estimate in part (a) larger or smaller than the actual answer? You must justify your decision.

Q6(a): Complete the missing number in the function diagram: 8 → [−5] → [×7] → ?

Q6(b): Complete the missing number in the function diagram: 12 → [÷ ?] → [×9] → 27. What is the missing number in the ÷ box?

Q6(c): Complete the missing number in the function diagram: ? → [÷2] → [+2] → 16. What is the missing input number?

Q7: Given that p = −2 and q = 25, find the value of p²q − (5p)².

Q8(a): The cost of petrol is £1.20 per litre. Alice buys £48 worth of petrol. How many litres of petrol does she buy?

Q8(b): Alice can drive 8.5km for every litre of petrol. How many km can she drive using the petrol she bought?

Q9: A jar contains 60 jelly beans. If 35% of the jelly beans are removed, how many remain in the jar?

Q10: In a mathematics competition, the winner won £100 more than twice the amount won by the runner-up. The total winnings were £2350. Let the amount won by the runner-up be r. Form an equation in r and solve it to find how much the winner received.

Q11: A 3×3 grid contains numbers where all rows, columns and diagonals have the same product. Some cells are given: Row 1 has 8, [?], 25. Row 2 has [?], 2, [?]. Row 3 has [?], 85, 12. Complete the grid by finding the four missing numbers. Give your answer as four values in order: Row 1 middle, Row 2 left, Row 2 right, Row 3 left. (Refer to original PDF for figure.)

Q12: A sports club has 65 men and 35 women as members. A new activity has just begun and 50 new members have joined. Given that the number of men is now 60% of the total members, how many of the 50 new members were women?

Q13(a): A rectangle is 50cm long and 40cm wide. Its length is extended by 12% and its width is reduced by 15%. Does the perimeter of the rectangle change? Justify your answer.

Q13(b): A rectangle is 50cm long and 40cm wide. Its length is extended by 12% and its width is reduced by 15%. Does the area of the rectangle change? Justify your answer.

Q14: Tasha scored an average of 78% across three of her five exams this year. She wants to score 85% minimum this year. What is the lowest score she can gain in her fourth exam to achieve her desired goal?

Q15: In a star (pentagram) formed by five intersecting lines with vertices A (top), B (upper-left), C (lower-left), D (lower-right), E (upper-right), the angles at B, C, D, and E are 30°, 35°, 36°, and 31° respectively. The angle at vertex A is split into x and y. T and S are intersection points on line BE near vertex A. Find the value of x, where x is the angle at intersection point T in triangle ATS. (Refer to original PDF for figure.)

Q15: In the same star diagram, find the value of y, which is the angle at vertex A (the star tip angle at A). (Refer to original PDF for figure.)

Q16: Nadia visits a restaurant every five days. She visited the restaurant on Sunday 1 January 2017. What is the date of her next Sunday visit?

Q17(a): A sequence is formed by 1 × 2², 2 × 3², 3 × 4², ... Find the next two terms of the sequence.

Q17(b): For the sequence 1 × 2², 2 × 3², 3 × 4², ... work out the 10th term of the sequence.

Q18: The prices of two items P and Q in a shop are in the ratio 4:5. When the price of P is increased by £12 and the price of Q is reduced by £6, then the items have the same price. Find the original price of P.

Q19: A measuring cylinder with diameter 5cm is partially filled with water. When a stone is placed in the cylinder, the water level rises by 3cm. Find the volume of the stone in terms of π. (Refer to original PDF for figure.)

Q20: Given the values w = 2^129 × 3^81 × 5^128, x = 2^127 × 3^81 × 5^128, y = 2^126 × 3^82 × 5^128, z = 2^125 × 3^82 × 5^129, write these numbers in ascending order.