Sevenoaks School — 13+ Maths Exam Paper 2021

Questions in this paper

1. Question 1short answer · 1 mark

   Q1: Work out the value of 3/8 of 24.

2. Question 2short answer · 2 marks

   Q2: Simplify 8x − 4x² − 5x − 4x².

3. Question 3short answer · 1 mark

   Q3(a): Simplify a⁶ ÷ a³.

4. Question 4short answer · 2 marks

   Q3(b): Simplify 2x⁴y² × 5y³.

5. Question 5short answer · 3 marks

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

6. Question 6short answer · 2 marks

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

7. Question 7short answer · 1 mark

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

8. Question 8short answer · 1 mark

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

9. Question 9short answer · 1 mark

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

10. Question 10short answer · 1 mark

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

11. Question 11short answer · 2 marks

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

12. Question 12short answer · 2 marks

    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?

13. Question 13short answer · 1 mark

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

14. Question 14short answer · 2 marks

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

15. Question 15short answer · 5 marks

    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.

16. Question 16short answer · 3 marks

    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, [?], 2/5. Row 2 has [?], 2, [?]. Row 3 has [?], 8/5, 1/2. 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.)

17. Question 17short answer · 3 marks

    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?

18. Question 18short answer · 3 marks

    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.

19. Question 19short answer · 2 marks

    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.

20. Question 20short answer · 3 marks

    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?

21. Question 21short answer · 2 marks

    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 trian…

22. Question 22short answer · 2 marks

    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.)

23. Question 23short answer · 3 marks

    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?

24. Question 24short answer · 2 marks

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

25. Question 25short answer · 1 mark

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

26. Question 26short answer · 3 marks

    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.

27. Question 27short answer · 3 marks

    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.)

28. Question 28short answer · 3 marks

    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.

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