: Edexcel past-paper questions pack
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Past-paper questions pack

Name
Class
Date set
Date due
Score/ 131

Questions are numbered; the mark schemes (the answer key) follow on separate pages so the question pages can be handed out alone. www.mathsaleveltutor.com

Edexcel AS and A-level Maths past-paper questions since June 2018 · 40 parts, 131 marks · mark schemes follow the questions · www.mathsaleveltutor.com · Questions and mark schemes © Pearson Education Ltd

1. June 2025 · AS Paper 1 · Q2(b) · 2 marks
y B C l R x A Figure 2 Figure 2 shows the line l and the curve C, which intersect at A and B. Given that 2 + 5x – 3 • C has equation y = 2x • the region R, shown shaded in Figure 2, is bounded by l and C (b) use inequalities to define R. (2)
2. June 2025 · AS Paper 1 · Q4(b) · 3 marks
The line with equation y = k, where k is a constant, cuts C at two distinct points. (b) Find the range of values for k, giving your answer in set notation. (3)
3. June 2025 · Paper 1 · Q7(a) · 2 marks
7. y –1 x –75 C Figure 1 Figure 1 shows a sketch of a curve C with equation y = f(x), where f(x) is a quartic expression in x. The curve • has maximum turning points at (–1, 0) and (5, 0) • crosses the y‑axis at (0, –75) • has a minimum turning point at x = 2 (a) Find the set of values of x for which f′(x) 0 writing your answer in set notation. (2)
4. June 2025 · AS Paper 1 · Q7(b) · 3 marks
Given that the company made an annual profit of more than £200 000 (b) find, according to the model, the highest possible selling price for the chair. You must show your working clearly. (3)
5. June 2025 · Paper 2 · Q8(c) · 4 marks
The equation f (x) = k, where k is a constant, has 4 distinct solutions. (c) Using algebra and showing all stages of your working, find the range of values of k. Give the answer using set notation. (Solutions relying on calculator technology are not acceptable.) (4)
6. June 2025 · Paper 2 · Q11(c) · 2 marks
Use the model given in part (b) to answer parts (c), (d) and (e). Given that the company wishes to make a profit on sales of the toy, (c) find the range of possible selling prices of the toy. (2)
7. June 2025 · Paper 3 (Statistics) · Q6(c) · 5 marks
When n = 20, a random value g of R is taken and the quadratic equation in x x 2 + gx + 3g = 5 is formed. (c) Find the exact probability that the equation has no real roots. (5)
8. June 2024 · Paper 1 · Q5(b) · 3 marks
(b) Hence, using algebra, find the values of x for which f is decreasing. You must show each step in your working. (3)
9. June 2024 · Paper 2 · Q14(b) · 5 marks
A different circle C2 • has centre with coordinates (–6, –8) • has radius k, where k is a constant Given that C1 and C2 intersect at 2 distinct points, (b) find the range of values of k, writing your answer in set notation. (5)
10. June 2023 · AS Paper 1 · Q1(b) · 4 marks
(b) Hence find the range of values of x for which y is decreasing. (4)
11. June 2023 · Paper 1 · Q3(b) · 2 marks
(b) Find the smallest value of a for which → > OA → OB (2)
12. June 2023 · AS Paper 1 · Q4(b) · 3 marks
(b) Hence or otherwise, solve x (3)
13. June 2023 · AS Paper 1 · Q6(b) · 3 marks
Given that C does not cut or touch the x-axis, (b) find the range of possible values for k. (3)
14. June 2023 · AS Paper 1 · Q8 · 5 marks
8. y C (10, 80) l R x Figure 3 Figure 3 shows a sketch of a curve C and a straight line l. Given that . / • C has equation y f x where f (x) is a quadratic expression in x • C cuts the x-axis at 0 and 6 • l cuts the y-axis at 60 and intersects C at the point 10, 80 use inequalities to define the region R shown shaded in Figure 3. (5)
15. June 2023 · Paper 1 · Q10(b) · 6 marks
The line with equation y = 2x – 1 intersects C at 2 distinct points. (b) Find the range of possible values of k. (6)
16. June 2023 · Paper 2 · Q12(c) · 5 marks
(c) Find the range of values of t for which NA > NB giving your answer in set notation. (5)
17. June 2022 · Paper 1 · Q6(b) · 2 marks
The line with equation y = k, where k is a constant, intersects C at only one point. (b) Find the set of values of k, giving your answer in set notation. (2)
18. June 2022 · AS Paper 1 · Q7(c) · 3 marks
The line l has equation y = k where k is a constant. Given that C and l intersect at 3 distinct points, (c) find the range of values for k, writing your answer in set notation. Solutions relying on calculator technology are not acceptable. (3)
19. June 2022 · Paper 1 · Q7(ii) · 2 marks
(ii) Given that x and y are integers such that • x < 0 • (x + y)2 < 9x2 + y2 show that y > 4x (2)
20. June 2022 · Paper 2 · Q12(b) · 3 marks
Given that the curve with equation y = f(x) has at least one stationary point, (b) find the range of possible values of k. (3)
21. June 2022 · Paper 2 · Q16(c) · 5 marks
The straight line with equation y = - 1 2 x + k where k is a constant intersects C at two distinct points. (c) Find the range of possible values for k. (5)
22. Oct 2021 · AS Paper 1 · Q1 · 3 marks
1. In this question you should show all stages of your working. Solutions relying on calculator technology are not acceptable. Using algebra, solve the inequality 2 – x > 20 x writing your answer in set notation. (3)
23. Oct 2021 · Paper 2 · Q11(b) · 4 marks
(b) Find, in terms of k, the set of values of x for which k – | 2x – 3k | > x – k giving your answer in set notation. (4)
24. Oct 2020 · Paper 1 · Q7 · 5 marks
7. y C R (-2, 13) l x Figure 1 Figure 1 shows a sketch of a curve C with equation y = f (x) and a straight line l. The curve C meets l at the points (-2, 13) and (0, 25) as shown. The shaded region R is bounded by C and l as shown in Figure 1. Given that ● f (x) is a quadratic function in x ● (-2, 13) is the minimum turning point of y = f (x) use inequalities to define R. (5)
25. Oct 2020 · AS Paper 1 · Q11(ii) · 4 marks
(ii) A different circle C2 has equation x2 + y2 – 8x + 12y + k = 0 where k is a constant. Given that C2 lies entirely in the 4th quadrant, find the range of possible values for k. (4)
26. Oct 2020 · Paper 2 · Q11(c) · 3 marks
A line l has equation y = ax, where a is a constant. Given that l intersects y = 2 | x + 4 | - 5 at least once, (c) find the range of possible values of a, writing your answer in set notation. (3)
27. Oct 2020 · Paper 2 · Q13(c) · 2 marks
(c) Find the range of values of a for which g (a) > 0 (2)
28. June 2019 · Paper 1 · Q3(b) · 1 marks
y (b) Hence deduce the range of values for x for which d x < 0 d (1)
29. June 2019 · AS Paper 1 · Q5(b) · 2 marks
(b) Hence find the exact range of values of x for which the curve is increasing. (2)
30. June 2019 · Paper 1 · Q9(b) · 2 marks
(b) Write down the full restriction on the value of b, explaining the reason for this restriction. (2)
31. June 2019 · Paper 1 · Q10(ii) · 2 marks
(ii) “Given x  <, the value of mu 3x – 28 mu is greater than or equal to the value of (x – 9).” State, giving a reason, if the above statement is always true, sometimes true or never true. (2)
32. June 2019 · Paper 2 · Q6(b) · 4 marks
(b) Find all values of x for which g(௘[࣠) < 28 (4)
33. June 2019 · Paper 2 · Q7(d) · 2 marks
Assuming that each bar of soap is sold on the day it is made, (d) find the least number of bars of soap that must be made on any given day for the factory to make a profit that day. (2)
34. June 2018 · AS Paper 1 · Q2(ii) · 2 marks
(ii) “If I add 3 to a number and square the sum, the result is greater than the square of the original number.” State, giving a reason, if the above statement is always true, sometimes true or never true. (2)
35. June 2018 · AS Paper 1 · Q6(b) · 3 marks
Given that the company made an annual profit of more than £80 000 (b) find, according to the model, the least possible selling price for the toy. (3)
36. June 2018 · AS Paper 1 · Q9(c) · 3 marks
y y = g(x) x Figure 2 Figure 2 shows a sketch of part of the curve with equation y = g(x) (c) Use your answer to part (b), and the sketch, to deduce the values of x for which (i) g(x) - 0 (ii) g(2x) = 0 (3)
37. June 2018 · AS Paper 1 · Q14(b) · 6 marks
The line with equation y = kx, where k is a constant, cuts C at two distinct points. (b) Find the range of values for k. (6)
38. June 2018 · Paper 1 · Q14(c) · 5 marks
The line with equation x + y = k, where k is a constant, intersects C at two distinct points. (c) State the range of values of k, writing your answer in set notation. (5)
39. June 2018 · AS Paper 2 · Q5(c) · 3 marks
The random variable Y = 12 X (c) Find P(Y – X - 4) (3)
40. June 2018 · Paper 3 · Q9(d) · 3 marks
The rope will break if the tension in it exceeds 5 Mg. (d) Explain how this will restrict the possible positions of P. You must justify your answer carefully. (3)

Mark schemes

Each mark scheme shows the whole question; the parts on this topic are the ones listed above.

June 2025 · AS Paper 1 · Q2
Mark scheme June 2025 Paper 1 Q2(b)
June 2025 · AS Paper 1 · Q4
Mark scheme June 2025 Paper 1 Q4(b)
June 2025 · Paper 1 · Q7
Mark scheme June 2025 Paper 1 Q7(a)
June 2025 · AS Paper 1 · Q7
Mark scheme June 2025 Paper 1 Q7(b)
June 2025 · Paper 2 · Q8
Mark scheme June 2025 Paper 2 Q8(c)
June 2025 · Paper 2 · Q11
Mark scheme June 2025 Paper 2 Q11(c)
June 2025 · Paper 3 (Statistics) · Q6
Mark scheme June 2025 Paper 3 (Statistics) Q6(c)
June 2024 · Paper 1 · Q5
Mark scheme June 2024 Paper 1 Q5(b)
June 2024 · Paper 2 · Q14
Mark scheme June 2024 Paper 2 Q14(b)
June 2023 · AS Paper 1 · Q1
Mark scheme June 2023 Paper 1 Q1(b)
June 2023 · Paper 1 · Q3
Mark scheme June 2023 Paper 1 Q3(b)
June 2023 · AS Paper 1 · Q4
Mark scheme June 2023 Paper 1 Q4(b)
June 2023 · AS Paper 1 · Q6
Mark scheme June 2023 Paper 1 Q6(b)
June 2023 · AS Paper 1 · Q8
Mark scheme June 2023 Paper 1 Q8
June 2023 · Paper 1 · Q10
Mark scheme June 2023 Paper 1 Q10(b)
June 2023 · Paper 2 · Q12
Mark scheme June 2023 Paper 2 Q12(c)
June 2022 · Paper 1 · Q6
Mark scheme June 2022 Paper 1 Q6(b)
June 2022 · AS Paper 1 · Q7
Mark scheme June 2022 Paper 1 Q7(c)
June 2022 · Paper 1 · Q7
Mark scheme June 2022 Paper 1 Q7(ii)
June 2022 · Paper 2 · Q12
Mark scheme June 2022 Paper 2 Q12(b)
June 2022 · Paper 2 · Q16
Mark scheme June 2022 Paper 2 Q16(c)
Oct 2021 · AS Paper 1 · Q1
Mark scheme Oct 2021 Paper 1 Q1
Oct 2021 · Paper 2 · Q11
Mark scheme Oct 2021 Paper 2 Q11(b)
Oct 2020 · Paper 1 · Q7
Mark scheme Oct 2020 Paper 1 Q7
Oct 2020 · AS Paper 1 · Q11
Mark scheme Oct 2020 Paper 1 Q11(ii)
Oct 2020 · Paper 2 · Q11
Mark scheme Oct 2020 Paper 2 Q11(c)
Oct 2020 · Paper 2 · Q13
Mark scheme Oct 2020 Paper 2 Q13(c)
June 2019 · Paper 1 · Q3
Mark scheme June 2019 Paper 1 Q3(b)
June 2019 · AS Paper 1 · Q5
Mark scheme June 2019 Paper 1 Q5(b)
June 2019 · Paper 1 · Q9
Mark scheme June 2019 Paper 1 Q9(b)
June 2019 · Paper 1 · Q10
Mark scheme June 2019 Paper 1 Q10(ii)
June 2019 · Paper 2 · Q6
Mark scheme June 2019 Paper 2 Q6(b)
June 2019 · Paper 2 · Q7
Mark scheme June 2019 Paper 2 Q7(d)
June 2018 · AS Paper 1 · Q2
Mark scheme June 2018 Paper 1 Q2(ii)
June 2018 · AS Paper 1 · Q6
Mark scheme June 2018 Paper 1 Q6(b)
June 2018 · AS Paper 1 · Q9
Mark scheme June 2018 Paper 1 Q9(c)
June 2018 · AS Paper 1 · Q14
Mark scheme June 2018 Paper 1 Q14(b)
June 2018 · Paper 1 · Q14
Mark scheme June 2018 Paper 1 Q14(c)
June 2018 · AS Paper 2 · Q5
Mark scheme June 2018 Paper 2 Q5(c)
June 2018 · Paper 3 · Q9
Mark scheme June 2018 Paper 3 Q9(d)