: Edexcel past-paper questions pack
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Partial fractions

Past-paper questions pack

Name
Class
Date set
Date due
Score/ 78

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 · 17 parts, 78 marks · mark schemes follow the questions · www.mathsaleveltutor.com · Questions and mark schemes © Pearson Education Ltd

1. June 2025 · Paper 1 · Q13 · 5 marks
13. In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Show that : x x d x ( ) (5)
2. June 2025 · Paper 2 · Q7 · 4 marks
7. Given that x x x C Ax B x ∈ ℝ x ≠ –1, 3 / / x x x x find the value of each of the constants A, B, C and D. (4)
3. June 2024 · Paper 2 · Q12(a) · 2 marks
12. (a) Express / in partial fractions. V V (2)
4. June 2024 · Paper 2 · Q12(b) · 5 marks
The volume, V microlitres, of a plant cell t hours after the plant is watered is modelled by the differential equation V d / V V t d The plant cell has an initial volume of 20 microlitres. (b) Find, according to the model, the time taken, in minutes, for the volume of the plant cell to reach 24 microlitres. (5)
5. June 2023 · Paper 2 · Q10(a) · 3 marks
kx x 10. 2 where k is a positive constant f ( ) x x ( )( ) (a) Express f (x) in partial fractions in terms of k. (3)
6. June 2023 · Paper 2 · Q10(b) · 4 marks
(b) Hence find the exact value of k for which ∫ 3f ( ) d x x = - (4)
7. June 2023 · Paper 2 · Q13(c) · 5 marks
(c) Find, using algebraic integration, the exact value of ∫ 0.4 x x d (3 + x ) 0.2 giving your answer in the form a ln b + c, where a, b and c are constants to be found. (5)
8. June 2022 · Paper 2 · Q14(a) · 3 marks
14. (a) Express in partial fractions. x - x + ( )( ) (3)
9. June 2022 · Paper 2 · Q14(b) · 5 marks
When chemical A and chemical B are mixed, oxygen is produced. A scientist mixed these two chemicals and measured the total volume of oxygen produced over a period of time. 3 , t hours after the chemicals were mixed, is The total volume of oxygen produced, V m modelled by the differential equation d V V t = V 0 t k d t - t + ( )( ) where k is a constant. 3 of Given that exactly 2 hours after the chemicals were mixed, a total volume of 3 m oxygen had been produced, (b) solve the differential equation to show that t - 3 2 ( ) V = t + ( ) (5)
10. Oct 2021 · Paper 1 · Q9(a) · 4 marks
9. x + x + f(x) = 50 x ≠ -2 5 x ≠ 1 ( ) ( ) x + - x Given that f(x) can be expressed in the form A B C + + ( ) x + - x x + where A, B and C are constants (a) (i) find the value of B and the value of C (ii) show that A = 0 (4)
11. Oct 2021 · Paper 1 · Q9(b) · 7 marks
(b) (i) Use binomial expansions to show that, in ascending powers of x f(x) = p + qx + rx2 + … where p, q and r are simplified fractions to be found. (ii) Find the range of values of x for which this expansion is valid. (7)
12. Oct 2021 · Paper 2 · Q14(b) · 6 marks
Given that when the tap was opened, the depth of water in the tank was 2 m, (b) show that, according to the model, h = A + B e–kt where A, B and k are constants to be found. (6)
13. Oct 2020 · Paper 1 · Q10(b) · 6 marks
(b) Hence, using algebraic integration, show that ∫ dx = a ( ) ln ( ) x - + x - 1 3 where a is a rational constant to be found. (6)
14. Oct 2020 · Paper 2 · Q6(b) · 4 marks
(b) Hence, using algebraic integration, find the exact value of ∫ x + x - x d x + giving your answer in the form a + b ln 2 where a and b are integers to be found. (4)
15. June 2019 · Paper 1 · Q13(b) · 8 marks
y C R x Figure 4 Figure 4 shows a sketch of part of the curve C. The region R, shown shaded in Figure 4, is bounded by the curve C, the x-axis and the line with equation x = 3 (b) Show that the exact value of the area of R is a ln 2 + b ln 3, where a and b are rational constants to be found. (8)
16. June 2018 · Paper 2 · Q11(a) · 4 marks
11. + x - x B C ≡ A + + x - - x x - - x ( 3 1 )( ) ( ) ( ) (a) Find the values of the constants A, B and C. (4)
17. June 2018 · Paper 2 · Q11(b) · 3 marks
+ x - x f (x) = 1 ) x > 3 x - - x ( 3 1 )( (b) Prove that f (x) is a decreasing function. (3)

Mark schemes

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

June 2025 · Paper 1 · Q13
Mark scheme June 2025 Paper 1 Q13
June 2025 · Paper 2 · Q7
Mark scheme June 2025 Paper 2 Q7
June 2024 · Paper 2 · Q12
Mark scheme June 2024 Paper 2 Q12(b)
June 2023 · Paper 2 · Q10
Mark scheme June 2023 Paper 2 Q10(b)
June 2023 · Paper 2 · Q13
Mark scheme June 2023 Paper 2 Q13(c)
June 2022 · Paper 2 · Q14
Mark scheme June 2022 Paper 2 Q14(b)
Oct 2021 · Paper 1 · Q9
Mark scheme Oct 2021 Paper 1 Q9(b)
Oct 2021 · Paper 2 · Q14
Mark scheme Oct 2021 Paper 2 Q14(b)
Oct 2020 · Paper 1 · Q10
Mark scheme Oct 2020 Paper 1 Q10(b)
Oct 2020 · Paper 2 · Q6
Mark scheme Oct 2020 Paper 2 Q6(b)
June 2019 · Paper 1 · Q13
Mark scheme June 2019 Paper 1 Q13(b)
June 2018 · Paper 2 · Q11
Mark scheme June 2018 Paper 2 Q11(b)