plumiFurther calculus: WJEC A‑Level Further Maths questions
Every WJEC A-Level Further Maths exam question on 4.5 Further calculus, 2018–2025, with its mark scheme and examiner’s report.
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All 15 questions on Further calculus, as a list
- Summer 2025, Unit 4, Q5 (6 marks): 5. The region R is bounded by the curve x = sinh 2y, the y-axis and the line y = 1. Find the volume of the solid generated when R is rotated through four right
- Summer 2025, Unit 4, Q7 (12 marks): 7. (a) Differentiate each of the following with respect to x, simplifying your answer where possible. cos 1 2 1 (i) y x [3] 3 sinh 4 (ii) y x x [3]
- Summer 2025, Unit 4, Q10 (18 marks): 3 2 12 5 2 6 x x x x 2 10. (a) (i) Show that can be written as . [2] 3 2 2 3 6 3 2 2 3 6 x x x x x x 3 2 2 x x 12 d x (ii) Hence, find
- Summer 2024, Unit 4, Q5 (14 marks): 5. Find each of the following integrals. 3 x (a) [8] d x 2 1 x x (b) sinh2 x [6] d x 4 2 cosh x 9cosh x
- Summer 2024, Unit 4, Q7 (12 marks): 7. (a) A curve C is defined by the equation y for 3 1 x X . X 16 6 2 x x 1 x and 3 x . 1 (i) Find the mean value of y between [4] 16 6 2 x x
- Summer 2023, Unit 4, Q8 (11 marks): 8. The function f is defined by 1 ( ) = f x . x2 + 4x + 3 (a) Find the mean value of the function f for 0 X x X 2, giving your answer correct to three decimal p
- Summer 2023, Unit 4, Q10 (8 marks): ) as sin y = 2x + 5, show that dy By writing y = sin−1 2x + 5 2 ( 10. (a) )2 . [5] dx = ( 1− 2x + 5 ( ) is valid. Deduce the range of values of x for which d dx
- Summer 2023, Unit 4, Q11 (14 marks): 11. Evaluate the integrals 0∫ (a) e2x [5] sinh xdx, −2 3 5 (b) d x [9] . 2 1 9 3 x x 2
- Summer 2022, Unit 4, Q4 (5 marks): The region R is bounded by the curve x = siny, the y-axis and the lines y = 1, y = 3. Find the 4. volume of the solid generated when R is rotated through four r
- Summer 2022, Unit 4, Q11 (15 marks): (a) Differentiate each of the following with respect to x. 11. y = e3x sin−1 x (i) ( ) y = ln cosh2 2x2 + 7x ( ) (ii) [7] Find the equations of the tangents to
- Summer 2022, Unit 4, Q14 (10 marks): 14. Evaluate the integral 6x2 + 2x +16 4∫ dx , x3 − x2 + 3x − 3 2 giving your answer correct to three decimal places. [10]
- Summer 2019, Unit 4, Q4 (16 marks): dy −1 4. (a) Given that y = cot–1x, show that . dx = [5] x2 +1 6x2 −10x − 9 (b) Express in terms of partial fractions. [5] (2x + 3)(x2 +1) 6x2 − 8x − 6 ∫ (c) He
- Summer 2019, Unit 4, Q5 (8 marks): Show that sinθ – sin3θ can be expressed in the form a cos bθ sinθ, where a, b are 5. (a) integers whose values are to be determined. [3] Find the mean value of
- Summer 2019, Unit 4, Q9 (14 marks): dy Given that y = sin–1(cosθ ), where 0 X θX π, show that , where the value of k is dθ = k 9. (a) to be determined. [4] x = π y = x3 tan−1 4x (b) Find the value
- Summer 2019, Unit 4, Q11 (9 marks): Find the area of the region enclosed by the curve y = x sinhx, the x-axis and the lines 11. (a) x = 0 and x = 1. [4] The region R is bounded by the curve y = co
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