plumiRoots of polynomials and series: WJEC A‑Level Further Maths questions
Every WJEC A-Level Further Maths exam question on 1.4 Roots of polynomials and series, 2018–2025, with its mark scheme and examiner’s report.
Paper
All papers
Exam
All years
All 13 questions on Roots of polynomials and series, as a list
- Summer 2025, AS Unit 1, Q1 (13 marks): 2 f x ( ) x 8 x 25 x 26 1. The function f is defined by . Show that f 3 2i . You must show all your working. 0 (a) [3] Solve the equation ( ) f
- Summer 2025, AS Unit 1, Q3 (10 marks): n 5 4 1 rA A for r x 2, find an expression for 3. (a) Given that , in the form r 1 r r 1 r r 2 a b c , where a, b, c are integers to be found.
- Summer 2024, AS Unit 1, Q3 (6 marks): x px q 0 has a repeated root α. 3. The quadratic equation A new quadratic equation has a repeated root 1 2 x mx m 0 and is of the form . Find the
- Summer 2024, AS Unit 1, Q5 (7 marks): 5. Given that 76 r 31 980 , r k show that there are two possible values of k. [7]
- Summer 2023, AS Unit 1, Q8 (9 marks): The roots of the cubic equation x3 + 5x2 + 2x + 8 = 0 are denoted by α, β, γ. 8. βγ, β γα, γ Determine the cubic equation whose roots are α αβ. Give your answer
- Summer 2023, AS Unit 1, Q10 (8 marks): 10. Gareth is investigating a series involving cube numbers. His series is 13 − 23 + 33 − 43 + 53 − 63 + 73 −… Gareth continues his series and ends with an odd
- Summer 2022, AS Unit 1, Q4 (7 marks): The positive integer N is such that 12 + 22 + 32 + … + N 2 = (3N – 2)2. 4. Write down and simplify an equation satisfied by N. Hence find the possible values of
- Summer 2022, AS Unit 1, Q6 (8 marks): 6. The roots of the cubic equation 2x3 + px2 – 126x + q = 0 form a geometric progression with common ratio −3. Find the possible values of p and q, giving your
- Summer 2022, AS Unit 1, Q9 (9 marks): 2 1 Ar = r +1 − r + 2 + Given that , show that Ar can be expressed 9. (a) r + 3 2 as . [2] (r +1)(r + 2)(r + 3) n (r +1)(r + 2)(r + 3) = 1 2 1 Hence, show that
- Summer 2019, AS Unit 1, Q7 (8 marks): 2m 1 3 m(am2 + bm + c) ∑ ( )2 r + 2 7. (a) Find an expression for in the form , where a, b, c are r=1 integers whose values are to be determined. [4] 20 ∑ ( )2
- Summer 2019, AS Unit 1, Q10 (9 marks): 10. The quadratic equation px2 + qx + r = 0 has roots α and β, where p, q, r are non-zero constants. (a) A cubic equation is formed with roots α, β, α + β. Find
- Summer 2018, AS Unit 1, Q3 (8 marks): 3. A cubic equation has roots α, β, γ such that α + β + γ = –9, αβ + β γ + γ α = 20, α β γ = 0. (a) Find the values of α, β, and γ. [4] (b) Find the cubic equat
- Summer 2018, AS Unit 1, Q5 (8 marks): 2 4 n −1 − 5. (a) Show that can be expressed as . [1] (n2 −1) n +1 n (an + b)(n + c) 4 ∑ (b) Hence, find an expression for in the form , (r2 −1) n(n +1) r=2 whe
Questions, mark schemes and examiner’s reports are © WJEC CBAC Ltd, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every WJEC A-Level Further Maths paper.
Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.