plumiPolynomials and the factor theorem: WJEC A‑Level Maths questions
WJEC A-Level Maths past-paper questions on 2.6 Polynomials and the factor theorem, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 9 questions on Polynomials and the factor theorem, as a list
- Summer 2025, Unit 3, Q8 (5 marks): 3 2 x 5 x 7 x 29 x 30 By algebraic division, or otherwise, simplify the expression . [5] 8. 3( 5)( 3)( 2) x x x
- Summer 2025, AS Unit 1, Q6 (16 marks): 2 f x ( ) = x 3 x 6 x . 8 6. The function f is defined by f x ( ) = 0 (a) Use an algebraic method to solve the equation . Show all your working. [6] y f
- Summer 2024, Unit 3, Q10 (14 marks): 10. The function f has domain 4, and is defined by 2 3 x 1 x f x . x 1 2 x 2 x 3 2 x f x (a) Show that . [4] x 3 Determine the
- Summer 2023, Unit 3, Q8 (7 marks): 4 x 12 x 9 The function f is defined by 0 8 f x , where x 1 1. 2 2 x x – 3 5 ( ) can be written as 2 + Show that f x a) x −1 . [3] 7∫ ( ) b) Hence fi
- Summer 2023, AS Unit 1, Q4 (10 marks): Find the remainder when the polynomial 3x3 + 2x2 + x −1 is divided by 3 x 0 4 a) . [3] ( ) = 2x3 − 3x2 + ax + 6 is divisible by x + 2 ( ), where a is a re
- Summer 2022, Unit 3, Q10 (5 marks): Solve the equation 1 0 6x5 −17x4 − 5x3 + 6x2 [5] = 0 . ( ) 3x + 2
- Summer 2022, AS Unit 1, Q12 (9 marks): 2 a) Solve the equation 2x3 – x2 – 5x – 2 = 0. [6] Find all values of θ in the range 0° < θ < 180° satisfying b) cos(2θ– 51°) = 0.891. [3]
- Summer 2019, AS Unit 1, Q3 (6 marks): Use an algebraic method to solve the equation 12x3 – 29x2 + 7x + 6 = 0. 0 3 Show all your working. [6]
- Summer 2018, AS Unit 1, Q8 (5 marks): 8 Given that (x – 2) and (x + 2) are factors of the polynomial 2x3 + px2 + qx – 12, a) find the values of p and q, [4] b) determine the other factor of the poly
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