plumiNumerical solution of equations: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP1.3 Numerical solution of equations, 2019–2025, with its mark scheme and examiner’s report.
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All 12 questions on Numerical solution of equations, as a list
- June 2025, Further Pure 1 (FP1), Q3 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) f (x) = x 2 + 5 – 8 5x Gi
- January 2025, Further Pure 1 (FP1), Q2 (9 marks): f(x) = x x x x x 2 3 7 4 0 − − > (a) Show that the equation f(x) = 0 has a root α in the interval [0.3, 0.4] (b) Determine f′(x). (c) Using x0 = 0.3 as a first
- June 2024, Further Pure 1 (FP1), Q3 (7 marks): f(x) = x x x 3 5 4 7 x 0 The equation f(x) = 0 has a root α in the interval [0.25, 1] (a) Use linear interpolation once on the interval [0.25, 1] to determine
- January 2024, Further Pure 1 (FP1), Q6 (8 marks): (i) f ( ) cos x x x x 4 5 0 > (a) Show that the equation f(x) = 0 has a root α in the interval [2.5, 3.5] (b) Use linear interpolation once on the interval [2.5
- June 2023, Further Pure 1 (FP1), Q7 (11 marks): f ( ) x x x 3 2 3 (a) Show that the equation f (x) = 0 has a root, α, in the interval [1, 2] (b) Starting with the interval [1, 2], use interval bisection twice
- January 2023, Further Pure 1 (FP1), Q4 (8 marks): f ( ) x x x x 1 1 8 2 7 0 4 7 The equation f(x) = 0 has a single root, α, that lies in the interval 0 15 0 25 . , . (a) (i) Determine ′f ( ) x (ii) Explain why
- June 2022, Further Pure 1 (FP1), Q2 (9 marks): f(x) = 10 – 2x – 1 2 1 3 x x − x > 0 (a) Show that the equation f(x) = 0 has a root α in the interval [0.4, 0.5] (b) Determine f′(x). (c) Using x0 = 0.5 as a fi
- January 2022, Further Pure 1 (FP1), Q8 (10 marks): f(x) = 2x 2 3 1 2 1 3 5 5 2 x x x ≠ 5 3 The table below shows values of f(x) for some values of x, with values of f(x) given to 4 decimal places where appropria
- October 2021, Further Pure 1 (FP1), Q2 (9 marks): f(x) = 7 x x x − − 1 2 5 3 3 x > 0 (a) Show that the equation f(x) = 0 has a root, α, in the interval [2.8, 2.9] (b) (i) Find f′(x). (ii) Hence, using x0 = 2.8
- June 2021, Further Pure 1 (FP1), Q1 (10 marks): (i) f (x) = x3 + 4x − 6 (a) Show that the equation f (x) = 0 has a root α in the interval [1, 1.5] (b) Taking 1.5 as a first approximation, apply the Newton Rap
- January 2021, Further Pure 1 (FP1), Q1 (5 marks): (a) Show that the equation 4x − 2 sin x − 1 = 0, where x is in radians, has a root α in the interval [0.2, 0.6] (b) Starting with the interval [0.2, 0.6], use i
- October 2020, Further Pure 1 (FP1), Q1 (7 marks): f(x) = x3 – 10 4 2 x x x − x > 0 (a) Show that the equation f(x) = 0 has a root α in the interval [1.4, 1.5] (b) Determine fʹ(x). (c) Using x0 = 1.4 as a first
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