plumiLocating roots by change of sign: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.09.1 Locating roots by change of sign, 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 8 questions on Locating roots by change of sign, as a list
- June 2025, Paper 3, Q5 (14 marks): (a) Use the substitution u cos x to show that = 1 cos x x + y d ln ( 1 cos x ) c . [4] = - + sin x Fig. 1 y x a O 1 cos x + Fig. 1 shows part of the curve y . =
- June 2024, Paper 2, Q4 (10 marks): - . 1 3 x 4 The diagram shows part of the graph of y xe = y 0.5 x 0 0.5 1 1.5 2 (a) Use the sign change method to determine, correct to 2 decimal places, the ro
- June 2023, Paper 1, Q10 (9 marks): f(x) x 0 1 2 3 4 ex The diagram shows part of the curve ( )x + . The equation ( )x f 2 f 0 has a positive root = = 2 4 x 1 - a close to x = 0.3. (a) Explain why
- June 2022, Paper 3, Q5 (14 marks): In this question you must show detailed reasoning. y x O P x 2 3 - The diagram shows the curve with equation y . The tangent to the curve at the point P = 2 4 x
- November 2021, Paper 2, Q2 (2 marks): The diagram shows part of the graph of y f( ) x , where f( )x is a cubic polynomial in x. = y x 0 0.5 1 Explain why one of the roots of the equation f( )x 0 can
- November 2021, Paper 3, Q6 (6 marks): 6 The equation 6 arcsin ( 2 x 1 ) x 0 has exactly one real root. - - = (a) Show by calculation that the root lies between 0.5 and 0.6. [2] In order to find the
- November 2020, Paper 3, Q4 (11 marks): 4 A curve has equation y 2 ln ( k 3 x ) x 3 x , where k is a positive constant. = - + - (a) Given that the curve has a point of inflection where x = 1, show tha
- June 2019, Paper 1, Q10 (11 marks): A i rad O 6cm B The diagram shows a sector AOB of a circle with centre O and radius 6 cm. The angle AOB is i radians. The area of the segment bounded by the cho
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