plumiNumerical methods: OCR A‑Level Maths questions
Every OCR A-Level Maths exam question on P.9 Numerical methods, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 Paper 3, question 5: (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 . =](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24003-jun25-05-qp.webp?v=3)
![November 2021 Paper 3, question 6: 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](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24003-nov21-06-qp.webp?v=3)
All 15 questions on Numerical methods, 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 2024, Paper 3, Q5 (13 marks): y x O M ^ h 3 2 y x x x The diagram shows the curve with equation 2 ln . The curve has a point of inflection = - at the point M. (a) (i) Show that the x-coordin
- 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 2023, Paper 3, Q7 (12 marks): 7 A car C is moving horizontally in a straight line with velocity ms v - at time t seconds, where - , of C is modelled by the equation 2 v 0 and t 0 . The accel
- June 2022, Paper 1, Q10 (12 marks): B irad O A M The diagram shows a sector OAB of a circle with centre O and radius OA. The angle AOB is i radians. M is the mid-point of OA. The ratio of areas OM
- 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 1, Q7 (9 marks): 7 The curve y ( x 2 )ln x has one stationary point which is close to x = . 1 = - 2 2 (a) Show that the x-coordinate of this stationary point satisfies the equat
- 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 1, Q7 (11 marks): Two students, Anna and Ben, are starting a revision programme. They will both revise for 30 minutes on Day 1. Anna will increase her revision time by 15 minutes
- 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
- June 2019, Paper 3, Q4 (14 marks): y P x O 1 r 2 1 The diagram shows the part of the curve y 3 x sin 2 x for which 0 x = G G . r 2 The maximum point on the curve is denoted by P. (a) Show that th
- June 2018, Paper 1, Q2 (4 marks): (i) Use the trapezium rule, with four strips each of width 0.5, to estimate the value of 2 y x 2 x e d 0 giving your answer correct to 3 significant figures. [3
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