plumiAreas between curves and lines: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.08.4 Areas between curves and lines, 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 Areas between curves and lines, as a list
- June 2025, Paper 1, Q10 (12 marks): ex e x 2 1 10 The graph of y can be transformed to the graph of y - by a stretch parallel to the = = x-axis followed by a translation. (a) (i) State the scale f
- June 2024, Paper 1, Q12 (11 marks): In this question you must show detailed reasoning. y 2 x O 2 2 The diagram shows the curve with parametric equations x , y 2 t 3 t for t 0 . = = + H 4 t2 ( 1 )
- June 2023, Paper 3, Q5 (9 marks): A mathematics department is designing a new emblem to place on the walls outside its classrooms. The design for the emblem is shown in the diagram below. y x O
- November 2021, Paper 1, Q11 (12 marks): 4 x y 4 2 2 2 2 11 (a) Use the substitution u x + to show that 3 d x ( x 6 ) x 3 c . [5] = = - + + 3 2 x 3 + (b) In this question you must show detailed reasoni
- November 2021, Paper 3, Q8 (11 marks): y L R P M O x 2 x The diagram shows the curve M with equation y xe - . = (a) Show that M has a point of inflection at the point P where x = . 1 [5] The line L p
- November 2021, AS Paper 2, Q8 (11 marks): y l ,16 ^ h x O 6 The diagram shows the curve y 1 x and the line l, which is the normal to the curve at the = - + x point (1, 6). (a) Determine the equation of
- November 2020, Paper 3, Q5 (12 marks): y P R C x O 1 6 The diagram shows the curve C with parametric equations 3 - , where t 3 2 t x , y t e 2 0 . = = t The maximum point on C is denoted by P. (a) De
- June 2018, Paper 2, Q7 (7 marks): The diagram shows a part ABC of the curve y = 3 - 2x2, together with its reflections in the lines y = x, 7 y = -x and y = 0. y B A C x Find the area of the shad
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