plumiInequalities: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.02.5 Inequalities, 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 21 questions on Inequalities, as a list
- June 2025, Paper 2, Q1 (3 marks): In this question you must show detailed reasoning. 2 Solve the inequality x 3 x 10 . [3] + G
- June 2025, Paper 3, Q4 (8 marks): Functions f and g are defined for all real values of x by x k - and ( )x 2 ( )x x kx , where k is a constant. f g 5 = = + + 2 1 ( )x kx You are given that the e
- June 2025, AS Paper 2, Q5 (5 marks): In this question you must show detailed reasoning. G H F E ( 2 x 1 ) cm + B C ( x 2 ) cm - A D 3 cm The diagram shows the cuboid ABCDEFGH where AD = 3 cm, AF (
- June 2024, Paper 3, Q2 (5 marks): In this question you must show detailed reasoning. A O 2rad (3x + 1) cm B The diagram shows a sector AOB of a circle with centre O and radius ( x . The angle AO
- June 2024, AS Paper 2, Q1 (5 marks): + 2 1 (a) Write x 3 24 x + in the form ( 5 a x b ) + , where a, b and c are constants to be determined. c + [3] 2 The finite region R is enclosed by the curve y
- June 2024, AS Paper 2, Q3 (6 marks): + 3 The quadratic equation kx 2 kx 2 k 3 x - , where k is a constant, has no real roots. 1 + = (a) Show that k satisfies the inequality 2 4 k 16 k 9 2 0 . [4] +
- June 2023, AS Paper 2, Q1 (3 marks): + 1 The quadratic equation kx 3 x k 0 has no real roots. + = Determine the set of possible values of k. [3]
- June 2023, AS Paper 2, Q7 (7 marks): y l2 C l1 1a k , 3 2 x O 2 The diagram shows the curve C with equation y 4 x 10 x + and two straight lines, l1 and l2. 7 = - 1a k. The line l2 is the normal to
- June 2022, Paper 1, Q3 (7 marks): (a) In this question you must show detailed reasoning. 2 Find the coordinates of the points of intersection of the curves with equations y x 2 x + 1 = - 2 and y
- June 2022, AS Paper 1, Q3 (7 marks): 3 The diagram in the Printed Answer Booklet shows part of the graph of y x 4 x + . 3 = - 2 - (a) It is required to solve the equation x 3 x 1 0 graphically by d
- June 2022, AS Paper 2, Q1 (2 marks): Write the solution of the inequality ( x 2 )( x 3 ) 2 0 using set notation. [2] - +
- November 2021, Paper 1, Q1 (4 marks): + 1 Determine the set of values of k such that the equation x 4 x ( k 3 ) 0 has two distinct real + + = roots. [4]
- November 2021, Paper 3, Q1 (3 marks): Show in a sketch the region of the x-y plane within which all three of the following inequalities hold. x2 y , x y 2 , x 0 . H + G H You should indicate the reg
- November 2021, AS Paper 2, Q2 (3 marks): y 4 x R O 2 –4 2 The diagram shows the line y x + and the curve y x - . The region R is the unshaded 2 4 4 = - = region together with its boundaries. Write down
- November 2020, Paper 2, Q5 (5 marks): - and n 2 + are positive integers. (a) Determine the set of values of n for which n 1 1 5 [3] 2 2 2 2 2 A ‘Pythagorean triple’ is a set of three positive intege
- November 2020, Paper 3, Q3 (11 marks): The functions f and g are defined for all real values of x by 2 f x ( ) 2 x 6 x and ( ) g x 3 x + . 2 = + = (a) Find the range of f. [3] (b) Give a reason why f
- November 2020, AS Paper 1, Q6 (13 marks): In this question you must show detailed reasoning. 2 (a) Solve the inequality x x 6 0 , giving your answer in set notation. [4] 2 + - 3 3 (b) Solve the equation
- June 2019, Paper 1, Q1 (4 marks): In this question you must show detailed reasoning. 2 Solve the inequality 10 x x 2 2 0 . [4] + -
- June 2019, Paper 3, Q2 (8 marks): 2 2 A circle with centre C has equation x y 6 x 4 y 4 0 . + - + + = (a) Find (i) the coordinates of C, [2] (ii) the radius of the circle. [1] (b) Determine the
- June 2018, Paper 3, Q3 (6 marks): In this question you must show detailed reasoning. A gardener is planning the design for a rectangular flower bed. The requirements are: • the length of the flo
- June 2018, AS Paper 1, Q2 (4 marks): + 2 (i) The equation x 3 x k 0 has repeated roots. Find the value of the constant k. [2] + = 2 2 (ii) Solve the inequality 6 x x 0 . [2] + -
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