Quadratics and the discriminant: OCR MEI A‑Level Maths questions

OCR MEI A-Level Maths past-paper questions on 2.3 Quadratics and the discriminant, 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.

All 17 questions on Quadratics and the discriminant, as a list

June 2025, Paper 1, Q8 (7 marks): (a) Determine the two values of k for which the line y x 3 + is a tangent to the curve 5 = x2 y k kx [4] . = - - x2 (b) These values of k are used to define two
June 2025, AS Paper 1, Q4 (4 marks): 2 4 (a) Show that the equation x kx k 0 has real roots for all real values of k. [2] + - = c m . – ! 1 5 2 2 (b) Show that the roots of the equation x kx k 0 ar
June 2024, Paper 2, Q8 (6 marks): The equation of a curve is 3 2 y 2 x 3 mx 9 mx + . 4 = + - Determine the range of values of m for which the curve has no stationary values. [6]
June 2024, Paper 3, Q18 (2 marks): 18 A student is investigating the intersection points of tangents to the curve y 6 x 7 x + . She 1 = - uses software to draw tangents at pairs of points with x‑
June 2024, AS Paper 1, Q6 (6 marks): 2 6 The polynomial x 4 x 10 x 21 is denoted by ( )x f . - + - (a) Use the factor theorem to show that ( x 3 ) is a factor of ( )x f . [2] - 2 (b) The polynomial
June 2024, AS Paper 2, Q2 (3 marks): - 2 (a) Find the discriminant of the equation x 3 2 x 5 0 . [2] + = 2 - (b) Use your answer to part (a) to find the number of real roots of the equation x 3 2 x
June 2023, AS Paper 1, Q9 (9 marks): x 9 The graph shows the function y e . = y x O x 2 x (a) Describe the transformation of the graph of y e that gives the graph of y e . [2] = = x A second functi
June 2023, AS Paper 2, Q2 (3 marks): - 2 2 (a) Express x 6 x + in the form ( 1 x a ) - , where a and b are integers to be determined. [2] b - 2 (b) Hence state the coordinates of the turning point
June 2023, AS Paper 2, Q11 (5 marks): In this question you must show detailed reasoning. 3 2 The equation of a curve is y 2 x 9 x 24 x - . 8 = + + Show that there are no stationary points on this cu
June 2022, AS Paper 1, Q4 (6 marks): 4 The quadratic function ( )x f is given by ( ) f x x 3 x 2 . = - + 2 (a) Write ( )x f in the form ( x a ) b , where a and b are constants. [2] + + (b) Write do
June 2022, AS Paper 2, Q2 (4 marks): - 2 (a) Factorise x 3 19 x 14 . [2] - 2 (b) Solve the inequality x 3 19 x 14 1 0 . [2] - -
November 2021, Paper 3, Q1 (5 marks): + 2 1 (a) Express x 8 x + in the form ( 2 x a ) + . b [2] + 2 (b) Write down the coordinates of the turning point of the curve y x 8 x + . 2 [1] = + x2 2 (c) St
June 2019, Paper 2, Q7 (5 marks): 288cm2. The angle of the sector is i radians and the radius of 7 The area of a sector of a circle is . the circle is r cm. (a) Find an expression for i in terms
June 2019, Paper 3, Q2 (5 marks): x2 2 2 (a) Find the transformation which maps the curve y to the curve y x 8 x - . 7 [4] = = + 2 (b) Write down the coordinates of the turning point of y x 8 x
June 2019, AS Paper 1, Q1 (3 marks): In this question you must show detailed reasoning. 2 2 Show that the equation x 7 x has no real roots. [3] = +
June 2018, Paper 2, Q16 (11 marks): In the first year of a course, an A-level student, Aaishah, has a mathematics test each week. The night before each test she revises for t hours. Over the cours
June 2018, AS Paper 2, Q5 (3 marks): Find the set of values of a for which the equation 2 + ax x 8 2 0 + = [3] has no real roots.

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