plumiQuadratics and the discriminant: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.02.3 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.
Questions from
Paper
All papers
Exam
All years
Loading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDF
All 34 questions on Quadratics and the discriminant, as a list
- June 2025, Paper 2, Q2 (9 marks): In this question you must show detailed reasoning. Solve the following equations. 2 3 (a) ( x 5 ) 8 [3] - = 2 3 = y (b) e 2 [2] 4 2 (c) x 3 x 4 0 [4] - - =
- June 2025, Paper 3, Q1 (5 marks): ^ h 2 - 2 1 (a) Express x 3 12 x 17 in the form a x b c where a, b and c are constants. [3] + - + 2 (b) State the coordinates of the minimum point of the curve
- 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 1, Q1 (8 marks): In this question you must show detailed reasoning. Solve the following equations. 2 - (a) x 11 = 5 [2] 6 3 (b) y 7 y 8 0 [4] + - = 10 = 3 z (c) 2 - 16 [2]
- June 2025, AS Paper 1, Q3 (5 marks): - 2 3 (a) Express x 6 x in the form ( x p ) + , where p and q are constants. q [2] + (b) Hence or otherwise determine the centre and radius of the circle with e
- June 2025, AS Paper 2, Q4 (10 marks): 2 4 The cubic polynomial x 2 kx 4 x + , where k is a constant, is denoted by ( )x k f . - + It is given that f ( ) 2 16 . l = (a) Show that k = 3. [4] For the r
- June 2025, AS Paper 2, Q7 (9 marks): y (1, 0) a x O (3, –16) The diagram shows the curve with equation y f ( ) x where ( ) f x is a quadratic function. The = curve intersects the x-axis at the poin
- June 2024, Paper 1, Q7 (10 marks): The point A has coordinates (1, 7), and the point B has coordinates (h, 10). (a) You are given that the gradient of the line AB is 2. Find the value of h. [2] (
- June 2024, AS Paper 1, Q7 (5 marks): In this question you must show detailed reasoning. 4 2 4 3 2 (a) Show that ( x 2 ) 6 ( x 2 ) 16 x 8 x 18 x 8 x 24 . [1] + - + - / + + + - 4 3 2 (b) Hence solve
- 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, Paper 2, Q1 (5 marks): - 2 1 (a) (i) Express x 8 x 11 in the form ( x a ) + where a and b are constants. b [2] + - 2 - (ii) Hence write down the minimum value of x 8 x 11 . [1] + 2 -
- June 2023, AS Paper 1, Q6 (11 marks): 3 6 (a) Determine the two real roots of the equation x x [3] 8 7 1 0 . + - = 7 49 4 (b) Determine the coordinates of the stationary points on the curve y x x x
- 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 2022, Paper 1, Q4 (8 marks): + 2 4 (a) Write x x p x q + , where p, q and r are constants. r [3] 2 6 + in the form 7 ( ) + 2 (b) State the coordinates of the minimum point on the graph of y
- June 2022, Paper 2, Q1 (8 marks): In this question you must show detailed reasoning. Solve the following equations. x x 1 - (a) x 0 [3] - = x 1 2 + + 8 7 (b) 1 0 [3] 6 - - = 3 x x 1 x 7 (c) 3 2
- June 2022, Paper 3, Q7 (8 marks): In this question you must show detailed reasoning. (a) Show that the equation m sec 3 cos 4 sin can be expressed in the form i + i = i 2i m tan 4 tan ( m 3 ) 0
- June 2022, AS Paper 1, Q7 (8 marks): (a) In this question you must show detailed reasoning. Find the range of values of the constant m for which the simultaneous equations y mx and = 2 2 x y 6 x 2
- June 2022, AS Paper 2, Q2 (4 marks): In this question you must show detailed reasoning. Solve the equation x 3 1 4 x . [4] + =
- 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, AS Paper 1, Q9 (6 marks): In this question you must show detailed reasoning. Find the equation of the straight line with positive gradient that passes through (0, 2) and is a 2 tangent t
- November 2020, Paper 1, Q11 (10 marks): In this question you must show detailed reasoning. y A P x O 2 2 The diagram shows a circle with equation x y 10 x 14 y 64 0 . A tangent is drawn from + - - + =
- 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
- November 2020, AS Paper 2, Q5 (5 marks): 5 A curve has equation y a x ( b ) + , where a, b and c are constants. The curve has a stationary c = + point at ( 3 2 , ) . - (a) State the values of b and c.
- June 2019, Paper 2, Q7 (5 marks): In this question you must show detailed reasoning. 6 2 4 3 2 Use the substitution u x + to solve the equation x 36 x 12 x 7 x x 2 0 . [5] = + + + - =
- 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 2019, AS Paper 2, Q2 (6 marks): ^ h 2 - 2 2 (a) Express x 5 20 x + in the form 3 p x q r , where p, q and r are integers. [3] + + 2 (b) State the coordinates of the minimum point of the curve
- June 2019, AS Paper 2, Q8 (8 marks): (a) Show that the equation x kx where k is a constant, can be expressed in 2 log log ( 1 ) 3 , = - + 2 2 2 - x kx [4] the form 8 8 0 . + = (b) Given that the eq
- June 2018, Paper 2, Q1 (7 marks): (i) Express 2x2 - 12x + 23 in the form a(x + b)2 + c. 1 [4] (ii) Use your result to show that the equation 2x2 - 12x + 23 = 0 has no real roots. [1] (iii) Given
- June 2018, Paper 3, Q4 (8 marks): In this question you must show detailed reasoning. The functions f and g are defined for all real values of x by ^ h ^ h x3 2 f x and g x x 2 . = = + (i) Write
- 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] + -
- June 2018, AS Paper 2, Q4 (6 marks): ^ h 2 - 2 4 (i) Express x 4 12 x 11 in the form a x b c . [3] + + + 2 - (ii) State the number of real roots of the equation x 4 12 x 11 0 . [1] + = ^ h 2 (iii)
- June 2018, AS Paper 2, Q5 (5 marks): In this question you must show detailed reasoning. 2 - The line x 5 y k is a tangent to the curve x 4 y 10 . Find the value of the constant k. [5] + = =
Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? OCR A-Level Maths past papers.
The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.