plumiTangents, normals and stationary points: WJEC A‑Level Maths questions
WJEC A-Level Maths past-paper questions on 7.3 Tangents, normals and stationary points, 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 14 questions on Tangents, normals and stationary points, as a list
- Summer 2025, Unit 3, Q5 (8 marks): 2 f x ( ) x 6 x 12 x . 5 5. A curve is defined by (a) Find the coordinates of the stationary point and determine its nature. [6] Determine the range of
- Summer 2025, Unit 3, Q13 (11 marks): 13. A curve is defined parametrically by 2 3 1 y 3 t 2 x t , . Show that the gradient of the curve at the point with parameter p is 1 (a) p . [4] t . 1
- Summer 2025, AS Unit 1, Q6 (16 marks): 2 f x ( ) = x 3 x 6 x . 8 6. The function f is defined by f x ( ) = 0 (a) Use an algebraic method to solve the equation . Show all your working. [6] y f
- Summer 2025, AS Unit 1, Q11 (9 marks): f x ( ) x 3 9 x 2 28 x 4 . 11. The function f is defined by f x is an increasing function. ( ) (a) Show that [4] y = f x . ( ) (b) Two straight lines, b
- Summer 2024, AS Unit 1, Q12 (10 marks): y x 3 12 x 20 12. A curve C has equation . (a) Find the coordinates of the stationary points of C and determine their nature. [7] (b) Determine the range
- Summer 2023, AS Unit 1, Q9 (11 marks): , find dy y x 2 3 x a) Given that dx from first principles. [5] 0 9 3 6 The function f is defined by f x 4 x b) 2 for x > 0. x ( ). Find ′f i) x [2]
- Summer 2022, Unit 3, Q13 (7 marks): A function is defined by f (x) = 2x3 + 3x – 5. 1 3 a) Prove that the graph of f (x) does not have a stationary point. [2] b) Show that the graph of f (x) does h
- Summer 2022, Unit 3, Q15 (9 marks): 5 A rectangle is inscribed in a semicircle with centre O and radius 4. The point P(x, y) is the vertex of the rectangle in the first quadrant as shown in the di
- Summer 2022, AS Unit 1, Q11 (15 marks): 1 The diagram below shows a sketch of the curve y = f (x), where f (x) = 10x + 3x2 − x3. The curve intersects the x-axis at the origin O and at the points A(–2,
- Summer 2022, AS Unit 1, Q14 (12 marks): ( ) = 3x3 − 5x2 + x − 6 1 4 A curve C has equation . f x a) Find the coordinates of the stationary points of C and determine their nature. [8] b) Without solvin
- Summer 2019, AS Unit 1, Q13 (11 marks): y = 1 9 x3 − kx + 5 1 3 A curve C has equation . A point Q lies on C and is such that the tangent to C at Q has gradient –9. The x-coordinate of Q is 3. Show th
- Summer 2019, AS Unit 1, Q15 (4 marks): Prove that f(x) = x3 – 6x2 + 13x – 7 is an increasing function. 1 5 [4]
- Summer 2018, AS Unit 1, Q13 (11 marks): 3 A curve C has equation y = x3 – 3x2. a) Find the stationary points of C and determine their nature. [7] b) Draw a sketch of C, clearly indicating the stationa
- Summer 2018, AS Unit 1, Q16 (5 marks): The curve C has equation y = 7 + 13x – 2x2. The point P lies on C and is such that the 1 6 tangent to C at P has equation y = x + c, where c is a constant. Find
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