OCR A Level Maths June 2024 Paper 1: question paper and mark scheme (H240/01)

3 A Level questions like these, with worked solutions

Written and checked by us, not taken from the OCR paper. Try each one, then tap "Worked solution" to see every step and its marks.

1. Trigonometry · 5 marks

   Solve ${\text{cosec}}^{2}x+{\cot }^{2}x=3$ for $0^{\circ }\le x\le {360}^{\circ }$.

   Worked solution

   1. M1 for using the identity ${\text{cosec}}^{2}x=1+{\cot }^{2}x$ to obtain $1+2{\cot }^{2}x=3$.
   2. M1 for rearranging to ${\cot }^{2}x=1$.
   3. M1 for taking the square root to find $\tan x=\pm 1$.
   4. A1 for finding the principal values ${45}^{\circ }$ and ${135}^{\circ }$.
   5. A1 for stating all four correct solutions: ${45}^{\circ },{135}^{\circ },{225}^{\circ },{315}^{\circ }$.

2. Differentiation · 5 marks

   A curve has the equation $y=e^{-x}\sin x$. Find the exact x-coordinate of the first positive turning point of the curve.

   Worked solution

   1. M1 for using the product rule to differentiate: $\frac{dy}{dx}=-e^{-x}\sin x+e^{-x}\cos x$.
   2. M1 for setting the derivative equal to 0 to find turning points: $e^{-x}(\cos x-\sin x)=0$.
   3. M1 for dividing by $e^{-x}$ (since $e^{-x}\ne 0$) to get $\cos x=\sin x$.
   4. M1 for dividing by $\cos x$ to obtain $\tan x=1$.
   5. A1 for identifying the first positive solution as $x=\frac{\pi }{4}$.

3. Integration · 5 marks

   The gradient of a curve is given by $\frac{dy}{dx}=4\sqrt{x}-1$. The curve passes through the point $(9,20)$. Find the equation of the curve.

   Worked solution

   1. M1 for rewriting as $4x^{\frac{1}{2}}-1$ and integrating: $y=\frac{4x^{\frac{3}{2}}}{\frac{3}{2}}-x+c$.
   2. A1 for simplifying the integral to $y=\frac{8}{3}{x}^{\frac{3}{2}}-x+c$.
   3. M1 for substituting the point $(9,20)$: $20=\frac{8}{3}(9{)}^{\frac{3}{2}}-9+c$.
   4. M1 for evaluating $9^{\frac{3}{2}}=27$ to solve for $c$: $20=72-9+c⟹c=-43$.
   5. A1 for the final equation $y=\frac{8}{3}{x}^{\frac{3}{2}}-x-43$.

More on these topics: Trigonometry · Differentiation · Integration

What this paper covers

What this paper is like

• Shape: 12 questions, 100 marks in 2 h (about 1.2 minutes a mark); questions from 6 to 12 marks.
• Biggest question: Q11, 12 marks: curve y = 5 ln(1 - cos 2x).
• Marks by main topic: Differentiation 20, Proof 15, Algebra and functions 14, Sequences and series 14, Integration 11, Coordinate geometry 10, Trigonometry 9, Numerical methods 7.
• More Differentiation in other sittings: June 2023 Q6 (9 marks), June 2025 Q7 (9 marks), June 2022 Q7 (8 marks).
• Against the other 7 sittings we mapped: more marks on Proof (15 marks here, 3 on average) and Differentiation (20 marks here, 15 on average); fewer on Exponentials and logarithms (0 marks here, 12 on average) and Algebra and functions (14 marks here, 20 on average).
• Not on this paper: Exponentials and logarithms, Vectors.
• Calculator: allowed.

H240/01: question by question

Labels and topics are ours, read from the H240/01 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Trapezium rule for x^2 e^(-x) (7 marks) · Numerical methods, Integration
2. Q2Direct and inverse proportion (6 marks) · Algebra and functions
3. Q3Counter-example about primes, then a proof (8 marks) · Proof
4. Q4Periodic sequence and a sum (6 marks) · Sequences and series
5. Q5Normal to a quadratic at a point (8 marks) · Differentiation, Coordinate geometry
6. Q6Factor theorem with a cubic (8 marks) · Algebra and functions
7. Q7Line through two points and a perpendicular (10 marks) · Coordinate geometry
8. Q8Inequality and a proof for integers (7 marks) · Proof, Algebra and functions
9. Q9Tidal river depth modelled with a trig function (9 marks) · Trigonometry
10. Q10Convergent geometric progression with terms in x (8 marks) · Sequences and series
11. Q11Curve y = 5 ln(1 - cos 2x) (12 marks) · Differentiation, Trigonometry, Exponentials and logarithms
12. Q12Area under a parametric curve (11 marks) · Integration, Coordinate geometry

What the examiners said about this paper

Summarised in our own words from the board's examiner report (Examiner Insights).

• H240/01: Rejecting a solution without a reason (Q6, Q10); "Explain" and "interpret" answers without context (Q9); Trig equations in context (Q9). Official examiner report ↗

Question-by-question topics, the top mistakes and what to focus on next →