Edexcel A Level Maths June 2025 Paper 1: question paper and mark scheme (9MA0/01)

Try 3 A Level questions like these

Written and checked by us, not taken from the Pearson Edexcel paper. Tap "Worked answer" to see every step.

1. Trigonometry · 5 marks

   Two identical circles of radius $8$ cm intersect such that the circumference of each passes through the centre of the other. Find the exact area of the overlapping region.

   Worked answer

   1. M1 for recognising that lines drawn from the intersection points to the centres form two equilateral triangles, hence the central angle in each circle covering the overlap is $\frac{2\pi}{3}$.
   2. M1 for establishing the overlapping region consists of two identical segments, so Area $= 2 \times \frac{1}{2}(8^2)(\frac{2\pi}{3} - \sin\frac{2\pi}{3})$.
   3. M1 for substituting $\sin\frac{2\pi}{3} = \frac{\sqrt{3}}{2}$.
   4. M1 for expanding the expression $64(\frac{2\pi}{3} - \frac{\sqrt{3}}{2})$.
   5. A1 for the exact simplified area $\frac{128\pi}{3} - 32\sqrt{3} \text{ cm}^2$.

2. Integration · 7 marks

   Find the exact total area of the finite regions bounded by the curves $y = x^3 + x^2$ and $y = 2x^2 + 2x$.

   Worked answer

   1. M1 for setting $x^3 + x^2 = 2x^2 + 2x \implies x^3 - x^2 - 2x = 0$.
   2. M1 for factoring $x(x-2)(x+1)=0$ to find the intersection points $x=-1, 0, 2$.
   3. M1 for recognising two distinct regions and setting up integrals: $\int_{-1}^{0} (x^3 - x^2 - 2x) \, dx$ and $\int_{0}^{2} (2x^2 + 2x - x^3 - x^2) \, dx$.
   4. M1 for integrating the generic polynomial to $\pm[\frac{x^4}{4} - \frac{x^3}{3} - x^2]$.
   5. M1 for evaluating the area of the first region to $\frac{5}{12}$.
   6. M1 for evaluating the area of the second region to $\frac{8}{3}$.
   7. A1 for calculating the combined total area: $\frac{5}{12} + \frac{8}{3} = \frac{37}{12}$.

3. Numerical methods · 6 marks

   The equation $\cos x = x$ has a unique root $\alpha$ in $[0, 1]$. Using the iteration $x_{n+1} = \cos x_n$ with $x_0 = 0.5$, find $x_1$, $x_2$, $x_3$, and $x_4$ each to $4$ d.p. (Angle in radians.)

   Worked answer

   $x_1 = \cos 0.5 = 0.8776$   M1 A1. $x_2 = \cos 0.8776 = 0.6390$   A1. $x_3 = \cos 0.6390 = 0.8027$   A1. $x_4 = \cos 0.8027 = 0.6948$   A1 A1.

More on these topics: Trigonometry · Integration · Numerical methods

What this paper covers

Pure Mathematics 1: any of the pure content (Edexcel Pure topics 1 to 10).

We haven't mapped this paper question by question yet, so these are the topics it can test, from the specification's paper structure. Each links to a page where you can learn the topic and then practise questions on it.

Pure

• Proof
• Algebra and functions
• Coordinate geometry
• Sequences and series
• Trigonometry
• Exponentials and logarithms
• Differentiation
• Integration
• Numerical methods
• Vectors

Practise these topics (opens the practice engine)

• Pure I
• Pure II
• Pure III (calculus)

What the examiners said about this paper

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

• 9MA0/01: "Show that" (Q5, Q14); Inverse and composite functions (Q1); Modelling (Q6, Q11). Official examiner report ↗

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

Formula booklet

Mathematical Formulae and Statistical Tables (A Level Mathematics and Further Mathematics) · Pearson Edexcel · For 9MA0 / 9FM0, first certification 2018 (current)