Edexcel A Level Maths June 2024 Paper 1: question paper and mark scheme (9MA0/01)

3 A Level questions like these, with worked solutions

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

1. Coordinate geometry · 7 marks

   The points $A(1,2)$ and $B(7,10)$ lie on a circle $C$ with $AB$ as a diameter.
   (a) Find the equation of $C$. (4)
   (b) The tangent to $C$ at $A$ meets the $y$-axis at $T$. Find the coordinates of $T$. (3)

   Worked solution

   (a) Centre $=$ midpoint $=(4,6)$   B1. Radius $=\frac{1}{2}|AB|=\frac{1}{2}\sqrt{36+64}=5$   M1 A1. Equation: $(x-4{)}^2+(y-6{)}^2=25$   A1.
   (b) Radius from centre to $A$ has gradient $\frac{2-6}{1-4}=\frac{4}{3}$   B1. Tangent gradient $=-\frac{3}{4}$; equation: $y-2=-\frac{3}{4}(x-1)$. Set $x=0$: $y=2+\frac{3}{4}=\frac{11}{4}$   M1 A1.

2. Exponentials and logarithms · 5 marks

   Solve the equation ${\log }_{2}x+{\log }_{x}2=2.5$ for $x>0,x\ne 1$.

   Worked solution

   1. M1 for applying the reciprocal rule: ${\log }_{x}2=\frac{1}{{\log }_{2}x}$.
   2. M1 for making the substitution $u={\log }_{2}x$ to form $u+\frac{1}{u}=2.5$.
   3. M1 for multiplying by $2u$ to form the quadratic $2u^2-5u+2=0$ and solving it.
   4. M1 for finding the roots $u=2$ and $u=\frac{1}{2}$.
   5. A1 for converting back to $x$ and finding both solutions: $x=4$ and $x=\sqrt{2}$.

3. Proof · 4 marks

   Prove by contradiction that there are infinitely many prime numbers.

   Worked solution

   1. M1 for assuming that there is a finite number of prime numbers, listing them as $p_1,p_2,\dots ,p_n$.
   2. M1 for constructing a new number $N=(p_1\times p_2\times \cdots \times p_n)+1$.
   3. M1 for arguing that dividing $N$ by any of the primes $p_i$ leaves a remainder of $1$, meaning $N$ has no prime factors from the finite list.
   4. A1 for concluding that $N$ must either be a new prime itself or have a prime factor not in the list, contradicting the assumption that the list contains all primes.

More on these topics: Coordinate geometry · Exponentials and logarithms · Proof

What this paper covers

What this paper is like

• Shape: 15 questions, 100 marks in 2 h (about 1.2 minutes a mark); questions from 3 to 11 marks.
• Biggest question: Q8, 11 marks: composite and inverse functions.
• Marks by main topic: Integration 34, Algebra and functions 20, Trigonometry 15, Sequences and series 10, Differentiation 9, Numerical methods 6, Proof 6.
• More Algebra and functions in other sittings: June 2023 Q7 (8 marks), June 2025 Q12 (8 marks), June 2022 Q5 (6 marks).
• Against the other 7 sittings we mapped: more marks on Integration (34 marks here, 12 on average) and Numerical methods (6 marks here, 1 on average); fewer on Differentiation (9 marks here, 19 on average) and Exponentials and logarithms (0 marks here, 9 on average).
• Not on this paper: Coordinate geometry, Exponentials and logarithms, Vectors.
• Calculator: allowed.

9MA0/01: question by question

Labels and topics are ours, read from the 9MA0/01 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Factor theorem with a cubic (3 marks) · Algebra and functions
2. Q2Binomial expansion with a fractional power (4 marks) · Sequences and series
3. Q3Root of an equation with tan and an iteration (6 marks) · Numerical methods, Trigonometry
4. Q4Differentiation from first principles (3 marks) · Differentiation
5. Q5Quotient rule and where a function increases (6 marks) · Differentiation
6. Q6Modulus graph and its vertex (6 marks) · Algebra and functions
7. Q7Differential equation for a draining tank (8 marks) · Integration
8. Q8Composite and inverse functions (11 marks) · Algebra and functions
9. Q9Geometric sequence with an unknown k (6 marks) · Sequences and series
10. Q10Area between two lines and a curve (9 marks) · Integration, Coordinate geometry
11. Q11Radians: a badge made of sectors (4 marks) · Trigonometry
12. Q12K cos(x + a) form and a model (11 marks) · Trigonometry
13. Q13Integration by substitution with sin^2 (8 marks) · Integration
14. Q14Differential equation for an inflating balloon (9 marks) · Integration
15. Q15Proof by contradiction and a quadratic (6 marks) · Proof

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, Q10); Inverse and composite functions (Q8); Modelling (Q7, Q14). Official examiner report ↗

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