Edexcel A Level Maths June 2024 Paper 2: question paper and mark scheme (9MA0/02)

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. Algebra and functions · 5 marks

   Let $f(x)=x^3+c{x}^2+dx-4$. Given $f(x)$ has a factor $(x+2)$ and leaves a remainder of $-10$ when divided by $(x-3)$, find the values of $c$ and $d$.

   Worked solution

   1. M1 for applying the Factor Theorem for $(x+2)$: $f(-2)=0⟹-8+4c-2d-4=0⟹4c-2d=12$.
   2. M1 for applying the Remainder Theorem for $(x-3)$: $f(3)=-10⟹27+9c+3d-4=-10⟹9c+3d=-33$.
   3. M1 for simplifying both equations (e.g., $2c-d=6$ and $3c+d=-11$).
   4. M1 for solving the simultaneous equations (e.g., adding them gives $5c=-5$).
   5. A1 for finding the correct values $c=-1$ and $d=-8$.

2. Integration · 4 marks

   Find $\int (\sin x+\cos x{)}^{2}dx$.

   Worked solution

   1. M1 for expanding the bracket to ${\sin }^{2}x+2\sin x\cos x+{\cos }^{2}x$.
   2. M1 for simplifying using ${\sin }^{2}x+{\cos }^{2}x\equiv 1$ and $2\sin x\cos x\equiv \sin 2x$.
   3. M1 for integrating $1+\sin 2x$.
   4. A1 for $x-\frac{1}{2}\cos 2x+c$.

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 solution

   $x_1=\cos 0.5=0.8776$   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: Algebra and functions · Integration · Numerical methods

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 12 marks.
• Biggest question: Q12, 12 marks: partial fractions and a growth differential equation.
• Marks by main topic: Differentiation 30, Algebra and functions 23, Sequences and series 10, Trigonometry 10, Exponentials and logarithms 9, Coordinate geometry 8, Vectors 5, Integration 5.
• More Algebra and functions in other sittings: June 2023 Q10 (7 marks), June 2025 Q11 (11 marks), June 2022 Q14 (10 marks).
• Against the other 7 sittings we mapped: more marks on Differentiation (30 marks here, 20 on average) and Algebra and functions (23 marks here, 18 on average); fewer on Integration (5 marks here, 17 on average) and Numerical methods (0 marks here, 4 on average).
• Not on this paper: Proof, Numerical methods.
• Calculator: allowed.

9MA0/02: question by question

Labels and topics are ours, read from the 9MA0/02 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1First and second derivatives and a point (5 marks) · Differentiation
2. Q2Loan repayments as an arithmetic series (5 marks) · Sequences and series
3. Q3Image of a point under graph transformations (4 marks) · Algebra and functions
4. Q4Recurrence relation with a constant k (5 marks) · Sequences and series
5. Q5Small-angle approximations (3 marks) · Trigonometry
6. Q6Equal gradients of e^(4x) and ln x, then iteration (7 marks) · Differentiation, Numerical methods
7. Q7Vector equation of a line (5 marks) · Vectors
8. Q8Proving a trig identity, then solving (7 marks) · Trigonometry
9. Q9Quadratic model for a ball's path (7 marks) · Algebra and functions
10. Q10Parametric curve and a tangent (6 marks) · Differentiation, Coordinate geometry
11. Q11Area under a curve with e^(3x) by parts (5 marks) · Integration
12. Q12Partial fractions and a growth differential equation (12 marks) · Algebra and functions, Integration
13. Q13Exponential model of world population (9 marks) · Exponentials and logarithms
14. Q14Circles, centres and radii (8 marks) · Coordinate geometry
15. Q15Implicit differentiation and tangents (12 marks) · Differentiation

What the examiners said about this paper

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

• 9MA0/02: "Show that" (Q2, Q4, Q8); Premature rounding and truncating (Q13); Integration by parts (Q11). Official examiner report ↗

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