Edexcel A Level Maths June 2022 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. Trigonometry · 6 marks

   Solve the equation $\cos 2x=\sin x$ for $-\pi \le x\le \pi$. Give your answers as exact radian values.

   Worked solution

   Substitute the double angle identity $\cos 2x=1-2{\sin }^{2}x$. M1
   $1-2{\sin }^{2}x=\sin x⟹2{\sin }^{2}x+\sin x-1=0$. A1
   Factorise the quadratic: $(2\sin x-1)(\sin x+1)=0$. M1A1
   Case 1: $2\sin x-1=0⟹\sin x=\frac{1}{2}$.
   Within the domain $-\pi \le x\le \pi$, solutions are $x=\frac{\pi }{6}$ and $x=\frac{5\pi }{6}$. A1
   Case 2: $\sin x+1=0⟹\sin x=-1$.
   Within the domain $-\pi \le x\le \pi$, the solution is $x=-\frac{\pi }{2}$. A1

2. Integration · 5 marks

   Find $\int \frac{x^2+1}{x(x-1)}dx$.

   Worked solution

   1. M1 for recognising the improper fraction and performing division to get $1+\frac{x+1}{x(x-1)}$.
   2. M1 for setting up partial fractions for the remainder: $\frac{x+1}{x(x-1)}=\frac{A}{x}+\frac{B}{x-1}$.
   3. A1 for determining the constants $A=-1$ and $B=2$.
   4. M1 for formulating the complete integral: $\int (1-\frac{1}{x}+\frac{2}{x-1})dx$.
   5. A1 for integrating the terms correctly to $x-\ln |x|+2\ln |x-1|+c$.

3. Sequences and series · 5 marks

   The first, third, and seventh terms of an arithmetic sequence (with a non-zero common difference) form three consecutive terms of a geometric sequence. Show that the first term is twice the common difference ($a=2d$).

   Worked solution

   1. M1 for writing the 1st, 3rd, and 7th terms as $a,a+2d,a+6d$.
   2. M1 for setting up the geometric ratio condition: $\frac{a+2d}{a}=\frac{a+6d}{a+2d}$.
   3. M1 for cross-multiplying and expanding: $(a+2d{)}^2=a(a+6d)⟹a^2+4ad+4d^2=a^2+6ad$.
   4. M1 for rearranging to $4d^2-2ad=0⟹2d(2d-a)=0$.
   5. A1 for concluding that since $d\ne 0$, $2d-a=0⟹a=2d$.

More on these topics: Trigonometry · Integration · Sequences and series

What this paper covers

What this paper is like

• Shape: 16 questions, 100 marks in 2 h (about 1.2 minutes a mark); questions from 3 to 12 marks.
• Biggest question: Q16, 12 marks: parametric curve, normal and its intersection.
• Marks by main topic: Algebra and functions 22, Differentiation 21, Sequences and series 19, Numerical methods 13, Integration 6, Vectors 6, Trigonometry 5, Exponentials and logarithms 4, Proof 4.
• More Differentiation in other sittings: November 2021 Q7 (9 marks), June 2023 Q7 (7 marks), October 2020 Q7 (10 marks).
• Against the other 7 sittings we mapped: more marks on Numerical methods (13 marks here, 2 on average) and Sequences and series (19 marks here, 9 on average); fewer on Integration (6 marks here, 16 on average) and Trigonometry (5 marks here, 13 on average).
• Not on this paper: Coordinate geometry.
• 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. Q1Modulus graph and an inequality (4 marks) · Algebra and functions
2. Q2Exponential graph and an equation (4 marks) · Exponentials and logarithms
3. Q3Periodic sequence and a sum (4 marks) · Sequences and series
4. Q4Differentiation from first principles (3 marks) · Differentiation
5. Q5Trapezium rule with a log function (6 marks) · Numerical methods, Exponentials and logarithms
6. Q6Locating a root of a trig equation (7 marks) · Numerical methods, Trigonometry
7. Q7Binomial expansion with a surd (5 marks) · Sequences and series
8. Q8Exact area between a curve and the x-axis (6 marks) · Integration
9. Q9Ferris wheel height modelled with cosine (5 marks) · Trigonometry
10. Q10Inverse function and a range (8 marks) · Algebra and functions
11. Q11Proof that an expression is always even (4 marks) · Proof
12. Q12Derivative of e^(3x) over a quadratic (6 marks) · Differentiation, Exponentials and logarithms
13. Q133D vectors, distance and a parallelogram (6 marks) · Vectors
14. Q14Partial fractions and a differential equation (10 marks) · Algebra and functions, Integration
15. Q15Geometric series with an unknown (10 marks) · Sequences and series
16. Q16Parametric curve, normal and its intersection (12 marks) · Differentiation, Coordinate geometry