Edexcel A Level Maths November 2021 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 · 7 marks

   Express ${\displaystyle \frac{x^3+1}{x^2-1}}$ in the form $Ax+B+{\displaystyle \frac{C}{x-1}}+{\displaystyle \frac{D}{x+1}}$ and find $A,B,C,D$.

   Worked solution

   Polynomial division: $\frac{x^3+1}{x^2-1}=x+\frac{x+1}{x^2-1}=x+\frac{1}{x-1}$ (since $\frac{x+1}{(x+1)(x-1)}=\frac{1}{x-1}$)   M1 M1 A1. So $A=1$, $B=0$, $C=1$, $D=0$   A1 A1 A1 A1.

2. Trigonometry · 5 marks

   Solve the equation $\tan 2x=4\tan x$ for $0^{\circ }\le x\le {180}^{\circ }$. Give your answers to 1 decimal place where appropriate.

   Worked solution

   1. M1 for substituting the identity $\tan 2x=\frac{2\tan x}{1-{\tan }^{2}x}$.
   2. M1 for rearranging to $2\tan x=4\tan x(1-{\tan }^{2}x)$.
   3. M1 for grouping terms on one side and factorising to get $2\tan x(2{\tan }^{2}x-1)=0$.
   4. A1 for finding solutions from $\tan x=0$, giving $x=0^{\circ }$ and ${180}^{\circ }$.
   5. A1 for finding solutions from ${\tan }^{2}x=0.5⟹\tan x=\pm \frac{1}{\sqrt{2}}$, giving $x={35.3}^{\circ }$ and $x={144.7}^{\circ }$.

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: Algebra and functions · Trigonometry · Sequences and series

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: Q14, 12 marks: differential equation for water in a tank.
• Marks by main topic: Differentiation 31, Trigonometry 19, Integration 19, Algebra and functions 15, Exponentials and logarithms 9, Sequences and series 7.
• More Integration in other sittings: June 2022 Q8 (6 marks), October 2020 Q12 (11 marks), June 2023 Q11 (10 marks).
• Against the other 7 sittings we mapped: more marks on Differentiation (31 marks here, 19 on average) and Trigonometry (19 marks here, 11 on average); fewer on Vectors (0 marks here, 6 on average) and Coordinate geometry (0 marks here, 5 on average).
• Not on this paper: Proof, Coordinate geometry, Numerical methods, Vectors.
• 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. Q1Arithmetic series: difference and sum (4 marks) · Sequences and series
2. Q2Range, inverse and composite functions (5 marks) · Algebra and functions
3. Q3Log equation with base 3 (3 marks) · Exponentials and logarithms
4. Q4Small-angle approximations to simplify (3 marks) · Trigonometry
5. Q5Stationary point and its nature on a quartic (7 marks) · Differentiation
6. Q6Radians: perimeter and area of a logo (5 marks) · Trigonometry
7. Q7Tangent to a cubic and an enclosed area (9 marks) · Differentiation, Integration
8. Q8Implicit differentiation with constants p and q (9 marks) · Differentiation
9. Q9Sum to infinity with cos(180n) (3 marks) · Sequences and series, Trigonometry
10. Q10Power-law model fitted by logs (6 marks) · Exponentials and logarithms
11. Q11Modulus graph and an equation in k (10 marks) · Algebra and functions
12. Q12Integration by substitution, exact value (7 marks) · Integration
13. Q13Parametric differentiation with cosec (6 marks) · Differentiation, Trigonometry
14. Q14Differential equation for water in a tank (12 marks) · Integration
15. Q15R cos(x + a) form and a modelling question (11 marks) · Trigonometry