Edexcel A Level Maths June 2018 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. Differentiation · 5 marks

   Find the equation of the tangent to the curve $2x^2-xy+y^2=8$ at the point $(2,2)$. Give your answer in the form $y=mx+c$.

   Worked solution

   1. M1 for differentiating $2x^2$ to $4x$ and $y^2$ to $2y\frac{dy}{dx}$.
   2. M1 for differentiating $-xy$ using the product rule to get $-y-x\frac{dy}{dx}$.
   3. M1 for setting the entire derivative to zero: $4x-y-x\frac{dy}{dx}+2y\frac{dy}{dx}=0$.
   4. M1 for substituting $x=2$ and $y=2$ to find the gradient $m$: $8-2-2\frac{dy}{dx}+4\frac{dy}{dx}=0⟹2\frac{dy}{dx}=-6⟹m=-3$.
   5. A1 for using $y-2=-3(x-2)$ to establish the final equation $y=-3x+8$.

2. 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 $d\ne 0$, $2d-a=0⟹a=2d$.

3. Exponentials and logarithms · 4 marks

   Solve the equation $2\ln x=\ln (3x+4)$.

   Worked solution

   1. M1 for applying the power law to the LHS: $\ln (x^2)=\ln (3x+4)$.
   2. M1 for equating the arguments: $x^2=3x+4$.
   3. M1 for rearranging to $x^2-3x-4=0$ and finding roots $x=4$ and $x=-1$.
   4. A1 for rejecting $x=-1$ (since $\ln x$ must have $x>0$) and giving $x=4$.

More on these topics: Differentiation · Sequences and series · Exponentials and logarithms

What this paper covers

What this paper is like

• Shape: 14 questions, 100 marks in 2 h (about 1.2 minutes a mark); questions from 5 to 10 marks.
• Biggest question: Q13, 10 marks: area between y = x ln x and its normal.
• Marks by main topic: Differentiation 22, Algebra and functions 19, Trigonometry 18, Integration 18, Sequences and series 7, Numerical methods 6, Vectors 5, Proof 5.
• More Integration in other sittings: June 2019 Q14 (15 marks), October 2020 Q12 (11 marks), November 2021 Q14 (12 marks).
• Against the other 7 sittings we mapped: more marks on Trigonometry (18 marks here, 11 on average); fewer on Exponentials and logarithms (0 marks here, 10 on average) and Coordinate geometry (0 marks here, 5 on average).
• Not on this paper: Coordinate geometry, Exponentials and logarithms.
• 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. Q1Composite and inverse functions, domain and range (6 marks) · Algebra and functions
2. Q2Position vectors in 3D and a parallelogram (5 marks) · Vectors
3. Q3Counter-example and a modulus graph (5 marks) · Proof, Algebra and functions
4. Q4Sigma notation and a periodic sequence (7 marks) · Sequences and series
5. Q5Newton-Raphson on a cubic (6 marks) · Numerical methods
6. Q6Factor theorem, proving the number of real roots (6 marks) · Algebra and functions, Proof
7. Q7Trig equations with sec and R sin(x - a) (9 marks) · Trigonometry
8. Q8Quadratic model of a ball's flight (7 marks) · Differentiation
9. Q9Differentiating cos from first principles (5 marks) · Differentiation, Trigonometry
10. Q10Model for a shrinking sphere, separating variables (8 marks) · Integration
11. Q11Partial fractions and a decreasing function (7 marks) · Algebra and functions, Proof
12. Q12Proving a trig identity, then solving with it (9 marks) · Trigonometry
13. Q13Area between y = x ln x and its normal (10 marks) · Integration
14. Q14Logistic population model and its growth rate (10 marks) · Differentiation, Exponentials and logarithms