Edexcel A Level Maths June 2018 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. Trigonometry · 5 marks

   Solve $2{\sin }^{2}x+3\cos x-3=0$ for $0^{\circ }\le x\le {360}^{\circ }$.

   Worked solution

   1. M1 for substituting ${\sin }^{2}x$ with $1-{\cos }^{2}x$ to get $2(1-{\cos }^{2}x)+3\cos x-3=0$.
   2. M1 for expanding and rearranging to form the quadratic $2{\cos }^{2}x-3\cos x+1=0$.
   3. M1 for factorising the quadratic as $(2\cos x-1)(\cos x-1)=0$.
   4. A1 for finding the solutions from $\cos x=0.5$ giving $x={60}^{\circ }$ and ${300}^{\circ }$.
   5. A1 for finding the solutions from $\cos x=1$ giving $x=0^{\circ }$ and ${360}^{\circ }$.

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. Proof · 6 marks

   Prove that $n^4-n^2$ is a multiple of 12 for every integer $n$.

   Worked solution

   Factorises: $n^4-n^2=n^2(n-1)(n+1)$ M1

   $(n-1)n(n+1)$ is a product of three consecutive integers, so one factor is a multiple of 3 B1

   Considers $n$ even and $n$ odd M1

   $n$ even: $n=2k$, so $n^2=4k^2$ is a multiple of 4 A1

   $n$ odd: $n-1$ and $n+1$ are both even, so $(n-1)(n+1)$ is a multiple of 4 A1

   The number is a multiple of 3 and of 4, which have no common factor, so it is a multiple of 12 A1 (cso)

More on these topics: Trigonometry · Integration · Proof

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 3 to 10 marks.
• Biggest question: Q6, 10 marks: circle with a tangent line.
• Marks by main topic: Differentiation 30, Coordinate geometry 20, Integration 14, Trigonometry 12, Sequences and series 10, Exponentials and logarithms 10, Numerical methods 4.
• More Coordinate geometry in other sittings: October 2020 Q11 (8 marks), November 2021 Q7 (9 marks), June 2022 Q3 (5 marks).
• Against the other 7 sittings we mapped: more marks on Coordinate geometry (20 marks here, 6 on average) and Differentiation (30 marks here, 16 on average); fewer on Algebra and functions (0 marks here, 19 on average) and Proof (0 marks here, 5 on average).
• Not on this paper: Proof, Algebra and functions, 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. Q1Small-angle approximations for a trig fraction (3 marks) · Trigonometry
2. Q2First and second derivatives, nature of a stationary point (7 marks) · Differentiation
3. Q3Radians: sector area and perimeter (4 marks) · Trigonometry
4. Q4Locating a root and a cobweb iteration with ln (4 marks) · Numerical methods, Exponentials and logarithms
5. Q5Quotient rule on a trig function (5 marks) · Differentiation, Trigonometry
6. Q6Circle with a tangent line (10 marks) · Coordinate geometry
7. Q7Definite integrals with a parameter k (7 marks) · Integration
8. Q8Modelling tide depth with a sine function (5 marks) · Trigonometry
9. Q9Implicit differentiation and a tangent condition (10 marks) · Differentiation
10. Q10Differential equation model for a ride height (8 marks) · Differentiation, Exponentials and logarithms
11. Q11Binomial expansion used to estimate a root (10 marks) · Sequences and series
12. Q12Exponential model of a car's value (10 marks) · Exponentials and logarithms
13. Q13Integration by substitution, exact answer (7 marks) · Integration
14. Q14Parametric curve converted to Cartesian form (10 marks) · Coordinate geometry