Edexcel A Level Maths June 2019 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. Coordinate geometry · 8 marks

   A curve $C$ has parametric equations $x=t^2$, $y=t^3-3t$.
   (a) Find ${\displaystyle \frac{dy}{dx}}$ in terms of $t$. (3)
   (b) Find the coordinates of the points on $C$ where the tangent is horizontal. (3)
   (c) Find the Cartesian equation of the tangent at $t=2$. (2)

   Worked solution

   (a) $\frac{dx}{dt}=2t$, $\frac{dy}{dt}=3t^2-3$   M1 A1. $\frac{dy}{dx}=\frac{3t^2-3}{2t}=\frac{3(t^2-1)}{2t}$   A1.
   (b) Horizontal iff $\frac{dy}{dt}=0$: $3t^2=3\Rightarrow t=\pm 1$   M1. $t=1$: $(1,-2)$; $t=-1$: $(1,2)$   A1 A1.
   (c) At $t=2$: $(x,y)=(4,2)$; gradient $=\frac{3\cdot 3}{4}=\frac{9}{4}$; equation: $y-2=\frac{9}{4}(x-4)$, i.e. $y=\frac{9}{4}x-7$   M1 A1.

2. Trigonometry · 5 marks

   Solve ${\text{cosec}}^{2}x+{\cot }^{2}x=3$ for $0^{\circ }\le x\le {360}^{\circ }$.

   Worked solution

   1. M1 for using the identity ${\text{cosec}}^{2}x=1+{\cot }^{2}x$ to obtain $1+2{\cot }^{2}x=3$.
   2. M1 for rearranging to ${\cot }^{2}x=1$.
   3. M1 for taking the square root to find $\tan x=\pm 1$.
   4. A1 for finding the principal values ${45}^{\circ }$ and ${135}^{\circ }$.
   5. A1 for stating all four correct solutions: ${45}^{\circ },{135}^{\circ },{225}^{\circ },{315}^{\circ }$.

3. Exponentials and logarithms · 5 marks

   Solve the equation ${\log }_{2}x+{\log }_{x}2=2.5$ for $x>0,x\ne 1$.

   Worked solution

   1. M1 for applying the reciprocal rule: ${\log }_{x}2=\frac{1}{{\log }_{2}x}$.
   2. M1 for making the substitution $u={\log }_{2}x$ to form $u+\frac{1}{u}=2.5$.
   3. M1 for multiplying by $2u$ to form the quadratic $2u^2-5u+2=0$ and solving it.
   4. M1 for finding the roots $u=2$ and $u=\frac{1}{2}$.
   5. A1 for converting back to $x$ and finding both solutions: $x=4$ and $x=\sqrt{2}$.

More on these topics: Coordinate geometry · Trigonometry · 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 3 to 15 marks.
• Biggest question: Q14, 15 marks: substitution in a differential equation model.
• Marks by main topic: Differentiation 33, Algebra and functions 17, Integration 15, Trigonometry 10, Coordinate geometry 6, Sequences and series 6, Vectors 6, Numerical methods 4, Exponentials and logarithms 3.
• More Integration in other sittings: June 2018 Q13 (10 marks), October 2020 Q12 (11 marks), November 2021 Q14 (12 marks).
• Against the other 7 sittings we mapped: more marks on Differentiation (33 marks here, 19 on average); fewer on Exponentials and logarithms (3 marks here, 9 on average) and Sequences and series (6 marks here, 10 on average).
• Not on this paper: Proof.
• 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. Q1Index laws to write y in terms of x (3 marks) · Exponentials and logarithms
2. Q2Trapezium rule from speed data (4 marks) · Numerical methods
3. Q3Finding a student's error in a sector calculation (3 marks) · Trigonometry
4. Q4Parametric curve meeting a circle (6 marks) · Coordinate geometry, Trigonometry
5. Q5Maximising a rectangle under a curve (3 marks) · Differentiation
6. Q6Piecewise function: composite and inverse (10 marks) · Algebra and functions
7. Q7Fitting a cost model to data (7 marks) · Algebra and functions
8. Q8Sum to infinity and a log sum (6 marks) · Sequences and series, Exponentials and logarithms
9. Q9Braking model with a quadratic (9 marks) · Differentiation, Algebra and functions
10. Q10Vectors in a triangle, ratio of lengths (6 marks) · Vectors
11. Q11Differentiating x^x by taking logs (11 marks) · Differentiation, Exponentials and logarithms
12. Q12Proving an identity, then solving an equation (7 marks) · Trigonometry
13. Q13Minimising surface area of a tank (10 marks) · Differentiation
14. Q14Substitution in a differential equation model (15 marks) · Integration, Exponentials and logarithms