Edexcel A Level Maths October 2020 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

   The line $L_1$ has equation $y=x+2$ and the line $L_2$ has equation $y=-2x+14$. The lines intersect at point $A$.

   1. Find the coordinates of $A$.

   2. Point $B$ lies on $L_1$ such that its $x$-coordinate is less than the $x$-coordinate of $A$. The distance $AB$ is exactly $\sqrt{18}$ units. Find the coordinates of $B$.

   3. The line $L_3$ passes through point $B$ and is perpendicular to $L_1$. Find the equation of $L_3$ and determine where it intersects $L_2$.

   Worked solution

   1. Solve simultaneously: $x+2=-2x+14⟹3x=12⟹x=4$. M1
      $y=4+2=6$. $A(4,6)$. A1

   2. Let $B$ be $(x,x+2)$. Distance $AB=\sqrt{18}$.
      $(x-4{)}^2+(x+2-6{)}^2=18⟹(x-4{)}^2+(x-4{)}^2=18$. M1
      $2(x-4{)}^2=18⟹(x-4{)}^2=9$. A1
      $x-4=\pm 3⟹x=7$ or $x=1$. A1
      Since $x$ for $B$ is less than $x$ for $A$ (which is $4$), $x=1$.
      $y=1+2=3$. $B(1,3)$. A1

   3. $L_3$ is perpendicular to $L_1$ ($m=1$), so $m_3=-1$. M1
      Passes through $B(1,3)$: $y-3=-1(x-1)⟹y=-x+4$.
      Intersection with $L_2$ ($y=-2x+14$):
      $-x+4=-2x+14⟹x=10$. $y=-10+4=-6$.
      Intersection point is $(10,-6)$. A1

2. Integration · 4 marks

   Find $\int (\cos x-\sin x{)}^{2}dx$.

   Worked solution

   1. M1 for expanding the bracket to ${\cos }^{2}x-2\sin x\cos x+{\sin }^{2}x$.
   2. M1 for simplifying to $1-\sin 2x$.
   3. M1 for integrating the expression term by term.
   4. A1 for $x+\frac{1}{2}\cos 2x+c$.

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: Coordinate geometry · 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 11 marks.
• Biggest question: Q12, 11 marks: area under a parametric curve.
• Marks by main topic: Algebra and functions 20, Integration 17, Exponentials and logarithms 15, Sequences and series 11, Differentiation 10, Trigonometry 8, Coordinate geometry 7, Numerical methods 5, Proof 4, Vectors 3.
• More Integration in other sittings: November 2021 Q14 (12 marks), June 2019 Q14 (15 marks), June 2022 Q8 (6 marks).
• Against the other 7 sittings we mapped: more marks on Exponentials and logarithms (15 marks here, 8 on average); fewer on Differentiation (10 marks here, 22 on average) and Trigonometry (8 marks here, 13 on average).
• Coverage: every topic on the list came up.
• 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. Q1Trapezium rule estimate and its accuracy (5 marks) · Numerical methods
2. Q2Collinear points with position vectors (3 marks) · Vectors
3. Q3Log equation reduced to a quadratic (5 marks) · Exponentials and logarithms
4. Q4Binomial coefficient to find a constant (3 marks) · Sequences and series
5. Q5Intersection of two exponential curves (4 marks) · Exponentials and logarithms
6. Q6Algebraic division, then integration (7 marks) · Algebra and functions, Integration
7. Q7Tangent and normal to a curve with ln x (10 marks) · Differentiation, Exponentials and logarithms
8. Q8Curve from its derivative and a point (6 marks) · Integration
9. Q9Exponential model for a heated liquid (6 marks) · Exponentials and logarithms
10. Q10Triple-angle identity used to solve an equation (8 marks) · Trigonometry
11. Q11Modulus graph, vertex and intersections (7 marks) · Algebra and functions
12. Q12Area under a parametric curve (11 marks) · Integration, Coordinate geometry
13. Q13Range and an asymptote of a log function (6 marks) · Algebra and functions, Exponentials and logarithms
14. Q14Circle touching both axes and a line (7 marks) · Coordinate geometry
15. Q15Geometric series: ratio and sum to infinity (8 marks) · Sequences and series
16. Q16Proof about squares and multiples of 3 (4 marks) · Proof