Edexcel A Level Maths October 2020 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. Algebra and functions · 4 marks

   A cubic curve crosses the x-axis at $x=-2$, $x=1$, and $x=4$. It crosses the y-axis at the point $(0,16)$. Find the equation of the curve in the form $y=a{x}^3+b{x}^2+cx+d$.

   Worked solution

   1. M1 for writing the equation in the factored form $y=k(x+2)(x-1)(x-4)$.
   2. M1 for substituting $(0,16)$ to find $k$: $16=k(2)(-1)(-4)⟹16=8k$.
   3. A1 for finding $k=2$.
   4. A1 for expanding to get $y=2(x^3-3x^2-6x+8)=2x^3-6x^2-12x+16$.

2. Differentiation · 4 marks

   Find the set of values of $x$ for which $f(x)=x^4-8x^2$ is an increasing function.

   Worked solution

   1. M1 for finding the derivative $f^{\prime }(x)=4x^3-16x$.
   2. M1 for setting $f^{\prime }(x)>0$ and factorising: $4x(x^2-4)>0⟹4x(x-2)(x+2)>0$.
   3. M1 for finding the critical values $x=-2,0,2$ and testing regions.
   4. A1 for stating the correct range: $-2<x<0$ or $x>2$.

3. Numerical methods · 6 marks

   The equation $\cos x=x$ has a unique root $\alpha$ in $[0,1]$. Using the iteration $x_{n+1}=\cos x_n$ with $x_0=0.5$, find $x_1$, $x_2$, $x_3$, and $x_4$ each to $4$ d.p. (Angle in radians.)

   Worked solution

   $x_1=\cos 0.5=0.8776$   M1 A1. $x_2=\cos 0.8776=0.6390$   A1. $x_3=\cos 0.6390=0.8027$   A1. $x_4=\cos 0.8027=0.6948$   A1 A1.

More on these topics: Algebra and functions · Differentiation · Numerical methods

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 2 to 10 marks.
• Biggest question: Q10, 10 marks: integration by substitution with surds.
• Marks by main topic: Differentiation 26, Sequences and series 18, Trigonometry 15, Algebra and functions 10, Integration 10, Coordinate geometry 8, Exponentials and logarithms 5, Vectors 4, Proof 4.
• More Integration in other sittings: November 2021 Q11 (8 marks), June 2019 Q8 (10 marks), June 2022 Q16 (9 marks).
• Against the other 7 sittings we mapped: more marks on Differentiation (26 marks here, 17 on average) and Sequences and series (18 marks here, 9 on average); fewer on Algebra and functions (10 marks here, 18 on average) and Integration (10 marks here, 16 on average).
• Not on this paper: Numerical methods.
• 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. Q1Binomial expansion, first four terms and validity (5 marks) · Sequences and series
2. Q2Solving an exponential equation with logarithms (3 marks) · Exponentials and logarithms
3. Q33D position vectors and a distance (4 marks) · Vectors
4. Q4Inverse and self-composite of a rational function (5 marks) · Algebra and functions
5. Q5Gear speeds as a geometric sequence (6 marks) · Sequences and series
6. Q6R sin(x + a) form and a maximum (7 marks) · Trigonometry
7. Q7Quadratic and a line: inequalities for a region (5 marks) · Algebra and functions, Integration
8. Q8Exponential growth from a proportional rate (2 marks) · Exponentials and logarithms
9. Q9Turning points of a curve with e^(-2x) (9 marks) · Differentiation, Exponentials and logarithms
10. Q10Integration by substitution with surds (10 marks) · Integration
11. Q11Two intersecting circles and an angle (8 marks) · Coordinate geometry, Trigonometry
12. Q12Proving a cosec identity, then solving (8 marks) · Trigonometry
13. Q13Recurrence relation with a constant k (7 marks) · Sequences and series
14. Q14Connected rates of change for a balloon (10 marks) · Differentiation
15. Q15Implicit curve with tan y, proving a point of inflection (7 marks) · Differentiation, Proof
16. Q16Proof by contradiction with a difference of squares (4 marks) · Proof