Edexcel A Level Maths June 2022 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. Sequences and series · 4 marks

   The first three terms of the expansion $(a+bx{)}^6$ are $64-192x+c{x}^2$. Find the values of the constants $a$, $b$, and $c$.

   Worked solution

   1. M1 for equating the first term: $a^6=64⟹a=2$.
   2. M1 for equating the $x$ coefficient to find $b$: $(\genfrac{}{}{0ex}{}{6}{1})a^{5}b=-192⟹6(32)b=-192⟹192b=-192$.
   3. A1 for obtaining $b=-1$.
   4. A1 for finding the $x^2$ coefficient: $c=(\genfrac{}{}{0ex}{}{6}{2})a^4{b}^2=15(16)(-1{)}^2=240$.

2. Numerical methods · 7 marks

   $f(x)=x^3-3x-4$.
   (a) Show that $f(x)=0$ has a root in $(2,3)$. (2)
   (b) Rewrite the equation in the form $x=\sqrt[3]{3x+4}$ and use this iteration with $x_0=2$ to find $x_1,x_2,x_3,x_4$ each to 4 d.p. State the value of the root to 3 d.p. (5)

   Worked solution

   (a) $f(2)=8-6-4=-2<0$; $f(3)=27-9-4=14>0$   M1 A1.
   (b) $x_1=\sqrt[3]{10}=2.1544$; $x_2=\sqrt[3]{10.4633}=2.1872$; $x_3=\sqrt[3]{10.5616}=2.1940$; $x_4=\sqrt[3]{10.5821}=2.1955$   M1 A1 A1 A1. Root $\approx 2.196$   A1.

3. Vectors · 7 marks

   Line $L_1$ has vector equation ${\mathbf{r}}_{\mathbf{1}}=\left(\begin{array}{c}1\\ 0\\ 1\end{array}\right)+\lambda \left(\begin{array}{c}2\\ 1\\ 1\end{array}\right)$ and line $L_2$ has equation ${\mathbf{r}}_{\mathbf{2}}=\left(\begin{array}{c}5\\ -3\\ 0\end{array}\right)+\mu \left(\begin{array}{c}-1\\ 2\\ 1\end{array}\right)$.

   1. Show that $L_1$ and $L_2$ intersect.
   2. Find the exact coordinates of the point of intersection.
   Worked solution

   1. M1 for equating the parametric equations: $1+2\lambda =5-\mu$, $\lambda =-3+2\mu$, and $1+\lambda =\mu$.
      M1 for taking two equations to solve for the parameters, e.g., $\lambda =\mu -1$ into $2\lambda +\mu =4$.
      M1 for $2(\mu -1)+\mu =4⟹3\mu -2=4⟹3\mu =6$.
      A1 for finding $\mu =2$ and $\lambda =1$.
      B1 for verifying with the unused equation: $\lambda -2\mu =1-4=-3$, which matches the second component equation, showing the lines intersect.
   2. M1 for substituting $\lambda =1$ into $L_1$ (or $\mu =2$ into $L_2$).
      A1 for the intersection point $(3,1,2)$.

More on these topics: Sequences and series · Numerical methods · Vectors

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 10 marks.
• Biggest question: Q15, 10 marks: radians: a toy's surface area, then optimising.
• Marks by main topic: Integration 24, Algebra and functions 19, Trigonometry 18, Differentiation 8, Exponentials and logarithms 8, Sequences and series 7, Vectors 6, Coordinate geometry 5, Proof 5.
• More Trigonometry in other sittings: November 2021 Q10 (8 marks), June 2023 Q8 (10 marks), October 2020 Q12 (8 marks).
• Against the other 7 sittings we mapped: more marks on Integration (24 marks here, 14 on average); fewer on Differentiation (8 marks here, 19 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. Q1Image of a point under graph transformations (4 marks) · Algebra and functions
2. Q2Factor theorem to find a constant (3 marks) · Algebra and functions
3. Q3Circle centre, radius and a tangent (5 marks) · Coordinate geometry
4. Q4Limit of a sum written as an integral (3 marks) · Integration, Exponentials and logarithms
5. Q5Tree height model fitted to data (6 marks) · Algebra and functions
6. Q6Cubic curve from its graph (6 marks) · Algebra and functions
7. Q7Proof by contradiction with even products (5 marks) · Proof
8. Q8Speed model with ln and the time to stop (8 marks) · Differentiation, Numerical methods
9. Q93D vectors in a parallelogram (6 marks) · Vectors
10. Q10Bee and wasp population models (8 marks) · Exponentials and logarithms
11. Q11Area between two curves (7 marks) · Integration
12. Q12Integration by parts with ln x (5 marks) · Integration
13. Q13Proving the arithmetic series sum (7 marks) · Sequences and series
14. Q14Trig equation from a compound angle (8 marks) · Trigonometry
15. Q15Radians: a toy's surface area, then optimising (10 marks) · Trigonometry, Differentiation
16. Q16Area under a parametric curve (9 marks) · Integration, Coordinate geometry