AQA A Level Maths November 2020 Paper 2: question paper and mark scheme (7357/2)

3 A Level questions like these, with worked solutions

Written and checked by us, not taken from the AQA paper. Try each one, then tap "Worked solution" to see every step and its marks.

1. Algebra and functions · 7 marks

   Let $f(x)=5-4x-2x^2$.
   
   (a) Express $f(x)$ in the form $A-B(x+C{)}^2$, where $A$, $B$, and $C$ are integers.
   (b) State the maximum value of $f(x)$ and the value of $x$ at which it occurs.
   (c) Solve $f(x)=0$, giving your answers in exact form.

   Worked solution

   (a) M1 Factors out $-2$ from the $x$ terms: $5-2(x^2+2x)$.

   1. M1 Completes the square inside the bracket: $5-2((x+1{)}^2-1)$.
   2. A1 Expands and simplifies to obtain $7-2(x+1{)}^2$.

   (b) B1 States the maximum value is $7$.

   1. B1 States this occurs at $x=-1$.

   (c) M1 Sets $7-2(x+1{)}^2=0$ and rearranges to $(x+1{)}^2=\frac{7}{2}$.

   1. A1 Solves for $x$ by square rooting, yielding $x=-1\pm \sqrt{\frac{7}{2}}$ (or equivalent exact surd).

2. 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: $c=(\genfrac{}{}{0ex}{}{6}{2})a^4{b}^2=15(16)(-1{)}^2=240$.

3. Kinematics · 5 marks

   A particle moving with constant acceleration passes three points $A$, $B$ and $C$, in that order, on a straight line. The distance $AB$ is $20\text{ m}$ and the distance $AC$ is $84\text{ m}$. The speed of the particle at $B$ is $12{\text{ m s}}^{-1}$ and its speed at $C$ is $20{\text{ m s}}^{-1}$. Find the acceleration of the particle and its speed at $A$.

   Worked solution

   1. M1 for $BC=84-20=64\text{ m}$.
   2. M1 for $v^2=u^2+2as$ from $B$ to $C$: ${20}^2={12}^2+2a(64)$.
   3. A1 for $128a=256\Rightarrow a=2{\text{ m s}}^{-2}$.
   4. M1 for $v^2=u^2+2as$ from $A$ to $B$: ${12}^2=u_A^2+2(2)(20)$.
   5. A1 for $u_A^2=64\Rightarrow u_A=8{\text{ m s}}^{-1}$.

More on these topics: Algebra and functions · Sequences and series · Kinematics

What this paper covers

What this paper is like

• Shape: 19 questions, 100 marks in 2 h (about 1.2 minutes a mark); questions from 1 to 13 marks.
• Biggest question: Q18, 13 marks: block on a rough inclined plane.
• Marks by main topic: Kinematics 33, Differentiation 21, Forces and Newton's laws 14, Coordinate geometry 8, Proof 7, Integration 6, Trigonometry 4, Sequences and series 3, Moments 3, Algebra and functions 1.
• More Forces and Newton's laws in other sittings: November 2021 Q15 (5 marks), June 2019 Q17 (9 marks), June 2022 Q19 (11 marks).
• Against the other 5 sittings we mapped: more marks on Differentiation (21 marks here, 8 on average) and Kinematics (33 marks here, 22 on average); fewer on Algebra and functions (1 marks here, 11 on average) and Exponentials and logarithms (0 marks here, 8 on average).
• Not on this paper: Exponentials and logarithms, Numerical methods, Vectors.
• Calculator: allowed.

7357/2: question by question

Labels and topics are ours, read from the 7357/2 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Decreasing functions (multiple choice) (1 marks) · Differentiation, Exponentials and logarithms
2. Q2Equations with no real solutions (tick one) (1 marks) · Algebra and functions
3. Q3Coefficient in a binomial expansion (3 marks) · Sequences and series
4. Q4Small-angle approximations for a limit (4 marks) · Trigonometry
5. Q5Integration by substitution with a root (6 marks) · Integration
6. Q6Circle tangent to a line (8 marks) · Coordinate geometry
7. Q7Proof about irrational numbers (7 marks) · Proof
8. Q8Parametric curve: gradient and normal (10 marks) · Differentiation, Coordinate geometry
9. Q9Maximising a cylinder cut from a hemisphere (10 marks) · Differentiation
10. Q10Constant speed (multiple choice) (1 marks) · Kinematics
11. Q11Resultant of forces (multiple choice) (1 marks) · Forces and Newton's laws
12. Q12Relative velocity of two particles (1 marks) · Kinematics
13. Q13Uniform rod on a pivot (3 marks) · Moments
14. Q14Position vector: velocity and acceleration (7 marks) · Kinematics
15. Q15Velocity-time graph: distance travelled (5 marks) · Kinematics
16. Q16Two particles released from rest (5 marks) · Kinematics
17. Q17Ball projected from a point (6 marks) · Kinematics
18. Q18Block on a rough inclined plane (13 marks) · Forces and Newton's laws
19. Q19Variable acceleration with calculus (8 marks) · Kinematics