Edexcel IAL P2 June 2022 mark scheme and question paper (WMA12/01)

3 P2 questions like these, with worked solutions

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

1. Circles · 5 marks

   The tangent to the circle $x^2+y^2=25$ at the point $P(3,4)$ meets the $x$-axis at $Q$. Find the coordinates of $Q$.

   Worked solution

   Radius $OP$ has gradient $\frac{4}{3}$   B1. Tangent gradient = $-\frac{3}{4}$ (perpendicular to radius)   M1. Equation: $y-4=-\frac{3}{4}(x-3)$   A1. Set $y=0$: $-4=-\frac{3}{4}(x-3)\Rightarrow x-3=\frac{16}{3}$   M1. So $x=\frac{25}{3}$   A1.

2. The Binomial Expansion · 5 marks

   The binomial expansion of $(1+ax{)}^b$, where $b$ is a positive integer, starts with $1-15x+90x^2$. Find the values of $a$ and $b$.

   Worked solution

   1. M1 for equating the $x$ coefficient: $ab=-15$.
   2. M1 for equating the $x^2$ coefficient: $\frac{b(b-1)}{2}{a}^2=90⟹b(b-1)a^2=180$.
   3. M1 for substituting $(ab)=-15$ or expanding to $a^2{b}^2-a^{2}b=180$ and substituting $a^2{b}^2=225$.
   4. M1 for solving for $a$: $225-a(-15)=180⟹15a=-45⟹a=-3$.
   5. A1 for finding the corresponding value $b=5$.

3. Integration (definite integrals and area) · 6 marks

   The curve with equation $y=x^3-4x$ intersects the x-axis at $x=-2$, $x=0$, and $x=2$. Find the total exact area enclosed between the curve and the x-axis.

   Worked solution

   1. M1 for recognising that the region between $0$ and $2$ is below the x-axis, so the integrals must be computed separately.
   2. M1 for integrating to find the generic primitive: $[\frac{1}{4}{x}^4-2x^2]$.
   3. M1 for evaluating the integral from $-2$ to $0$: $(0)-(4-8)=4$.
   4. M1 for evaluating the integral from $0$ to $2$: $(4-8)-(0)=-4$.
   5. M1 for taking the absolute value of the negative area before combining.
   6. A1 for the total correct area: $4+|-4|=8$.

More on these topics: Circles · The Binomial Expansion · Integration (definite integrals and area)

What's on this paper

What this paper is like

• Shape: 10 questions, 75 marks in 1 h 30 min (about 1.2 minutes a mark); questions from 4 to 12 marks.
• Biggest question: Q10, 12 marks: circle and a tangent line.
• Marks by main topic: Logarithms and Exponentials 23, Circles 12, Sequences and Series 8, Differentiation (stationary points) 8, Proof 7, Algebraic Methods 7, Further Trigonometry 6, The Binomial Expansion 4.
• More Circles in other sittings: January 2022 Q6 (8 marks), January 2023 Q6 (10 marks), October 2021 Q6 (8 marks).
• Against the other 16 sittings we mapped: more marks on Logarithms and Exponentials (23 marks here, 10 on average) and Circles (12 marks here, 7 on average); fewer on Integration (definite integrals and area) (0 marks here, 9 on average) and Sequences and Series (8 marks here, 13 on average).
• Not on this paper: Integration (definite integrals and area).
• Calculator: allowed.

WMA12/01: question by question

Labels and topics are ours, read from the WMA12/01 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Binomial expansion with a fractional term (4 marks) · P2 The Binomial Expansion
2. Q2Graph of a log of sin x (8 marks) · P2 Logarithms and Exponentials, P2 Further Trigonometry
3. Q3Disproving a claim about cubes, then a proof (7 marks) · P2 Proof
4. Q4Simultaneous equations with logarithms (6 marks) · P2 Logarithms and Exponentials
5. Q5Trig equation in degrees (6 marks) · P2 Further Trigonometry
6. Q6Geometric sequence from two conditions (8 marks) · P2 Sequences and Series
7. Q7Factor theorem with two constants (7 marks) · P2 Algebraic Methods
8. Q8Stationary points of a curve with negative powers (8 marks) · P2 Differentiation (stationary points)
9. Q9Carbon-14 dating with an exponential model (9 marks) · P2 Logarithms and Exponentials
10. Q10Circle and a tangent line (12 marks) · P2 Circles

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