Edexcel IAL P2 October 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 · 7 marks

   The points $A(1,2)$ and $B(7,10)$ lie on a circle $C$ with $AB$ as a diameter.
   (a) Find the equation of $C$. (4)
   (b) The tangent to $C$ at $A$ meets the $y$-axis at $T$. Find the coordinates of $T$. (3)

   Worked solution

   (a) Centre $=$ midpoint $=(4,6)$   B1. Radius $=\frac{1}{2}|AB|=\frac{1}{2}\sqrt{36+64}=5$   M1 A1. Equation: $(x-4{)}^2+(y-6{)}^2=25$   A1.
   (b) Radius from centre to $A$ has gradient $\frac{2-6}{1-4}=\frac{4}{3}$   B1. Tangent gradient $=-\frac{3}{4}$; equation: $y-2=-\frac{3}{4}(x-1)$. Set $x=0$: $y=2+\frac{3}{4}=\frac{11}{4}$   M1 A1.

2. Algebraic Methods · 5 marks

   Let $f(x)=x^3+c{x}^2+dx-4$. Given $f(x)$ has a factor $(x+2)$ and leaves a remainder of $-10$ when divided by $(x-3)$, find the values of $c$ and $d$.

   Worked solution

   1. M1 for applying the Factor Theorem for $(x+2)$: $f(-2)=0⟹-8+4c-2d-4=0⟹4c-2d=12$.
   2. M1 for applying the Remainder Theorem for $(x-3)$: $f(3)=-10⟹27+9c+3d-4=-10⟹9c+3d=-33$.
   3. M1 for simplifying both equations (e.g., $2c-d=6$ and $3c+d=-11$).
   4. M1 for solving the simultaneous equations (e.g., adding them gives $5c=-5$).
   5. A1 for finding the correct values $c=-1$ and $d=-8$.

3. Differentiation (stationary points) · 4 marks

   Find the coordinates of the stationary points on the curve $y=2x^3-15x^2+24x+6$.

   Worked solution

   1. M1 for differentiating to find $\frac{dy}{dx}=6x^2-30x+24$.
   2. M1 for setting to $0$ and factorising: $6(x^2-5x+4)=0⟹6(x-4)(x-1)=0$.
   3. A1 for finding the x-coordinates $x=1$ and $x=4$.
   4. A1 for finding the y-coordinates to state the full points: $(1,17)$ and $(4,-10)$.

More on these topics: Circles · Algebraic Methods · Differentiation (stationary points)

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 3 to 12 marks.
• Biggest question: Q9, 12 marks: tangent to a cubic and an enclosed area.
• Marks by main topic: Integration (definite integrals and area) 19, Logarithms and Exponentials 15, Sequences and Series 14, Differentiation (stationary points) 9, Further Trigonometry 8, The Binomial Expansion 7, Proof 3.
• More Integration (definite integrals and area) in other sittings: January 2023 Q9 (8 marks), June 2023 Q1 (3 marks), January 2022 Q9 (10 marks).
• Against the other 16 sittings we mapped: more marks on Integration (definite integrals and area) (19 marks here, 8 on average) and Logarithms and Exponentials (15 marks here, 10 on average); fewer on Circles (0 marks here, 8 on average) and Algebraic Methods (0 marks here, 7 on average).
• Not on this paper: Circles, Algebraic Methods.
• 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. Q1Proof by exhaustion with three integers (3 marks) · P2 Proof
2. Q2Binomial expansion with a constant k (7 marks) · P2 The Binomial Expansion
3. Q3Sequence defined with cos^2 (7 marks) · P2 Sequences and Series, P2 Further Trigonometry
4. Q4Log model for a baby mammal's weight (8 marks) · P2 Logarithms and Exponentials
5. Q5Trig equation with cos and tan (8 marks) · P2 Further Trigonometry
6. Q6Trapezium rule from a table (7 marks) · P2 Integration (definite integrals and area)
7. Q7Writing in index form, then a stationary point (9 marks) · P2 Differentiation (stationary points)
8. Q8Geometric series with a given sum to infinity (7 marks) · P2 Sequences and Series
9. Q9Tangent to a cubic and an enclosed area (12 marks) · P2 Integration (definite integrals and area), P2 Differentiation (stationary points)
10. Q10Logs in terms of a = log 3 (7 marks) · P2 Logarithms and Exponentials

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