Edexcel IAL P2 June 2024 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. Logarithms and Exponentials · 5 marks

   Solve the equation ${\log }_{2}x+{\log }_{x}2=2.5$ for $x>0,x\ne 1$.

   Worked solution

   1. M1 for applying the reciprocal rule: ${\log }_{x}2=\frac{1}{{\log }_{2}x}$.
   2. M1 for making the substitution $u={\log }_{2}x$ to form $u+\frac{1}{u}=2.5$.
   3. M1 for multiplying by $2u$ to form the quadratic $2u^2-5u+2=0$ and solving it.
   4. M1 for finding the roots $u=2$ and $u=\frac{1}{2}$.
   5. A1 for converting back to $x$ and finding both solutions: $x=4$ and $x=\sqrt{2}$.

2. 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.

3. Algebraic Methods · 4 marks

   Fully factorise the polynomial $f(x)=2x^3-5x^2-4x+3$.

   Worked solution

   1. M1 for using the factor theorem to find one root, e.g., evaluating $f(-1)=-2-5+4+3=0$, to deduce $(x+1)$ is a factor.
   2. M1 for performing algebraic division to find the quadratic quotient.
   3. A1 for obtaining the correct quadratic quotient $2x^2-7x+3$.
   4. A1 for fully factorising the quadratic to provide the final answer $(x+1)(2x-1)(x-3)$.

More on these topics: Logarithms and Exponentials · Circles · Algebraic Methods

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 5 to 12 marks.
• Biggest question: Q8, 12 marks: trig equations in radians.
• Marks by main topic: Logarithms and Exponentials 23, Further Trigonometry 12, Algebraic Methods 8, Differentiation (stationary points) 8, Sequences and Series 7, Proof 6, Circles 6, The Binomial Expansion 5.
• More Further Trigonometry in other sittings: October 2024 Q9 (7 marks), January 2024 Q9 (14 marks), October 2023 Q3 (7 marks).
• Against the other 16 sittings we mapped: more marks on Logarithms and Exponentials (23 marks here, 10 on average) and Further Trigonometry (12 marks here, 8 on average); fewer on Integration (definite integrals and area) (0 marks here, 9 on average) and Sequences and Series (7 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, first four terms (5 marks) · P2 The Binomial Expansion
2. Q2Arithmetic series from two conditions (7 marks) · P2 Sequences and Series
3. Q3Log equation with base change (6 marks) · P2 Logarithms and Exponentials
4. Q4Remainder and factor theorem with k (8 marks) · P2 Algebraic Methods
5. Q5Proof of an inequality (6 marks) · P2 Proof
6. Q6Exponential graph and an intersection (9 marks) · P2 Logarithms and Exponentials
7. Q7Circle centre, radius and a second circle (6 marks) · P2 Circles
8. Q8Trig equations in radians (12 marks) · P2 Further Trigonometry
9. Q9Stationary point and two areas (8 marks) · P2 Differentiation (stationary points), P2 Integration (definite integrals and area)
10. Q10Dormouse and vole population models (8 marks) · P2 Logarithms and Exponentials

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What the examiners said about this paper

Summarised in our own words from the board's examiner report (Examiner Insights).

• WMA12/01: Logarithms (Q3); Factor theorem (Q4); Proof (Q5). Official examiner report ↗

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