Edexcel IAL P3 June 2024 mark scheme and question paper (WMA13/01)

3 P3 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. Functions · 5 marks

   Solve the inequality $|2x+1|\le |x-5|$.

   Worked solution

   1. M1 for squaring both sides to remove the modulus signs: $(2x+1{)}^2\le (x-5{)}^2$.
   2. M1 for expanding the brackets: $4x^2+4x+1\le x^2-10x+25$.
   3. M1 for rearranging to form a quadratic inequality: $3x^2+14x-24\le 0$.
   4. M1 for factorising to find the critical values: $(3x-4)(x+6)\le 0$, yielding critical values $-6$ and $\frac{4}{3}$.
   5. A1 for stating the correct closed interval $-6\le x\le \frac{4}{3}$.

2. Further Integration · 4 marks

   Find $\int (\cos x-\sin x{)}^{2}dx$.

   Worked solution

   1. M1 for expanding the bracket to ${\cos }^{2}x-2\sin x\cos x+{\sin }^{2}x$.
   2. M1 for simplifying to $1-\sin 2x$.
   3. M1 for integrating the expression term by term.
   4. A1 for $x+\frac{1}{2}\cos 2x+c$.

3. Trigonometric Functions · 5 marks

   Solve ${\text{cosec}}^{2}x+{\cot }^{2}x=3$ for $0^{\circ }\le x\le {360}^{\circ }$.

   Worked solution

   1. M1 for using the identity ${\text{cosec}}^{2}x=1+{\cot }^{2}x$ to obtain $1+2{\cot }^{2}x=3$.
   2. M1 for rearranging to ${\cot }^{2}x=1$.
   3. M1 for taking the square root to find $\tan x=\pm 1$.
   4. A1 for finding the principal values ${45}^{\circ }$ and ${135}^{\circ }$.
   5. A1 for stating all four correct solutions: ${45}^{\circ },{135}^{\circ },{225}^{\circ },{315}^{\circ }$.

More on these topics: Functions · Further Integration · Trigonometric Functions

What's on this paper

What this paper is like

• Shape: 9 questions, 75 marks in 1 h 30 min (about 1.2 minutes a mark); questions from 6 to 10 marks.
• Biggest question: Q5, 10 marks: functions with ln: inverse and composite.
• Marks by main topic: Further Differentiation 29, Trigonometric Addition Formulae 17, Functions 16, Algebraic Methods 7, Exponentials and Logarithms 6.
• More Functions in other sittings: October 2024 Q6 (8 marks), January 2024 Q8 (11 marks), January 2025 Q6 (8 marks).
• Against the other 14 sittings we mapped: more marks on Further Differentiation (29 marks here, 19 on average) and Trigonometric Addition Formulae (17 marks here, 10 on average); fewer on Exponentials and Logarithms (6 marks here, 14 on average) and Further Integration (0 marks here, 5 on average).
• Not on this paper: Numerical Methods, Further Integration, Trigonometric Functions.
• Calculator: allowed.

WMA13/01: question by question

Labels and topics are ours, read from the WMA13/01 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Modulus graph and an equation (6 marks) · P3 Functions
2. Q2Writing a fraction as quotient and remainder (7 marks) · P3 Algebraic Methods
3. Q3Sketching y = 3^x and a log graph (6 marks) · P3 Exponentials and Logarithms
4. Q4Double-angle form and its maximum (9 marks) · P3 Trigonometric Addition Formulae
5. Q5Functions with ln: inverse and composite (10 marks) · P3 Functions, P3 Exponentials and Logarithms
6. Q6Curve, a tangent and an area (9 marks) · P3 Further Differentiation, P3 Further Integration
7. Q7Compound-angle equation (8 marks) · P3 Trigonometric Addition Formulae
8. Q8Model for a golf ball's path (10 marks) · P3 Further Differentiation
9. Q9x = 4 sin^2 y - 1: dy/dx and a tangent (10 marks) · P3 Further Differentiation

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What the examiners said about this paper

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

• WMA13/01: Functions (Q5); Modulus equations and inequalities (Q1); Exponential models (Q8). Official examiner report ↗

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