Edexcel IAL P4 June 2024 mark scheme and question paper (WMA14/01)

3 P4 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. Partial Fractions · 7 marks

   Express ${\displaystyle \frac{x^3+1}{x^2-1}}$ in the form $Ax+B+{\displaystyle \frac{C}{x-1}}+{\displaystyle \frac{D}{x+1}}$ and find $A,B,C,D$.

   Worked solution

   Polynomial division: $\frac{x^3+1}{x^2-1}=x+\frac{x+1}{x^2-1}=x+\frac{1}{x-1}$ (since $\frac{x+1}{(x+1)(x-1)}=\frac{1}{x-1}$)   M1 M1 A1. So $A=1$, $B=0$, $C=1$, $D=0$   A1 A1 A1 A1.

2. Differential Equations · 4 marks

   Use the method of separation of variables to find the general solution to the differential equation: $$\frac{dy}{dx}=\frac{x}{y}$$ Express your answer in the form $y^2=f(x)$.

   Worked solution

   Separate the variables by multiplying both sides by $y$ and $dx$: M1
   $ydy=xdx$.
   Integrate both sides: $\int ydy=\int xdx$. M1
   $\frac{y^2}{2}=\frac{x^2}{2}+C$. A1
   Multiply entirely by 2 to isolate $y^2$:
   $y^2=x^2+2C$. (Note: $2C$ can just be written as a new constant $K$). A1

3. Coordinate Geometry (parametric) · 5 marks

   A curve $C$ has parametric equations $x=\sin \theta$ and $y=\cos 2\theta$ for $0\le \theta \le \pi$. Find the exact coordinates of the points where $C$ intersects the line $y=x$.

   Worked solution

   1. M1 for setting $x=y$, resulting in $\sin \theta =\cos 2\theta$.
   2. M1 for substituting the double angle formula: $\sin \theta =1-2{\sin }^2\theta$.
   3. M1 for rearranging into a quadratic $2{\sin }^2\theta +\sin \theta -1=0$ and factorising $(2\sin \theta -1)(\sin \theta +1)=0$.
   4. A1 for finding valid solutions for $\sin \theta$: $\sin \theta =\frac{1}{2}$ (rejecting $\sin \theta =-1$ since $0\le \theta \le \pi$).
   5. A1 for calculating the corresponding $(x,y)$ coordinates: $(\frac{1}{2},\frac{1}{2})$.

More on these topics: Partial Fractions · Differential Equations · Coordinate Geometry (parametric)

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 5 to 13 marks.
• Biggest question: Q5, 13 marks: parametric curve: area of a region.
• Marks by main topic: Vectors 16, Integration 14, Differentiation 13, Parametric Equations 13, Differential Equations 11, The Binomial Expansion 8.
• More Parametric Equations in other sittings: October 2024 Q3 (9 marks), January 2024 Q9 (12 marks), January 2025 Q9 (12 marks).
• Against the other 14 sittings we mapped: more marks on Vectors (16 marks here, 11 on average) and Differential Equations (11 marks here, 6 on average); fewer on Partial Fractions (0 marks here, 6 on average) and Proof (0 marks here, 4 on average).
• Not on this paper: Partial Fractions, Proof, Coordinate Geometry (parametric).
• Calculator: allowed.

WMA14/01: question by question

Labels and topics are ours, read from the WMA14/01 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Integration by parts with x cos 3x (5 marks) · P4 Integration
2. Q2Position vectors in 3D (6 marks) · P4 Vectors
3. Q3Implicit curve: tangent at a point (7 marks) · P4 Differentiation
4. Q4Rate of change of a segment's area (6 marks) · P4 Differentiation
5. Q5Parametric curve: area of a region (13 marks) · P4 Parametric Equations, P4 Integration
6. Q6Vector equations of two lines (10 marks) · P4 Vectors
7. Q7Current in an electrical circuit (11 marks) · P4 Differential Equations
8. Q8Binomial expansion of a cube root (8 marks) · P4 The Binomial Expansion
9. Q9Area under a curve with arctan (9 marks) · P4 Integration

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What the examiners said about this paper

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

• WMA14/01: Differential equations (Q7); Binomial (any index) (Q8); Connected rates of change (Q4). Official examiner report ↗

Question-by-question topics, the top mistakes and what to focus on next →