Edexcel IAL P3 October 2022 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. Further Differentiation · 4 marks

   Differentiate $y=\frac{e^{2x}}{x^2+1}$ with respect to $x$, giving your answer as a single algebraic fraction in its simplest form.

   Worked solution

   1. M1 for correctly identifying $u=e^{2x}$ and $v=x^2+1$, and their derivatives $2e^{2x}$ and $2x$.
   2. M1 for substituting into the quotient rule: $\frac{(x^2+1)2e^{2x}-e^{2x}(2x)}{(x^2+1{)}^2}$.
   3. M1 for factorising out $2e^{2x}$ in the numerator.
   4. A1 for the correct simplified expression: $\frac{2e^{2x}(x^2-x+1)}{(x^2+1{)}^2}$.

2. Algebraic Methods · 5 marks

   Express $\frac{x+2}{x^2-5x+6}-\frac{x-1}{x^2-4x+3}$ as a single fraction in its simplest form.

   Worked solution

   1. M1 for factorising $x^2-5x+6$ to $(x-2)(x-3)$.
   2. M1 for factorising $x^2-4x+3$ to $(x-1)(x-3)$.
   3. M1 for simplifying the second fraction: $\frac{x-1}{(x-1)(x-3)}$ cancels to $\frac{1}{x-3}$.
   4. M1 for creating a common denominator $(x-2)(x-3)$ and subtracting: $\frac{x+2}{(x-2)(x-3)}-\frac{x-2}{(x-2)(x-3)}$.
   5. A1 for reaching the final simplified answer $\frac{4}{(x-2)(x-3)}$.

3. Exponentials and Logarithms · 4 marks

   Solve the equation $2\ln x=\ln (3x+4)$.

   Worked solution

   1. M1 for applying the power law to the LHS: $\ln (x^2)=\ln (3x+4)$.
   2. M1 for equating the arguments: $x^2=3x+4$.
   3. M1 for rearranging to $x^2-3x-4=0$ and finding roots $x=4$ and $x=-1$.
   4. A1 for rejecting $x=-1$ (since $\ln x$ must have $x>0$) and giving $x=4$.

More on these topics: Further Differentiation · Algebraic Methods · Exponentials and Logarithms

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 12 marks.
• Biggest question: Q7, 12 marks: modulus graphs and their intersections.
• Marks by main topic: Functions 26, Trigonometric Addition Formulae 18, Exponentials and Logarithms 16, Algebraic Methods 9, Further Differentiation 6.
• More Functions in other sittings: January 2023 Q6 (8 marks), June 2022 Q2 (9 marks), June 2023 Q6 (9 marks).
• Against the other 14 sittings we mapped: more marks on Functions (26 marks here, 16 on average) and Trigonometric Addition Formulae (18 marks here, 10 on average); fewer on Further Differentiation (6 marks here, 21 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. Q1Algebraic division of a cubic (9 marks) · P3 Algebraic Methods
2. Q2Composite and inverse functions (7 marks) · P3 Functions
3. Q3Transformations of a graph through (2, 0) (7 marks) · P3 Functions
4. Q4Log function: x in terms of y and a gradient (5 marks) · P3 Exponentials and Logarithms, P3 Further Differentiation
5. Q5Company profit model (11 marks) · P3 Exponentials and Logarithms
6. Q6Quotient rule with sin and cos (6 marks) · P3 Further Differentiation, P3 Trigonometric Functions
7. Q7Modulus graphs and their intersections (12 marks) · P3 Functions
8. Q8R sin(x - a) form and its maximum (9 marks) · P3 Trigonometric Addition Formulae
9. Q9Identity with cos 2x, then an equation (9 marks) · P3 Trigonometric Addition Formulae

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