Edexcel IAL P3 January 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 · 4 marks

   Given that $f(x)=\frac{x+1}{x-2}$, $x\ne 2$, find an expression for $ff(x)$ in its simplest form.

   Worked solution

   1. M1 for substituting $f(x)$ into itself: $ff(x)=\frac{\frac{x+1}{x-2}+1}{\frac{x+1}{x-2}-2}$.
   2. M1 for multiplying the numerator and the denominator by $(x-2)$ to clear the nested fractions.
   3. M1 for obtaining the expanded fraction $\frac{(x+1)+(x-2)}{(x+1)-2(x-2)}$.
   4. A1 for fully simplifying to $\frac{2x-1}{5-x}$ (or $\frac{1-2x}{x-5}$).

2. Algebraic Methods · 4 marks

   Simplify fully $\frac{2x^2-x-1}{x^2-x}÷\frac{4x^2-1}{x}$.

   Worked solution

   1. M1 for rewriting the division as multiplication by the reciprocal: $\times \frac{x}{4x^2-1}$.
   2. M1 for factorising $2x^2-x-1$ to $(2x+1)(x-1)$ and $x^2-x$ to $x(x-1)$.
   3. M1 for factorising $4x^2-1$ to $(2x-1)(2x+1)$.
   4. A1 for cancelling all common factors to yield $\frac{1}{2x-1}$.

3. Exponentials and Logarithms · 4 marks

   Solve the equation $e^{2x}+4e^x-12=0$, giving your answer(s) in exact form.

   Worked solution

   1. M1 for identifying the hidden quadratic and factorising: $(e^x+6)(e^x-2)=0$.
   2. M1 for extracting the roots $e^x=2$ and $e^x=-6$.
   3. M1 for rejecting $e^x=-6$ since an exponential function must be positive.
   4. A1 for the exact valid solution $x=\ln 2$.

More on these topics: Functions · 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 4 to 13 marks.
• Biggest question: Q4, 13 marks: algebraic fractions and an inverse function.
• Marks by main topic: Functions 22, Exponentials and Logarithms 14, Algebraic Methods 13, Further Differentiation 12, Trigonometric Addition Formulae 8, Numerical Methods 6.
• More Algebraic Methods in other sittings: June 2024 Q2 (7 marks), January 2023 Q4 (7 marks), January 2025 Q4 (9 marks).
• Against the other 14 sittings we mapped: more marks on Algebraic Methods (13 marks here, 5 on average) and Functions (22 marks here, 16 on average); fewer on Further Differentiation (12 marks here, 20 on average) and Further Integration (0 marks here, 5 on average).
• Not on this paper: 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. Q1Image of a point under transformations (4 marks) · P3 Functions
2. Q2Root of a quartic and an iteration (6 marks) · P3 Numerical Methods
3. Q3Charity fund-raising model (7 marks) · P3 Exponentials and Logarithms
4. Q4Algebraic fractions and an inverse function (13 marks) · P3 Algebraic Methods, P3 Functions
5. Q5Air temperature model (7 marks) · P3 Exponentials and Logarithms
6. Q6Transformed graph through three points (7 marks) · P3 Functions
7. Q7Curve with a constant k: gradient and tangent (12 marks) · P3 Further Differentiation
8. Q8Modulus graph with constants a and b (11 marks) · P3 Functions
9. Q9Trig identity and an equation (8 marks) · P3 Trigonometric Addition Formulae, P3 Trigonometric Functions

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