Edexcel IAL P3 January 2021 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. 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 $\frac{4}{(x-2)(x-3)}$.

2. Trigonometric Addition Formulae · 6 marks

   Solve the equation $\cos 2x=\sin x$ for $-\pi \le x\le \pi$. Give your answers as exact radian values.

   Worked solution

   Substitute the double angle identity $\cos 2x=1-2{\sin }^{2}x$. M1
   $1-2{\sin }^{2}x=\sin x⟹2{\sin }^{2}x+\sin x-1=0$. A1
   Factorise the quadratic: $(2\sin x-1)(\sin x+1)=0$. M1A1
   Case 1: $2\sin x-1=0⟹\sin x=\frac{1}{2}$.
   Within the domain $-\pi \le x\le \pi$, solutions are $x=\frac{\pi }{6}$ and $x=\frac{5\pi }{6}$. A1
   Case 2: $\sin x+1=0⟹\sin x=-1$.
   Within the domain $-\pi \le x\le \pi$, the solution is $x=-\frac{\pi }{2}$. A1

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: Algebraic Methods · Trigonometric Addition Formulae · Exponentials and Logarithms

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 3 to 11 marks.
• Biggest question: Q5, 11 marks: oven temperature model.
• Marks by main topic: Exponentials and Logarithms 18, Further Differentiation 18, Functions 15, Trigonometric Addition Formulae 9, Algebraic Methods 8, Further Integration 7.
• More Exponentials and Logarithms in other sittings: October 2020 Q6 (9 marks), June 2021 Q8 (13 marks), October 2021 Q3 (6 marks).
• Against the other 14 sittings we mapped: more marks on Exponentials and Logarithms (18 marks here, 14 on average).
• Not on this paper: Numerical Methods, 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. Q1Integrating powers of x (3 marks) · P3 Further Integration
2. Q2Graph transformations through two points (6 marks) · P3 Functions
3. Q3Combining algebraic fractions (8 marks) · P3 Algebraic Methods
4. Q4Modulus graph and an equation (9 marks) · P3 Functions
5. Q5Oven temperature model (11 marks) · P3 Exponentials and Logarithms
6. Q6Derivative of x cos(x/3) and an iteration (8 marks) · P3 Further Differentiation, P3 Numerical Methods
7. Q7Double-angle identity, then an equation (9 marks) · P3 Trigonometric Addition Formulae
8. Q8Model for internet access (7 marks) · P3 Exponentials and Logarithms
9. Q9Two integrals: a fraction and an exponential (4 marks) · P3 Further Integration, P3 Exponentials and Logarithms
10. Q10dx/dy for a curve with sec (10 marks) · P3 Further Differentiation, P3 Trigonometric Functions

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