Edexcel IAL P3 January 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. 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 $\frac{1}{2x-1}$.

2. 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: ${45}^{\circ },{135}^{\circ },{225}^{\circ },{315}^{\circ }$.

3. Trigonometric Addition Formulae · 4 marks

   Given that $\sin A=\frac{4}{5}$ and $\cos B=\frac{12}{13}$, where both $A$ and $B$ are acute angles, find the exact value of $\sin (A+B)$.

   Worked solution

   1. M1 for using a right-angled triangle or identity to find $\cos A=\frac{3}{5}$.
   2. M1 for finding $\sin B=\frac{5}{13}$.
   3. M1 for applying the formula $\sin (A+B)=\sin A\cos B+\cos A\sin B$.
   4. A1 for calculating $(\frac{4}{5})(\frac{12}{13})+(\frac{3}{5})(\frac{5}{13})=\frac{48}{65}+\frac{15}{65}=\frac{63}{65}$.

More on these topics: Algebraic Methods · Trigonometric Functions · Trigonometric Addition Formulae

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 4 to 11 marks.
• Biggest question: Q6, 11 marks: rational function: range and inverse.
• Marks by main topic: Functions 21, Further Differentiation 20, Exponentials and Logarithms 15, Trigonometric Functions 13, Further Integration 6.
• More Functions in other sittings: October 2021 Q2 (10 marks), June 2022 Q2 (9 marks), June 2021 Q4 (10 marks).
• Against the other 14 sittings we mapped: more marks on Trigonometric Functions (13 marks here, 3 on average) and Functions (21 marks here, 16 on average); fewer on Trigonometric Addition Formulae (0 marks here, 11 on average) and Algebraic Methods (0 marks here, 6 on average).
• Not on this paper: Numerical Methods, Algebraic Methods, Trigonometric Addition Formulae.
• 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. Q1Stationary point using calculus (4 marks) · P3 Further Differentiation, P3 Exponentials and Logarithms
2. Q2Equation with cos and cosec (5 marks) · P3 Trigonometric Functions
3. Q3Integrals by algebraic integration (6 marks) · P3 Further Integration
4. Q4Weed growth model (7 marks) · P3 Exponentials and Logarithms
5. Q5Curve with 6 ln: tangent and normal (9 marks) · P3 Further Differentiation, P3 Exponentials and Logarithms
6. Q6Rational function: range and inverse (11 marks) · P3 Functions, P3 Further Differentiation
7. Q7Modulus graph with a vertex (10 marks) · P3 Functions
8. Q8Antibiotic dose model (8 marks) · P3 Exponentials and Logarithms
9. Q9Trig equations in radians (8 marks) · P3 Trigonometric Functions, P3 Trigonometric Addition Formulae
10. Q10x = y e^(2y): dy/dx and a tangent (7 marks) · P3 Further Differentiation

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