Edexcel IAL P3 June 2022 question paper and mark scheme (WMA13/01)

Try 3 P3 questions like these

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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 answer

   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. Numerical Methods · 6 marks

   The equation $\cos x = x$ has a unique root $\alpha$ in $[0, 1]$. Using the iteration $x_{n+1} = \cos x_n$ with $x_0 = 0.5$, find $x_1$, $x_2$, $x_3$, and $x_4$ each to $4$ d.p. (Angle in radians.)

   Worked answer

   $x_1 = \cos 0.5 = 0.8776$   M1 A1. $x_2 = \cos 0.8776 = 0.6390$   A1. $x_3 = \cos 0.6390 = 0.8027$   A1. $x_4 = \cos 0.8027 = 0.6948$   A1 A1.

3. Further Integration · 4 marks

   Find $\int (\cos x - \sin x)^2 \, dx$.

   Worked answer

   1. M1 for expanding the bracket to $\cos^2 x - 2\sin x \cos x + \sin^2 x$.
   2. M1 for simplifying to $1 - \sin 2x$.
   3. M1 for integrating the expression term by term.
   4. A1 for $x + \frac{1}{2}\cos 2x + c$.

More on these topics: Functions · Numerical Methods · Further Integration

P3 topics this paper can test

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• Functions
• Numerical Methods
• Further Differentiation
• Further Integration
• Algebraic Methods
• Trigonometric Functions
• Trigonometric Addition Formulae
• Exponentials and Logarithms

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Formula booklet

Mathematical Formulae and Statistical Tables (International AS/A Level Mathematics) · Pearson Edexcel · For the 2018 IAL specification (current)