Edexcel IAL P3 October 2020 question paper and mark scheme (WMA13/01)

Try 3 P3 questions like these

Written and checked by us, not taken from the Pearson paper. Tap "Worked answer" to see every step.

1. Further Integration · 4 marks

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

   Worked answer

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

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 answer

   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 · 5 marks

   The variables $x$ and $y$ satisfy the equation $y = a b^x$. A graph of $\ln y$ against $x$ is plotted and forms a straight line passing through $(0, 2)$ and $(4, 10)$. Find the exact values of the constants $a$ and $b$.

   Worked answer

   1. M1 for taking natural logarithms of both sides to get $\ln y = \ln a + x \ln b$.
   2. M1 for calculating the gradient of the line: $\ln b = \frac{10 - 2}{4 - 0} = 2$.
   3. A1 for solving to find exactly $b = e^2$.
   4. M1 for identifying the y-intercept from the coordinate $(0, 2)$, so $\ln a = 2$.
   5. A1 for solving to find exactly $a = e^2$.

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

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)