Edexcel IAL P2 June 2021 question paper and mark scheme (WMA12/01)

Try 3 P2 questions like these

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1. Further Trigonometry · 5 marks

   Solve $2\sin^2 x + 3\cos x - 3 = 0$ for $0^\circ \le x \le 360^\circ$.

   Worked answer

   1. M1 for substituting $\sin^2 x$ with $1 - \cos^2 x$ to get $2(1 - \cos^2 x) + 3\cos x - 3 = 0$.
   2. M1 for expanding and rearranging to form the quadratic $2\cos^2 x - 3\cos x + 1 = 0$.
   3. M1 for factorising the quadratic as $(2\cos x - 1)(\cos x - 1) = 0$.
   4. A1 for finding the solutions from $\cos x = 0.5$ giving $x = 60^\circ$ and $300^\circ$.
   5. A1 for finding the solutions from $\cos x = 1$ giving $x = 0^\circ$ and $360^\circ$.

2. Differentiation (stationary points) · 4 marks

   Find the set of values of $x$ for which $f(x) = x^4 - 8x^2$ is an increasing function.

   Worked answer

   1. M1 for finding the derivative $f'(x) = 4x^3 - 16x$.
   2. M1 for setting $f'(x) > 0$ and factorising: $4x(x^2 - 4) > 0 \implies 4x(x-2)(x+2) > 0$.
   3. M1 for finding the critical values $x = -2, 0, 2$ and testing regions.
   4. A1 for stating the correct range: $-2 < x < 0$ or $x > 2$.

3. Integration (definite integrals and area) · 6 marks

   The curve with equation $y = x^3 - 4x$ intersects the x-axis at $x = -2$, $x = 0$, and $x = 2$. Find the total exact area enclosed between the curve and the x-axis.

   Worked answer

   1. M1 for recognising that the region between $0$ and $2$ is below the x-axis, so the integrals must be computed separately.
   2. M1 for integrating to find the generic primitive: $[\frac{1}{4}x^4 - 2x^2]$.
   3. M1 for evaluating the integral from $-2$ to $0$: $(0) - (4 - 8) = 4$.
   4. M1 for evaluating the integral from $0$ to $2$: $(4 - 8) - (0) = -4$.
   5. M1 for taking the absolute value of the negative area before combining.
   6. A1 for the total correct area: $4 + |-4| = 8$.

More on these topics: Further Trigonometry · Differentiation (stationary points) · Integration (definite integrals and area)

P2 topics this paper can test

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• Sequences and Series
• Logarithms and Exponentials
• Circles
• Further Trigonometry
• Algebraic Methods
• Proof
• The Binomial Expansion
• Differentiation (stationary points)
• Integration (definite integrals and area)

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Formula booklet

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