Edexcel IAL P2 October 2024 question paper and mark scheme (WMA12/01)

Try 3 P2 questions like these

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

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. The Binomial Expansion · 5 marks

   The binomial expansion of $(1+ax)^b$, where $b$ is a positive integer, starts with $1 - 15x + 90x^2$. Find the values of $a$ and $b$.

   Worked answer

   1. M1 for equating the $x$ coefficient: $ab = -15$.
   2. M1 for equating the $x^2$ coefficient: $\frac{b(b-1)}{2} a^2 = 90 \implies b(b-1)a^2 = 180$.
   3. M1 for substituting $(ab) = -15$ or expanding to $a^2b^2 - a^2b = 180$ and substituting $a^2b^2 = 225$.
   4. M1 for solving for $a$: $225 - a(-15) = 180 \implies 15a = -45 \implies a = -3$.
   5. A1 for finding the corresponding value $b = 5$.

3. 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 $x > 2$.

More on these topics: Further Trigonometry · The Binomial Expansion · Differentiation (stationary points)

P2 topics this paper can test

Every P2 paper can test any of the 9 P2 topics in the specification.

We haven't mapped this paper question by question yet. Each topic below opens our P2 page at that topic: what it covers, a worked example with its mark scheme, then practice questions.

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

Practise these topics (opens the practice engine)

• IAL P2

Practise every P2 topic free →

What the examiners said about this paper

Summarised in our own words from the board's examiner report (Examiner Insights).

• WMA12/01: Logarithms (Q6); Trapezium rule (Q1); Proof (Q11). Official examiner report ↗

Question-by-question topics, the top mistakes and what to focus on next →

Formula booklet

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