Edexcel IAL P2 June 2025 question paper and mark scheme (WMA12/01)

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1. Logarithms and Exponentials · 4 marks

   Given that $\log_2 x = p$ and $\log_2 y = q$, express $\log_2(8x^2 y^3)$ in terms of $p$ and $q$.

   Worked answer

   1. M1 for splitting the logarithm into a sum: $\log_2 8 + \log_2 x^2 + \log_2 y^3$.
   2. B1 for evaluating $\log_2 8 = 3$.
   3. M1 for applying the power law: $2\log_2 x + 3\log_2 y$.
   4. A1 for the final expression $3 + 2p + 3q$.

2. Proof · 6 marks

   Prove that \(n^4-n^2\) is a multiple of 12 for every integer \(n\).

   Worked answer

   Factorises: \(n^4-n^2=n^2(n-1)(n+1)\) M1

   \((n-1)n(n+1)\) is a product of three consecutive integers, so one factor is a multiple of 3 B1

   Considers \(n\) even and \(n\) odd M1

   \(n\) even: \(n=2k\), so \(n^2=4k^2\) is a multiple of 4 A1

   \(n\) odd: \(n-1\) and \(n+1\) are both even, so \((n-1)(n+1)\) is a multiple of 4 A1

   The number is a multiple of 3 and of 4, which have no common factor, so it is a multiple of 12 A1 (cso)

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: Logarithms and Exponentials · Proof · Integration (definite integrals and area)

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)

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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 (Q5); Factor theorem (Q4). Official examiner report ↗

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Formula booklet

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