Edexcel IAL P2 January 2020 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. Sequences and Series · 5 marks

   The first, third, and seventh terms of an arithmetic sequence (with a non-zero common difference) form three consecutive terms of a geometric sequence. Show that the first term is twice the common difference ($a = 2d$).

   Worked answer

   1. M1 for writing the 1st, 3rd, and 7th terms as $a, a+2d, a+6d$.
   2. M1 for setting up the geometric ratio condition: $\frac{a+2d}{a} = \frac{a+6d}{a+2d}$.
   3. M1 for cross-multiplying and expanding: $(a+2d)^2 = a(a+6d) \implies a^2 + 4ad + 4d^2 = a^2 + 6ad$.
   4. M1 for rearranging to $4d^2 - 2ad = 0 \implies 2d(2d - a) = 0$.
   5. A1 for concluding that since $d \ne 0$, $2d - a = 0 \implies a = 2d$.

2. 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 $360^\circ$.

3. 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)

More on these topics: Sequences and Series · Further Trigonometry · Proof

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 →

Formula booklet

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