Edexcel IAL P2 January 2022 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. Algebraic Methods · 5 marks

   Let $f(x) = x^3 + cx^2 + dx - 4$. Given $f(x)$ has a factor $(x+2)$ and leaves a remainder of $-10$ when divided by $(x-3)$, find the values of $c$ and $d$.

   Worked answer

   1. M1 for applying the Factor Theorem for $(x+2)$: $f(-2) = 0 \implies -8 + 4c - 2d - 4 = 0 \implies 4c - 2d = 12$.
   2. M1 for applying the Remainder Theorem for $(x-3)$: $f(3) = -10 \implies 27 + 9c + 3d - 4 = -10 \implies 9c + 3d = -33$.
   3. M1 for simplifying both equations (e.g., $2c - d = 6$ and $3c + d = -11$).
   4. M1 for solving the simultaneous equations (e.g., adding them gives $5c = -5$).
   5. A1 for finding the correct values $c = -1$ and $d = -8$.

3. 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 $b = 5$.

More on these topics: Sequences and Series · Algebraic Methods · The Binomial Expansion

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)