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

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1. Sequences and Series · 5 marks

   The second term of a geometric series is 12 and its sum to infinity is 64. Find the two possible values of the common ratio, $r$, and the corresponding values of the first term, $a$.

   Worked answer

   1. M1 for setting up the two equations: $ar = 12$ and $\frac{a}{1-r} = 64$.
   2. M1 for substituting $a = \frac{12}{r}$ to get $\frac{12/r}{1-r} = 64 \implies 12 = 64r(1-r)$.
   3. M1 for forming the quadratic $16r^2 - 16r + 3 = 0$.
   4. A1 for finding $r = 0.25$ and $r = 0.75$.
   5. A1 for finding the corresponding first terms: $a = 48$ and $a = 16$.

2. Further Trigonometry · 5 marks

   Solve the equation $2\cos^2 x - \sin x - 1 = 0$ for $0^\circ \le x \le 360^\circ$.

   Worked answer

   1. M1 for using the identity $\cos^2 x = 1 - \sin^2 x$ to rewrite the equation: $2(1 - \sin^2 x) - \sin x - 1 = 0$.
   2. M1 for simplifying to a quadratic in $\sin x$: $2\sin^2 x + \sin x - 1 = 0$.
   3. M1 for factorising the quadratic to $(2\sin x - 1)(\sin x + 1) = 0$.
   4. A1 for finding the solutions from $\sin x = 0.5$, which are $x = 30^\circ, 150^\circ$.
   5. A1 for finding the solution from $\sin x = -1$, which is $x = 270^\circ$.

3. The Binomial Expansion · 4 marks

   The first three terms of the expansion $(a+bx)^6$ are $64 - 192x + cx^2$. Find the values of the constants $a$, $b$, and $c$.

   Worked answer

   1. M1 for equating the first term: $a^6 = 64 \implies a=2$.
   2. M1 for equating the $x$ coefficient to find $b$: $\binom{6}{1}a^5 b = -192 \implies 6(32)b = -192 \implies 192b = -192$.
   3. A1 for obtaining $b = -1$.
   4. A1 for finding the $x^2$ coefficient: $c = \binom{6}{2}a^4 b^2 = 15(16)(-1)^2 = 240$.

More on these topics: Sequences and Series · Further Trigonometry · The Binomial Expansion

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)