CAIE A-Level Mathematics A2 3.1.5 Binomial Expansion Questions

Practise binomial expansions, coefficients and validity intervals within the AS mathematics syllabus.

Exam points

expand binomial expressions to a stated power
find coefficients and use binomial terms in products
state validity intervals for binomial expansions

[Maximum number: 5]

Let $\mathrm{f}(x)=\frac{2+11 x-10 x^{2}}{(1+2 x)(1-2 x)(2+x)}$ .

Hence obtain the expansion of f(x) in ascending powers of x, up to and including the term in $x^{2}$ .

Use a correct method to find the first two terms of the expansion of one of
$(1+2x)^{-1},\quad (1-2x)^{-1},\quad (2+x)^{-1},\quad \left(1+\frac12x\right)^{-1}.$
Obtain correct unsimplified expansions up to the term in $x^2$ of each partial fraction.
A1FT + A1FT + A1FT

The follow-through is on A, B, and C.

Final answer:
$1+5x-\frac72x^2.$

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CAIE A-Level Mathematics A2 3.1.5 Binomial Expansion Questions question 1