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: 4]

Expand $(3+x)(1-2 x)^{\frac{1}{2}}$ in ascending powers of x, up to and including the term in $x^{2}$ , simplifying the coefficients.

State correct unsimplified first two terms of the expansion of $(1-2 x)^{\frac{1}{2}}$ ,
e.g. $1+\frac{1}{2}(-2 x)$
Symbolic coefficients are not sufficient.
1-x

State correct unsimplified term in $x^{2}$ , e.g. $\frac{\frac{1}{2}\left(\frac{1}{2}-1\right)(-2 x)^{2}}{2!}$
Symbolic coefficients are not sufficient.
$-\frac{1}{2} x^{2}$

Obtain sufficient terms of the product of (3+x) and the expansion up to the term
in $x^{2}$
Obtain final answer $3-2 x-\frac{5}{2} x^{2}$

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