CAIE IGCSE Additional Math 12.2 Use the General Binomial Term Questions

Practise using the general binomial term to locate specified powers, find terms independent of x and connect coefficients in Cambridge International Additional Mathematics questions.

Exam points

Use the general binomial term to find a specified term, such as the term independent of x, and solve coefficient relationships.

[Maximum number: 6]

Find the exact value of the term independent of x in the expansion of $\left(2+\frac{3}{x^{2}}\right)^{10}\left(1-4 x^{2}\right)^{2}$ .

$2^{10}+10\times2^9\times\frac{3}{x^2}+45\times2^8\times\left(\frac{3}{x^2}\right)^2\ \text{oe, soi}$
and
$1-8x^2+16x^4\ \text{soi}$
B2 for the first expansion;
B1 for two correct terms in the first expansion;
B1 for $1-8x^2+16x^4$ .
$2^{10}+$ their $15360\times$ their (-8)+ their $103680\times$ their 16
M2 FT expansions;
M1 FT for any two correct terms in this sum.
1537024

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CAIE IGCSE Additional Math 12.2 Use the General Binomial Term Questions question 1