CAIE IGCSE Additional Math 12.1 Use the Binomial Theorem Questions

Practise the binomial theorem by expanding powers of (a + b)^n, simplifying coefficients and selecting the required terms in Cambridge International Additional Mathematics questions.

Exam points

Use the binomial theorem to expand powers of (a + b)^n, simplifying coefficients and retaining the required terms.

[Maximum number: 5]

In this question a, b and n are constants.
When $5(2+a x)^{n}$ is written in ascending powers of x, the first three terms are $640+b^{2} x+30240 x^{2}$ . Find the value of a and the possible values of b.

n=7 soi
$5\times\frac{7\times6}{2}\times2^5\times a^2=30240$ oe
$5\times7\times2^6\times a=b^2$ a=3 only, nfww
$b=\pm\sqrt{6720}$ oe, isw, nfww
If first B1 only scored then SC1 for $a=3\sqrt5$ or $\sqrt{45}$ or 6.71 or 6.708... only, and SC1 for $b=\pm\sqrt{1344\sqrt5}$ or $\pm54.8...$ .

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CAIE IGCSE Additional Math 12.1 Use the Binomial Theorem Questions question 1