Maths Core WMA01/WMA02: BINOMIAL EXPANSION Topical Past Paper Questions

(a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of $$ \left(\frac{1}{4}-3x\right)^{\frac{1}{2}} $$ giving each coefficient in its simplest form. (5) By substituting $ x = \frac{1}{100} $ into the answer for (a), (b) find an approximation for $ \sqr…

(a) Use the binomial series to find the expansion of $$ \frac{1}{(2+3x)^{3}}\quad|x| (5) (b) Hence or otherwise, find the coefficient of $ x^{2} $ in the series expansion of (i) $$ \frac{1}{(2+6x)^{3}}\quad\left|x\right|<\frac{1}{3} $$ $$ \frac{4-x}{\left(2+3x\right)^{3}}\quad\le…

$$ \mathrm{f}(x)=\left(125-5x\right)^{\frac{2}{3}}\qquad|x| (4) (b) Use your expansion to find an approximate value for $120^{\overline{3}}$, stating the value of $x$ which you have used and showing your working. Give your answer to 5 decimal places. (3)