Binomial expansion for positive integer powersEdexcel A-Level Maths: Mind map

Exam questions on Binomial expansion for positive integer powers

1. The expression $(1+2x)^5$ is expanded in ascending powers of $x$.
   Use the first three terms of the expansion, with a suitable value of $x$, to estimate $1.02^5$.2 marks
2. The random variable $X$ is the number of heads obtained when a fair coin is tossed 6 times, so $X\sim B\left(6,\frac12\right)$.
   Without evaluating either probability, explain why $P(X=4)=P(X=2)$.2 marks
3. The expression $(2+kx)^5$, where $k$ is a positive constant, is expanded in ascending powers of $x$. The coefficient of $x^2$ in the expansion is $720$.
   Find the value of $k$.3 marks