# Browsing category STEP

## What I learnt from a STEP Speedrun

I’ve been doing some work on STEP recently – maths exams used mainly for entrance at Cambridge and Warwick, who want some way to differentiate between very good A-level candidates. When I was in Year 13, I had an interview – in fact, two interviews – at Cambridge; at one

## Ask Uncle Colin: A STEP vectors problem

Dear Uncle Colin, I’m struggling with this STEP question. The first two parts are fine — equality holds when there is some constant $k$ for which $a = kx$, $b = ky$ and $c=kz$, and part (i) follows directly from the original inequality. I can get an answer to part

## A STEP expansion

A STEP question (1999 STEP II, Q4) asks: By considering the expansions in powers of $x$ of both sides of the identity $(1+x)^n (1+x)^n \equiv (1+x)^{2n}$ show that: $\sum_{s=0}^{n} \left( \nCr{n}{s} \right)^2 = \left( \nCr{2n}{n} \right)$, where $\nCr{n}{s} = \frac{n!}{s!(n-s)!}$. By considering similar identities, or otherwise, show also that: (i)