1.1 Proof by Contradiction

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Relative to a fixed origin $O$ , the points $P$ , $Q$ , and $R\,$ have position vectors $p\mathbf{p}$ , $q\mathbf{q}$ , and $r\mathbf{r}$ respectively. The points $P$ , $Q$ , and $R\,$ lie on a straight line such that $Q\,$ lies between $P\,$ and $R$ . Given that $P Q : P R = 1 : 4$ , show that: $r=4q−3p\mathbf{r} = 4\mathbf{q} - 3\mathbf{p}$

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ii.

Given that $\in \mathbb{Z}$ , prove by contradiction that if $n^2\,$ is a multiple of 5, then $n\,$ is a multiple of 5.

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1.1 Proof by Contradiction Questions

Practise Edexcel A Level Maths 1.1 Proof by Contradiction with exam-style questions for A Level Maths. 100 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.