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1.1 Proof by Contradiction

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Question 81

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:

\mathbf{r} = 4\mathbf{q} - 3\mathbf{p}

[3]

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.

[4]

Markscheme

1.1 Proof by Contradiction Questions

A Level
Maths
1.1 Proof by Contradiction

107 exam-style questions on Edexcel A Level Maths 1.1 Proof by Contradiction. Each one has a worked solution and a mark scheme showing where the marks go.

1.1 Proof by Contradiction

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1.1 Proof by Contradiction

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Question 81

\mathbf{r} = 4\mathbf{q} - 3\mathbf{p}

[3]

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.

[4]

Markscheme

1.1 Proof by Contradiction Questions

A Level
Maths
1.1 Proof by Contradiction

107 exam-style questions on Edexcel A Level Maths 1.1 Proof by Contradiction. Each one has a worked solution and a mark scheme showing where the marks go.