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1.1 Proof

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Question 71

Relative to a fixed origin $O$ , the position vectors of three collinear sensors $A$ , $B$ , and $C\,$ are $a\mathbf{a}$ , $b\mathbf{b}$ , and $c\mathbf{c}$ respectively. The sensor $B\,$ is located such that the distance $AC\,$ is triple the distance $A B$ . Given that $B\,$ lies between $A\,$ and $C$ , show that:

\mathbf{c} = 3\mathbf{b} - 2\mathbf{a}

[3]

ii.

Prove by contradiction that for any integer $n$ , if $n^2\,$ is divisible by 3, then $n\,$ is divisible by 3.

[4]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof

132 exam-style questions on OCR (MEI) A Level Maths 1.1 Proof, covering 1.1.1 Structure of mathematical proof, 1.1.2 Disproof by counter example, 1.1.3 Proof by contradiction (A-level only), and 1.1 Proof. Each one has a worked solution and a mark scheme showing where the marks go.

1.1 Proof

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1.1 Proof

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Question 71

\mathbf{c} = 3\mathbf{b} - 2\mathbf{a}

[3]

ii.

Prove by contradiction that for any integer $n$ , if $n^2\,$ is divisible by 3, then $n\,$ is divisible by 3.

[4]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof