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1.1 Proof

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Question 81

A laser beam travels in a straight line from a source $S\,$ to a detector $D$ , passing through a filter $F$ . The points $S$ , $F$ , and $D\,$ have position vectors $s\mathbf{s}$ , $f\mathbf{f}$ , and $d\mathbf{d}$ respectively. Given that $F\,$ lies between $S\,$ and $D\,$ such that the ratio of distances $S F : S D = 2 : 7$ , show that:

\mathbf{d} = \frac{1}{2}(7\mathbf{f} - 5\mathbf{s})

[3]

ii.

Given that $\in \mathbb{Z}$ , prove by contradiction that if $n^2\,$ is a multiple of 3, then $n\,$ is a multiple of 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 81

\mathbf{d} = \frac{1}{2}(7\mathbf{f} - 5\mathbf{s})

[3]

ii.

Given that $\in \mathbb{Z}$ , prove by contradiction that if $n^2\,$ is a multiple of 3, then $n\,$ is a multiple of 3.

[4]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof