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Question 95

A structural engineer calculates that the side length, $s$ decimetres, of a square support column must satisfy the equation $s^2 = 13$ to meet safety specifications.

Use proof by contradiction to prove that $s$ is an irrational number.

(You may assume that for any integer $n$ , if $n^2$ is a multiple of 13, then $n$ is a multiple of 13).

[6]

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 95

A structural engineer calculates that the side length, $s$ decimetres, of a square support column must satisfy the equation $s^2 = 13$ to meet safety specifications.

Use proof by contradiction to prove that $s$ is an irrational number.

(You may assume that for any integer $n$ , if $n^2$ is a multiple of 13, then $n$ is a multiple of 13).

[6]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof