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Question 96

A systems architect models the relationship between the number of active server nodes, $n$ , and the number of concurrent maintenance processes, $m$ , using the equation

n^2 - 12m - 10 = 0

Assume that $n\,$ and $m\,$ are both integers.

Prove that $n\,$ is even.

[2]

Hence, prove that $6 m + 5$ is even and explain why this leads to a contradiction.

[3]

Explain what can be deduced about the possible integer values for $n\,$ and $m\,$ in this model.

[1]

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 96

A systems architect models the relationship between the number of active server nodes, $n$ , and the number of concurrent maintenance processes, $m$ , using the equation

n^2 - 12m - 10 = 0

Assume that $n\,$ and $m\,$ are both integers.

Prove that $n\,$ is even.

[2]

Hence, prove that $6 m + 5$ is even and explain why this leads to a contradiction.

[3]

Explain what can be deduced about the possible integer values for $n\,$ and $m\,$ in this model.

[1]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof