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1.1 Proof

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Question 56

Assume that $x$ and $y$ are integers such that

x^2 - 8y - 6 = 0

Prove that $x$ is even.

[2]

Hence, prove that $4 y + 3$ is even and explain why this leads to a contradiction.

[3]

Explain what can be deduced about the integer solutions to the equation $x^2 - 8y - 6 = 0$ .

[1]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof

107 exam-style questions on OCR A Level Maths 1.1 Proof, covering 1.1.1 Structure of mathematical proof, 1.1.2 Logical connectives, 1.1.3 Disproof by counter example, 1.1.4 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 56

Assume that $x$ and $y$ are integers such that

x^2 - 8y - 6 = 0

Prove that $x$ is even.

[2]

Hence, prove that $4 y + 3$ is even and explain why this leads to a contradiction.

[3]

Explain what can be deduced about the integer solutions to the equation $x^2 - 8y - 6 = 0$ .

[1]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof