Course home

1.1 Proof by Contradiction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92

Question 90

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 by Contradiction Questions

A Level
Maths
1.1 Proof by Contradiction

107 exam-style questions on Edexcel A Level Maths 1.1 Proof by Contradiction. Each one has a worked solution and a mark scheme showing where the marks go.

1.1 Proof by Contradiction

Question bank

1.1 Proof by Contradiction

Easy Medium Hard

Question 90

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 by Contradiction Questions

A Level
Maths
1.1 Proof by Contradiction

107 exam-style questions on Edexcel A Level Maths 1.1 Proof by Contradiction. Each one has a worked solution and a mark scheme showing where the marks go.