Course home

1.1 Proof

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 93 94 95 96 97 98 99 100

Question 73

Expand and simplify $p + 3q)^2$ .

[1]

An electronics engineer claims that for any non-zero voltage ratio $v$ , the expression $\frac{9}{v}$ is always greater than or equal to 6.

The engineer tests two values: When $v = 9$ , $\frac{9}{9} = 10 \ge 6$ . When $v = 3$ , $\frac{9}{3} = 6 \ge 6$ .

Provide a counter-example to show that the engineer's claim is incorrect.

[1]

Given that $x$ and $y$ are positive real numbers such that $\neq 3y$ , use proof by contradiction to prove that:

\frac{x}{y} + \frac{9y}{x} > 6

[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

Question bank

1.1 Proof

Easy Medium Hard

Question 73

Expand and simplify $p + 3q)^2$ .

[1]

An electronics engineer claims that for any non-zero voltage ratio $v$ , the expression $\frac{9}{v}$ is always greater than or equal to 6.

The engineer tests two values: When $v = 9$ , $\frac{9}{9} = 10 \ge 6$ . When $v = 3$ , $\frac{9}{3} = 6 \ge 6$ .

Provide a counter-example to show that the engineer's claim is incorrect.

[1]

Given that $x$ and $y$ are positive real numbers such that $\neq 3y$ , use proof by contradiction to prove that:

\frac{x}{y} + \frac{9y}{x} > 6

[4]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof