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1.1 Proof by Contradiction

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Question 66

Expand and simplify $5x - 2y)^2$ .

[1]

An environmental scientist claims that for any non-zero real number $v$ , the sum of $v$ and its scaled reciprocal, $\frac{49}{v}$ , is always greater than or equal to 14.

The scientist tests two values: When $v = 7$ , $\frac{49}{7} = 14 \ge 14$ . When $v = 10$ , $\frac{49}{10} = 14.9 \ge 14$ .

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

[1]

Given that $x$ and $y$ are positive real numbers such that $\neq 2y$ , use proof by contradiction to prove that:

\frac{5x}{2y} + \frac{2y}{5x} > 2

[4]

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

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1.1 Proof by Contradiction

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Question 66

Expand and simplify $5x - 2y)^2$ .

[1]

An environmental scientist claims that for any non-zero real number $v$ , the sum of $v$ and its scaled reciprocal, $\frac{49}{v}$ , is always greater than or equal to 14.

The scientist tests two values: When $v = 7$ , $\frac{49}{7} = 14 \ge 14$ . When $v = 10$ , $\frac{49}{10} = 14.9 \ge 14$ .

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

[1]

Given that $x$ and $y$ are positive real numbers such that $\neq 2y$ , use proof by contradiction to prove that:

\frac{5x}{2y} + \frac{2y}{5x} > 2

[4]

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.