Question 78 – 1.4 A: Proof - AQA A Level Maths Questions

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

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.

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

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

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.

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

1.4 A: Proof

Question 66

1.4 A: Proof

Question 66

1.4 A: Proof

Question 66

1.4 A: Proof Questions

1.4 A: Proof

Question 66

1.4 A: Proof Questions