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 69

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]

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.

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]

1.1 Proof

Question 69

Markscheme

1.1 Proof

Question 69

Markscheme

1.1 Proof

Question 69

1.1 Proof Questions

1.1 Proof

Question 69

1.1 Proof Questions