Edexcel A-Level Mathematics A2 P4.1.1 Proof By Contradiction Questions

Practise Edexcel IAL P4.1.1 proof by contradiction: assume the negation, derive an impossible algebraic consequence, and conclude clearly.

Exam points

Set up the contradiction by assuming the negation of the stated claim
Derive an impossible parity, algebraic, sign or inequality consequence
Conclude that the contradiction proves the original statement

[Maximum number: 4]

Prove by contradiction that for all positive numbers k

k+\frac{9}{k} \geqslant 6

Assume that there exists a positive number k such that $k+\frac9k<6$ .
$k+\frac9k<6\Rightarrow k^2+9<6k\Rightarrow k^2-6k+9<0$ $(k-3)^2<0$
But numbers squared are $\ge 0$ , hence $k+\frac9k\ge 6$ .
A1*

All question bank results loaded

Edexcel A-Level Mathematics A2 P4.1.1 Proof By Contradiction Questions question 1