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2022 Mathematics Extension 2 Q13 (b) (ii) | HSC Atlas

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2022TrialShort answer

Q13 (b) (ii)

2 marks

Question

Prove by contraposition that if $n^2$ is not divisible by $18$ , then $n$ is not divisible by $6$ .

Try the question before revealing the answer.

Solution

(ii) Contrapositive:

If $n$ is divisible by $6$ ,

$n^2$ is divisible by $18$ .

Let $n=6k$ .

n^2=36k^2

=18\times2k^2,

which is divisible by $18$ .

Supplied marking guidance · human reviewed

Compare this with your working, not only your final sentence.

Syllabus alignment

Proof

The Nature of ProofUse formal proof language, contradiction, counter-examples and rigorous arguments involving numbers and inequalities.

Source

Girraween 2022 4U Trial PaperGirraweenQuestion paper page 7Guidance page 18View original source ↗

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