smc-1019-10-Divisibility

Proof, EXT1 P1 2024 HSC 12d

Use mathematical induction to prove that is divisible by 7 for all integers . (3 marks)

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Proof, EXT1 P1 2022 HSC 12f

Use mathematical induction to prove that is divisible by 7 for all integers . (3 marks)

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Proof, EXT1 P1 2017 HSC 14a

Prove by mathematical induction that is divisible by 7, for any integer . (3 marks)

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Proof, EXT1 P1 2007 HSC 4b

Use mathematical induction to prove that is divisible by 12, for all integers . (3 marks)

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Proof, EXT1 P1 SM-Bank 3

Prove by mathematical induction that is divisible by 9 for integral . (3 marks)

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IMPORTANT: In cases where substitution doesn’t work, remember that

can be used to illustrate divisibility as well (Tony Lantry special).

Proof, EXT1 P1 2014 HSC 13a

Use mathematical induction to prove that is divisible by 3 for all integers . (3 marks)

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Proof, EXT1 P1 2010 HSC 7a

Prove by induction that

is divisible by for all integers . (3 marks)

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♦ Mean mark 51%.
IMPORTANT: Making

the subject helps the substitution in the proof for

. Students must state that

is an integer. NOTE: using

develops proof for

Proof, EXT1 P1 2012 HSC 12a

Use mathematical induction to prove that is divisible by for . (3 marks)

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IMPORTANT: Making

the subject helps for the substitution required in the proof for

. Important to state that

is an integer.