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Date May 2014 Marks available 8 Reference code 14M.2.hl.TZ1.7
Level HL only Paper 2 Time zone TZ1
Command term Prove Question number 7 Adapted from N/A

Question

Prove, by mathematical induction, that 78n+3+2, nN, is divisible by 5.

Markscheme

if n=0

73+2=345 which is divisible by 5, hence true for n=0     A1

 

Note:     Award A0 for using n=1 but do not penalize further in question.

 

assume true for n=k     M1

 

Note:     Only award the M1 if truth is assumed.

 

so 78k+3+2=5p, p     A1

if n=k+1

78(k+1)+3+2     M1

=7878k+3+2     M1

=78(5p2)+2     A1

=78.5p2.78+2

=78.5p11529600

=5(78p2305920)     A1

hence if true for n=k, then also true for n=k+1. Since true for n=0, then true for all n     R1

 

Note:     Only award the R1 if the first two M1s have been awarded.

 

[8 marks]

Examiners report

[N/A]

Syllabus sections

Topic 1 - Core: Algebra » 1.4 » Proof by mathematical induction.

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