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, n∈N, 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(5p−2)+2 A1
=78.5p−2.78+2
=78.5p−11529600
=5(78p−2305920) 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]