Date | November Example questions | Marks available | 8 | Reference code | EXN.1.AHL.TZ0.9 |
Level | Additional Higher Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 0 |
Command term | Prove | Question number | 9 | Adapted from | N/A |
Question
It is given that . (Do not prove this identity.)
Using mathematical induction and the above identity, prove that for .
Markscheme
* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.
let be the proposition that for
considering :
and
so is true R1
assume is true, i.e. M1
Note: Award M0 for statements such as “let ”.
Note: Subsequent marks after this M1 are independent of this mark and can be awarded.
considering
M1
A1
M1
Note: Award M1 for use of with and .
A1
A1
is true whenever is true, is true, so is true for R1
Note: Award the final R1 mark provided at least five of the previous marks have been awarded.
[8 marks]