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Mathematical Induction: What will the NSW HSC Markers accept for a
conclusion?

One of my students asked me this question last year. Here is my research and response. **2008 Ext 1 Mathematical Induction Question**

From the marker comments (produced by the Board of Studies) they seem to suggest that there was:

- 1 mark for step,

- 1 mark for 'the inductive step' (assuming true for )

- 1 mark for proving true for

In addition, from 2009, the BOS has started to provide "sample answers"

The marking guideline clearly gives one mark for proving true for n = 1 (this is actually part (i) of the question). For part (ii), one mark is given for the 'inductive step' --- i.e. assuming true for n = k and one mark for proving true for n = k+1. It looks like NO marks are allocated to the conclusion.At MANSW's Markers Reports and advice days in the past it has been said that a conclusion as brief as "Hence proved by Mathematical Induction" would be sufficient.

However, there is no harm in taking the 5-10 seconds to write a conclusion.

In 2010, Q7(a) was a reasonable typical divisibility induction question. The marker's notes affirm one mark for proving *n* = 1, The inductive step and proving *n* = *k* + 1 are both important steps. The conclusion was not mentioned in the notes, except to say that there is no point writing out the structure of an induction proof (conclusion) without any attempt at a proof. The conclusion given is very similar to the previous year: "**result is true for all integers n > 1 by induction."**
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