Proof is the best bit of Maths!
Really… but what is proof?
Proof is the process of showing something is true in every case, often by using algebra.
Given an algebraic expression…
Just do it!
- Expand brackets.
- Simplify. (Work with left hand side only if = sign involved)
- Make sure you finish with the statement you are proving
Exam Tip: “A multiple of k” means it can be written as k(……) – ie. k × …
This is a bit trickier but turning it into algebra is usually the best thing to do.
- Give things names (use as few letters as possible):
- n is “any integer” (or m or k or…)
- n + 1 is the integer after n (“consecutive”)
- 2n is an even integer (2n + 2 is the next one)
- 2m is a different even integer
- 2n + 1 is an odd integer (and 2n + 3 is the next one)
- Then go on as above (“Given an Algebraic Expression”)