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What you need to know
What you need to know:
Mathematical proof is a very important idea, and it crops up in every corner of mathematics, including in many parts of the GCSE maths course. The majority of this topic is aimed towards the higher course, however it is still important for all who are taking foundation or higher to understand the structure of a proof. The idea of using existing facts and information (using things given to you in the question as well as known truths, e.g. all angles in a triangle add up to 180), and constructing an argument in order to learn something new, is the primary idea on the topic of proof. A lot of the time this is understood implicitly, but that does not diminish its importance.
For those taking the higher course, proof is made slightly more explicit in a few ways. You will be expected to be familiar with using algebra to construct mathematical arguments and prove facts about numbers. An example of this might be:
- Prove that the sum of three consecutive odd numbers is a multiple of 6.
In this case you should ascertain that 2n + 1 is an algebraic way of representing a general odd number, and moreover you can express the next two odd numbers algebraically. Then, follow the argument through and try to demonstrate that it is indeed a multiple of 6.
You may also be asked to prove certain geometric facts using vectors. The principle is the same, use the information in the question as well as existing facts about vectors to try to construct an argument, and prove something new (naturally, you’ll be asked to prove a specific statement).
One final point is that sometimes you are asked to disprove something. This is usually easier, as all it requires is for you to find one counterexample – a single example for which the statement in question doesn’t work. Then you have successfully shown the statement to be false.
Proof and algebraic proof are one of the most difficult topics to teach and yet there are very few great resources out there to help tutors and teachers to deliver this topic. Thankfully at Maths Made Easy we have taken the time to research the best resources out there as well as add in much of our own to help create a super resource for proof.
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