This video is a quick reminder of algebraic proof for GCSE maths, and is aimed at around grade 8. The questions are fairly challenging, and you really need to read the questions carefully.
– stop the video
– work through the question
– compare your solution
I hope the video helps and please leave a comment – thanks!
Here’s the questions:
1. Show algebraically that the sum of any 3 consecutive even numbers is always a multiple of 6.
2. Prove that (3n + 1)² – (3n – 1)² is a multiple of 4, for all positive integer values of n.
3. Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.
4. Prove algebraically that the sum of the squares of any 2 odd positive integers is always even.
5. 5(x – c) = 4x – 5 where c is an integer. Prove that x is a multiple of 5.
Download a copy of the question here:
Here’s a copy of the written answers:
These problems are fairly popular for GCSE maths, and appear on all the main examination boards such as Edexcel, AQA, OCR and Educas.
- any number is ‘n’
- any even number 2n
- any odd number is 2n + 1
- Work methodically
- Practice factorising
Here’s other posts that also might be of interest:
Please do leave a comment below if you are not sure. Alternately you can view my YouTube channel and leave a comment there – I’ll always try to respond as quickly as possible.
Watch on YouTube:
I’d really appreciate a like, if you found it useful! If you subscribe to the channel, you’ll also be notified of new uploaded videos 🙂