Download Algebraic Proof

Diophantus of Alexandria
Born about 200AD
Died about 284 AD
Sometimes called ‘the father of algebra’ , he was the
author of a series of books called ‘Arithmetica’.
Although most of his work is now lost his texts dealt with
solving algebraic equations which included the proof
that the quadratic formula could solve any
real quadratic equation.
Algebraic Proof
Monday 12th November 2014
Mathematical Proof
In order to prove that a conjecture is true for all
values we must use algebra.
Here are a couple of useful things that you need to
know:
Here are a couple of useful things that you need to know:
An algebraic expression to represent
an even number is:
An algebraic expression to represent
an odd number is:
In algebra we write consecutive numbers like this:
In algebra we write consecutive even numbers like
this:
In algebra we write consecutive odd numbers like this:
Here are a couple of useful things that you need to know:
Even + Even =
Even + Odd =
Odd + Odd=
Even × Even =
Even × Odd =
Odd × Odd =
Mathematical Skills that you
must be confident with are:
• Simplifying algebraic
expressions
• Expanding brackets
• Factorising
• Solving Equations
Show that:
2
2
2
(2n-1) + (2n+1) = 8n + 2
We need to manipulate the
algebra on the LHS to show
that is equal to the RHS
Hence prove that the sum of the two squares of any two
consecutive odd numbers is even.
Matching Activity
Can you sequence the proofs that you have been
given?
Each of you has two proofs you need to sort them
into two separate proofs and glue them down to a
sheet of A4 with a title.
Proving the
Quadratic Formula
RAG 123
RAG your learning so far, then log into the blog.
Pick the appropriate task for you.