# Algebraic Proof Worksheets and Answers

# Teach Maths The Easy Way

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## Algebraic Proof Practice

Algebraic Proof worksheets for year 11 working at grades 5 and grades 8 for 9-1 GCSE Maths as well as international maths curriculum. This section contains questions on algebraic proof with the answers. Algebraic proof worksheets 1 contains questions with expression for given statements taking n as a positive integer. Algebraic proof worksheet number two is more difficult and students prove more difficult statements. This algebraic proof worksheet contains 3 different questions. The final algebraic proof worksheets contains far more tricky questions involving more complex algebraic techniques. Students will have a strong knowledge of Bodmas and Simplifying Expressions beforehand.

## Algebraic Proof Written as Expressions

Algebraic Proof statements can be written as expressions usually using the letter "n". In the graphic below there are 6 statements that can written as an expression of n.

## Algebraic Proof Example Question

The algebraic proof example below asks students to prove that the difference between 8^{12} and 12^{7} is a multiple of 4. To answer this question first show that 8^{12} is the same as 8^{1} x 8^{11} which is the same as (4 x 2 x 8^{11}). Next show that 12^{7} is the same as 12^{1} x 12^{6} which is the same as (4 x 3 x 12^{6}). As an extension to this problem students could show that the diference between 8^{a} and 12^{b} necessarily equals 4n.

## 'Prove that!'

Consider the conjecture below. Use proof by mathematical induction to come up with a solution.

## Algebraic Proof Key Words

Terminology is important when applying algebraic proof. You'll want to have a good grasp of all the key words.

When proving a statement algebraically you will use expressions usually in the form of the letters n or x. For example, to prove that a number is even we show that n is divisible by 2, or that n is a multiple of 2.

The graphic above asks students to explain the difference between a 'conjecture' and a 'proof'. A **conjecture** presents an idea which is yet to be proven. To learn more about the Poincare Conjecture see the article Grigori Perelman - The Mathematician Who Proved the Poincare Conjecture.

# Algebraic Proof Questions And Answers

**For Simplifying Expressions Cazoomy Worksheets try: Simplifying Expressions Worksheets. For Functions Cazoomy Worksheets try: Functions Worksheets. For Rearranging Formulae Cazoomy Worksheets try: Rearranging Formulae Worksheets.**