Algebraic Proof Starter Questions
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 812 and 127 is a multiple of 4. To answer this question first show that 812 is the same as 81 x 811 which is the same as (4 x 2 x 811). Next show that 127 is the same as 121 x 126 which is the same as (4 x 3 x 126). As an extension to this problem students could show that the diference between 8a and 12b necessarily equals 4n.
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.