Algebraic Proof

Summary and Exam Tips for Algebraic Proof

Algebraic Proof is a subtopic of Equations, Formulae, and Identities, which falls under the subject Mathematics in the Edexcel IGCSE curriculum. In this topic, you will learn to prove mathematical statements using algebraic methods. A mathematical proof is a logical argument that demonstrates the truth of a statement in all cases. The process often begins with known facts or definitions and proceeds through logical steps to reach a conclusion.

There are several methods to prove statements:

• Proof by Deduction: This involves starting from known facts and using logical reasoning to prove a statement. For example, proving that the product of two odd numbers is odd.
• Proof by Exhaustion: This method involves breaking a statement into smaller cases and proving each one separately. It is useful for a limited number of cases, such as proving the sum of two consecutive square numbers between 100 and 200 is odd.
• Disproof by Counter-Example: To disprove a statement, you only need one counter-example that does not fit the statement, such as showing that $3n + 3$ is not a multiple of 6 for all $n$.

In algebraic proofs, it is crucial to state any assumptions, show each step clearly, ensure logical progression, cover all cases, and conclude with a statement of proof. For identities, manipulate one side of the equation until it matches the other, showing all algebraic steps.

Exam Tips

• Understand the Methods: Familiarize yourself with different proof methods such as deduction, exhaustion, and counter-examples. Knowing when to use each method is crucial.

• Show Your Work: Clearly show each step of your proof. This not only helps in getting partial credit but also ensures you don't miss any logical steps.

• State Assumptions: Always state any assumptions or known facts you are using in your proof. This provides a solid foundation for your argument.

• Practice with Past Papers: Work through past paper questions to get a feel for the types of proofs you may be asked to complete. This will also help you manage your time effectively during the exam.

• Check Your Logic: Ensure that each step logically follows from the previous one. Double-check your work for any errors in reasoning or calculation.