GCSE Secondary Maths Age 13-17 - Algebra: Algebraic Proof - Explained

The video tutorial covers solving algebraic problems by expanding and simplifying double brackets, and proving expressions algebraically. Part A focuses on expanding brackets using the FOIL method, while Part B involves proving that a given expression is even for all positive integers. The tutorial emphasizes the importance of algebraic proof over numerical examples and highlights common mistakes students make.

What is the first step in expanding double brackets using the FOIL method?

• Subtract the terms inside the brackets

• Multiply the first terms of each bracket

• Add the terms inside the brackets

• Divide the terms inside the brackets

What is the final simplified form of the expression y^2 - 5y - 2y + 10?

• y^2 - 7y + 10

• y^2 - 3y + 10

• y^2 - 7y - 10

• y^2 + 7y + 10

What is the key requirement for solving Part B of the question?

• Guess the answer

• Use numerical examples

• Use a calculator

• Prove algebraically

What is the expanded form of (2N + 1)^2?

• 2N^2 + 4N + 1

• 4N^2 + 4N + 1

• 2N^2 + 2N + 1

• 4N^2 + 2N + 1

What is the result of factorizing 4N^2 + 2N?

• 2(N^2 + 2N)

• 2(2N^2 + N)

• 4(2N^2 + N)

• 4(N^2 + N)

Why is the expression 4N^2 + 2N always even for positive integer values of N?

• It is a multiple of 2

• It is a multiple of 3

• It is a multiple of 5

• It is a multiple of 4

What was a common mistake made by students in Part B?

• Using numerical examples instead of algebraic proof

• Using a calculator

• Guessing the answer

• Skipping the question