Page 2: Basic Algebra and Substitution

This page covers fundamental algebraic concepts and the substitution method, along with practical examples of factorisation.

Definition: Variables are letters used to represent numbers, while expressions are combinations of letters and numbers.

Vocabulary: An equation contains an equals sign and at least one variable, while a formula involves multiple variables.

Highlight: When performing substitution, always use brackets around negative numbers to avoid calculation errors.

Example: To find the value of 3x² - 5 when x = 3:

1. Write 3(3)² - 5
2. Calculate the result using proper order of operations

The page emphasizes the importance of identifying common factors in factorisation:

• Look for common coefficients first
• Then identify common variables
• Express the factored form using brackets

Page 1: Quadratic Expressions and Factorisation

This page introduces the fundamental concepts of quadratic expressions and their manipulation through expansion and factorisation. The content focuses on methods for expanding bracket expressions and factorising quadratic terms.

Definition: Quadratic expressions are algebraic expressions where the highest power of a variable is 2, such as y² or 3t².

Example: When expanding (x + 3)(x + 4), multiply each term in the first bracket by each term in the second bracket.

Highlight: For factorisation of expressions like x² + ax + b, the expression inside each bracket will start with x, and the signs in the brackets depend on the original expression's signs.

Vocabulary: Factorisation is the process of converting a quadratic expression back into its bracket form.

The page outlines different patterns for factorising quadratic expressions:

• x² + ax + b = (x + ?)(x + ?)
• x² + ax - b = (x + ?)(x - ?)
• x² - ax + b = (x - ?)(x - ?)