This section delves deeper into quadratic factorisation and introduces the method of completing the square.

Example: 3x² + 11x + 6 is factored as 3x+2$$x+3

The page provides multiple examples of factoring quadratic expressions, including those with a coefficient other than 1 for the x² term. It then transitions to completing the square, a technique used to rewrite quadratic expressions in a specific form.

Definition: Completing the square is a method used to convert a quadratic expression into the form $x+p$² + q.

Highlight: The completing the square quadratic example with solution shown is x² + 8x - 5, which is rewritten as $x+4$² - 21.

This page covers rules for indices, further examples of expanding brackets, and an introduction to surds.

Vocabulary: Indices (or exponents) are the powers to which a number or variable is raised.

The page provides examples of simplifying expressions with indices and expanding brackets with more complex terms. It also introduces the concept of surds and their simplification.

Example: 3a³ × 4a / 8a² is simplified to 3/2a²

Highlight: The section on surds introduces important rules for simplifying and rationalising expressions involving square roots.

This page continues with more advanced surd operations and introduces scientific notation.

Definition: A surd is a root (usually a square root) of a number that cannot be simplified to a whole or rational number.

The page provides examples of simplifying and rationalising surds, emphasizing the importance of fully simplifying expressions. It then transitions to scientific notation, demonstrating how to represent very large or small numbers.

Example: √27 + √48 - √12 is simplified to 5√3

Highlight: The scientific notation section includes practical examples, such as calculating the surface area of Jupiter relative to Earth.

This page focuses on applying scientific notation to real-world problems, particularly in astronomy and space travel.

Vocabulary: Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

The page provides examples of using scientific notation to perform calculations involving very large distances and speeds. It demonstrates how to use the distance-speed-time formula in conjunction with scientific notation.

Example: A rocket traveling at 1.32 × 10⁵ miles per second for 4 minutes covers a distance of 3.168 × 10⁸ miles.

Highlight: This section emphasizes the practical applications of scientific notation in fields like astronomy and space exploration.

The final page focuses on simplifying algebraic fractions, a crucial skill in advanced algebra.

Definition: An algebraic fraction is a fraction where the numerator, denominator, or both contain algebraic expressions.

The page provides examples of simplifying complex algebraic fractions, including those involving quadratic expressions. It demonstrates techniques for factoring and canceling common terms to simplify fractions.

Example: $b²-49$ / $b²-16$ is simplified to $b+7$ / $b+4$

Highlight: The simplifying algebraic fractions questions and answers provided here offer valuable practice for students preparing for advanced mathematics exams.

This page covers techniques for expanding brackets and factorising expressions. It provides several examples to illustrate these important algebraic skills.

Example: $2x-3$² is expanded as 4x²-12x+9

The page demonstrates the step-by-step process of expanding squared terms and multiplying two binomials. It also covers factorising techniques, including the difference of two squares and quadratic expressions.

Highlight: Factorising quadratic expressions is a crucial skill in algebra, often used in solving equations and simplifying complex expressions.

Vocabulary: Difference of two squares - a special case in algebra where an expression can be factored into the product of two binomials.