Algebra & Graphs

Solving Linear Equations

A linear equation contains a variable (usually ) raised to the power of 1. Solving means finding the value of the variable that makes the equation tru...

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Rearranging Formulae

Rearranging a formula means making a different variable the subject. The subject is the variable on its own on one side of the formula. In , the subje...

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Expanding Brackets and Factorising

Expanding means removing brackets by multiplying. Factorising is the reverse — putting expressions into brackets. Expanding Single Brackets Multiply e...

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Quadratic Equations

A quadratic equation has the form where . Solving by Factorising If you can factorise the quadratic, set each bracket equal to zero. Either → Or → The...

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Straight-Line Graphs

The Equation of a Straight Line - = gradient (steepness of the line) - = y-intercept (where the line crosses the y-axis) Finding the Gradient - Positi...

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Simultaneous Equations

Simultaneous equations are two (or more) equations that are both true at the same time. We find values of and that satisfy both equations. Method 1: E...

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Sequences: nth Term

What is a Sequence? A sequence is a list of numbers that follow a pattern. Each number is called a term. Example: 3, 7, 11, 15, 19, ... (common differ...

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Inequalities

Inequality Symbols | Symbol | Meaning | |--------|---------| | | Less than | | | Greater than | | | Less than or equal to | | | Greater than or equal...

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Functions H

A function is a rule that takes an input, does something to it, and produces exactly one output. Function Notation Instead of writing , we write: This...

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Algebraic Fractions

Algebraic fractions work just like numerical fractions, but with variables in the numerator, denominator, or both. Simplifying Algebraic Fractions To...

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Graphs of Non-Linear Functions

Non-linear graphs curve – they're not straight lines. Each type has a distinctive shape you should recognise. Quadratic Graphs: Shape: Parabola (U-sha...

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