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A1.1 Algebraic operations

This section introduces the basic skills for addition, subtraction, multiplication and division (+ - × ÷) of algebraic expressions.

A1.3 Removing brackets

What do I do with the brackets? Brackets are useful to group numbers, pronumerals and operations together as a whole. Whatever is around the brackets affects all the things inside the brackets. View...

A1.4 Algebraic fractions: Addition and subtraction

How do I deal with fractions involving pronumerals? Adding and subtracting fractions always requires a common denominator (which is the lower half of the fraction). These need to be the same before...

A1.5 Algebraic fractions: Multiplication and division

What is an algebraic fraction? The numerator(top) or denominator(bottom) of a fraction can be in algebraic form involving numbers and variables (represented by pronumerals or letters). In this...

A2.1 Rearranging formulae

Learn how to manipulate or rearrange formulas that involve fractions and brackets.

A2.3 Transposition of formulas with challenges

Are you still trying to get that variable on its own from the formula, but it is in a tricky place – or maybe it appears more than once? Here we demonstrate manipulating or rearranging complex...


What is algebra? Why are there letters in the equation? Algebraic expressions involve pronumerals (letters) to represent values. Pronumerals can take many different values. We often need to plug...

FG1 Functions and relations

A relation is a set of ordered pairs.

FG10 (T8) Graphs of sine and cosine functions

Both the functions y = sin x and y = cos x have a domain of R and a range of [-1,1].

FG2 Interval notation

Often the domain of a function will be restricted to a subset of R. This subset is called an interval, and the end points are a and b.

FG3 Inverse notation

If f to the power of -1 times (x) is the inverse function of a one-to-one function f(x) then f to the power of -1 times (x) is the set of ordered pairs obtained by interchanging the first and...

FG4 Absolute value functions

The absolute value of a number x gives a measure of its size or magnitude regardless of whether it is positive or negative. If a number is plotted on a number line then its absolute value can be...

FG5 Hybrid functions

Functions which have different rules for each subset of the domain are called hybrid functions. Sometimes they are referred to as piecewise defined functions.

FG6 (T6) Circular functions

The trigonometric ratios that have been defined in right-angled triangles can be extended to angles greater than 90 degrees

FG7 Linear graphs

Understanding a linear graph is the simplest way of representing data or a functional relationship. This module explains the equations and visuals of a linear graph.

FG8 Quadratic graphs

The graph of a quadratic function is called a parabola.

FG9 Graphs and transformations

The known graphs of some simple functions and relations can be used to sketch related, but more complicated functions.

Functions and graphs

Information about functions and graphs to improve your maths skills in these areas

T1 Pythagoras’ theorem

Pythagoras’ Theorem shows the relationship between the sides of a right-angled triangle. Knowing the length of two sides of a right-angled triangle, the length of the third side can be calculated.

T2 Right triangle trigonometry

Sine, cos and tan can be defined using side lengths of a right-angled triangle. These side lengths are identified as either the hypotenuse or the opposite or adjacent sides to the angle.