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Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved to find solutions to a range of problems in science and engineering.

Forming, using and solving equations are skills needed in many different situations. From balancing accounts to making sense of a mobile phone bill, solving equations is a vital skill.

Simultaneous equations require algebraic skills to find the values of letters within two or more equations. They are called simultaneous equations because the equations are solved at the same time.

Solve quadratic equations by factorising, using formulae and completing the square. Each method also provides information about the corresponding quadratic graph.

Formulae are used in everyday life, from working out areas and volumes of shapes to converting units of measurement. Knowing how to use and rearrange formulae are very useful skills.

Inequalities show the relationship between two expressions that are not equal to one another. Inequalities are useful when projecting profits and breakeven figures.

Sequences can be linear, quadratic or practical and based on real-life situations. Finding general rules helps find terms in sequences.

y = mx + c is an important real-life equation. The gradient, m, represents rate of change (eg, cost per concert ticket) and the y-intercept, c, represents a starting value (eg, an admin. fee).

The most commonly occurring graphs are quadratic, cubic, reciprocal, exponential and circle graphs. Their equations can be used to plot their shape.

Functions of graphs can be transformed to show shifts and reflections. Graphic designers and 3D modellers use transformations of graphs to design objects and images.

Using graphs is not just about reading off values. In real-life contexts, the intercept, gradient and area underneath the graph can have important meanings such as a fixed charge, speed or distance.

Algebraic expressions in fraction form are rational. Methods of adding, subtracting, multiplying and dividing fractions plus expanding and factorising can be used to simplify rational expressions.