Terms

Meet some of the notation used in algebra, see what makes up an algebraic ‘term’, and begin simplifying terms.

Expressions

See how ‘sums’ are made up of ‘terms’, try simplifying expressions by ‘collecting like terms’, and meet some of the names given to particular types of terms and expressions.

Building Algebraic Expressions

Learn to recognise what each operation in an expression is acting on. See how the operations in an expression can be thought of as happening in a particular order, and, starting with x, apply a sequence of operations to build up a given algebraic expression.

Get Back To x

Operate on given expressions to ‘cancel’ things out until we ‘get back to x’ on its own. This topic deals only with expressions, but the skills developed here are important in solving equations.

Expanding A Single Bracket

See how to ‘expand’ a single bracket that is being multiplied by another factor, then practise number and simplification skills as we continue expanding brackets within expressions.

Factorisation: Common Factors

An introduction to factorisation. Learn how to ‘take out’ common factors from the terms in a sum to express that sum as a product of factors.

Expanding Multiple Brackets

See how to ‘expand’ brackets when there is more than one bracket factor being multiplied together, including terms with a squared bracket factor, and expressions with more than one term to expand.

One Step Linear Equations

An introduction to solving equations. Meet the underlying concepts and practise number skills as we attempt linear equations that can be solved in a single step.

Multi-step Linear Equations

See how to solve linear equations by applying a sequence of operations to each side, and practise number skills as we continue solving.

Unknown On Both Sides

Learn how to solve equations in which the expressions on each side both have a term containing the unknown.

Unknown In A Denominator

Learn to solve equations that have the unknown in a denominator, including when the unknown is a factor of the denominator, and when the denominator is a sum.

Simultaneous Equations (Linear)

‘Simultaneous’ means ‘at the same time’. Learn to solve linear equations in more than one unknown, by using more than one equation simultaneously.

Changing The Subject

Change the ‘subject’ of a formula by applying operations to it, so that it becomes equal to something else.

Using Formulae

Substitute values into a formula and simplify the result, including giving answers in terms of τ and π.

Number Practice

Practise times tables, negatives, fractions, decimals, and powers.

Exponents

Deepen your understanding of exponents (also known as ‘powers’ or ‘indices’). Meet some ‘laws of exponents’ and see what zero and negative exponents mean. (We’ll deal mainly with integer exponents here.)

Quadratics

The next set of topics we hope to release are about quadratic expressions and equations. We intend these to cover: factorisation of quadratic polynomials into double brackets (including the difference of two squares); completing the square; simplifying expressions that include quadratics within algebraic fractions; using these skills, as well as the quadratic formula, to solve quadratic equations; and the solving of simultaneous equations that include quadratics.

Trigonometry

We have done significant development on solving trigonometric equations and hope to create topics on this, as well as on the use of trigonometric formulae and identities.

Exponentials And Logarithms

One topic on exponents is already included in Algebra Tutor and we have at least one more planned, as well as topics introducing logarithms, their rules, and their use in simplifying and solving equations.