Algebra

Mathematical language

This video provides useful background material on the different mathematical symbols used in mathematical work. It also describes conventions used by mathematicians, engineers, and scientists.

Powers or Indices

Powers (also called exponents or indices) are a short way of writing multiplication of the same factor. A knowledge of powers, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules for manipulating them through a number of worked examples.

Logarithms

Before calculators logarithms were used to assist in multiplication and division. They still appear in a number of calculations in engineering, science, business and economics. This video looks at what a logarithm is, why use it and examples on how to use them.

Substitution & Formulae

In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities, the values of others can be calculated. This video looks at several formulae and how they are used.

Expanding and Removing Brackets

Expanding brackets means being able to rewrite the expression in an equivalent form without any brackets. This video investigates the mathematics behind expanding and removing brackets and then shows examples using simple expressions through to nesting brackets (brackets inside other brackets).

Pascal's triangle and Binomial Expansion

A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a power higher than 2 it is very cumbersome to do this by repeatedly multiplying x+1 or 3x+2y by itself. In this video you will learn how Pascal's triangle can be used to obtain the required result quickly.

Factorising Quadratic Equations

Factorising can be thought of as reversing the process used to 'remove' brackets from an expression. This video looks at factorising by inspection and then other methods of factorising used for example when the coefficient of x2 is not 1 or when there is no constant term.

Transposition or Re-arranging Formulae

It is often useful to rearrange, or transpose, a formula in order to write it in a different, but equivalent form. This video explains what it means to "transpose", the procedure for doing this through simple examples and then shows some more complex examples.

Simple Linear Equations

This video gives examples of simple linear equations and shows how the unknown quantity can be found. This involves collecting terms, removing brackets, and solving linear equations with fractions.

Completing the Square - By Inspection

Quadratic expressions can be written in an equivalent form using the technique known as completing the square. This video explains the basic ideas behind completing the square and how to use the method to solve quadratic equations.

Completing the Square - Maxima & Maxima

This video shows how to find the maximum or minimum values of quadratic functions by using the 'completing the square' technique.

Solving quadratic equations

This video is about the solution of quadratic equations. These take the form ax2+bx+c = 0. We will look at four methods: factorisation, completing the square, using a formula, and solution using graphs.

Simultaneous Linear Equations

Solving a pair of simultaneous equations is equivalent to finding the location of the point of intersection of two straight lines This video looks at the main methods of solving simultaneous linear equations - elimination, substitution and then looks at further examples and how to approach them.

Solving Inequalities

This video explains linear and quadratic inequalities and how they can be solved both algebraically and graphically. It includes information on inequalities in which the modulus symbol is used.

Solving Cubic Equations

Cubic equations have either one real root, or three real roots. In this video we explore why this is so, how to solve them to find the roots and how to use graphs to solve them.

Simplifying Algebraic Fractions

This involves simplifying fractions to their lowest equivalent form, fractions that need to be factorised before simplifying and looks at common mistakes made when cancelling.

Polynomial Division

In order to simplify certain sorts of algebraic fraction we need a process known as polynomial division. This video describes this process using normal long division as a parallel example.

Partial_Fractions

This video looks algebraic fractions, adding and subtracting fractions and spliting fractions into partial fractions, It explains the meaning of the terms 'proper fraction' and 'improper fraction', and how to express an algebraic fraction as the sum of its partial fractions.

Year 10 & 11 Algebra Expanding and Factorising

This booklet contains 70 pages of worksheets (with answers) cover simple expanding and factorising through to harder work with quadratics. In most cases there are 5 parallel question papers that you can complete. It is an ideal Algebra resource for Year 10 students through to Year 11 especially those that want to sit the MCAT exam AS91027 Apply algebraic procedures in solving problems.

Year 10 & 11 Simplifying and Solving Equations

This 82 page booklet contains work on simplifying expressions, exponents, solving simultaneous equations using algebra and graphs. The pages are ideal for Year 10 and Year 11 Algebra and specifically work for the MCAT AS91027 Apply algebraic procedures in solving problems external examination.

Algebra Skills for NCEA Level 2

This document was sent to us by another teacher. It can be used to determine whether you have the algebra skills needed to proceed into a Year 12, mathematics course or it can also be used to study for AS91027 (the Level 1 MCAT - Maths Common Assessment Task). There are worked examples, practice questions, and practice assessments with all answers provided. Topics include indices, manipulating brackets, expanding and factorising, solving linear equations and other algebraic expressions. The booklet is 26 pages in length.

Algebra II for Dummies

Contents at a Glance:

Introduction
Chapter 1: Going Beyond Beginning Algebra
Chapter 2: Toeing the Straight Line: Linear Equations
Chapter 3: Cracking Quadratic Equations
Chapter 4: Rooting Out the Rational, Radical, and Negative
Chapter 5: Graphing Your Way to the Good Life
Chapter 6: Formulating Function Facts
Chapter 7: Sketching and Interpreting Quadratic Functions
Chapter 8: Staying Ahead of the Curves: Polynomials
Chapter 9: Relying on Reason: Rational Functions
Chapter 10: Exposing Exponential and Logarithmic Functions
Chapter 11: Cutting Up Conic Sections
Chapter 12: Solving Systems of Linear Equations
Chapter 13: Solving Systems of Nonlinear Equations and Inequalities
Chapter 14: Simplifying Complex Numbers in a Complex World
Chapter 15: Making Moves with Matrices
Chapter 16: Making a List: Sequences and Series
Chapter 17: Everything You Wanted to Know about Sets
Chapter 18: Ten Multiplication Tricks
Chapter 19: Ten Special Types of Numbers

Mathematics For The Next Generation

Mathematics For the Next Generation was originally written for New Zealand Year 11 examination classes. It features dozens of examples to study and exercises to work through. The book is loaded with tips and techniques for answering all common exam-type questions. There are also a series of reviews and extra challenges. It is a good revision book leading up to exams.

The book features 8 chapters from number, measurement, shape and space, transformation geometry, algebra, graphs, statistics and probability. Use this book for homework, for revision or of you didn't understand a concept.