• Substitution and Formula
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.
• Expanding and Removing Brackets
Expanding brackets means being able to rewrite the expression in an equivalent form without any brackets. This video shows examples using simple expressions through to brackets inside other brackets (nesting).
• Solving 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.
• 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.
• Simultaneous 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 - elimination and substitution and then looks at further examples.
• 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.
The video and PDF look 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.
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.
• Solving Cubic Equations
• Simplify and Solve
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 "Apply Algebraic Procedures in Solving Problems" external examination.
• Expand and Factorise
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 11 Algebra Skills
This resource can either 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 Aiming for Achievement
To gain "Achievement" in Year 11, students need to work on algebraic fractions, exponents, expanding, factorising, forming and solving linear equations or inequations, quadratic equations, rearranging formulae, simplifying, solving pairs of simultaneous equations and substituting values into formulae. The booklet contains separate worksheet pages on all of these at an Achievement level. There are also 6 pages of general revision at the back.
• Apply Algebraic Procedures
This booklet is designed for the MCAT (Mathematics Common Assessment Task). There are specific achievement, merit and excellence examples and exercises to cater for all student levels. The booklet contains both write-on sheets and worksheets that could be used as homework or classwork sheets. At the back are some actual old exam papers (and answers).
• Systems of Equations (NCEA Level 2)
AS91269 is a Year 12, Level 2 Achievement Standard worth 2 credits. This booklet provides a number of situations and problems that require you to form and use pairs of simultaneous equations and inequations. Both linear and non linear equations are used. There are 40 pages with many worked examples, lots of hints, tips and full answers.
• 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. There is a video that looks at what a logarithm is, why use it and examples on how to use them. There is also a PDF booklet with further information.