Math Section 9 - Equations

In this set of Math Tutorials we cover Equations in details with clear guides, Equations formulas and working examples. Each tutorial includes example questions, a revision guide and supporting Equations calculators

We also provide online Equations Calculators which allow you to calculate specific Equations formula in support of the tutorials or to check and verify your own calculations in support of your Equations homework, math coursework or to help you improve your own understanding so it is easier to teach your children Equations.

Equations Learning Material and Equations Study Aide
Tutorial IDTitleTutorialVideo
9.1Variables, Coefficients and Constants. First Order Equations with One Variable
9.2Word Problems Involving Equations
9.4Iterative Methods for Solving Equations
9.5Quadratic Equations
9.6The Quadratic Formula
9.7Systems of Linear Equations. Methods for Solving Them.
9.8Relationship between Equations in Linear Systems. Systems of Equations with One Linear and One Quadratic Equation

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Equations Tutorials Snapshot

This chapter deals with equations and related concepts. The first tutorial discusses some introductory concepts preceding equations such as mathematical sentences (open and close); then it discusses the definition of equations and their components elements. In addition, the regular form of equations (in general) is explained before starting to deal in more detail with first-order equations with one variable.

The second tutorial focuses on word problems involving equations, where some daily-life situations are used to illustrate the application of equations in practice. These problems are solved with one two or more steps depending on the complexity of their clues. This tutorial also includes problems with second-order equations with one variable and first-order equations with two variables, as an introduction to such equations that are discussed more extensively in the other tutorials of this chapter.

The third tutorial is about identities and their meaning in math. The three types of equations: identities, conditional identities and inconsistent equations are explained by illustrating them with various examples. Two other things you can learn in this tutorial are how to solve a question in math by proof, and how to disproof a claim in math using counter-examples.

The fourth tutorial of this chapter deals with the iterative methods used to solve equations, where the most frequent ones are the two 'change-in-sign' methods that we use when the other methods are not applicable. Other related concepts such as the recursive iteration and iteration machines are also discussed in this tutorial.

The fifth tutorial of this chapter deals with quadratic equations - another name used for second-degree equations with one or two variables. This tutorial explains how to solve quadratic equations using two methods: simple factorisation and the completing-the-square method.

The sixth tutorial of this chapter focuses exclusively on the quadratic formula used to solve quadratic equations more simply and comprehensively. Besides the meaning of discriminant and its importance in determining the number of roots in quadratic equations, this tutorial also explains how to use Vieta's Formulas to find the original coefficients and constant of a quadratic equation when the roots are known.

The seventh tutorial of this chapter focuses on systems of first-order equations with two variables (also known as linear equations). The three methods available for solving such systems (elimination, substitution and graphing methods) are explained through numerous examples. Last, you will learn how to verify the correct solution of a system of linear equations.

The eighth and last tutorial of this chapter deals again with systems of equations where one is linear and the other is quadratic, or both equations are quadratic. This tutorial highlights the graphing method (one of the three methods used for solving systems of equations) which is the most appropriate in such situations. Moreover, we deal with some specific situations where a system of linear equations may have no or multiple solutions.

Equations Calculators

The following Math Calculators are provided in support of the Equations tutorials.