We will look at 2 examples Example 1 is determining if the y-intercept goes through a specific point given 2 known points on the line Example 2 […]More…

# Category: Algebra

# Finding the Equation of a Parabola

To find the equation of a parabola, you need some specific data points from the parabola. The following 2 scenarios describe this process. SCENARIO 1 – YOU […]More…

# Domain & Range of a Function

Sometimes you are given a function on a graph and asked to find the domain and range of that function. But what are the domain and the […]More…

# Inverse Functions

To find the inverse of a function, all you need to do is follow a few basic steps. Below are some examples with increasing level of complexity.

# nth Term of a Linear Sequence

When asked to find the n-th term of a linear sequence, you are asked to find the rule or the formula that allows you to find any […]More…

# Inequalities – Solving for x

In a previous article, we saw examples of solving inequalities using a number line. In this article, we will look at solving inequalities using Algebra. Below are […]More…

# Equation of a Circle – Part II

In part I we saw what the equation of a circle looks like. In this article, we look at a few examples and show you how to […]More…

# Equation of a Circle

There are two versios for the equation of a circle. A simplified version where the center of the circle is at coordinates (0, 0) and a generic […]More…

# Changing the subject of the formula

If you are given an algebraic formula and asked to make one variable the subject – e.g. make ‘x’ the subject – then you are asked to […]More…

# Simultaneous Equations

Solving simultaneous equations can be done in one of 3 ways: by substitution, by elimination, and by using graphs. In this article, we will look at solving […]More…

# Nth Term of a Quadratic Sequence

This is one method of working out the nth term of a quadratic sequence. Other methods are also possible. Now, just as linear sequence has an nth […]More…

# Quadratic Curve – Coordinates of the Turning Point (Part II)

In Part (I), we saw how to work out the coordinates of the turning point on quadratic curve that has solutions – that is the curve crosses […]More…

# How To determine if 2 linear equations are parallel or perpendicular to each other

Very often students get asked to show whether 2 linear equations are parallel (or perpendicular – they meet at a 90° angle) to each other when drawn […]More…

# Solving quadratic equations using completing the square

Sometimes you are asked to solve a quadratic equation using completing the square. This means you first need to get the quadratic equation into the Square form, […]More…

# Fibonacci Sequence

The Fibonacci sequence is a special type of sequence. It starts with 0 and 1, then every subsequent number is the sum of the two preceding ones. […]More…

# By Substitution when Elimination Fails

Sometimes solving simultaneous equations cannot be done using the elimination method. For these – usually complex – cases, you can use substitution. Here is an example.

# Composite Functions

Composite functions are functions that are combined together. This article will present 3 examples showing you how to work with composite functions. EXAMPLE I EXAMPLE II EXAMPLE […]More…

# Collecting Like Terms

Collecting like terms generally means simplifying an algebraic expression having mutliple terms. This means we are grouping ‘like terms’ together and performing whatever operation needs to be […]More…

# Algebra – Plotting a linear equation using the slope and y-intercept.

Suppose you are given this equation y = 5x + 1 – how do you then plot this equation on a graph using just the equation – […]More…

# Distance between 2 points on a Graph

If you have two points on a graph and are asked to find the distance between these two points, then this can easily be done using Pythagoras […]More…

# Inequalities using a Number Line

With inequalities, you are solving for a variable where the operator is one of 4 operators. These are: Less than, Less than or equal to, Greater than, […]More…

# Simultaneous Equations – using Graphs

Solving simultaneous equations by graphs means plotting the 2 equations and finding the x and y coordinates of the intersection point or points. These values will be […]More…

# Is my Term in the Sequence

Very often, when working with sequences, one of the questions you might get asked is whether a number is a term in the sequence you are given. […]More…

# Finding the Coordinates of the Turning Point

There are 3 possible ways of working out the coordinates of the vertex of a quadratic equation on a graph. These are: 1) Using the Axis of […]More…

# How To Determine the Equation of a Straight Line

Given a straignt line on a graph, how do you determine the equation for this line? We know that a straight line is of the form y […]More…

# (R&F) Algebra – Expanding Brackets

Expanding brackets in algebra means you need to multiply the terms inside the brackets by the term (or terms) that are outside the brackets. Below are some […]More…