There is no doubt that if you want to achieve a high grade in Maths, then you must be able to solve complex problems. Unfortunalty, very often, […]More…

# Numbers – Highest Common Factor (HCF) & Lowest Common Multiple (LCM)

The best way to work out the HCF and LCM of two numbers is to use the prime factor decomposition and Venn Diagram method as it is […]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…

# Compound Measures – Density (Mass/Volume)

Next on the compound measures is Density. This measure give you the mass of the material PER UNIT OF VOLUME. In terms of formula for the density, […]More…

# Stem & Leaf Diagrams

A Stem & Leaf diagram is a way of representing data in a tabular format. The left section of the diagram is called the ‘STEM’ and the […]More…

# Surface Area of Solid Shapes

A reference page showing the formulas of the surface area of some common basic and composite shapes, including: Rectangular Prism Triangular Prism Square Pyramid Cone Sphere Cylinder […]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…

# Frequency Polygons

A frequency polygon is a line graph that is based on a frequency table. Frequency polygons are similar to histograms. Here is an example below.

# 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…

# Trig Ratios – Must Know Values

There are many ways that allow you to work out the values for the trigonometric ratios of the most common angles (0°, 30°, 45°, 60°, and 90° […]More…

# Circle Theorems (IV – VII)

This article is a continuation of part 1 on circle theorems and covers theorems 4 to 7.

# Outcomes / Sample Spaces

Listing outcomes and samples spaces is a way to list all possible outcomes of an experiment. This can be very useful when working with probabilities where we […]More…

# Rounding to – the nearest… / a significant figure

There are two ways to round a number. You can round a number to a specific place value or to a specific significant figure. Rounding to a […]More…

# Circle Theorems (I – III)

Circle theorems are a set or rules you can use to arrive at the correct value of angles in a circle. In this article we will look […]More…

# Cumulative Frequency Diagram

The next step after completing your Cumulative Frequency table is to draw a Cumulative Frequency Diagram; and the question that is most likely to come up is […]More…

# Find a missing angle – non right angle triangle

For non right angle triangles, finding a missing angle requires the use of either the sine rule of the cosine rule. Which one to use will depend […]More…

# Bearings – three examples

Bearings measure direction of travel from the north, clockwise. There are three points that MUST be considered when working with bearings. Measurememts MUST be done clockwise. All […]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…

# Numbers – Factors, Multiples & Prime Factors

Getting confused with Factors, Multiples and Prime factors ??? Well! here are some examples that will hopefully shed some light on the meaning of these terms. Let’s […]More…

# Determine if a point is on a line

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…

# 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…

# Compound Measures – Speed (Distance/Time)

Speed is probably the easiest of the 3 compound measures to understand (the other 2 compound measures are Density and Force). We all know about the speed […]More…

# Recurring Decimals to Fractions

Writing numbers containing recurring decimals into fractions involves a few steps. These are described here using a few examples. First, we start with… Key to the above […]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…

# Multiplication – Lattice Method

There are few ways to multiply numbers. The method shown in the video below is one of them

# Box Plots

Box plots are used to represent the 5 data items listed below graphically, which are: Lowest value in the dataset Lower Quartile (LQ) Median Upper Quartile (UQ) […]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.

# 3D Shapes

Below are the most common 3D shapes you will come across and with 3D shapes, you need to be able to work out the volume of these […]More…

# Rationalise the Denominator

Rationalise the denominator means eliminating the SURD from the denominator. Here are a few examples showing how to do this operation. A full video lesson on working […]More…

# Finding the probability of an Event using Outcomes

Sometimes, we are asked to find the probability of an event happening but we are not given the list of all possible outcome. This means that as […]More…

# Finding the Upper Bound and Lower Bound

With rounding, you often get asked to find two values. These are the Upper Bound (UB) and the Lower Bound (LB) and when these 2 values are […]More…

# Trigonometric Ratios (Sine / Cosine / Tangent)

You use the trigonometric ratios when you are given a side and an angle in a right angle triangle and are asked to find a missing side. […]More…

# Similar Shapes – Area & Volume

Calculating the area or volume of similar shapes relies on two very simple formulae you need to know. These are the ‘Area Scale Factor (Area SF)’ and […]More…

# 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…

# Find a missing angle – right angle triangle

In a right-angle triangle, if you are given the triangle sides and are asked to find the corresponding angles, you use the inverse trigonometric ratios: inverse sine, […]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…