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…

# 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. […]More…

# 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…

# Algebra – 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…

# Similar Shapes

Similarity in mathematics has a precise meaning, unlike its usage in everyday life. 2 shapes are said to be similar if they fulfill the following 2 conditions:

# Completing a Cumulative Frequency Table

Completing a Cumulative Frequency table is a simple exercise. This is done by simply performing some addition on the data you are given. Here are a couple […]More…

# Estimate the Area under a Curve

When estimating the area under a curve, you need to split the area under the curve into a number of distinct shapes; the total area of those […]More…

# Negative Numbers – Multiplying & Dividing

The rules for multiplying and dividing involving negative numbers are relatively simple compared to adding and subtracting involving negative numbers. Here they are: Dividing works the EXACT […]More…

# Negative Numbers – Adding & Subtracting

Adding and subtracting involving negative numbers can be challenging to some students if the rules on negatives numbers are not well understood. This article aims to provide […]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…

# 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 to […]More…

# 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.

# 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…

# 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…

# Best Fit on a Scatter Diagram

When drawing a ‘best fit’ line on a scatter diagram, you need to keep in mind a few points as these will determine whether you best fit […]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…

# Scatter Diagrams

A scatter diagram is a way of visually representing information on two variables on a graph. You can get 3 possible outcomes with scatter diagrams, these are: […]More…

# Congruent vs Similar Shapes

The question of whether 2 shapes are congruent or similar is often asked of students. In fact the answer to this question is very simple.

# Range vs. Interquartile Range

Both the ‘Range’ and ‘Interquartile Range’ measure the spread of our data set. That is they both tell us how spread out our data set is; so […]More…