# Math

## How to Do Long Multiplication Using Napier's Method

Find out how to do long multiplication using Napier's Method, also known as Lattice multiplication, in this quick maths article.

## How to Answer the 'Impossible' Question on the Edexcel GCSE Maths Paper 2022

The final question on the 2022 Edexcel GCSE Mathematics paper has been branded as 'impossible' by many people. In this article we take a look at how to solve it.

## How to Expand a Pair of Brackets, an Algebra Walkthrough

Learn how to expand a pair of brackets such as (x+1)(x+3) in this quick algebra maths lesson.

## An Introduction to Linear Algebra

Linear Algebra is a branch of Mathematics that deals with the study of Linear Equations, Vector Spaces and Linear Maps. It is used in one way or another in plethora of fields such as Computer science, Quantum Physics and Quantum Informatics, Biology and Data Science.

## How to Find the Averages and Range From Grouped Data

Learn how to find the mean, median, mode and range from grouped data in a frequency table in this quick maths article.

## Prime Numbers, Composite Numbers, and Prime Factorization

Prime numbers and composite numbers are types of numbers based on the number of factors that a number has. Factor is a value or a number that can divide a number or an expression evenly; which means that when a number is divided by its factor, no remainder exists.

## How to Find the Average From a Frequency Table

Learn how to find the mean, median, mode and range from a frequency table in this quick maths article.

## Whole Numbers: Basic Concepts, Properties, and Applications

Whole Numbers is the union set of zero and set of natural numbers (counting numbers/positive integers). It is conventionally denoted with W. It can be written as W: { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14...}.

## How to Find the Average of a Group of Numbers

Find out how to calculate the different averages and the range of a group of numbers in this quick maths article all about the mean, median, mode and range.

## How Many Gifts Did I Get Over the Twelve Days of Christmas?

Have you ever wondered just how many gifts you would receive if your true love actually gave you all of the gifts from the Twelve Days of Christmas carol? Find out in this Christmas-themed maths article.

## How to Use Pythagoras' Theorem to Find Missing Sides on Right-Angled Triangles

Find out how to use Pythagoras' theorem to find the length of missing sides on right-angles triangles in this quick maths article.

## How to Find the Lowest Common Multiple and Highest Common Factor of Two Numbers

In this quick maths article we look at how to find the lowest common multiple and highest common factor of two numbers quickly and efficiently using prime factors.

## How to Write a Number as a Product of Its Prime Factors

In this quick maths article, find out what prime factors are, how to find them using a factor tree and how any number can be written as a product of its prime factors.

## What Do the Angles in a Polygon Add Up To?

In this quick maths article, find out what the angles in a polygon add up to, as well as the difference between interior and exterior angles.

## What Are Triangular Numbers?

What are the triangular numbers? Find out how the sequence is defined and more interesting facts in this quick maths article.

## Why Do We Split a Circle Into 360 Degrees? A Look at the Origins of 360

Ever wondered why circles have 360 degrees? Why not a simpler number such as 10 or 100? Find out some possible reasons in this quick maths article.

## How to Factorise a Quadratic Algebraic Equation

How do you factorise quadratic equations quickly and easily? Find out in this quick algebra maths lesson.

## How to Prove Pi Equals 2: A Mathematical Paradox

Do you know what pi equals? 3.141... right? Here's a curious geometric proof that pi equals 2.

## How to Calculate a Percentage of an Amount Using a Decimal Multiplier

Learn how to calculate a percentage of an amount quickly and easily by using the decimal multiplier method.

## What Is a Dudeney Number?

Find out about Dudeney numbers and how to find them in this quick maths article.

## Alternate Interior Angles (Theorem and Examples)

This article helps you learn the concept of alternate interior angles in geometry through solving various examples. The article also includes the converse of the alternate interior angles theorem and its proof.

## Double Angle Formula (Sine, Cosine, and Tangent)

In this article, you will learn how to use each double angle formula for sine, cosine, and tangent in simplifying and evaluating trigonometric functions and equations. This article also includes double angle formulas proof and word problems.

## Direct Variation: Equation, Graph, Formula, and Examples

Learn how to solve direct variation examples. This article also includes a definition of direct variation, as well as the corresponding formula, graph, and an explanation of how to create formula equations.

## Coterminal Angles: How to Find Coterminal Angles in Radians and Degrees

This article will teach you how to find coterminal angles in degrees and radians.

## How to Solve a Quadratic Equation - Three Methods for Solving Quadratic Equations

Learn about three ways of solving quadratic equations in this quick maths article.

## Dividing Complex Numbers

Learn how to divide complex numbers in polar form by learning the step-by-step procedures shown in the examples.

## Inverse Variation: Definition, Formula, Graph and Examples

Learn how to solve inverse variation problems in algebra. This article also includes definitions, formulas, graphs, and examples explaining how to translate mathematical statements of inverse variations to equations and vice versa.

## Joint Variation: Solving Joint Variation Problems in Algebra

Learn how to solve joint variation problems in algebra. This article includes definitions and various examples about joint variation and combined variation that will help you gauge your understanding of the topic.

## Vertical Line Test: Definition and Examples

Learn how to perform the vertical line test in identifying if a graph is a function or not. This article also includes definitions and various examples that will gauge your understanding of the topic.

## How to Find the Area of the Shaded Region Using the Area Decomposition Method

Learn how to calculate the area of the shaded region using the area decomposition method. This article also includes step-by-step procedures for all types of problems involving shaded areas.

## Cotangent Graph: How to Graph a Cotangent Function

Learn how to sketch a cotangent graph by learning its properties such as period, horizontal shift, vertical shift, amplitude, vertical asymptotes and more. This article also includes examples of step-by-step procedures on how to graph secant functions with different forms.

## How to Find the Sum of a Geometric Sequence

How do we find the sum of a geomtric sequence? Discover how to quickly add up the first terms of a geometric sequence in this quick maths article.

## Secant Graph: How to Graph a Secant Function

Learn how to sketch a secant graph by learning its properties such as period, horizontal shift, vertical shift, amplitude, and more. This article also includes examples of step-by-step procedures on how to graph secant functions with different natures.

## What Are Hexadecimal Numbers?

What are hexadecimal numbers, what are they used for and how do we convert them into decimal numbers? Find out all of this and more in this quick math article.

## Reciprocal Identities in Trigonometry (With Examples)

Learn the different reciprocal identities in trigonometry together with other fundamental identities such as Pythagorean and quotient identities. This article includes several examples that can help in understanding the trig reciprocal identities.

## Sum and Difference Formulas (With Proofs and Examples)

Learn how to apply sum and difference formulas in solving trigonometric equations. This article also includes the definition of sum and difference identities, proofs, and examples with solutions.

## Similar Polygons: Ratio of Areas, Perimeters, and Side Lengths

Learn how to solve problems about similar polygons using the concepts of ratio of areas, perimeters, side lengths, diagonals, and angle bisectors. This article also includes practice problems with solutions and answers that will help you gauge your understanding of the topic.

## How Many Socks Make a Pair? - A Mathematics Problem

You keep pulling socks out of a messy drawer, desperately trying to find a matching pair, but all you seem to get are odd socks. How many socks will you need to pull out of the drawer in order to be guaranteed a matching pair? Find out in this quick mathematics article.

## Mutually Inclusive Events: Definition, Examples, and Word Problems

Learn how to solve mutually inclusive events in probability by going through the examples written in this article.

## Triangle Proportionality Theorem (With Proof and Examples)

Learn how to use the triangle proportionality theorem to complete triangle proportions, solve word problems, and find the value of the missing sides of a triangle. This article includes the triangle proportionality theorem proof and examples that can help you fully gauge your understanding of it.

## A Quick Way to Solve 1000^2 − 999^2: The Difference of Two Squares

A look at how using the difference of two squares can speed up your mental arithmetic with large numbers.

## How to Prove That the Square Root of 2 Is Irrational

It's common knowledge that the square root of two is an irrational number, but how can we prove it? Find out in this quick mathematics article.

## Rationalizing the Denominator: Dealing With Surds/Radicals in Fractions

Struggling with surds and radicals in fractions? You're not alone. I'll explain it to you. Learn how to rationalize the denominator in this quick high school mathematics article.

## Why Do We Rationalise the Denominator? Standard Notation While Using Surds/ Radicals

When learning about surds/radicals at school, we are always told to rationalise the denominator. But what does this mean and why do we do it? Find out why in this quick mathematics article.

## The Prisoner's Dilemma: Using Game Theory to Achieve the Optimal Solution

Two criminals have been arrested for a crime, but the police don't have enough evidence to convict. They offer each criminal the chance to reduce their sentence by testifying against the other, but is this the best option? Find out in this quick math article about the prisoner's dilemma.

## Being Careful When You Average an Average: A Basketball Problem

Alan has the best scoring average in the first half of the basketball season and the best scoring average for the second half of the season, but when everything is tallied together he finds that it is Brian who has the highest average over the season. Find out how in this quick math article.

## Hilbert's Paradox of the Grand Hotel: Another Look at Infinity

This article will provide a look at Hilbert's Paradox of the Grand Hotel, also known as the 'Infinite Hotel Paradox'. Find out how to fit extra guests into the infinite hotel, even when every room is occupied!

## L'Hopital's Rule: Evaluating Limits of Indeterminate Forms

Learn how to evaluate and simplify the limits of indeterminate forms using L'Hopital's rule. This article includes L'Hopital's rule proof, when to use it, and examples with solutions about finding the limit of various functions.

## Cylindrical Coordinates: Rectangular to Cylindrical Coordinates Conversion and Vice Versa

This article includes problems with solutions teaching how to convert rectangular to cylindrical coordinates and vice versa, identify the surfaces in the cylindrical coordinate system, and find a cylindrical equation of three-dimensional spaces.

## Divergence Test: Determining if a Series Converges or Diverges

Learn how to use the divergence test in determining the convergence or divergence of a series.