A look at how using the difference of two squares can speed up your mental arithmetic with large numbers
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.
Learn how to rationalise the denominator in this quick high school mathematics article.
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.
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.
The village of Smallville and the Intergalactic Gods have both had five metres of boundary rope stolen from their circular cricket pitches. They have vastly different sized pitches, so whose pitch will reduce in radius the most?
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.
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!
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.
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.
Learn how to use the Divergence Test in determining the convergence or divergence of a series.
Learn how to solve the derivative of constant times a function through a step-by-step Constant Multiple Rule method.
Learn how to solve problems about cofunction identities in trigonometry. This article also includes formulas, proofs, and examples with solutions that can help you fully apply the cofunction trigonometric identities.
Learn how to find the linear approximation or differentials of a function at a given point. This article also includes formulas, proof, and examples with solutions that can help you fully understand the Linear Approximation topic in Calculus.
The slope of a line is the direction in which the line goes. You can calculate it as the ratio between horizontal change and vertical change, or you can use the derivative.
Finding the intersection is something that comes up a lot in math. To do this you need to set the expressions equal and solve for x. Then you can determine y by filling in the x you found.
The variance of a probability distribution is a measure to quantify the spread of a distribution. If the variance is low, all outcomes are close to the mean, while distributions with a high variance have outcomes that could be far away from the mean.
The mean is the most important measure of probability distributions. It tells a lot about the likelihood that certain events will happen.
If you were asked to add together all of the numbers from 1 to 100, what would you do? Would you go through each number, adding to your total as you went or is there a quicker way? Find out in this article.
A right triangle is a triangle in which one angle is right, meaning it is exactly 90°. For these triangles, it is possible to calculate the other angles using goniometric functions as the sine, cosine and tangent.
The limit of a function describes how the function behaves in the neighborhood of some value. Often, it is interesting to look at the limit for x to infinity. This describes what happens when you would follow the line of the graph of the function until "the end".
Finding the minimum or maximum of a function is very important in mathematics. It can help you finding the optimal solution to a problem. Often you want some quantity to be maximal, such as profits or capacity. Also minima can be very useful, for example, when looking at a cost function.
Finding the derivative is something that comes up a lot in maths, but what is it actually? The derivative tells you what the slope of the function is in a certain point. The derivative of a function can be calculated using the definition, but mostly it is done by using standard rules.
In this article, you can learn how to use the power-reducing formulas in simplifying and evaluating trigonometric functions of different powers.
The theorem of Pythagoras is well known, showing the relationship between the areas of squares on the sides of right-angled triangles. However, it may not be realised that the theorem can also be used to show relationships between shapes other than squares.
In this article, you can learn the concept of the Same-Side Interior Angles Theorem in Geometry through solving various examples provided. The article also includes the Converse of the Same-Side Interior Angles Theorem and its proof.
Linear equations pop up everywhere and solving them is one of the most basic tools in mathematics.
Learn to use Descartes' Rule of Signs in determining the number of positive and negative zeros of a polynomial equation. This article is a full guide that defines Descartes' Rule of Signs, the procedure on how to use it, and detailed examples and solutions.
This article is a full guide in solving problems involving the use of the factor theorem. It includes the definition, proof, examples and solutions about the factor theorem.
This article is a full guide to solving problems on 30-60-90 triangles. It includes pattern formulas and rules necessary to understand the concept of 30-60-90 triangles. There are also examples provided to show the step-by-step procedure on how to solve certain kinds of problems.
Bayes' Law is an important tool to calculate conditional probabilities, such as the probability that A happens given B happened. It has many applications, but is often interpreted incorrectly.
Complex numbers are an extension of the real numbers that allow us to calculate the square root of negative numbers. All numbers can be represented as a complex number, and we can do all kinds of computations with them.
A look at what fractals are and three of the most popular examples: the middle third Cantor Set, the Koch curve, and the Sierpinski triangle.
The tangent line of a function in a point is a straight line that has the same slope as the function has in that point.