The graph and location of a parabola depend on its equation. This is a step-by-step guide in graphing different forms of a parabola in the Cartesian coordinate system.

### Graphing a Parabola in a Cartesian Coordinate System

This first part of a two part tutorial covers the concept of limits, differentiating by first principles, rules of differentiation and applications of differential calculus.

### How to Understand Calculus: A Beginner's Guide to Limits and Differentiation

One of the best tools for statistical analysis is Microsoft Excel. In this article, I will cover how to find relative distribution in a list of data using the COUNTIF() function.

### Using Excel COUNTIF Function in Frequency Distribution

This guide shows you the math behind working out a bolt circle diameter (BCD) or pitch circle diameter (PCD) and gives tables you can use in your calculations.

### How to Calculate Bolt Circle Diameter (BCD) for Chainrings and Bash Guards

Like all important fields of study, Calculus had its growing pains. Here is the journey to the foundations of that amazing field.

### Who Developed Indivisibles? The Precursor to Infintesimal Calculus

Solving problems related to plane geometry especially polygons can be easily solved using a calculator. Here is a comprehensive set of problems about polygons solved using calculators.

### Calculator Techniques for Polygons in Plane Geometry

The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of its faces.

### How to Find the Surface Area of Right-Angled and Isosceles Triangular Prisms

Learn how to solve problems on different types of depreciation methods in Engineering Economics using the formulas and solutions provided.

### Methods of Depreciation: Formulas, Problems, and Solutions

In this article, learn about the history and how to perform addition on the abacus. Also, learn about terms related to the use of the abacus and how to set numerical values from an expert in the use of the counting tool.

### How to Count to Ninety-Nine on an Abacus With Addition

How many people do you need to have in a room before you have a better than 50% chance of at least two people sharing a birthday? The answer is surprisingly low.

### The Birthday Paradox

Covering bases and exponents, laws of exponents. log to the base 10, natural logs, rules of logs, working out logs on a calculator, graphs of log functions, log scales and using logs to perform multiplication.

### An Introduction to Logarithms: How to Use the Rules of Logs and Exponents

Finding the nth term of a decreasing linear sequence can by harder to do than increasing sequences, as you have to be confident with your negative numbers. A decreasing linear sequence is a sequence that goes down by the same amount each time....

### Finding the nth term of decreasing linear sequences (math help)

Speed, distance and time can be calculated using a magic triangle. D (the distance) goes in the top of the triangle, S (speed) goes in the bottom left of the triangle and T (time) goes in the bottom right of the triangle. If you want to calculate...

### Using the Magic Triangle for Speed, Distance and Time (Compound Measures)

A composite shape or compound shape is a shape that is made from other shapes such as two rectangles (L-shape) or a triangle and a rectangle. If you are going to calculate the area of a composite shape then you need to break up composite shape into...

### How To Calculate The Area Of A Composite Or Compound Shape (rectangles, triangles, circles).

Once I was preparing to take a difficult standardized test, which evaluates math and logic skills for university entrance. It was an online exam with a timer and I had to make calculations without using a calculator. Techniques of fast mental math discussed here became a true godsend for me!

### How to Calculate Quickly Without a Calculator

This article shows you how to multiply fractions in four easy steps. How do you multiply mixed numbers? What is an improper fraction? This article, which includes a short video, will answer all these questions and leave you with the knowledge and confidence to multiply any fractions.

### How to Multiply Fractions in Four Easy Steps

This is a full guide in finding the general term of sequences. There are examples provided to show you the step-by-step procedure in finding the general term of a sequence.

### How to Find the General Term of Sequences

The mean average from an ungrouped frequency table can be found by following these three simple steps: Step 1. First you will need to add a new column onto the end of the frequency table. You can label this column fx as you are going to multiply...

### How to Get the Mean Average From a Frequency Table

Need high school geometry homework help? This Math Made Easy! Geometry Tutorial explains how to find the circumference of a circle with easy to follow problems and solutions.

### Math Made Easy—How to Find the Circumference of a Circle

Working out the odds of an event occurring allows us to estimate the number of times that event will take place in future trials. Permutations/combinations are also an important part of the analysis.

### How to Find the Probability of an Event and Calculate Odds, Permutations and Combinations

If the angles in a triangle are given as algebra (usually in terms of x), and you are asked to find out the size of each angle, then you can follow these 3 simple steps to find all of the angles. Step 1 Add up the 3 angles that are given and...

### How to Work Out the Angles in a Triangle When the Angles Are in Algebra.

How to develop a cone or how to create a flat pattern of a cone can be achieved in a few easy geometrical steps. The geometrical method shown below does however have inaccuracy, so at the end of this hub I have included a mathematical formula to...

### How to Develop a Cone - Cone Development

The grid method is a great fool proof method to help you with multiplication. As long as you follow these simple steps and have good knowledge of place value and your timetables this is a great method

### Math Help: How Do You Multiply Using the Grid Method? Partition the Units, Tens and Hundreds to Make It Simplier

The dumbest smart jokes, the stupidest funny answers. These are the best of the worst math puns and wisecracks!

### The Dumbest, Cleverest, Funniest Math Jokes & Puns

This is an action research proposal which seeks to address the failure of some students to solve and analyze mathematics word problems due to poor reading comprehension.

### Action Research Proposal: Mathematics Problem-Solving Skill and Reading Comprehension

The use of right spherical triangle is a technique to solved the angles easily. This article will help you understand the concept of the right spherical triangle and Napier's Circle.

### Right Spherical Triangles

The article is written in rather technical level, providing an overview of linear regression. Linear regression is based on the ordinary list squares technique, which is one possible approach to the statistical analysis. Both univariate and multivariate linear regression are illustrated on small concrete examples. In addition to the explanation of basic terms like explanatory and dependent variables, we will see how to interpret results obtained by a regression analysis.

### Univariate and Multivariate Linear Regression

Defines polynomials by showing the elements that make up a polynomial and rules regarding what's NOT considered a polynomial. Learn about different types, how to find the degree, and take a quiz to test your knowledge.

### What Is a Polynomial?

Pythagoras and trigonometry (basic) both work in right angled triangles. In this hub you will be shown how to choose the correct one. Pythagoras is used when you have a right angled triangle and you need to work out one of the missing side...

### Pythagoras vs. Trigonometry—How to Know When to Use Trig or Pythag in Your Math Exams

A basic discussion on the null hypothesis, z-scores, and probability. This article includes examples of the null hypothesis, one-tailed, and two-tailed tests. A coin is tossed and comes up tails ten times: is this just random chance, or is an unfair coin being used? Learn when to reject the null hypothesis: if the probability (P) is less than the chosen significance level, the null must be rejected.

### Null Hypothesis and Formulas: A Definition With Examples

A simple, step by step guide about how to find the Pearson's correlation coefficient, r, and how to calculate the coefficient of determination on your TI-89 calculator.

### How to Find the Correlation Coefficient on a TI-89 Calculator

Follow these instructions below to develop a truncated cone. A truncated cone is a conical shape which has had it's top cut off at an angle. Sometimes you might need to develop these truncated cones as duct elements. Developing a truncated cone can...

### How to Develop a Truncated Cone

A quick way to divide by 0.5 or ½ is to double the number (or multiply number by 2). The reason for this is because two halves go into a whole.

### Dividing by 0.5: A Simple Method to Divide by a Half

In this article I want to use a specific polynomial equation to introduce the Whittaker method for finding the root that has the smallest absolute value.

### Whittaker Formula and the Fibonacci Numbers

If you are asked to translate a shape then you need to move the shape to a new position on the coordinate grid. Usually, the directions of the translation are given in terms of a vector. The vector contains 2 numbers which are written vertically...

### How to translate a shape on a coordinate grid using a vector. Math help.

Card game problems are a recurring theme in probability. In fact, a small set of basic principles allows you to crack game problems with ease, including the notorious poker hand problems.

### Cracking Probability and Combinatorics: Card Game Problems

A compound H-shape is made up of 3 rectangles. Make sure you can work out the area of an L-shape first before you attempt this one. If you are finding the area of a compound H-shape all you need to do is split the H-shape up into 3 rectangles and...

### Calculating the Area of Compound H Shapes

Here you will be shown how to simplify expressions involving brackets and powers. The general rule is: (xm)n = xmn So basically all you need to do is multiply the powers. This may also be called the exponent bracket rule or indices bracket rule...

### Powers in Brackets: How to Use the Bracket Power Rule

There is no biggest number, but really, how much is a thousand, a million, a googolplex or even a googolplexian? This look into big numbers may give you an idea how big they are.

### Taking a Perspective Look Into Big Numbers

In this article, we explore the ubiquitous Fibonacci sequence and its presence in nature and in many aspects of our life.

### What Are Fibonacci Numbers?

To work out a fraction of a number all you need to do is divide the number by the denominator of the fraction and multiply this answer by the numerator. Example 1 Work out 3/8 of 48. First of all divide 48 by the denominator: 48 ÷ 8 =...

### Math Help: How to Work Out a Fraction of a Number

When solving division problems, it can be challenging for students to learn how to interpret the remainder. With these 40 example division problems, you can learn more about four possible ways to interpret the meaning of the remainder.

### Interpreting the Remainder: 40 Example Division Word Problems for Student Practice

Zenos Paradox has been around since before Christ and has baffled many people. An explanation and debunking of the paradox; why it is no paradox at all but a simple mathematical description of what we see happening all around us.

### Understanding and Solving Zeno's Paradox

Game Theory is one of the most fascinating branches of mathematics with tons of applications to fields ranging from the social sciences to the biological sciences. In this article, we will look at some basic examples of game theory and its application to real-world situations.

### What Is Game Theory? A Basic Introduction and Example

Roman numerals have been around for about 3,000 years, and they became a recognized number system that was used around the world.

### How To Understand Roman Numerals

How to do the standard deviation manually in six straightforward steps, includes a step by step of how to do this using Excel, with screenshots and a link to a sample Excel sheet.

### How to Calculate Standard Deviation

In this hub I will show you how to find the area of circle giving your answer in terms of Pi (π). First of all you need to remember the formula for calculating the area of a circle: A = πr² A stands for area, π stands for Pi and r is...

### Math Help: How to Calculate the Area of Circle and Get an Answer in Terms of Pi

How do you add and subtract fractions on the abacus? Mixed numbers? Complex fractions? Introduce children to fractions? Learn from this article.

### Adding and Subtracting Fractions With the Abacus in Easy Steps

Here you will be shown to work out the area and perimeter of a C shape. A C shape is a compound shape made up of 3 rectangles. Make sure you know how to find the area and perimeter of an L shape before you attempt this lesson on C shapes. To work...

### Compound C Shapes: How to Calculate the Perimeter and Area of a C Shape.

Do you have problems converting between cups, pints, quarts, and gallons? Many people do. Learn a method of conversion that will help you to remember the units and will give you a visual way to go about converting between units. This method is useful for children and adults.

### How to Remember Customary System Measurement Conversions: Cups, Pints, Quarts, Gallons

Calculus! We all love it, but who were the early pioneers that led the fight over indivisibles, a cornerstone for this topic?

### Does Calculus Represent Reality? The Early Fights Over Indivisibles

Understanding percentages and learning how to calculate them is a fundamental skills of mathematics. This articles describes how to calculate a variety of types of percentages that are used in our world each and every day.

### How to Calculate Percentages

Do you ever wonder how Magic Squares are created? Well, stop worrying. I'll show you how to construct them using just a few easy to follow rules.

### How to create magic squares

The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if you wanted to work out the...

### The Density, Mass and Volume Magic Triangle: How to Calculate Density of a Solid Shape

The Viral Equation 8 ÷ 2(2 + 2) has only one answer and that is 1 not 16. PEMDAS and BODMAS are being incorrectly applied to this equation by the proponents of 16 as a result, probably due to calculators and spreadsheets applying incorrect rules and not being challenged many years ago.

### 8 ÷ 2(2 + 2) The Viral Equation Has Only One Answer and That Is 1 Not 16

This article describes a technique for performing multiplication of equations with three digits on the abacus. Learn from an expert in the use of the counting tool.

### Multiplying and Mastering Equations With Three Digits on the Abacus

Step-by-step guide to multiplying different types of polynomials. Learn how to multiply binomials using the FOIL method. Use the grid method and know why it's the best way to multiply polynomials.

### Multiply Polynomials (With Examples) - FOIL & Grid Method

Solving problems related to plane geometry especially circles and triangles can be easily solved using a calculator. Here is a comprehensive set of calculator techniques for circles and triangles in plane geometry.

### Calculator Techniques for Circles and Triangles in Plane Geometry

A quadrant is a quarter of a circle. So to work out the area of a quadrant, first work out the area of the whole circle (use the formula A = π ×r²) and then divide the answer by 4. Alternatively, you could substitute the radius of the quadrant...

### How to Find the Area of a Quadrant (a Quarter of a Circle)

Percentile refers to the position of a piece of data in a distribution, while percent refers to rate per 100.

### What Is Percentile Rank? How Is It Different From Percentage?

A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple steps: Step 1: Work out the...

### Compound Shapes: How to Find the Area of an L-Shape

This guide teaches you how to solve the surface area and volume of different polyhedrons such as prisms, pyramids. There are examples to show you how to solve these problems step-by-step.

### How to Solve for the Surface Area and Volume of Prisms and Pyramids

The special theory of relativity is a theory by Albert Einstein, which can be based on the two postulates Postulate 1: The laws of physics are the same (invariant) for all inertial (non-accelerating) observers.* Postulate 2: In a vacuum the speed...

### Minkowski Diagram

Al-Biruni a pioneering Muslim scientist figured out a truly remarkable and ingenious method to calculate the radius of the earth (and subsequently its circumference etc.). This was very simple yet accurate requiring just four measurements in all to...

### Al-Biruni's Classic Experiment: How to Calculate the Radius of the Earth

Area and perimeter can be difficult to work out if you can't remember which one is which. Here is a great hub to help you remember and also help you work out more complicated maths in compound shapes.

### Math Help: What Are Area and Perimeter? How to Work out the Area and Perimeter of a Compound Shape

Finding the mean, median, and mode of a data set is an important first step in learning and implementing basic statistical techniques. This hub will teach you how to calculate these measures.

### Measures of Central Tendency: Mean, Median, and Mode

If you are asked to work out the product of two numbers, then you need to multiply the two numbers together. If you are asked to find the sum of two numbers, then you need to add the numbers together.

### How to Find the Product and Sum of Two (Or More) Numbers

This hub is all about calculating lottery probability or odds. In order to make it relevant, I decided to base it on the Grandlotto 6/55, the lottery game with the biggest prize money here in the Philippines. There will be two different cases in the hub: the probability of winning the game with all six numbers matching, and the probability of having n numbers matching.

### How to Calculate Lottery Probability

This geometry tutorial shows how to find the area of a circle. Included are math tips and easy to follow problems and answers for finding the area of a circle.

### Math Made Easy! How to Find the Area of a Circle

How do you learn to calculate percentages in your head? Practice, practice, practice. Seriously, doing mental math in your head isn't that hard when you understand a few shortcuts. Here are our tips.

### How Much Is 70 Percent Off? (Calculating Percentages in Your Head)

A hands-on math activity for middle schoolers. The topic being taught here is circumference and area of circles and the hands-on activity is using two different types of baked pies.

### Circumference and Area of a Circle: A Middle School Math Hands-On Lesson

A farmer has 100 metres of fence and wants to make a rectangular enclosure with the largest possible area. What size should the sides of his rectangle be?

### Which Rectangle Gives the Biggest Area?

Through the use of negations, conjunctions and disjunctions in logic, we can build up to De Morgan's Laws, a very powerful tool in logic.

### Negations, Conjunctions, Disjunctions, and De Morgan's Laws

Trig graphs are easy once you get the hang of them. Once you learn the basic shapes, you shouldn't have much difficulty. The main problems A-Level students have, in my experience, are: Remembering which is y = sin x and which is y = cos x....

### Trigonometry—Graphing the Sine, Cosine and Tangent Functions

This Hub shows how to analyze data obtained from a statistical survey. The methods prescribed in this Hub are basic, yet effective.

### How to Analyze a Statistical Survey: Standard Deviation, Outliers, and More

Stuck on long division of polynomials? Here's an easy, step-by-step guide to "synthetic division" to help you with tricky Algebra homework.

### Math Help: How to Do Long Division of Polynomials Easily (Synthetic Division)

Need help with math? Get math help online with the Math Made Easy! series of geometry tutorials, including surface area of a cylinder.

### Math Made Easy! How to Find the Surface Area of a Cylinder

Learn what trigonometry is and get a view of this area of mathematics throughout history—its development, uses, and why it's important.

### What is Trigonometry? Description & History of Trig

Equation of a parabola, meaning of locus, directrix, focus, quadratic equation, maxima and minima etc.

### How to Understand the Equation of a Parabola, Directrix and Focus

The marginal rate of technical substitution of Labor (L) for Capital (K) is the slope of an isoquant multiplied by -1. Since the slope of an isoquant is moving down, the isoquant is given by –ΔK/ΔL...

### Marginal Rate of Technical Substitution

The nth term of a number sequence is a formula that gives you the values in the numbers sequence from the position number (some people call it the position to term rule). Example 1 Find the nth term of this sequence. 5 8 11 14 17 First of...

### How to Find the nth Term of an Increasing Linear Sequence.

The main property of a trapezium (as known in Great Britain) or trapezoid (as known in the United States) is that it is a 4 side shape with exactly one pair of parallel sides. Depending on how the trapezium is drawn determines how many lines of...

### Properties of a trapezium or trapezoid (math facts)

Not everybody knows why a plus b whole square is i.e. (a+b) 2 = a2+b2+2ab and why exactly it has been generalized.So, here I come up with the geometrical proof that shows up the results.

### Why (a+b) 2 = a2+b2+2ab ?

How to convert a hexadecimal to a decimal and a decimal to a hexadecimal without using any calculators or special knowledge.

### How to Convert Hexadecimal to Decimal and Decimal to Hex Manually

To calculate the 3 point moving averages form a list of numbers, follow these steps: 1. Add up the first 3 numbers in the list and divide your answer by 3. Write this answer down as this is your first 3 point moving average. 2. Add up the next 3...

### How to Calculate the 3 Point Moving Averages from a List of Numbers and Describe the Trend

Finding the modal class from a grouped frequency table is actually quite easy to do. All you need to do is to look for the group that has the highest frequency. This is because the mode is the number that comes up the most times. Make sure you write...

### How to Work out the Modal Class Interval from a Grouped Frequency Table

Age and mixture problems are tricky questions in Algebra. It requires deep analytical thinking skills and great knowledge in creating mathematical equations. Practice these age and mixture problems with solutions in Algebra.

### Age and Mixture Problems and Solutions in Algebra

Though we all know how to use the Pythagorean Theorem, few know of the many proofs that accompany this theorem. Many of them have ancient and surprising origins.

### Early Proofs of the Pythagorean Theorem by Leonardo Da Vinci, Ptolemy, Thabit ibn Qurra, and Garfield

Regression equations are frequently used by scientists, engineers, and other professionals to predict a result given an input. These equations have many applications and can be developed with relative ease. In this article I show you how easy it is to create a simple linear regression equation from a small set of data.

### How to Create Your Own Simple Linear Regression Equation

The Monty Hall Problem is a popular example of how intuition can often lead you to make mistakes in probability. In this hub, I will describe this interesting problem and the mathematics behind it.

### The Monty Hall Problem

A guide to solving for centroids and centers of gravity of different compound shapes using the method of geometric decomposition. Learn how to obtain the centroid from different examples provided.

### Calculating the Centroid of Compound Shapes Using the Method of Geometric Decomposition

Learn how to easily solve math problems using divisibility rules in math. These important math techniques will help you excel in your math subject.

### Math Techniques: Learn the Divisibility Rules

Find out how to perform AC test in determining if a trinomial is factorable. Once proven factorable, proceed with finding the factors of the trinomial using a 2 x 2 grid.

### Factoring Quadratic Trinomials Using the AC Test

To keep our calendar in sync with solar time requires more than adding a day every four years. We need to add a second occasionally. We also need to skip some leap years.

### The Algorithmic-Rule for Leap Years and Leap Seconds

Converting between digital binary words and decimal, octal, or hexadecimal number systems, for human use, is essential to understand the inner workings of the vast tech world of gaming, gadgets, computers, and computerized most things. I describe the best ways to perform these tasks.

### Converting Number Systems

The uses of math for the layperson are essentially endless. No matter whether you are a struggling student, a homeowner, or someone simply trying to lose weight, math is the universal language that has an something to offer everyone.

### Practical Applications of Mathematics in Everyday Life

Numbers are represented using different number systems dependant on their application. For example, numbers within computers use binary or hexadecimal. How do these different number systems work and how can numbers be converted between them?

### Alternative Number Systems: What Are Binary Numbers?

How many cats fit into the trunk of a Honda Civic....and other fun math problems involving our favorite feline friends

### Cat Mathematics: How Many Cats Fit Into the Trunk of a Honda Civic...

How to learn your times tables fast. There are a few tricks to help you with your times tables and even a link to my video "How to Learn Your Times Tables Fast"

### How to Learn Times Tables

When solving complex arithmetic expressions, the order in which you perform which functions is crucial in getting the correct answer. The acronym PEMA is a good mnemonic tool for these problems.

### How to Use PEMA to Guide Order of Operations in Arithmetic Problems

Need help with trig homework or a review of the basics? This article explains in plain English how to visualize the unit circle as just a set of triangles, how a sine and cosine work, and radians.

### Trigonometry: The Unit Circle [in Plain English]

Don't let mind readers and magicians mess with your mind with number tricks. Learn their secrets and beat them at their own game.

### It's Not Magic, It's Mathematics

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