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Introduction to Algebra - MATH

Details: Introduction to Algebra. Algebra is great fun - you get to solve puzzles! A Puzzle. What is the missing number? −

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Introduction to Measurement

Details: Area. Area is the size of a surface: how much is inside the boundary of a flat (2-dimensional) object such as a triangle or circle. Here Ariel the Dog is waiting patiently inside 1 square meter.

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Differential Equations - Introduction

Details: Differential Equations can describe how populations change, how heat moves, how springs vibrate, how radioactive material decays and much more. They are a very natural way to describe many things in the universe. What To Do With Them? On its own, a Differential Equation is a wonderful way to express something, but is hard to use.. So we try to solve them by turning the Differential Equation

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Multiplication - Times Tables - MATH

Details: Why Learn The Multiplication Table? While it is generally more important to know why things work, with the tables I recommend pure memory, it makes future math work much easier.. Much like walking, you don't want to think what your feet are doing, you want to enjoy the adventure.

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Binary Number System - MATH

Details: Position. In the Decimal System there are Ones, Tens, Hundreds, etc. In Binary there are Ones, Twos, Fours, etc, like this:. This is 1×8 + 1×4 + 0×2 + 1 + 1×(1/2) + 0×(1/4) + 1×(1/8) = 13.625 in Decimal Numbers can be placed to the left or right of the point, to show values greater than one and less than one.

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The Method of Variation of Parameters

Details: The simpler case where f(x) = 0: d 2 ydx 2 + P(x) dydx + Q(x)y = 0. is "homogeneous" and is explained on Introduction to Second Order Differential Equations.Please learn that method first to help you understand this page. Two Methods

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Converting Fractions to Decimals - MATH

Details: Another Method Yet another method you may like is to follow these steps: Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.; Step 2: Multiply both top and bottom by that number.; Step 3.Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero

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Amplitude, Period, Phase Shift and Frequency

Details: Amplitude, Period, Phase Shift and Frequency. Some functions (like Sine and Cosine) repeat forever and are called Periodic Functions.. The Period goes from one peak to the next (or from any point to the next matching point):. The Amplitude is the height from the center line to the peak (or to the trough). Or we can measure the height from highest to lowest points and divide that by 2.

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Chi-Square Test - MATH

Details: Important points before we get started: This test only works for categorical data (data in categories), such as Gender {Men, Women} or color {Red, Yellow, Green, Blue} etc, but not numerical data such as height or weight.; The numbers must be large enough. Each entry must be 5 or more. In our example we have values such as 209, 282, etc, so we are good to go.

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Matrices

Details: Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

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Fractional Exponents - MATH

Details: First, let us look at whole number exponents:. The exponent of a number says how many times to use the number in a multiplication.. In this example: 8 2 = 8 × 8 = 64

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Imaginary Numbers - MATH

Details: Imaginary Numbers are not "Imaginary". Imaginary Numbers were once thought to be impossible, and so they were called "Imaginary" (to make fun of them).. But then people researched them more and discovered they were actually useful and important because they filled a gap in mathematics but the "imaginary" name has stuck.. And that is also how the name "Real Numbers" came about (real is not

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Laws of Exponents - MATH

Details: Laws of Exponents. Exponents are also called Powers or Indices. The exponent of a number says how many times to use the number in a multiplication.. In this example: 8 2 = 8 × 8 = 64

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Introduction to Calculus - MATH

Details: Wow! Sam got an answer! Sam: "I will be falling at exactly 10 m/s". Alex: "I thought you said you couldn't calculate it?". Sam: "That was before I used Calculus!". Yes, indeed, that was Calculus. The word Calculus comes from Latin meaning "small stone". · Differential Calculus cuts something into small pieces to find how it changes. · Integral Calculus joins (integrates) the small pieces

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Eigenvector and Eigenvalue - MATH

Details: Eigenvector and Eigenvalue. They have many uses! A simple example is that an eigenvector does not change direction in a transformation:. The Mathematics Of It. For a square matrix A, an Eigenvector and Eigenvalue make this equation true:. We will see how to find them (if they can be found) soon, but first let us see one in action:

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Quick Subtraction - MATH

Details: Quick Subtraction. This is a special method of subtraction which many people find quickest (once they get used to it!).. Start Normally. We start the same way as Subtraction by Regrouping (but we aren't going to be doing any regrouping):. write down the larger number first and the smaller number directly below it

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Solving SSA Triangles

Details: Note there is only one answer in this case. The "12.4" line only joins up one place. The other possible answer for L is 149.9°. But that is impossible because we already have M = 125° and a triangle can't have two angles greater than 90°.. Conclusion: When solving a "Side, Side, Angle" triangle we need to check if there could be another possible answer!

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Hyperbolic Functions - MATH

Details: Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

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Infinite Series - MATH

Details: More Examples Arithmetic Series. When the difference between each term and the next is a constant, it is called an arithmetic series. (The difference between each term is 2.) Geometric Series. When the ratio between each term and the next is a constant, it is called a geometric series.. Our first example from above is a geometric series:

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Matrix Rank - Math is Fun

Details: It also has uses in communication, stability of systems and more. Linear Dependence. Instead of "not made of" we say they are linearly independent which is an important idea.. Linear means we can multiply by a constant, but no powers or other functions. The constant can be any real number (0, 1, any whole number, fraction, negatives, etc.).

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Exact Equations and Integrating Factors

Details: Exact Equations and Integrating Factors. Hi! You should have a rough idea about differential equations and partial derivatives before proceeding!. Exact Equation. An "exact" equation is where a first-order differential equation like this:

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Inflection Points - MATH

Details: Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

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Limits to Infinity - MATH

Details: Limits to Infinity. Please read Limits (An Introduction) first. Infinity is a very special idea. We know we can't reach it, but we can still try to work out the value of functions that have infinity in them.

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The Time - Converting AM/PM to 24 Hour Clock - MATH

Details: Footnote on "Meridiem" vs "Meridian" Should "AM" be "ante meridiem" or "ante meridian" (likewise for PM)?. The official (according to an American, Australian and British dictionary I checked), and most common spelling for AM is "ante meridiem" which is a Latin phrase.I recommend that spelling!

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Convert Decimals to Percents - MATH

Details: Example: Convert 0.125 to percent. Multiply 0.125 by 100%: 0.125 × 100% = 12.5% Don't forget the % sign! Answer 0.125 = 12.5%

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Sine, Cosine, Tangent - MATH

Details: Sine, Cosine and Tangent. Sine, Cosine and Tangent (often shortened to sin, cos and tan) are each a ratio of sides of a right angled triangle:. For a given angle θ each ratio stays the same no matter how big or small the triangle is. To calculate them: Divide the length of one side by another side

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Subtracting Fractions - MATH

Details: Subtracting Mixed Fractions. I have a special page on Adding and Subtracting Mixed Fractions.. Making the Denominators the Same. In the previous example it was easy to make the denominators the same, but it can be harder so you may need to use either the

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Copy a Line Segment Construction - MATH

Details: Copy a Line Segment. How to copy a line segment using just a compass and a straightedge

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Inverse Sine, Cosine, Tangent

Details: And now for the details: Sine, Cosine and Tangent are all based on a Right-Angled Triangle. They are very similar functions so we will look at the Sine Function and then Inverse Sine to learn what it is all about.. Sine Function. The Sine of angle θ is:. the length of the side Opposite angle θ; divided by the length of the Hypotenuse; Or more simply:

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Solids of Revolution by Disks and Washers

Details: Solids of Revolution by Disks. We can have a function, like this one: And revolve it around the x-axis like this: To find its volume we can add up a series of disks:. Each disk's face is a circle:

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Introduction to Sets - MATH

Details: Now you don't have to listen to the standard, you can use something like m to represent a set without breaking any mathematical laws (watch out, you can get π years in math jail for dividing by 0), but this notation is pretty nice and easy to follow, so why not?. Also, when we say an element a is in a set A, we use the symbol to show it. And if something is not in a set use .

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Bayes' Theorem - MATH

Details: Example: An internet search for "movie automatic shoe laces" brings up "Back to the future" Has the search engine watched the movie? No, but it knows from lots of other searches what people are probably looking for.. And it calculates that probability using Bayes' Theorem.

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Confidence Intervals - MATH

Details: Example: Average Height. We measure the heights of 40 randomly chosen men, and get a mean height of 175cm,. We also know the standard deviation of men's heights is 20cm.. The 95% Confidence Interval (we show how to calculate it later) is:. 175cm ± 6.2cm. This says the true mean of ALL men (if we could measure all their heights) is likely to be between 168.8cm and 181.2cm.

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Inverse of a Matrix

Details: 2x2 Matrix. OK, how do we calculate the inverse? Well, for a 2x2 matrix the inverse is: In other words: swap the positions of a and d, put negatives in front of b and c, and divide everything by the determinant (ad-bc). Let us try an example: How do we know this is the right answer?

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Finding Parallel and Perpendicular Lines - MATH

Details: Example: Find the equation of the line that is: parallel to y = 2x + 1 ; and passes though the point (5,4) The slope of y=2x+1 is: 2. The parallel line needs to have the same slope of 2.

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Seismic Waves - MATH

Details: P-Waves are fastest at about 6 km/s (kilometers per second) and arrive first.. They can travel through solids, liquids, and gases and pass right through the Earth in a special pattern. S-Waves are slower at about 3.6 km/s and arrive second.. They can only pass through solids and so cannot pass through the earth’s liquid core.

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Solving Word Questions - MATH

Details: Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

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Solution of First Order Linear Differential Equations

Details: Here we will look at solving a special class of Differential Equations called First Order Linear Differential Equations. First Order. They are "First Order" when there is only dy dx, not d 2 y dx 2 or d 3 y dx 3 etc. Linear. A first order differential equation is linear when it can be made to look like this:. dy dx + P(x)y = Q(x). Where P(x) and Q(x) are functions of x.. To solve it there is a

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Percentage Difference, Percentage Error, Percentage Change

Details: Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

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Integral Approximations

Details: Integral Approximations . Integration is the best way to find the area from a curve to the axis: we get a formula for an exact answer.

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Activity: Lengths of Leaves

Details: If this is not clear, then let me explain: The three shortest leaves in my sample have lengths 22 mm, 25 mm and 27 mm.These are all between 20 mm and 29 mm, so each of them adds a tally mark for the group 20 - 29. So there are three tally marks altogether in the group 20 - 29, and the frequency for this group is 3 (i.e. there are 3 leaves in this group).

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Inverse Functions - MATH

Details: Inverse Functions. An inverse function goes the other way! Let us start with an example: Here we have the function f(x) = 2x+3, written as a flow diagram:. The Inverse Function goes the other way:. So the inverse of: 2x+3 is: (y-3)/2

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Adding and Subtracting Positive and Negative Numbers

Details: How to Add and Subtract Positive and Negative Numbers Numbers Can be Positive or Negative. This is the Number Line:

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The Binomial Distribution - MATH

Details: Let's draw a tree diagram:. The "Two Chicken" cases are highlighted. The probabilities for "two chickens" all work out to be 0.147, because we are multiplying two 0.7s and one 0.3 in each case.In other words. 0.147 = 0.7 × 0.7 × 0.3

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Dividing Decimals Animations

Details: Dividing Decimals Animations How to Divide Decimals. Dividing Decimals (read that page if you want) has two steps:. Use Long Division (ignoring the decimal point); Then put the decimal point in the same spot as the dividend (the number being divided)

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Chi-Square Table

Details: The table below can help you find a "p-value" (the top row) when you know the Degrees of Freedom "DF" (the left column) and the "Chi-Square" value (the values in the table).

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Pythagoras Theorem in 3D - MATH

Details: c 2 = a 2 + b 2. c = √(a 2 + b 2). You can read more about it at Pythagoras' Theorem, but here we see how it can be extended into 3 Dimensions.. In 3D. Let's say we want the distance from the bottom-most left front corner to the top-most right back corner of this cuboid:

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Homogeneous Differential Equations - MATH

Details: Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

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Activity: Currency Conversion - MATH

Details: Activity: Currency Conversion. In this activity, you will learn how to convert money between different currencies using an exchange rate table and a calculator.

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