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Algebra
How to Add and Subtract Fractions in Algebra (Video)
In algebra, adding and subtracting fractions is easy when you find the common denominator. This video shows you how to convert fractions for the common denominator. After you determine the common denominator, you can add and subtract fractions, including story problems, with ease. [more…]
Calculus
How to Find the Volume of a Solid with a Circular Cross-Section (Video)
Calculus allows you to calculate the volume of conical objects by dividing the object into an infinite number of circular cross-sections - geometrical shapes resembling pancakes or washers - and adding up the volume of all those cross-sections through integration. This video tutorial shows you how. [more…]
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Geometry
Mastering the Formal Geometry Proof
Suppose you need to solve a crime mystery. You survey the crime scene, gather the facts, and write them down in your memo pad. To solve the crime, you take the known facts and, step by step, show who committed [more…]
Geometry
Sizing Up the Area of a Polygon
Not only can polygons be classified by the number of sides they have and by their angles, but they can also be grouped according to some of their qualities. Polygons can have three personality characteristics [more…]
Geometry
Simple and Easy Geometry Tips and Tools
The first rule of life? Life (as well as geometry) can be difficult. But why make it more difficult than it has to be? Do you need help with geometry? Here are 11 tried-and-true tips to make your forays [more…]
Geometry
Measuring and Making Angles
On a map, you trace your route and come to a fork in the road. Two diverging roads split from a common point and form an angle. The point at which the roads diverge is the [more…]
Geometry
Classifying Three Types of Triangles
Triangles are classified according to the length of their sides or the measure of their angles. These classifications come in threes, just like the sides and angles themselves. That is, a triangle has [more…]
How to Find Area with the Shortcut Version of the Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus has a shortcut version that makes finding the area under a curve a snap. Here it is. Let F be any antiderivative of the function [more…]
Integration by Parts Problems where You Go around in Circles
Sometimes if you use integration by parts twice, you get back to where you started from — which, unlike getting lost, is not a waste of time. [more…]
How to Integrate Sine/Cosine Problems with an Odd, Positive Power of Sine
Here’s how you integrate a trig integral that contains sines and cosines where the power of sine is odd and positive. You lop off one sine factor and put it to the right of the rest of the expression, [more…]
How to Integrate Sine/Cosine Problems with Even, Nonnegative Powers of Both Sine and Cosine
Here’s how you integrate a trig integral that contains sines and cosines where the powers of both sine and cosine are even and nonnegative (in other words, zero or positive). You first convert the integrand [more…]
How to Find the Area between Two Curves
To find the area between two curves, you need to come up with an expression for a narrow rectangle that sits on one curve and goes up to another. [more…]
How to Find the Area of a Surface of Revolution
A surface of revolution is a three-dimensional surface with circular cross sections, like a vase or a bell or a wine bottle. For these problems, you divide the surface into narrow circular bands, figure [more…]
How to Use L'Hôpital's Rule to Solve Limit Problems
L’Hôpital’s rule is a great shortcut for doing some limit problems. (And you may need it someday to solve some improper integral problems, and also for some infinite series problems.) [more…]
How to Decompose Partial Fractions
A process called partial fractions takes one fraction and expresses it as the sum or difference of two other fractions. In calculus, this process is useful before you integrate a function. Because integration [more…]
How to Factor a Polynomial Expression
In mathematics, factorization or factoring is the breaking apart of a polynomial into a product of other smaller polynomials. If you choose, you could then multiply these factors together, and you should [more…]
How to Graph a Circle
The first thing you need to know in order to graph the equation of a circle is where on a plane the center is located. The equation of a circle appears as [more…]
How to Graph an Ellipse
An ellipse is a set of points on a plane, creating an oval, curved shape, such that the sum of the distances from any point on the curve to two fixed points [more…]
How to Graph a Hyperbola
Think of a hyperbola as a mix of two parabolas — each one a perfect mirror image of the other, each opening away from one another. The vertices of these parabolas are a given distance apart, and they open [more…]
How to Solve Linear Systems
When you solve systems with two variables and therefore two equations, the equations can be linear or nonlinear. Linear systems are usually expressed in the form Ax + By [more…]
How to Solve Systems that Have More than Two Equations
Larger systems of linear equations involve more than two equations that go along with more than two variables. These larger systems can be written in the form Ax + By + Cz + . . . [more…]
How to Graph a Rational Function When the Numerator Has the Higher Degree
Rational functions where the numerator has the greater degree don’t actually have horizontal asymptotes. Instead, they have oblique asymptotes which you find by using long division. [more…]
How to Graph a Parabola
In order to graph a parabola correctly, it is important to note whether it is a horizontal or a vertical parabola. This is because while the variables and constants in the equations for both curves serve [more…]
How to Measure Angles with Radians
Degrees aren’t the only way to measure angles. You can also use radians. Degrees and radians are just two different ways to measure angles, like inches and centimeters are two ways of measuring length. [more…]
What Is a Geometry Proof?
A geometry proof — like any mathematical proof — is an argument that begins with known facts, proceeds from there through a series of logical deductions, and ends with the thing you’re trying to prove. [more…]
Getting to Know the Five Simplest Geometric Objects
The study of geometry begins with the definitions of the five simplest geometric objects — point, line, segment, ray, and angle — as well as two extra definitions [more…]
Getting to Know Points
Although individual points have no features, when you group them, you can create several different types of points: collinear, non-collinear, coplanar, and non-coplanar. Each type merits an explanation [more…]
Getting to Know Lines
There are different types of lines (or segments or rays) or pairs of lines (or segments or rays). You can identify single lines based on the direction they’re pointing [more…]
Getting to Know Planes
When two geometric planes interact with each other, it is in one of two ways: as parallel planes or as intersecting planes. Here are the definitions for these two types of relationships between a pair [more…]
Getting to Know Angles
Angles are one of the basic building blocks of triangles and other polygons. There are five types of angles: acute, right, obtuse, straight, and reflex. You see angles on virtually every page of any geometry [more…]
Getting to Know Angle Pairs
Adjacent angles and vertical angles always share a common vertex, so they’re literally joined at the hip. Complementary and supplementary angles can share a vertex, but they don’t have to. Here are the [more…]
How to Measure Line Segments
To find the measure or size of a segment, you simply measure its length. What else could you measure? After all, length is the only feature a segment has. You’ve got your short, your medium, and your long [more…]
