Calculus is the study of change. It is focused on limits, functions, derivatives, integrals, and infinite series. It has two major branches, differential calculus the measure the rate of change at any given point on a curve, and integral calculus the measure the exact area under a curve.
Algebra - Completing the Square | Algebra - Slope |
When you are unable to solve a quadratic equation of the form ax² +bx+c by factoring, then you can use the technique called completing the square. To complete the square means to create a polynomial with three terms (trinomial) that is a perfect square. Algebra - Quadratic Formula The quadratic formula is the solution of the quadratic equation. There are other ways to solve the quadratic equation, however, using the quadratic formula is often the most convenient way. |
The slope of a line defines the steepness of the line and whether the line rises or falls. The definition of slope is the rise divided by the run, written as:
Slope = rise / run The slope is calculated by counting the rise and then counting the run. We then write the slope as a fraction. Algebra - Mean You find the mean of a set of data by adding up all the numbers in the data set and then dividing by the number of data points you added up. |
Algebra - Area | Algebra - Volume |
Area is the number of square units inside of a shape. The shape is two dimensional. Since the area is measuring the number of square units inside of the shape, the units must be written as squared units. Area of a Rectangle A rectangle is a 4 sided figure with two pairs of parallel lines. Each set of parallel lines has the same length. To find the area of a rectangle we are going to multiply the length x the width. |
Volume is the amount of space enclosed by an object. You must have a three-dimensional object in order to find volume. You are trying to figure out how many cubic units the object can hold inside. Volume of a Rectangular Prism A rectangular prism is your basic box, that is not a cube. In order to find the volume, we will multiply the length x width x height. These dimensions may all be different. |
Algebra - Scientific Notation | Algebra - Factoring |
Scientific Notation Scientific notation is a way of writing numbers that are too big or too small to be conveniently written in decimal form. Cramer's Rule In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. |
Factoring A "quadratic" is a polynomial that looks like "ax2 + bx + c", where "a", "b", and "c" are just numbers.
For the easy case of factoring, you will find two numbers that will not only multiply to equal the constant term "c", but also add up to equal "b", the coefficient on the x-term. Lateral Area lateral area ( mathematics ) The area of a surface of a 3-D figure with the bases (if any) excluded. |
Algebra - Vectors | Algebra - Conics |
A Vector is something that has two and only two defining charactersitcs. Magnitude: the meaning of magnitude is 'size' or 'quantity' Direction: simply means that the vector is directed from one place to another. Vector Addition the process of finding one vector that is equivalent to the result of the successive application of two or more given vectors. |
Conic Section Definition:
A conic section is the intersection of a cone by a plane. By changing the angle and location of intersection, we can produce a circle, ellipse, parabola or hyperbola. Logarithm The logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: |