Integration

Definition Integration is used to find areas, volumes, central points and often is used to find the area underneath the graph of a function. Common Functions of Integration   Function Integral Constant ∫ a dx ax + c Variable ∫ x dx Square ∫ x2 dx   Reciprocal ∫ (1/x) dx ln|x| + c Exponential ∫

Consecutive Interior Angles

Definitions When two lines are crossed by another line (Transversal), Consecutive Interior Angles are the pairs of angles on one side of the transversal, but inside the two lines. The 2 angles in purple (d and e) make one pair of consecutive interior angles, and the other 2 angles in red (c and f) make another

Percentage Change

What Is Percentage Change? Percentage change can be applied to any quantity. Let’s say you are tracking the the grow of height. If the height increased, use the formula (New Height – Old Height)/Old Height Then, multiply that number by 100%. If the price decreased, use the formula (Old Height – New Height)/Old Height Then

Zero Product Property

Definition If   a × b = 0   then   a = 0   or   b = 0   or  a = b = 0 A product of factors is zero if and only if one or more of the factors is zero. Standard Form of an Equation The Standard Form of an equation is: “some expression” = 0 Learn More Partial Sum General Form of

Partial Sum

A series is the sum of the terms in a sequence (not the list of terms, like a sequence). The series with a finite number of terms is a easy to find the sum of the series just by adding the terms. However, for the series with an infinite number of terms, the summation is more difficult and complicated.

Prime Factorization

Prime Numbers A Prime Number is a whole number greater than 1 that can not be made by multiplying other whole numbers. The number that we can make by multiplying other whole numbers is a Composite Number. Factors Factors are the numbers you multiply together to get another number 4 × 2 = 8 From

Common Derivatives

Derivative of a function of a real variable measures the sensitivity to change of the function value (output) with respect to a change in its argument (input). Derivatives are a fundamental tool of calculus. The derivative of a function of a single variable at a chosen input value (when it exists) is the slope of the tangent

General Form of Equation of a Line

Definition General Form of the equation of a straight line is: Ax + By + C = 0 Note: A or B can’t be zero at the same time. (if A = 0 then B ≠ 0, vice versa) The General Form is not always the most useful form, and you may prefer to use: Slope-Intercept Form

Parallel Lines

Lines are parallel if they are always the same distance apart (called “equidistant“), and will never meet. Definition of Parallel Lines Parallel lines in geometry are lines in a plane which do not meet. They don’t intersect each other at any point. By extension, a line & a plane, or 2 planes, in 3D Euclidean

Subtracting Fractions

Definition A fraction like 2/3 says we have 2 out of the 3 parts the whole is divided into. The top number is called numerator The bottom number is called denominator There are 3 simple steps to subtract fractions Make sure the bottom numbers (the denominators) are the same Subtract the top numbers (the numerators).