degree of a monomial: sum of the exponents of the variables ( x squared = degree 2, [x^4][y^3][z^2] = degree 9)
polynomial: the sum/difference of monomials
degree of a polynomial: degree of the term with the highest degree
standard form of a polynomial: written with therms in order by degree
System of Equations
A system of linear equations is 2 or more equations containing 2 or more variables. The solution of a system of equations is an ordered pair that satisfies all equations in the system. It is the point of intersection.
Exponents
The exponent tells you how many times to use the base as a factor.
Counterexamples
An example that disproves a statement. One counterexample is enough to disprove a statement.
Parallel and Perpendicular
Lines with the same slope are parallel. Perpendicular lines have slopes that are opposite reciprocals.
Slope and Intercept
Any line can be described by its slope and intercepts. Lines heading up from right to left have a positive slope. Lines heading down to the right have a negative slope.
Relations and Functions
relation: a set of ordered pairs
domain: the set of the first numbers of the ordered pairs/ x values/ possible inputs
range: the set of the second numbers of the ordered pairs/ y values/ possible outputs
function: a relation that pairs up each x value with exactly one y value
Solving Inequalities
An inequality is a statement that two expressions are not equal. To solve inequalities use inverse operations to isolate variables, but when you multiply/divide by a negative number, you must flip the direction of the inequality (< or >).
G E M D A S
G = grouping
E = exponents
M/D = multiplying/dividing
A/S = adding/subtracting
Solving Absolute Value Equations
1. Use inverse operations to isolate the absolute-value expression.
2. Branch off - write two cases that don't involve absolute values, with the answers as opposites of each other.
3. Solve the equation in each of the two cases.
Special Cases: If the absolute value expression equals zero, there is only one solution. If the equation states the absolute value is negative, there are no solutions.
Inverse or Reciprocal
Two numbers are reciprocals (or inverses) if they multiply to make 1.
Multiplying and Dividing Real Numbers
Both are positive > answer is positive
Both are negative > answer is positive
One positive, one negative > answer is negative
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