Math 101: Exam 2 (Study Guide)
"Transforming"Equations into simpler Linear or Quadratic equations. (Ch 1.4)
What can you Transform: 1. Radical Equations 2. Quadratic Equations 3. Factorable Equations * Can use substitution or factoring
Absolute Value Equations and Inequalities (ch. 1.7): Definiton
describes the distance of a number on the number line from 0 without considering which direction from zero the number lies. The absolute value of a number is never negative. (Ex: The absolute value of 5 is 5) See Example!!
Graph a Set and Write as Interval
see example
LInear Inequality Word Problem Example
see example
Solve "Polynomial" inequality, express solution set in interval notation
see example
Solve "Rational" inequality, graph solution set on real number line
see example
Solve "Rational" inequality, graph solution set on real number line (second example)
see example
Transform "Radical" to "Linear" equation
see example
Transforming: Solve Radical for Given Variable (Substitution)
see example
Transforming: Using Factoring
see example
Transforming: Using Substitution
see example
Use Substitution to transform to Quadratic
see example
Write a statement as an "inequality"
see example
Write inequality using "interval notation" and "graph"
see example
Solving Quadratic Equations: Complete the Square
see image
Solving Quadratic Equations: Factoring
see image
Solving Quadratic Equations: Quadratic Formula
see image
Solving Quadratic Equations: Square Root
see image
Solving Quadratic Equations: Use Any Method
see image
Liner Inequality - Mult/Div by Negative Number
KEY: Must REVERSE the inequality sign see example
How To Determine Quadrant Where POINTS lie
See Example
Absolute Value: Graph Solution Set on Number Line
See Example!
Absolute Value: Solve Equation
See Example!
Determine Quadrants that Satisfy Condition
See Example!
Theorem: Absolute Value Inequalities
See Example!
Definition: Distance Between 2 Numbers
See Example!!
Solve absolute value equations (not inequality)
See Example!!
Theorem: Absolute Value
See Example!!
Theorem: Absolute Value Equation
See Example!!
Linear Inequalities: Ch. 1.5
* For any 2 real numbers "a" and "b", one of 3 things must be true: a = b, 2. a > b; 3. a < b * solved using the same procedures as "linear equations" EXCEPT FOR: When you mult/div by a "negative" number, you must REVERSE the inequality sign.
Basic Tools: Cartesian Plan, Distance, Midpoint (Ch. 2.1)
1. A Cartesian plane is a graph with one x-axis and one y-axis. These two axes are perpendicular to each other. 2. Distance Formula, as evident from its name, is used to measure the shortest (straight-line) distance between two points. 3. The midpoint is halfway between the two end points: Its x value is halfway between the two x values. Its y value is halfway between the two y values.
4 methods for solving Quadratic Equations (Ch. 1.3)
1. Factoring 2. The square root method (if possible) 3. Complete the square (ALWAYS WORKS) 4. Quadratic Formula (ALWAYS WORKS)
Solving Linear Inequalties
1. Solve Linear Inequality 2. Show solution set (inequality) interval notation 3. Graph the solution set * see example
Procedure to solve Rational or Polynomial Inequalities
1. Write inequality in standard form (Expression > 0) 2. Identify Zeros 3. Draw Number Line with Zeros Labeled 4. Determine the "sign of expression" in each interval * see example
Polynomial and Rational Inequalities: (Ch. 1.6)
1. rational inequality: is an inequality which contains a rational expression. The trick to dealing with rational inequalities is to always work with zero on one side of the inequality. 2. Polynomial inequalities: a polynomial on one side of the inequality symbol and zero on the other side. Solutions to polynomial inequalities are intervals of values, such that any number in the interval makes a true statement when plugged into the inequality
Solve absolute inequality using 3 steps
1. solve given inequality 2. write solution set using interval notation 3. graph the solution set see example!
Definition of Quadratic Equation
Any equation having the form where: x represents an unknown a, b, and c represent known numbers, with a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term
Rectangular Coordinate System
Formed by two perpendicular lines (axes) that intersect at the point corresponding to zero on each line.
