Math 101: Exam 2 (Study Guide)

Pataasin ang iyong marka sa homework at exams ngayon gamit ang Quizwiz!

"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.


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