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Illinois Licensure Testing System: Mathematics Test Framework Study Guide

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Translating Phrases to Expressions

  • Translating Word Phrases to Expressions Example 2
    01:25
  • Translating Word Phrases to Expressions
    07:32
  • Translating Word Phrases to Expressions Example 1
    01:31

Translating Sentences to Equations

  • Translating Sentences to Equations Example 1
    01:21
  • Translating Sentences to Equations
    04:36
  • Translating Sentences to Equations Example 2
    01:15

Simplifying Expressions

  • Like Terms Example 1
    02:12
  • Like Terms Example 2
    01:50
  • Like Terms Example 3
    01:21

Solving Linear Equations

  • Strategy for Solving Linear Equations
    06:21
  • 가이드 코스
    Solving Linear Equations with Fraction or Decimal Coefficients
    06:25
  • 가이드 코스
    Solving Linear Equations with Fraction or Decimal Coefficients Example 2
    05:27

Linear Inequalities in One Variable

  • Solving Linear Inequalities
    05:29
  • Solving Linear Inequalities Example 3
    02:46
  • 가이드 코스
    Solving Three Part Inequalities
    05:13

Introduction to Problem Solving

  • Consecutive Integers Problems Example 2
    02:11
  • Consecutive Integers Problems Example 3
    02:17
  • Word Problem Solving Strategy
    07:08

Formulas

  • Solve Applied Problems Using Formulas
    04:45
  • Solve a Formula for a Specific Variable
    04:10
  • Solve a Formula for a Specific Variable Example 2
    03:00

Percent Problem Solving

  • Simple Interest Example 5
    01:45
  • Translating Percent Problems Example 3
    03:09
  • Translating Percent Problems Example 2
    00:44

Mixture Problem Solving

  • Example 2: Mixing Simple Interest
    04:10
  • Intro to Mixture Problems
    05:18
  • Mixture Problems Involving Percents
    05:55

The Rectangular Coordinate System

  • Completing Ordered Pair Solutions
    05:09
  • Determining Whether an Ordered Pair is a Solution to an Equation
    05:09
  • Graphs & the Rectangular Coordinate System
    05:10

Graph Linear Equations in Two Variables

  • Graphing Linear Equations in Two Variables Example 2
    02:35
  • Graphing Linear Equations in Two Variables Example 1
    03:07
  • Graphing Linear Equations in Two Variables
    05:51

Slope of a Line

  • Graphing a Line From Its Slope Example 4
    03:41
  • Finding the Slope of a Line Example 2
    03:03
  • Finding the Slope of a Line
    05:13

Slope-Intercept Form

  • Graphing Lines in Slope-Intercept Form
    02:35
  • Parallel and Perpendicular Lines Example 3
    03:32
  • Graphing in Slope-Intercept Form Example 2
    05:57

Point Slope Form

  • Finding the Equation of a Line Given 2 Points Example 2
    05:26
  • Point Slope Form of a Line Example 1
    03:29
  • Point Slope Form of a Line
    05:41

Solving Systems of Linear Equations by Graphing

  • Solve a System of Linear Equations by Graphing Example 2
    04:42
  • Solve a System of Linear Equations by Graphing Example 1
    3:09
  • Determining Number of Solutions in a System
    06:06

Solving Systems of Linear Equations by Substitution

  • Solving Systems of Linear Equations - Substitution
    5:48

Solving Systems of Linear Equations by Elimination

  • Choosing a Method to Solve a System
    06:26
  • Solving Systems of Linear Equations - Elimination Example 1
    4:32
  • Choosing a Method to Solve a System Example 4
    01:57

Intro to Polynomials

  • Introduction to Polynomials
    05:13
  • Degree of Polynomials
    05:20

Adding and Subtracting Polynomials

  • Adding and Subtracting Polynomials
    07:43

Multiplying Polynomials

  • Multiply Polynomials Using the Distributive Property Example 2
    02:47
  • Multiply Polynomials by Monomials
    03:46
  • Multiply Binomials Using the FOIL Method Example 1
    01:34

Factoring by Greatest Common Factor & Grouping

  • GCF of Terms
    05:42
  • Factoring Polynomials by Grouping Example 4
    02:47
  • Factoring Polynomials by Grouping Example 5
    03:23

Factoring Trinomials of the Form x² + bx + c

  • Factoring Trinomials of the Form x² + bx + c Example 1
    02:03
  • Factoring Trinomials of the Form x² + bx + c
    07:23

Factoring Trinomials of the Form ax² + bx + c

  • Factoring Trinomials by Grouping (AC Method)
    04:23
  • Factoring Trinomials Using Trial and Error
    08:18
  • Factoring Trinomials Using Trial and Error Example 2
    03:07

Factoring Special Products

  • Difference of Squares Example 3
    01:17
  • Difference of Squares
    04:13
  • Sum & Difference of Cubes Example 6
    02:49

Quadratic Equations & Applications

  • Solving Quadratic Equations by Factoring
    04:41
  • Applications of Quadratic Equations Example 2
    02:49
  • Applications of Quadratic Equations Example 6
    01:41

Simplifying Fractions

  • Types of Fractions
    05:25
  • Simplify Fractions (Write Fractions in Lowest Terms)
    06:15
  • Intro to Fractions Example 1
    03:42

Simplifying Rational Expressions

  • Simplifying Rational Expressions Example 2
    03:24
  • Intro To Rational Expressions
    04:37
  • Simplifying Rational Expressions
    04:13

Multiplying and Dividing Rational Expressions

  • Multiplying Rational Expressions Example 1
    03:58
  • Dividing Rational Expressions
    03:43
  • Multiplying Rational Expressions
    03:41

Adding and Subtracting Rational Expressions with Common Denominators

  • Adding and Subtracting Rational Expressions with Common Denominators Example 1
    04:35
  • Adding and Subtracting Rational Expressions with Common Denominators
    06:00

Least Common Denominators

  • Write Equivelant Expressions With Common Denominators Example 1
    03:32
  • Write Equivelant Expressions With Common Denominators Example 2
    03:28
  • Write Equivalent Expressions With Common Denominators
    05:30

Adding and Subtracting Rational Expressions with Different Denominators

  • Adding and Subtracting Rational Expressions with Unlike Denominators
    06:23
  • Adding and Subtracting Rational Expressions with Unlike Denominators Example 1
    08:03

Rational Equations

  • Restrictions on Rational Equations
    05:21
  • Solving Rational Equations Example 1
    08:59
  • Solving Rational Equations
    05:56

Introduction to Relations and Functions

  • Determining if a Relation is a Function Given an Equation Example 3
    05:13
  • Determining if a Relation is a Function Given an Equation
    06:28
  • Domain and Range Example 4
    02:49

Function Notation

  • Function Notation
    05:50
  • Function Notation Example 1
    02:46
  • Function Notation Example 2
    04:20

Graphing Common Functions

  • Graphs of Common Functions
    5:57

Composition of Functions

  • Domain Restrictions of Composed Functions
    3:51
  • Evaluating Composed Functions
    4:26
  • Function Compositions
    4:56

Direct & Inverse Variation

  • Direct Variation
    04:31
  • Inverse Variation
    05:33
  • Inverse Variation Example 2
    03:07

Introduction to Radical Expressions

  • Finding Higher Roots: Even Roots
    04:44
  • Simplifying nth Root of nth Power
    05:20
  • Approximating Roots
    03:15

Simplifying Radical Expressions

  • Product Rule of Radicals Example 1
    01:05
  • Quotient Rule of Radicals
    05:04
  • Simplifying Radicals Example 3
    04:06

Adding and Subtracting Radicals

  • Adding & Subtracting LIKE Radicals
    03:50
  • Adding & Subtracting UNLIKE Radicals
    5:48
  • Adding & Subtracting UNLIKE Radicals Example 1
    01:40

Multiplying, Dividing, and Rationalizing Radicals

  • Rationalizing Denominators Example 3
    02:34
  • Rationalizing Denominators
    02:58
  • Multiplication of Radical Expressions Example 2
    05:00

Introduction to Complex Numbers

  • Adding and Subtracting Complex Numbers
    03:18
  • Introduction to Complex Numbers
    03:31
  • Square Roots of Negative Numbers
    05:02

Multiplying and Dividing Complex Numbers

  • Complex Conjugates
    05:33
  • Multiplying Complex Numbers
    05:02
  • Higher Powers of i
    05:10

The Square Root Property

  • Imaginary Solutions
    02:26
  • Using The Square Root Property
    05:34
  • Using The Square Root Property Example 3
    03:56

Completing the Square

  • Complete the Square Example 1
    08:50
  • Complete the Square
    07:06
  • Complete the Square Example 2
    02:40

The Quadratic Formula

  • Choosing a Method to Solve Quadratic Equations
    03:45
  • Introduction to the Quadratic Formula
    06:08
  • The Discriminant
    04:11

Graphing Quadratic Equations

  • Intro to Graphing Quadratic Equations
    04:10
  • Vertex Form of Quadratics Example 4
    04:04
  • Horizontal and Vertical Shifts of Quadratics Example 2
    03:42