Courses

# Math for Grade 10 (Intermediate Algebra)

Teacher: Amy
Customers Who Have Viewed This Course: 102
\$499.99

#### 0 Course Introduction 03:00

Why should you take this course? 1) Huge amount of resources 2) Step-by-step instruction 3) Highly qualified instructor 4) Build your mathematics confidence

#### 1 Lesson #1 Factors 26:22

Objectives:

1.    Be able to determine all of the factors of a given natural number.
2.    Be able to determine the prime factorization for a given natural number.
3.    Be able to determine the least common multiple for a given set of natural numbers.

#### 2 Lesson #1 Factors Homework Key 02:21

Objectives:

1.    Be able to determine all of the factors of a given natural number.
2.    Be able to determine the prime factorization for a given natural number.
3.    Be able to determine the least common multiple for a given set of natural numbers.

#### 3 Lesson #2 Fractions 24:36

Objectives:

1. Understand why no number can be written as a fraction with a denominator of zero
2. Be able to write any fraction as a reduced fraction where the numerator and denominator have no common factors other than 1.
3. Be able to create an equivalent fraction with a given denominator.
4. Be able to multiply and divide fractions and write the result as a reduced fraction.

#### 4 Lesson #2 Fractions Homework Key 01:43

Objectives:

1. Understand why no number can be written as a fraction with a denominator of zero
2. Be able to write any fraction as a reduced fraction where the numerator and denominator have no common factors other than 1.
3. Be able to create an equivalent fraction with a given denominator.
4. Be able to multiply and divide fractions and write the result as a reduced fraction.

#### 5 Lesson #3 Real Numbers 18:28

Objectives:

1.    Be familiar with the basic definition of a set and the notation used to define a set.
2.    Be able to give examples and non-examples of natural numbers.
3.    Be able to give examples and non-examples of whole numbers.
4.    Be able to give examples and non-examples of integers.
5.    Be able to give examples and non-examples of rational numbers.
6.    Be able to give examples and non-examples of irrational numbers.
7.    Be able to identify problems that can be addressed with each subset of the real numbers.
8.    Be familiar with the basic definition of the absolute value of a real number.
9.    Be able to determine the absolute value of a given real number

#### 6 Lesson #3 Real Numbers Homework Key 01:43

Objectives:

1.    Be familiar with the basic definition of a set and the notation used to define a set.
2.    Be able to give examples and non-examples of natural numbers.
3.    Be able to give examples and non-examples of whole numbers.
4.    Be able to give examples and non-examples of integers.
5.    Be able to give examples and non-examples of rational numbers.
6.    Be able to give examples and non-examples of irrational numbers.
7.    Be able to identify problems that can be addressed with each subset of the real numbers.
8.    Be familiar with the basic definition of the absolute value of a real number.
9.    Be able to determine the absolute value of a given real number

#### 7 Lesson #4 Exponents 31:32

Objectives:

1.    Understand and be able to utilize the rules for multiplying and dividing exponential expressions.
2.    Understand and be able to utilize the rule for simplifying the power of an exponential expression.
3.    Understand and be able to utilize the rule for simplifying the powers of products and quotients.
4.    Be able to interpret and simplify an exponential with a zero as an exponent.
5.    Be able to interpret and simplify an exponential with a negative number exponent.

#### 8 Lesson #4 Exponents Homework Key 04:09

Objectives:

1.    Understand and be able to utilize the rules for multiplying and dividing exponential expressions.
2.    Understand and be able to utilize the rule for simplifying the power of an exponential expression.
3.    Understand and be able to utilize the rule for simplifying the powers of products and quotients.
4.    Be able to interpret and simplify an exponential with a zero as an exponent.
5.    Be able to interpret and simplify an exponential with a negative number exponent.

#### 9 Lesson #5 Order of Operations 12:58

Objective:

1. Be able to use the order of operations to evaluate and simplify an expression.

#### 10 Lesson #5 Order of Operations Homework Key 02:03

Objective:

1. Be able to use the order of operations to evaluate and simplify an expression.

#### 11 Lesson #6 Simplifying & Evaluating Algebraic Expressions 22:10

Objectives:

1.    Be able to simplify variable expressions using the algebraic properties of addition and multiplication.
2.    Be able to simplify variable expressions using the distributive property.

#### 12 Lesson #6 Simplifying & Evaluating Algebraic Expressions Homework Key 02:44

Objectives:

1.    Be able to simplify variable expressions using the algebraic properties of addition and multiplication.
2.    Be able to simplify variable expressions using the distributive property.

#### 13 Lesson #7 Polynomials 26:07

Objectives:

1.    Define polynomial.

#### 14 Lesson #7 Polynomials Homework Key 02:08

Objectives:

1.    Define polynomial.

#### 15 Lesson #8 Multiplying Polynomials (Part One) 10:46

Objectives:

1.    Multiply terms, any two polynomials, binomials, and polynomial functions.
2.    Find the product of the sum and difference of two terms.
3.    Find the square of a binomial.

#### 16 Lesson #8 Multiplying Polynomials Homework Key 05:22

Objectives:

1.    Multiply terms, any two polynomials, binomials, and polynomial functions.
2.    Find the product of the sum and difference of two terms.
3.    Find the square of a binomial.

#### 17 Lesson #8 Multiplying Polynomials (Part Two) 10:33

Objectives:

1.    Multiply terms, any two polynomials, binomials, and polynomial functions.
2.    Find the product of the sum and difference of two terms.
3.    Find the square of a binomial.

#### 18 Lesson #9 Dividing Polynomials 33:21

Objectives:

1.    Divide a polynomial by a monomial.
2.    Divide a polynomial by a polynomial of two or more terms.

#### 19 Lesson #9 Dividing Polynomials Homework Key 02:35

Objectives:

1.    Divide a polynomial by a monomial.
2.    Divide a polynomial by a polynomial of two or more terms.

#### 20 Lesson #10 Factors and the Greatest Common Factor 20:18

Objectives:

1.    Factor out the greatest common factor.
2.    Factor by grouping.

#### 21 Lesson #10 Factors and the Greatest Common Factor Homework Key 03:50

Objectives:

1.    Factor out the greatest common factor.
2.    Factor by grouping.

#### 22 Lesson #11 Factoring by Grouping 18:59

Objectives:

1.    Factor out the greatest common factor.
2.    Factor by grouping.

#### 23 Lesson #11 Factoring by Grouping Homework Key 04:15

Objectives:

1.    Factor out the greatest common factor.
2.    Factor by grouping.

#### 24 Lesson #12 Factoring Trinomials 25:12

Objectives/Hints:

1.    Use the “OI” to factor.
2.    Can you factor out a monomial?
3.    Negative leading coefficients should be factored out.

#### 25 Lesson #12 Factoring Trinomials Homework Key 05:29

Objectives/Hints:

1.    Use the “OI” to factor.
2.    Can you factor out a monomial?
3.    Negative leading coefficients should be factored out.

#### 26 Lesson #13 Special Factoring Formulas 19:05

Objectives:

1.    Factor a difference of squares.
2.    Factor a perfect square trinomial.

#### 27 Lesson #13 Special Factoring Formulas Homework Key 05:55

Objectives:

1.    Factor a difference of squares.
2.    Factor a perfect square trinomial.

#### 28 Lesson #14 Rational Expressions 21:28

Objectives:

1.    Define rational expressions and functions and describe their domain.
2.    Write rational expressions in lowest terms.

#### 29 Lesson #14 Rational Expressions Homework Key 04:42

Objectives:

1.    Define rational expressions and functions and describe their domain.
2.    Write rational expressions in lowest terms.

#### 30 Lesson #15 Multiplying and Dividing Rational Expressions 27:49

Objectives:

1.    Define rational expressions and functions and describe their domain.
2.    Write rational expressions in lowest terms.
3.    Multiply and divide rational expressions.
4.    Find reciprocals of rational expressions.

#### 31 Lesson #15 Multiplying & Dividing Rational Expressions Homework Key 04:28

Objectives:

1.    Define rational expressions and functions and describe their domain.
2.    Write rational expressions in lowest terms.
3.    Multiply and divide rational expressions.
4.    Find reciprocals of rational expressions.

#### 32 Lesson #16 Adding & Subtracting Rational Expressions 22:33

Objectives:

1.    Add and subtract rational expressions with common denominators.
2.    Find a least common denominator.
3.    Add and subtract rational expressions with different denominators.

#### 33 Lesson #16 Adding & Subtracting Rational Expressions Homework Key 03:13

Objectives:

1.    Add and subtract rational expressions with common denominators.
2.    Find a least common denominator.
3.    Add and subtract rational expressions with different denominators.

#### 34 Lesson #17 Radical Expressions 23:17

Objectives:

1.    Find roots of numbers.
2.    Find principal roots.

#### 35 Lesson #17 Radical Expressions Homework Key 04:01

Objectives:

1.    Find roots of numbers.
2.    Find principal roots.

#### 36 Lesson #18 Simplifying Radical Expressions (Part One) 29:02

Objectives:

1.    Use the product and quotient rule for radicals.
3.    Simplify products and quotients of radicals with different indexes.

#### 37 Lesson #18 Simplifying Radical Expressions Homework Key 06:59

Objectives:

1.    Use the product and quotient rule for radicals.
3.    Simplify products and quotients of radicals with different indexes.

#### 38 Lesson #18 Simplifying Radical Expressions (Part Two) 20:36

Objectives:

1.    Use the product and quotient rule for radicals.
3.    Simplify products and quotients of radicals with different indexes.

#### 39 Lesson #19 Logarithmic Functions 13:24

Objectives:

1.    Write from logarithmic form to exponential form.
2.    Write from exponential form to logarithmic form.
3.    Evaluate logarithmic expressions.

#### 40 Lesson #19 Logarithmic Functions Homework Key 01:32

Objectives:

1.    Write from logarithmic form to exponential form.
2.    Write from exponential form to logarithmic form.
3.    Evaluate logarithmic expressions.

#### 41 Lesson #20 Sets and Notation for Sets 16:29

Objectives:

1.    List elements of sets.
2.    Graph inequalities.
3.    Write inequalities in interval notation.
4.    Express intervals as inequalities.
5.    Write sets using the roster method.

#### 42 Lesson #20 Sets and Notation for Sets Homework Key 02:38

Objectives:

1.    List elements of sets.
2.    Graph inequalities.
3.    Write inequalities in interval notation.
4.    Express intervals as inequalities.
5.    Write sets using the roster method.

#### 43 Lesson #21 Solutions of Equations and Properties of Equality 11:44

Objectives:

1.    Determine if a given number is a solution or is not a solution of a given equation.
2.    Write a given sentence as an equation or inequality.
3.    Solve equations.

#### 44 Lesson #21 Solutions of Equations and Properties of Equality Homework Key 03:33

Objectives:

1.    Determine if a given number is a solution or is not a solution of a given equation.
2.    Write a given sentence as an equation or inequality.
3.    Solve equations.

#### 45 Lesson #22 Solving Linear Equations 35:36

Objectives:

1.    Solve equations.
2.    Solve application problems.

#### 46 Lesson #22 Solving Linear Equations Homework Key 03:33

Objectives:

1.    Solve equations.
2.    Solve application problems.

#### 47 Lesson #23 Solving Absolute Value Equations 15:28

Objectives:

1.    Solve absolute value equations.
2.    Write solutions in solution sets.

#### 48 Lesson #23 Solving Absolute Value Equations Homework Key 03:57

Objectives:

1.    Solve absolute value equations.
2.    Write solutions in solution sets.

#### 49 Lesson #24 Solving Equations (Zero-Factor Property) 38:16

Objectives:

1.    Learn and use the zero-factor property.
2.    Solve applied problems that require the zero-factor property.

#### 50 Lesson #24 Solving Equations (Zero-Factor Property) Homework Key 05:08

Objectives:

1.    Learn and use the zero-factor property.
2.    Solve applied problems that require the zero-factor property.

#### 51 Lesson #25 Solving Rational Equations (Part One) 30:49

Objectives:

1.    Determine the domain of the variable in a rational equation.
2.    Solve rational equations.

#### 52 Lesson #25 Solving Rational Equations (Part Two) 22:47

Objectives:

1.    Determine the domain of the variable in a rational equation.
2.    Solve rational equations.

#### 53 Lesson #25 Solving Rational Equations Homework Key 03:32

Objectives:

1.    Determine the domain of the variable in a rational equation.
2.    Solve rational equations.

#### 54 Lesson #26 Solving Equations with Radical Terms 28:29

Objectives:

1.    Solve radical equations by using the power rule.
3.    Solve radical equations with indexes greater than 2.

#### 55 Lesson #26 Solving Equations with Radical Terms Homework Key 05:43

Objectives:

1.    Solve radical equations by using the power rule.
3.    Solve radical equations with indexes greater than 2.

#### 56 Lesson #27 Solving Equations (Square Root Property) 20:06

Objectives:

1.    Learn the square root property.
2.    Solve quadratic equations by extending the square root property.
3.    Solve quadratic equations by completing the square.

#### 57 Lesson #27 Solving Equations (Square Root Property) Homework Key 04:20

Objectives:

1.    Learn the square root property.
2.    Solve quadratic equations by extending the square root property.
3.    Solve quadratic equations by completing the square.

#### 58 Lesson #28 The Quadratic Formula 27:30

Objective:

#### 59 Lesson #28 The Quadratic Formula Homework Key 03:56

Objective:

#### 60 Lesson #29 Solving Linear Inequalities 27:50

Objectives:

1.    Solve linear inequalities by using the addition property.
2.    Solve linear inequalities by using the multiplication property.
3.    Solve applied problems by using linear inequalities.

#### 61 Lesson #29 Solving Linear Inequalities Homework Key 03:59

Objectives:

1.    Solve linear inequalities by using the addition property.
2.    Solve linear inequalities by using the multiplication property.
3.    Solve applied problems by using linear inequalities.

#### 62 Lesson #30 Solving Inequalities (Absolute Value) 24:57

Objectives:

1.    Use the definition of absolute value.
2.    Solve inequalities. graph the solution set, and write in interval notation.

#### 63 Lesson #30 Solving Inequalities (Absolute Value) Homework Key 03:10

Objectives:

1.    Use the definition of absolute value.
2.    Solve inequalities. graph the solution set, and write in interval notation.

#### 64 Lesson #31 Functions 31:44

Objectives:

1.    Distinguish between independent and dependent variables.
2.    Define and identify relations and functions.
3.    Find the domain and range.
4.    Identify functions defined by graphs and equations.

#### 65 Lesson #31 Functions Homework Key 08:19

Objectives:

1.    Distinguish between independent and dependent variables.
2.    Define and identify relations and functions.
3.    Find the domain and range.
4.    Identify functions defined by graphs and equations.

#### 66 Lesson #32 Two-Variable Equations and Graphs 20:05

Objectives:

1.    Find the x- and y-coordinates of labeled points. State in which quadrant or on which axis the point lies.
2.    Complete tables of ordered pairs for linear equations.

#### 67 Lesson #32 Two-Variable Equations and Graphs Homework Key 03:48

Objectives:

1.    Find the x- and y-coordinates of labeled points. State in which quadrant or on which axis the point lies.
2.    Complete tables of ordered pairs for linear equations.

#### 68 Lesson #33 Linear Equations and Their Graphs 29:51

Objectives:

1.    Graph linear equations.
2.    Graph linear equations by finding and plotting its intercepts.
3.    Write the coordinates of x- and y-intercepts.

#### 69 Lesson #33 Linear Equations and Their Graphs Homework Key 04:21

Objectives:

1.    Graph linear equations.
2.    Graph linear equations by finding and plotting its intercepts.
3.    Write the coordinates of x- and y-intercepts.

#### 70 Lesson #34 Slope of a Line 27:32

Objectives:

1.    Graph a line, given its slope and a point on the line.
2.    Use slopes to determine whether two lines are parallel, perpendicular, or neither.
3.    Solve problems involving average rate of change.

#### 71 Lesson #34 Slope of a Line Homework Key 03:13

Objectives:

1.    Graph a line, given its slope and a point on the line.
2.    Use slopes to determine whether two lines are parallel, perpendicular, or neither.
3.    Solve problems involving average rate of change.

#### 72 Lesson #35 Determining the Equation for a Line 35:32

Objectives:

1.    Use the slope-intercept form to graph the equations.
2.    Find an equation of the line passing through the pair of points.
3.    Solve problems involving average rate of change.

#### 73 Lesson #35 Determining the Equation for a Line Homework Key 02:29

Objectives:

1.    Use the slope-intercept form to graph the equations.
2.    Find an equation of the line passing through the pair of points.
3.    Solve problems involving average rate of change.

#### 74 Lesson #36 Graphs and Basic Transformations 23:48

Objective:

1.     Recognize the graphs of elementary functions and graph their translations.
2.     Determine a graph's domain and range.

#### 75 Lesson #36 Graphs and Basic Transformations Homework Key 03:53

Objective:

1.     Recognize the graphs of elementary functions and graph their translations.
2.     Determine a graph's domain and range.

#### 76 Lesson #37 Solving Systems of Equations 44:37

Objective:

1.     Solve linear systems by graphing, substitution, and elimination.

#### 77 Lesson #37 Solving Systems of Equations Homework Key 04:56

Objective:

1.     Solve linear systems by graphing, substitution, and elimination.

TOPICS COVERED:

This course is an intermediate course in algebra that begins with a review of introductory algebra concepts. The course is comprised of three units: Manipulating and Simplifying Expressions, Solving Equations and Inequalities, and Graphing Equations and Inequalities. Each unit will consider real-world applications of the associated concepts and procedures and will incorporate the following expression types: linear, quadratic, general polynomial, rational, roots and radicals, exponential, and logarithmic.

IDEA COURSE OBJECTIVES:

This course will involve the following objectives:

- Objective 1: Gaining factual knowledge (terminology, classifications, methods, trends).
- Objective 2: Learning fundamental principles, generalizations, and/or theories

COURSE INCLUDES:

• 37 Video-Lessons
• 36 Practice Worksheets
• 18 hr 37 min 26 sec of video-lessons
• Guided powerpoint for each lesson
• 36 Practice worksheet review videos
• 22 Quizzes (Quick concept/vocabulary checks)
• 10 Comprehension Tests
• Answer keys to all practice worksheets and tests (Additional Resources for Parents)
• Completed copies of all of the notes (Additional Resources for Parents)

COURSE TOPICS:

• Factors
• Fractions
• Real Numbers
• Exponents
• Order of Operations
• Simplifying and Evaluating Algebraic Expressions
• Polynomials
• Multiplying Polynomials
• Dividing Polynomials
• Factors and the Greatest Common Factor
• Factoring by Grouping
• Factoring Trinomials
• Special Factoring Formulas
• Rational Expressions
• Multiplying and Dividing Rational Expressions
• Adding and Subtracting Rational Expressions
• Logarithmic Functions
• Sets and Notation for Sets
• Solutions of Equations and Properties of Equality
• Solving Linear Equations
• Solving Absolute Value Equations
• Solving Equations Using the Zero-Factor Property
• Solving Rational Equations
• Solving Equations with Radical Terms
• Extracting Square Roots to Solve an Equation
• Solving Linear Inequalities
• Solving Inequalities that Contain an Absolute Value Term
• Functions
• Two-Variable Equations and Graphs
• Linear Equations and their Graphs
• Slope of a Line
• Determining the Equation for a Line
• Graphs of Common Functions and Basic Transformations
• Solving Systems of Equations

• Teacher: Amy
• Areas of expertise: Mathematics
• Education: Bachelor of Science in Math Education, Masters in Educational Leadership and Policy
• Interests: Running, hiking, reading, swimming, playing at the park with my kids, crocheting
• Skills: I have earned many teaching awards: Jordan School District Teacher of the Year, Canyons School District Teacher of the Year, and Utah State University's Teaching Adjunct of the Year (Twice)
• Associations: NCTM, UCTM
• Issues I care about: I am passionate about making math accessible to all types of learners. You can do this!

I am an outstanding teacher-leader who has served in numerous leadership capacities. I taught at the middle school level for eight consecutive years, then at the university level for four consecutive years, and I currently work at a local high school helping at-risk students.

#### Lesson #1 Factors Homework Key

Practice Worksheet Key

Filled-in notes

#### Lesson #1 Factors Powerpoint

Blank powerpoint, but the key to the homework is included at the end.

#### Lesson #2 Fractions

Adding, Subtracting, Multiplying, Dividing, and Writing Equivalent Fractions

#### Lesson #3 Real Numbers

Sets of Numbers, Absolute Value

#### Lesson #4 Exponents

Objectives:

1.    Understand and be able to utilize the rules for multiplying and dividing exponential expressions.
2.    Understand and be able to utilize the rule for simplifying the power of an exponential expression.
3.    Understand and be able to utilize the rule for simplifying the powers of products and quotients.
4.    Be able to interpret and simplify an exponential with a zero as an exponent.
5.    Be able to interpret and simplify an exponential with a negative number exponent.

#### Lesson #5 Order of Operations

Objective:

1. Be able to use the order of operations to evaluate and simplify an expression.

#### Lesson #6: Simplifying Algebraic Expressions and Evaluating Algebraic Expressions

Objectives:

1.    Be able to simplify variable expressions using the algebraic properties of addition and multiplication.
2.    Be able to simplify variable expressions using the distributive property.

#### Lesson #7 Polynomials

Objectives:

1.    Define polynomial.

#### Lesson #8 Multiplying Polynomials

Objectives:

1.    Multiply terms, any two polynomials, binomials, and polynomial functions.
2.    Find the product of the sum and difference of two terms.
3.    Find the square of a binomial.

#### Lesson #9 Dividing Polynomials

Objectives:

1.    Divide a polynomial by a monomial.
2.    Divide a polynomial by a polynomial of two or more terms.

Factors, GCF

#### Lesson #11 Factoring by Grouping

GCF, Factoring by Grouping

FOIL, Factoring

#### Lesson #13 Special Factoring Formulas

Factoring, Difference of Squares, Perfect Square Trinomials

#### Lesson #14 Rational Expressions

Domain, Simplifying Rational Expressions

#### Lesson #15 Multiplying and Dividing Rational Expressions

Domain, Multiplying and Dividing Rational Expressions

#### Lesson #16 Adding & Subtracting Rational Expressions

Rational Expressions, LCD, Add, & Subtract

Radical Expressions, Roots, Principal Roots, Negative Roots

#### Lesson #18 Simplifying Radical Expressions

Simplify radicals, product rule, quotient rule

#### Lesson #19 Logarithmic Functions

Logarithmic Form, Exponential Form, Solving Logarithms

#### Lesson #20 Sets and Notation for Sets

Sets, Inequalities, Interval Notation, Graphing Intervals, Roster Method

#### Lesson #21 Solutions of Equations and Properties of Equality

Solve equations, determine solutions and non-solutions, write sentences as equations or inequalities

#### Lesson #22 Solving Linear Equations

Solve equations and application problems

#### Lesson #23 Solving Absolute Value Equations

Equations containing absolute values, solution sets

#### Lesson #24 Solving Equations Using the Zero-Factor Property

Zero-Factor Property, Zero-Product Property

#### Lesson #25 Solving Rational Equations

Domain, rational equations

#### Lesson #26 Solving Equations with Radical Terms

Radical Equations, Power Rule, Indexes Greater than 2

#### Lesson #27 Extracting Square Roots to Solve an Equation

Square Root Property

#### Lesson #29 Solving Linear Inequalities

Linear Inequalities

#### Lesson #30 Solving Inequalities that Contain an Absolute Value Term

Absolute Value Inequalities

#### Lesson #31 Functions

Relations, Functions, Domain, Range, Graphs

#### Lesson #33 Linear Equations and Their Graphs

Graph Linear Equations, Intercepts

#### Lesson #34 Slope of a Line

Graph Lines, Parallel and Perpendicular Slopes, Average Rate of Change

#### Lesson #35 Determining the Equation for a Line

Slope-Intercept Form, Point-Slope Form, Parallel and Perpendicular

#### Lesson #36 Graphs of Common Functions and Basic Transformations

Absolute Value Function, Parabolic Function, Square Root Function, Domain and Range

#### Lesson #37 Solving Systems of Equations

Graphing, Substitution, Elimination