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In this lesson, we discuss what sets and set operations are. We talk about sets, number of elements, subsets, finite and infinite sets, complement, union, intersection and difference. We also learn to represent sets in a Venn diagram.

Lesson 1 - Worksheet Review

In this lesson, we look at set problems and how we can solve them using Venn diagrams and the inclusion exclusion principle.

Lesson 2 - Worksheet Review

In this lesson, we consider number sets, such as natural numbers, integers, rational, irrational and real numbers. We look at the subset/superset relationships between these sets and decide which number set(s) a given number belongs to.

Lesson 3 - Worksheet Review

In this lesson, we work with properties, such as the closure property, the commutative property, the associative property, the distributive property, the identity element, the zero product property and the equality property.

Lesson 4 - Worksheet Review

In this lesson, we talk about the inverse property of addition and multiplication. We learn to find additive and multiplicative inverses. Then, we calculate numerical expressions with integer and rational exponents.

Lesson 5 - Worksheet Review

In this lesson, we discuss properties of exponents and radicals and apply these properties to the task of simplifying algebraic expressions.

Lesson 6 - Worksheet Review

In this lesson, we work with propositions and their truth values. We look at compound propositions made with negation, conjunction and disjunction. We cover de Morgan's laws and truth tables.

Lesson 7 - Worksheet Review

In this lesson, we look at conditional statements, their inverses, converses and contrapositives. We also define biconditional statements and use truth tables and properties to prove statements and simplify expressions.

Lesson 8 - Worksheet Review

In this lesson, we learn about variables and like terms. We express verbal contexts with expressions and equations and learn to simplify algebraic expressions bu combining like terms.

Lesson 9 - Worksheet Review

In this lesson, we solve multistep linear equations. We also look at finding coefficients given a solution, and situations where there is no solution or where any real number is a solution.

Lesson 10 - Worksheet Review

In this lesson, we solve multistep inequalities and pay special attention to situations where the inequality sign must be reversed in the working of the solution.

Lesson 11 - Worksheet Review

In this lesson, we solve word problems by setting up and solving multistep linear equations.

Lesson 12 - Worksheet Review

In this lesson, we solve word problems by setting up and solving multistep linear inequalities.

Lesson 13 - Worksheet Review

In this lesson, we look at the definition of absolute value and formulate some simple expressions from this definition.

Lesson 14 - Worksheet Review

In this lesson, we work on solving absolute value equations. We also discuss extraneous solutions.

Lesson 15 - Worksheet Review

In this lesson, we look at the different types of absolute value inequalities and we learn how to solve them.

Lesson 16 - Worksheet Review

In this lesson, we work with slope and intercepts to write equations of lines. We also graph lines given their equations.

Lesson 17 - Worksheet Review

In this lesson, we graph and solve systems of linear equations in two variables. We go over the methods of substitution and elimination. We also create a system of linear equations from a word problem.

Lesson 18 - Worksheet Review

In this lesson, we derive systems of linear inequalities from word problems. Then, we graph and solve these systems of linear inequalities in two variables.

Lesson 19 - Worksheet Review

In this lesson, we introduce key terms, such as degree, term, coefficient, related to polynomials. We perform addition, subtraction and multiplication on polynomials.

Lesson 20 - Worksheet Review

In this lesson, we use the division algorithm on polynomials.

Lesson 21 - Worksheet Review

In this lesson, we factor out the common factor and use identities and other strategies to factor trinomials.

Lesson 22 - Worksheet Review

In this lesson, we learn to factor sums and differences of cubes.

Lesson 23 - Worksheet Review

In this lesson, we learn to add and subtract rational expressions.

Lesson 24 - Worksheet Review

In this lesson, we learn to multiply and divide rational expressions.

Lesson 25 - Worksheet Review

In this lesson, we learn about properties of angles in triangles, in polygons and on parallel lines cut by a transversal.

Lesson 26 - Worksheet Review

In this lesson, we work with the triangle inequality and the Pythagorean theorem to find missing side lengths in a triangle.

Lesson 27 - Worksheet Review

In this lesson, we work with the 30-60-90 triangle and the 45-45-90 triangle to find missing side lengths.

Lesson 28 - Worksheet Review

In this lesson, we work with congruence and similarity postulates and theorems to prove statements and find missing parts of triangles.

Lesson 29 - Worksheet Review

In this lesson, we use the area formula to compute the areas of various types of triangles. We also learn Heron's formula.

Lesson 30 - Worksheet Review

**Course Description**

This course builds on the math skills you have developed in middle school to provide an integrated comprehension-based and problem-solving centered approach. This math course covers the entire ninth grade!

**The course includes:**

The course comprises 7 units and 30 lessons

Over 9 hours of video-lessons!

Each lesson includes a video lecture, a worksheet, a worksheet review video and an online quiz.

30 video lectures

30 worksheets

30 worksheet review videos with every question solved step-by step by the instructor

30 online quizzes

30 answer keys for the online quizzes

2 midterm exams (on paper)

1 final exam (on paper)

The solutions to online quizzes, midterm exams and final exam are uploaded under Resources.

**COURSE GOALS**

Upon course completion, you will learn how to:

- work with sets and set operations
- solve set problems
- recognize and work with natural numbers, integers, rational numbers, irrational numbers and real numbers
- apply properties of arithmetic operations
- calculate additive inverses, reciprocals and evaluate exponential expressions
- work with exponents and radicals
- work with propositions, simplify propositions and express truth tables
- find the inverse, converse and contrapositive of a conditional statement and express a biconditional statement
- simplify algebraic expressions by combining like terms
- solve multistep linear equations and inequalities
- solve word problems with multistep linear equations and inequalities
- define absolute value
- solve absolute value equations and inequalities
- calculate slope
- write an equation of a line and sketch its graph
- solve and graph systems of linear equations and inequalities
- add, subtract, multiply and divide polynomials and rational expressions
- factor polynomials
- apply properties about angles in triangles, polygons and on parallel lines
- work with the triangle inequality and the Pythagorean theorem
- find missing lengths of sides in 30-60-90 and 45-45-90 triangles
- prove statements about congruence and similarity
- use congruence and similarity postulates and theorems to find missing parts of a triangle
- find the area of a triangle

**TARGET AUDIENCE **

This video-course is primarily intended for 9th grade students who would like to enhance their mathematical skills and knowledge in the integrated Mathematics curriculum.

**COURSE REQUIREMENTS**

Students taking this course will need to have completed Math for 8th grade or an equivalent Math course prior to enrolling in this course.

UNIT 1 SETS AND NUMBER SETS

Sets and Set Operations

Set Problems

Number Sets

UNIT 2 OPERATIONS AND PROPOSITIONS

Properties of Arithmetic Operations

Opposites, Reciprocals and Exponents

Properties of Exponents and Radicals

Propositions

Conditionals and Biconditionals

UNIT 3 LINEAR EQUATIONS AND INEQUALITIES

Variables, Like Terms, Simplifying Algebraic Expressions

Multistep Linear Equations

Multistep Linear Inequalities

Word Problems with Multistep Linear Equations

Word Problems with Multistep Linear Inequalities

UNIT 4 ABSOLUTE VALUE

Absolute Value

Absolute Value Equations

Absolute Value Inequalities

UNIT 5 GRAPHS OF LINEAR EQUATIONS AND INEQUALITIES

Equations of Lines

Systems of of Linear Equations and Their Graphs

Systems of Linear Inequalities and Their Graphs

UNIT 6 POLYNOMIALS AND RATIONAL EXPRESSIONS

Operations with Polynomials

Long Division of Polynomials

Factoring Polynomials

Sum and Difference of Cubes

Rational Expressions: Addition and Subtraction

Rational Expressions: Multiplication and Division

UNIT 7 GEOMETRY OF TRIANGLES

Angles in Triangles and on Parallel Lines

The Triangle Inequality and The Pythagorean Theorem

Special Right Triangles

Congruent and Similar Triangles

Area of a Triangle

- Teacher: Ebru
- Areas of expertise: Mathematics
- Education: Oberlin College, BA in Mathematics and Anthropology 1993 Texas A&M University MSc in Mathematics 2011
- Interests: Epistemology, Acting
- Skills: Learning Languages
- Associations: National Council of Teachers of Mathematics (NCTM)
- Issues I care about: Sustainability, Social Responsibility, Giving Back to the Community

I am happy to start working with Lernsys students as I reach out to you all beyond the physical boundaries of the classroom.

Lesson 1 online quiz answers

Lesson 2 online quiz answers

Lesson 3 online quiz answers

Lesson 4 online quiz answers

Lesson 5 online quiz answers

Lesson 6 online quiz answers

Lesson 7 online quiz answers

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Lesson 30 online quiz answers

Midterm 1 Solutions

Midterm 2 Solutions

Final Exam Solutions