# Math for 10th Grade

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Teacher: Ebru
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#### 0 Introduction 01:58

A short introduction to the course.

#### 1 Lesson 1 - Arithmetic Operations on Complex Numbers 15:31

In this lesson, we go over addition, subtraction, multiplication and division of rational numbers, especially with numbers written in fraction form. We also consider converting decimals to fractions and order of operation.

#### 2 Lesson 1 - Worksheet Review 07:35

Lesson 1 - Worksheet Review

#### 3 Lesson 2 - Rational & Irrational Numbers and Rationalizing the Denominator 12:57

In this lesson, we discuss and classify numbers as rational and irrational. In the second half of the lesson, we go over rationalizing the denominator of a fraction.

#### 4 Lesson 2 - Worksheet Review 09:48

Lesson 2 - Worksheet Review

#### 5 Lesson 3 - Complex Numbers 15:23

This lesson introduces imaginary and complex numbers. We work on identifying the real and imaginary parts of a complex number and the conjugate of a complex number. We also plot complex numbers in the complex plane and finish the lesson with an example where we calculate the square roots of a complex number.

#### 6 Lesson 3 - Worksheet Review 09:54

Lesson 3 - Worksheet Review

#### 7 Lesson 4 - The Arithmetic of Complex Numbers 13:52

In this lesson, we add, subtract, multiply and divide complex numbers. We also look at powers of i and solve an equation with complex coefficients.

#### 8 Lesson 4 - Worksheet Review 11:19

Lesson 4 - Worksheet Review

#### 9 Lesson 5 - Complex Numbers in the Complex Plane 10:46

In this lesson, we represent complex numbers and their operations in the complex plane. We apply polar form to complex numbers and see how polar form is useful in multiplication and division and how rectangular form is useful in addition and subtraction.

#### 10 Lesson 5 - Worksheet Review 05:11

Lesson 5 - Worksheet Review

#### 11 Lesson 6 - Operations on Vectors 15:56

In this lesson, we cover the basics of vectors in Cartesian coordinates. We discuss operations with vectors and unit vectors.

#### 12 Lesson 6 - Worksheet Review 07:02

Lesson 6 - Worksheet Review

#### 13 Lesson 7 - Vectors in Real Life Applications 11:27

In this lesson, we work with vector quantities in solving real life problems.

#### 14 Lesson 7 - Worksheet Review 03:39

Lesson 7 - Worksheet Review

#### 15 Lesson 8 - Matrix Operations 13:53

In this lesson, we look at operations on matrices and certain features of matrices. We cover matrix addition and subtraction, multiplication by a scalar and matrix multiplication. We also look at identity matrices, the dimensions of a matrix, square matrices and the transpose of a matrix. At the end of the video, we illustrate properties of matrix multiplication.

#### 16 Lesson 8 - Worksheet Review 05:59

Lesson 8 - Worksheet Review

#### 17 Lesson 9 - Representations of Data With Matrices and Inverse Matrices 17:01

In this lesson, we see examples of data with matrices, such as incidence matrices, payoff matrices and augmented matrices. We then look at inverse matrices and learn how we can find the inverse of a 2x2 matrix by hand. Lastly, we use the inverse of a matrix to solve a matrix equation.

#### 18 Lesson 9 - Worksheet Review 08:27

Lesson 9 - Worksheet Review

#### 19 Lesson 10 - Transformations with Matrices 11:41

In this lesson, we look at multiplication of vectors with matrices and then we consider performing transformations on vectors using matrix multiplication.

#### 20 Lesson 10 - Worksheet Review 09:01

Lesson 10 - Worksheet Review

#### 20 Midterm Exam 1 00:00

This exam covers material from lessons 1 through 10. The duration is 60 minutes. Good luck!

#### 21 Lesson 11 - Common Factors and Factoring Trinomials 10:20

In this lesson, we work with factoring the greatest common factor out of expressions and factoring trinomials, with a leading coefficient equal to 1 and not equal to 1.

#### 22 Lesson 11 - Worksheet Review 04:55

Lesson 11 - Worksheet Review

#### 23 Lesson 12 - Dividing Polynomials by Binomials 14:00

In this lesson, we learn and practice the division algorithm on polynomials.

#### 24 Lesson 12 - Worksheet Review 06:54

Lesson 12 - Worksheet Review

#### 25 Lesson 13 - Remainder Theorem, Factor Theorem, Zeros of Polynomials and Graphs 18:05

In this lesson, we go over the remainder theorems, the factor theorem, define zeros pf polynomials and sketch some polynomials based on their zeros and shape.

#### 26 Lesson 13 - Worksheet Review 05:26

Lesson 13 - Worksheet Review

#### 27 Lesson 14 - Quadratic Equations with Real Coefficients 12:38

In this lesson, we solve quadratic equations using completing the square and the quadratic formula. We also use the discriminant to distinguish between the number and types of roots.

#### 28 Lesson 14 - Worksheet Review 07:09

Lesson 14 - Worksheet Review

#### 29 Lesson 15 - Polynomial Identities 10:25

In this lesson, we look at polynomial identities and we use polynomial identities in solving polynomial equations.

#### 30 Lesson 15 - Worksheet Review 10:25

Lesson 15 - Worksheet Review

#### 31 Lesson 16 - The Fundamental Theorem of Algebra 10:32

In this lesson, we apply the fundamental theorem of algebra to polynomial equations and graphs. We also consider multiplicity of roots in detail.

#### 32 Lesson 16 - Worksheet Review 08:34

Lesson 16 - Worksheet Review

#### 33 Lesson 17 - The Binomial Theorem 13:36

In this lesson, we work with the binomial theorem to expand polynomials.

#### 34 Lesson 17 - Worksheet Review 06:27

Lesson 17 - Worksheet Review

#### 35 Lesson 18 - Creating Equations 10:47

In this lesson, we create one-variable equations (including absolute value) and systems of linear equations in two variables from contexts. We also look at solving literal equations.

#### 36 Lesson 18 - Worksheet Review 06:01

Lesson 18 - Worksheet Review

#### 37 Lesson 19 - The Parabola 11:38

In this lesson, we look at graphing parabolas. We find the vertex and intercepts of a parabola and whether the parabola opens up or down.

#### 38 Lesson 19 - Worksheet Review 09:37

Lesson 19 - Worksheet Review

#### 39 Lesson 20 - Systems of Equations 10:32

In this lesson, we graph systems of equations in two variables. We solve these systems and interpret the solutions geometrically.

#### 40 Lesson 20 - Worksheet Review 12:38

Lesson 20 - Worksheet Review

#### 41 Lesson 21 - Systems of Inequalities 11:42

In this lesson, we create systems of inequalities from contexts and we solve these systems by graphing in the coordinate plane. Finally, we interpret the solutions in their context.

#### 42 Lesson 21 - Worksheet Review 10:30

Lesson 21 - Worksheet Review

#### 42 Midterm Exam 2 00:00

This midterm exam covers the material in lessons 11 through 21. The duration is 60 minutes. Good luck!

#### 43 Lesson 22 - Units in Contexts and Scales of Graphs 11:05

In this lesson, we consider the best unit to use in different problem solving contexts. We also look at scaling in graphical displays and the significance of slope and y-intercept in a context involving a linear equation.

#### 44 Lesson 22 - Worksheet Review 04:48

Lesson 22 - Worksheet Review

#### 45 Lesson 23 - Quadrilaterals 13:42

In this lesson, we define special quadrilaterals and look at their properties. We prove some of these properties and also use the properties to solve problems.

#### 46 Lesson 23 - Worksheet Review 09:48

Lesson 23 - Worksheet Review

#### 47 Lesson 24 - The Pythagorean Theorem and Its Converse 10:36

In this lesson, we look at the Pythagorean Theorem and its converse. We also consider the situations where the side lengths given belong to an acute triangle, a right triangle or an obtuse triangle.

#### 48 Lesson 24 - Worksheet Review 07:31

Lesson 24 - Worksheet Review

#### 49 Lesson 25 - Theorems About Circles 10:02

In this lesson, we will be working with theorems that apply to angles and segments in circles.

#### 50 Lesson 25 - Worksheet Review 09:16

Lesson 25 - Worksheet Review

#### 51 Lesson 26 - Arc Length and Areas of Sectors 10:46

In this lesson, we calculate arc length, areas of sectors and central angles using the fact that a sector encompasses a fraction of a circle.

#### 52 Lesson 26 - Worksheet Review 04:28

Lesson 26 - Worksheet Review

#### 53 Lesson 27 - Right Triangle Trigonometry and Applications 10:01

In this lesson, we look at the six trigonometric ratios in a right triangle. We solve for missing angles and sides in a triangle and we also apply these ratios to problems involving angles of elevation and depression.

#### 54 Lesson 27 - Worksheet Review 13:29

Lesson 27 - Worksheet Review

#### 55 Lesson 28 - SI and US Standard Units 12:18

In this lesson, we learn about metric and US Standard units of mass, length and volume. We also perform conversions between these units.

#### 56 Lesson 28 - Worksheet Review 04:31

Lesson 28 - Worksheet Review

#### 57 Lesson 29 - Surface Areas of Solids 14:06

In this lesson, we learn to calculate surface areas of solids, such as cubes, prisms, cylinders, pyramids, cones and spheres.

#### 58 Lesson 29 - Worksheet Review 05:40

Lesson 29 - Worksheet Review

#### 59 Lesson 30 - Volumes of Solids 10:13

In this lesson, we learn to calculate volumes of solids, such as cubes, prisms, cylinders, pyramids, cones and spheres.

#### 60 Lesson 30 - Worksheet Review 05:36

Lesson 30 - Worksheet Review

#### 61 Final Exam 00:00

This final exam covers all the material in this course. The duration is 120 minutes. Good luck!

Course Description

This course builds on the math skills you have developed in grade 9 to provide an integrated comprehension-based and problem-solving centered approach.

The course includes:

The course comprises 6 units and 30 lessons

Over 10 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

2 midterm exams (on paper)

1 final exam (on paper)

COURSE GOALS

Upon course completion, you will learn how to:

• work with rational, irrational and complex numbers
• sketch complex numbers in the complex plane
• perform operations on vectors
• examine real-life applications of vectors
• perform operations on matrices
• represent data with matrices
• perform transformations with matrices
• factor polynomials
• divide polynomials by binomials
• use the remainder theorem, the factor theorem, find zeros of polynomials
• use the quadratic formula
• apply the Fundamental Theorem of Algebra
• apply the Binomial Theorem
• create equations
• sketch the graph of a parabola
• solve systems of equations and inequalities
• interpret units in contexts and determine scales on graphs
• examine and apply properties of special quadrilaterals
• apply the Pythagorean Theorem and its converse
• apply theorems about circles
• find arc lengths and areas of sectors
• apply right triangle trigonometry
• convert between SI ans US Standard units
• find surface area and volume of solids

TARGET AUDIENCE

This video-course is primarily intended for 10th 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 9th grade or an equivalent Math course prior to enrolling in this course.

UNIT 1 RATIONAL, IRRATIONAL AND COMPLEX NUMBERS

Arithmetic Operations on Complex Numbers

Rational & Irrational Numbers and Rationalizing the Denominator

Complex Numbers

The Arithmetic of Complex Numbers

Complex Numbers in the Complex Plane

UNIT 2 VECTORS

Operations on Vectors

Vectors in Real Life Applications

UNIT 3 MATRICES

Matrix Operations

Representations of Data With Matrices and Inverse Matrices

Transformations with Matrices

UNIT 4 FACTORING AND POLYNOMIALS

Common Factors and Factoring Trinomials

Dividing Polynomials by Binomials

Remainder Theorem, Factor Theorem, Zeros of Polynomials and Graphs

Quadratic Equations with Real Coefficients

Polynomial Identities

The Fundamental Theorem of Algebra

The Binomial Theorem

UNIT 5 EQUATIONS AND INEQUALITIES

Creating Equations

The Parabola

Systems of Equations

Systems of Inequalities

UNIT 6 MEASUREMENT, GEOMETRY AND TRIGONOMETRY

Units in Contexts and Scales of Graphs

The Pythagorean Theorem and Its Converse

Arc Length and Areas of Sectors

Right Triangle Trigonometry and Applications

SI and US Standard Units

Surface Areas of Solids

Volumes of Solids

• 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.

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#### Midterm 1 Solutions

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#### Midterm 2 Solutions

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#### Final Exam Solutions

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