Course Description
Math for 9th – 11th Grade weaves together previous study of Algebra concepts into a preparatory course for Algebra 2, Trigonometry, and Precalculus. The course progresses from foundational concepts like understanding the real number system and conversion of units of measure to linear equations and inequalities before moving into a study of polynomials with an emphasis on quadratic equations. It then extends into the complex number system and explores topics like vectors, matrices, and right triangle properties and trigonometry. The course topics address both abstract mathematical concepts as well as real-world problem situations, uniquely blending both algebraic and geometric concepts and approaches. There is consistent emphasis on explaining mathematical terminology, knowing that this is key for overcoming common stumbling blocks and reaching deeper understanding and therefore confidence. The course focuses on the mastery of critical and foundational skills and exposure to new skills necessary for success in subsequent math courses.
Course Includes
- 16+ hours of engaging instructional video
- 6 Units
- 50 video lessons
- 47 practice worksheets with printable answer keys
- 47 worksheet review videos where I go over each of the exercises
- 47 online “Knowledge Check” quizzes
- 15 “Challenge Problems” as extensions to each unit’s knowledge
- Solutions sets to each of the 47 “Knowledge Check Quizzes”
- Solutions sets to each of the 15 challenge problems
- Guided solutions showing step by step work to each of the 15 challenge problems
- Final Exam for Units 1-3
- Final Exam for Units 4-6
- Solutions sets for both final exams
- Introduction to Desmos video showing helpful hints for first time users
Course Goals
Upon completion of this course, students will be prepared to move on to math courses which demands strong algebra skills such as: Trigonometry, analytic Geometry, Precalculus, Linear Algebra, and eventually courses like Calculus and Statistics.
Course Requirements
Student taking this course are expected to have basic algebra skills such simplify expressions using order of operations, plotting points and graphing lines in slope-intercept form (y = mx + b) .
Target Audience
This video course is primarily intended for students who have already mastered Algebra 1 concepts and is designed so that it can be taken before or after both Geometry and Algebra 2. This course will also help students in building their mathematical and analytical skills which will prepare them for taking other courses in mathematics and the sciences.
Technology
Students will need a calculator capable of performing the basic operations, as well as square roots and trigonometric functions.
The majority of the lessons are taught so that technology is not needed. However there are some where the use of a calculator or computer is required. If the student has a scientific calculator (performs basic operations as well as square roots and trigonometric functions) or graphing calculator such as a TI-83 or 84 that will be sufficient, or a student can use the free online resources www.wolframalpha.com and www.desmos.com.
Under the Additional Resources for Parents are tutorial videos that show how to use either online resources or a calculator to perform the work needed.
Course Topics
Unit 1- Foundational Skills
Understand the Real Number System
Perform Arithmetic Operations on Rational Numbers
Rationalize the denominator
Understand the key components of graphing
Scaling graphs of data
Understand different measurement systems
Convert between units and systems of measure (Dimensional Analysis)
Solve application problems using measurement conversions
Area of 3D objects
Volume of 3D objects
Pythagorean Theorem
Unit 2- Linear Equations and Inequalities
Translate statements into mathematical expressions/equations/inequalities
Solve equations and inequalities with one variable
Substitution method to solve systems of linear equations
Elimination method to solve systems of linear equations
Graphing to solve systems of linear equations by graphing
Graphing systems of linear inequalities
Applications of systems
Unit 3- Polynomials
Factor polynomials using the GCF
Factor quadratic trinomials
Factor using the difference of two squares
Factor perfect square trinomials
Solve quadratic equations by square root method
Solve quadratic equations by factoring
Understand and apply the Zero Product Property
Solve quadratic equations by graphing, finding intersections
Solve quadratic equations by the quadratic formula
Long division of polynomials
Polynomial Remainder Theorem
Write polynomial equations from roots
Find real and non-real roots of polynomial equations
Key characteristics of polynomial equations
Graphing polynomial equations
Fundamental Theorem of Algebra
Unit 4- Complex Numbers
Understand the complex number system
Powers of i
Understanding the complex plane
Conjugates of complex numbers
Adding/Subtracting complex numbers
Multiplying/Dividing complex numbers
Absolute Value of complex numbers
Graphing complex numbers
Unit 5- Vectors and Matrices
Understanding vectors v. scalars
Vector notation
Graphing vectors
Unit Vectors
Scalar multiplication on vectors
Addition/subtraction of vectors
Magnitude of vectors
Matrix notation and dimensions
Scalar multiplication on matrices
Addition/subtraction of matrices
Matrix multiplication
Zero Matrix
Identity Matrix
Determinant of a matrix
Inverse Matrices
Unit 6- Right Triangles
Converse of the Pythagorean Theorem
Classifying triangles by sides and angles
Right Triangle Trigonometry
Solving for Unknown Sides using trigonometry
Solving for unknown angles using trigonometry
Trigonometry applications
