Course Description
This course is a gateway to Precalculus and it provides you with all the knowledge and skills you need in Precalculus.
The course includes:
The course comprises 10 units and 39 lessons
Over 15 hours of video-lessons!
Each lesson includes a video lecture, a worksheet, a worksheet review video and an online quiz.
39 video lectures
39 worksheets
39 worksheet review videos with every question solved step-by step by the instructor
39 online quizzes
2 midterms (on paper)
1 final exam (on paper)
COURSE GOALS
Upon course completion, you will learn how to:
- solve quadratic equations, including complex solutions
- solve radical equations
- work with exponents and radicals
- solve systems of inequalities in two variables and linear systems in three variables
- perform operations on polynomials and rational expressions
- define and graph a parabola
- define logarithms and apply properties of logarithms
- solve logarithmic and exponential equations
- choose between models and model with a logarithmic or a trigonometric function
- apply the concept of a function and function notation
- perform operations on functions, including function composition and transformations
- find the inverse of a function and decide if a function is odd, even or neither
- find the average rate of change of a function over a given interval
- work with linear, quadratic, trigonometric, exponential and logarithmic functions
- calculate probabilities and conditional probabilities from probability rules and Venn or tree diagrams
- examine the center, spread and shape of distributions
- work with the normal distribution and the standard normal distribution
- consider types of statistical studies, estimation of a population characteristic and sampling variability in the distribution of sample means
- work with proportional reasoning
- apply theorems about angles in triangles and circles
- use the unit circle in finding trigonometric values
- prove trigonometric identities and simplify trigonometric expressions
TARGET AUDIENCE
This video-course is primarily intended for 11th grade students who would like to solidify their mathematical skills and knowledge before they take Precalculus.
COURSE REQUIREMENTS
Students taking this course will need to have completed Algebra I, Math for 10th Grade or an equivalent Math course prior to enrolling in this course.
UNIT 1 FACTORING AND SOLVING QUADRATIC EQUATIONS
The Complex Number System
The Zero Product Rule and Factoring
UNIT 2 EXPONENTS AND RADICALS
Radical Equations
Integer and Rational Exponents
Properties of Exponents and Radicals
UNIT 3 SYSTEMS OF EQUATIONS AND INEQUALITIES
Problems with Systems of Inequalities in Two Variables
Linear Systems in Three Variables
UNIT 4 POLYNOMIALS AND RATIONAL EXPRESSIONS
Arithmetic Operations on Polynomials
Successive Differences in Polynomials
Polynomial Identities and Equations
Adding and Subtracting Rational Expressions
Multiplying and Dividing Rational Expressions
UNIT 5 MORE ON SYSTEMS OF EQUATIONS WITH QUADRATIC EQUATIONS
Completing the Square, the Quadratic Formula and Types of Roots of a Quadratic Equation
Defining and Graphing a Parabola
Graphing and Solving Systems of Equations
UNIT 6 EXPONENTS AND LOGARITHMS
Logarithms
Properties of Logarithms
Logarithmic Equations
Exponential Equations
Choosing a Model and Modeling with Exponential Functions
UNIT 7 FUNCTIONS AND TYPES OF FUNCTIONS
Concept of a Function, Function Notation and Building Functions
Creating New Functions from Existing Functions
Even/Odd Functions and Inverse Functions
Rates of Change and Linear Functions
Characteristics of Quadratic Functions and Comparing Properties of Functions
Exponential Functions
Trigonometric Functions
Logarithmic Functions
UNIT 8 PROBABILITY
Probability and Venn Diagrams
Probability Rules, Conditional Probability, Tree Diagrams
UNIT 9 STATISTICS
Center, Spread and Shape of Distributions
The Normal Distribution
Types of Statistical Studies, Estimation of Population Characteristic, Sampling Variability
UNIT 10 GEOMETRY AND CIRCULAR FUNCTIONS
Square Roots and Proportional Reasoning
Properties of Angles in Triangles
Theorems About Circles
The Unit Circle
Modeling Periodic Data with Trigonometric Functions
Proving Trigonometric Identities