Course Description

This course is designed to cover topics in Algebra ranging from polynomial, rational, and exponential functions to conic sections. Trigonometry concepts such as Law of Sines and Cosines will be introduced. Students will then begin analytic geometry and calculus concepts such as limits, derivatives, and integrals. This class is important for any student planning to take a college algebra or college pre-calculus class.

Course Format

15 live online sessions - 2 hrs each - 2 additional make-up sessions to accomodate for unforeseen schedule changes.

Dates:
to be announced

Course Layout:

Unit 1: Relations and Functions (1 session)
1. Introduction to families of functions
2. Four ways to represent functions
3. Domain and range
4. Rational expressions and complex fractions
5. Arithmetic operations on functions
6. Composition of functions
7. Inverses of functions
8. Vertical and horizontal line tests

Unit 2: Linear and Quadratic Functions (2 sessions)
1. Linear functions
2. Degree, coefficients, end behavior of linear functions
3. Graphs of linear functions, x- and y- intercepts, slopes
4. Point-slope, slope-intercept, and standard forms of equations
5. Systems of linear equations
6. Modeling with linear functions
8. Absolute value functions and inequalities with absolute value functions
9. Quadratic functions, expression, equation, and the quadratic formula
10. Graphing quadratic functions - 5 key parts of a parabola
11. Intersection of two functions (linear and quadratic; quadratic and quadratic)

Unit 3: Polynomial and Rational Functions (2 sessions)
1. Graphs of polynomial functions
2. Local maxima and minima, and end behavior
3. Remainder and factor theorems
4. Rational zeros theorem
5. Finding zeros of polynomials
6. Rational functions, graphs of rational functions
7. Inequalities and their application

Unit 4: Exponential and Logarithmic Functions (2 sessions)
1. Graphs of exponential and logarithmic functions
2. Inverse of an exponential function and logarithmic function
3. Evaluating logarithmic expressions
4. Change of base formula
5. Expanding and condensing logarithmic expressions
6. Exponential and logarithmic equations
7. Applications of logarithms in problem solving

Review - Unit 1 - 4 (1 session)

Unit 5: Trigonometric Functions of Real Numbers (2 sessions)
1. 17 special angles used to graph the trigonometric functions
2. Terminal point of an arc and its coordinates
3. Graphs of the six trigonometric functions
4. Domain, range, period, amplitude, and phase-shift

Unit 6: Trigonometric Functions of Angles (2 sessions)
1. Right triangle trigonometry and its application
2. 30-60-90 and 45-45-90 triangles
3. Six trigonometric functions
4. Degree measure and radian measure
5. Coterminal, reference, and quadrantal angles
6. “All Students Take Calculus” rule
7. Law of sines and cosines
8. Fundamental trigonometric identities

Unit 7: Analytic Trigonometry (2 sessions)
1. Trigonometric identities
2. The addition and subtraction formulas
3. Inverse sine and cosine functions
4. Analyzing the graphs of the inverse sine and cosine functions

Review - Unit 5 - 7 (1 session)

Course Registration: