Precalculus

What: One academic year of live instruction and grading.

When: Mon/Tues/Fri 3:50-4:50pm (Eastern), class meets 3x per week

Prerequisites: Successful completion of Algebra 1, Algebra 2, and Geometry. Recommended grade of 80% or higher in these courses as this course relies heavily on retained knowledge. Students should plan on putting time into this course.

Includes: Includes 96 hours of live instruction through the school year. Also, includes curriculum, grading, and support through the year.

Scope and Sequence

Unit 1: Review - this unit is not done live. There are pre-recorded videos that students may use if they do not remember these topics. They are critical prerequisite topics but due to limited time are not reviewed live.

• Exponents and Polynomial Operations

• Factoring Polynomials

• Rational Expressions

• Radicals and Rational Exponents

• Complex Numbers

• Linear Equations & Absolute Value Equations

• Quadratic Equations

• Radical Equations

• Rational Equations

• Inequalities

Unit 2: Functions & Their Graphs

• Functions Review including domain, range, notation, and evaluating

• Intercepts: Zeros, Critical Points, Increasing and Decreasing Intervals

• Continuity and End Behavior

• Parent Functions and Transformations

• Graphing Functioons

• Piecewise Functions

• Function Operations and Compositions of Functions

• Inverse Relations and Functions

Unit 3: Polynomial & Rational Functions

• Graphing Power Functions, also with rational exponents

• Graphing Polynomial Functions

• Zeros of Polynomials, Linear Factors and Multiplicity

• Dividing Polynomials

• Remainder and Factor Theorems

• Rational Zero Theorem, Find Rational Zeros

• Irrational Zeros, Decartes’ Rule of Signs

• Complex Zeros, Fundamental Theorem of Algebra

• Using Zeros to Write Polynomial Functions

• Graphing Rational Functions

• Rational Functions with Slant Asymptotes

• Nonlinear Inequalities

Unit 4: Exponential & Logarithmic Functions

• Graphing Exponential Functions and the Natural Base

• Transformations of Exponential Functions

• Exponential Growth and Decay Applications

• Compound Interest and Continuous Compound Interest

• Logarithms

• Graphing Logarithms

• Solving Exponential Equations

• Solving Logarithmic Equations

• Applications

• Nonlinear Regression

Unit 5: Trigonometric Functions

• Standard form of an angle

• Arc length and area of sectors

• circular motion

• Trig values in special right triangles

• Finding side and angle measures

• Trig functions for any angle, the unit circle

• Law of Sines

• Law of Cosines

• Graphing sine, cosine, and tangent functions

• Graphing reciprocal functions

• Inverse trig functions

• Compositions of trig functions

Unit 6: Trigonometric Identities & Equations

• Basic trig identities

• Simplify and rewrite trig expressions

• Sum and Difference of angle identities

• Double-angle and half-angle identities

• Product-sum and power-reducing identities

• Solving trig equations

Unit 7: Systems and Matrices

• Two-variable systems of equations

• Nonlinear systems of equations

• System in 3 variables

• Introduction to matrices

• Multiplying matrices

• Determinants and inverse matrices

• Solving Systems with Cramer’s Rule

• Solving Systems with Inverse Matrices

• Solving Systems with Gaussian Elimination

• Partial Fractions

Unit 8: Sequences & Seriues

• Explicit and Recursive Sequences

• Arithmetic Sequences

• Geometric Sequences

• Series and Sigma Notation: Arithmetic Series

• Geometric Series

• Mathematical Induction

• Binomial Expansion: Pascal’s Triangle and The Binomial Theorem

Unit 9: Introduction to Calculus

• Limit Notation

• One-sided limits

• Finding limits algebraically

• Limits at infinity, limits of sequences

• Tangent lines

• Derivatives

• Applications: average vs instantaneous rate of change and velocity