Pre-Calculus
Course Summary
Ensure preparedness for calculus by mastering advanced mathematical concepts such as logarithms, trigonometry, and parabolas. Students gain an understanding of a range of pre-calculus topics including radicals, fractional exponents, polynomials, rational functions, and more. In this course, maximize your understanding and retention of key math concepts through lessons and effective skill assessments.
Course Prerequisite(s):
Algebra 2 or Integrated Math 3
Curriculum
This is a 2-semester course. We do not recommend taking both semesters simultaneously.
Unit 1: Algebraic Functions
- Linear Equations and Their Graphs
- Functions Operations
- Inverse Functions
- Graphing Quadratic Functions
- Polynomial Division and Complex Roots
- Graphs of Polynomial Functions
- Graphing Rational Expressions
- Solving Radical Equations
- Sketching Graphs Using Function Transformations
Unit 2: Exponential and Logarithmic Functions
- Exponential Functions and Their Graphs
- Logarithmic Functions and Their Graphs
- Properties of Logarithms
- Change of Base
- Rewriting Logarithmic Expressions
- Solving Exponential Equations
- Solving Logarithmic Equations
- Exponential Growth and Decay Models
- Logarithmic Models
Unit 3: Systems of Equations
- The Substitution Method
- Nonlinear Systems of Equations
- Solving Systems of Equations Graphically
- The Elimination Method
- Modeling and Optimization with Two-Variable Linear Systems
- Modeling with Non-Linear Systems
- Absolute Value Graphs, Equations, and Inequalities
Unit 4: Topics of Analytic Geometry
- Introduction to Conics: Parabolas
- Finding the Standard Equation of a Parabola
- Applications of Parabolas
- Finding the Standard Equation of an Ellipse
- Graphing an Ellipse
- Applications of Ellipses
- Finding the Standard Equation of a Hyperbola
- Using Asymptotes to Sketch a Hyperbola
- Using Asymptotes to Find the Standard Equation
Unit 5: Trigonometry
- Trigonometric Ratios and Special Right Triangles
- Applications Involving Right Triangles
- Radian Measures
- Arc Length and the Area of a Circle
- The Unit Circle
- Evaluate Trigonometric Functions Using the Unit Circle
- Evaluate Trigonometric Functions Given a Point
- Find Reference Angles
- Use Reference Angles to Evaluate Trigonometric Functions
Unit 6: Graphs and Inverses of Trigonometric Functions
- Sine and Cosine Curves
- Amplitude and Period
- Translations of Sine and Cosine Curves
- Graph of the Tangent Function
- Graph of the Cotangent Function
- Graph of Secant
- Graph of the Cosecant Function
- Inverse Sine and Cosine Functions
- Inverse Tangent Function
Unit 7: Analytic Trigonometry
- Basic Trigonometric Identities
- Simplifying Trigonometric Expressions
- Factoring Trigonometric Expressions
- Combining Rational Trigonometric Expressions
- Finding Trigonometric Values
- Verifying Trigonometric Identities
- Using Standard Algebraic Techniques to Solve Trigonometric Identities
- Solving Quadratic Trigonometric Equations
- Solving Trigonometric Equations Involving Multiple Angles
- Using Sum and Difference Formulas to Evaluate Trigonometric Functions
- Using Sum and Difference Formulas to verify Identities and Solve Trigonometric Equations
Unit 8: Additional Topics in Trigonometry
- Using the Law of Sines and Law of Cosines to Solve an Oblique Triangle
- Applications of the Law of Sines and Law of Cosines
- Finding the Area of an Oblique Triangle
Unit 9: Additional Topics for Advanced Mathematics
- Vectors and Vector Operations
- Unit Vectors and Directional Analysis
- Application of Vectors
- Parametric Equations
- Limits of Functions
- The Complex Number System