In Pre-Calculus Part 1, students develop a deeper understanding of functions and their graphs. The function types covered in depth in this course include polynomial, rational, exponential, logarithmic, and trigonometric. Topics covered in relation to polynomial and rational functions include complex numbers, zeroes of polynomial functions, and synthetic division. Some exponential and logarithmic topics discussed are change of base formulas, properties of logs, growth and decay, and logistic growth models. Pre-Calculus Part 1 concludes with the unit circle, trigonometric functions, and their inverses.
It is recommended that students possess a solid understanding of the concepts covered in Algebra II and Geometry or equivalent course work before enrolling in this course.
Unit 1: Essential Content and Skills
- Sketch the graphs of equations.
- Find and use the slopes of lines to write and graph linear equations in two variables.
- Evaluate functions and find their domains.
- Identify and graph rigid and nonrigid transformations of functions.
- Find arithmetic combinations and compositions of functions.
- Find inverse functions graphically and algebraically.
- Write algebraic models for direct, inverse, and joint variation.
Unit 2: Essential Content and Skills
- Sketch and analyze graphs of polynomial functions.
- Use long division and synthetic division to divide polynomials by other polynomials.
- Perform operations with complex numbers.
- Determine the numbers of rational and real zeros of polynomial functions, and find the zeros.
- Determine the domains of rational functions and find asymptotes of rational functions.
- Sketch the graphs of rational functions.
Unit 3: Essential Content and Skills
- Recognize and evaluate exponential and logarithmic functions.
- Chart exponential and logarithmic functions.
- Use the change-of-base formula to rewrite and evaluate logarithmic expressions.
- Use properties of logarithms to evaluate, rewrite, expand, or condense logarithmic expressions.
- Solve exponential and logarithmic equations.
- Use exponential growth models, exponential decay models, Gaussian models, logistic growth models, and logarithmic models to solve real-life problems.
Unit 4: Essential Content and Skills
- Describe an angle and convert between radian and degree measures.
- Identify a unit circle and its relationship to real numbers.
- Evaluate trigonometric functions at any angle.
- Use the fundamental trigonometric identities.
- Sketch the graphs of trigonometric functions and translations of graphs of the sine and cosine functions.
- Evaluate the inverse trigonometric functions.
- Evaluate the compositions of trigonometric functions and inverse trigonometric functions.
- Pre-Calculus 7th (textbook)
- Pre-Calculus Study And Solutions Guide
- Pre-Calculus (program DVD)