Course Syllabus
Syllabus Precalculus A
Welcome
Welcome to Precalculus A! We’re so glad you’re here.
Every lesson is designed to help you grow as a thinker, problem solver, and global learner. As a Mizzou Academy global student, you will complete lessons and assignments on your own schedule, interacting with course content, participating in interactives, and completing practice activities, as well as drafting and revising assignments, preparing for quizzes and assessments, and taking exams.
To stay on track, we recommend using a pacing guide. You can find more information about pacing in the Course Resources section, along with helpful tools, technology support, and tips for online learning success.
As you begin, remember that online learning requires both independence and communication. Be curious, stay organized, and don’t hesitate to reach out to your teacher if you need support.
We’re excited to learn with you, and we’re happy you’re part of our Mizzou Academy community!
Pacing
This course can be completed in as few as six weeks or take up to 6 months (180 calendar days). The six weeks are counted from the date of the first lesson submission and not the date of enrollment.
This course is asynchronous, meaning you can complete lessons and assignments at your own pace.
Most students spend approximately 10 hours per lesson interacting with course content, participating in interactive activities, and completing practice exercises, as well as drafting and revising assignments, preparing for quizzes and assessments, and taking exams. Your time may vary depending on your goals and learning style.
We encourage you to work at a consistent pace, allowing time to absorb new ideas, build skills, and reflect on what you’ve learned. Use a pacing guide to plan ahead, stay organized, and finish strong.
Course Description
The principle goal of Precalculus is to prepare you for the rigors of calculus. This course is designed to give you a better understanding of the concepts, functions, and applications of calculus, and to deepen your understanding of mathematical concepts previously studied to make the transition to calculus as smooth as possible. It is in Precalculus that all of the earlier material studied in mathematics begins to come together. Concepts and applications that might have seemed abstract and useless at times will take on new and more concrete meaning! Precalculus A will cover linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric equations and functions; graphing and analyzing these various types of functions and their transformations; linear and nonlinear inequalities. In Precalculus B we will dive into analytic trigonometry; and how to use the laws of trigonometry to solve triangles and represent vectors and further ease your transition into Calculus.
Course Overview
LESSON
OBJECTIVES
QUIZ
ASSIGNMENT
1: Review and Functions
1.1a: Plot and identify points.
1.1b: Find the distance between points.
1.1c: Find the midpoints of segments.
1.2a: Find x- and y-intercepts.
1.2b: Sketch and identify the graphs of equations.
1.2c: Find equations of circles and sketch their graphs.
1.3a: Determine the slope of lines and use slope to sketch linear equations.
1.3b: Use slope to determine if lines are parallel, perpendicular, or neither.
1.3c: Write the linear equation of a line and sketch its graph using limited information.
1.4a: Determine if relations are functions.
1.4b: Write and evaluate functions using function notation.
1.4c: Find the domain and range of a function (algebraically and graphically).
1.5a: Use the Vertical Line Test to determine if relations are functions.
1.5b: Use the Horizontal Line Test to determine if functions are one-to-one.
1.5c: Evaluate the nature and change of functions on intervals.
1.5d: Identify even and odd functions.
20 multiple-choice questions
N/A
2:Functions and Their Graphs
2.1a: Graph, identify, and write functions, including linear, squaring, cubic, square root, reciprocal, and piecewise-defined functions.
2.1b: Identify graphs of parent functions.
2.2: Use transformations to sketch graphs of functions and write equations of functions.
2.3a: Perform basic operations on functions.
2.3b: Find and use composite functions.
2.4a: Find inverse functions and verify that functions are inverses.
2.4b: Determine whether a function has an inverse.
2.5a: Find least-squares regression models and assess “goodness-of-fit"
2.5b: Write mathematical models for direct, inverse, and joint variation.
20 multiple-choice questions
N/A
3: Polynomial Functions and Complex Number
3.1a: Sketch and analyze the graphs of quadratic functions.
3.1b: Identify, write, and analyze quadratic functions, including finding minimum and maximum values.
3.2a: Use transformations to sketch graphs of polynomial functions.
3.2b: Determine end behavior of polynomial functions, including using the Leading Coefficient Test.
3.2c: Find and use zeros of polynomial functions, including using the Intermediate Value Theorem.
3.3a: Divide polynomials using long and synthetic division.
3.3b: Use the Remainder Theorem and Factor Theorem with division of polynomials.
3.4a: Write and perform basic operations on complex numbers.
3.4b: Find solutions to quadratic equations that involve complex numbers.
20 multiple-choice questions
N/A
4: Zeros of Polynomial Functions, Rational Functions, and Nonlinear Inequalities
4.1a Apply the Fundamental Theorem of Algebra, Linear Factorization Theorem, Rational Zero Test, Descartes’ Rule of Signs, and upper and lower bound rules to find possible zeros of polynomial functions.
4.1b Find zeros (and factors) of polynomial functions (including in the complex number system), and find polynomial functions given zeros.
4.2a Find zeros, domains, and asymptotes of rational functions.
4.2b Analyze and sketch graphs of rational functions, including those with slant-asymptotes.
4.3a Solve polynomial inequalities.
4.3b Solve rational inequalities.
20 multiple-choice questions
Assignment 1: Lesson 1-4
5: Exponential and Logarithmic Functions
5.1 Recognize, evaluate, and graph exponential functions with base a and base e.
5.2 Recognize, evaluate, and graph logarithmic functions both with base a and the natural logarithmic functions.
5.3a Use the change of base formula to evaluate logarithmic functions.
5.3b Use properties of logarithms to evaluate, expand, and condense logarithmic expressions.
5.4 Solve simple and complex logarithmic and exponential equations/functions.
5.5a Recognize common types of models involving exponential and logarithmic functions
5.5b Use exponential growth and decay functions to model and solve problems.
5.5c Use Gaussian functions to model and solve problems.
5.5d Use logistic growth functions to model and solve problems.
5.5e Use logarithmic functions to model and solve problems.
20 multiple-choice questions
N/A
Midterm Exam
6: Introduction to Trigonometry
6.1a Find angle measures in degrees and radians.
6.1b Use angles to model and solve real-life problems.
6.2a Evaluate trigonometric functions using the unit circle.
6.2b Use domains and periods to evaluate sine and cosine functions.
6.2c Use trigonometric functions to model and solve problems.
6.3a Find and use reference angles.
6.3b Evaluate trigonometric functions for any real numbers.
6.4a Evaluate trigonometric functions of acute angles.
6.4b Use fundamental trigonometric identities.
6.4c Use trigonometric functions to model and solve real-life problems.
20 multiple-choice questions
N/A
Graphs of Trigonometric Functions, Inverse Functions, and Applications
7.1a Sketch graphs of sine and cosine functions with transformations.
7.1b Use amplitude and period with sketches of sine and cosine functions.
7.1c Model situations using sine and cosine functions.
7.2a Sketch graphs of tangent and cotangent functions.
7.2b Sketch graphs of secant and cosecant functions.
7.2c Identify and graph damped trigonometric functions.
7.3a Evaluate and graph inverse trigonometric functions.
7.3b Evaluate compositions of trigonometric and inverse trigonometric functions.
7.4a Apply trigonometric and inverse trigonometric functions to right triangles.
7.4b Solve real-life problems using trigonometry including directional bearings and harmonic motion.
20 multiple-choice questions
N/A
8: Trigonometric Identities and Solving Trigonometric Equations
8.1a: Recognize and write the fundamental trigonometric identities.
8.1b: Use the fundamental trigonometric identities to simplify trigonometric expressions.
8.1c: Use the fundamental trigonometric identities to evaluate trigonometric functions.
8.2: Verify trigonometric identities.
8.3a: Use algebra to solve trigonometric equations.
8.3b: Solve quadratic trigonometric equations.
8.3c: Solve trigonometric equations containing multiple angles.
8.3d: Solve trigonometric equations using inverse trigonometric functions.
20 multiple-choice questions
Assignment 2: Lesson 6-8
9: Trigonometric Formulas and Laws
9.1a: Use sum and difference formulas to evaluate trigonometric expressions.
9.1b: Use sum and difference formulas to verify identities.
9.1c: Use sum and difference formulas to solve trigonometric equations.
9.2a: Evaluate trigonometric functions using multiple-angle formulas.
9.2b: Evaluate trigonometric functions using half-angle formulas.
9.2c: Evaluate trigonometric functions using product-to-sum and sum-to-product formulas.
9.3a: Use the Law of Sines to solve oblique triangles.
9.3b: Find the areas of oblique triangles.
9.4a: Use the Law of Cosines to solve oblique triangles.
9.4b: Use Heron's Formula to find the areas of triangles.
20 multiple-choice questions
N/A
10: Vectors and Complex Numbers
10.1a Represent vectors as directed line segments and in component form.
10.1b Perform basic vector operations and represent them with graphs.
10.1c Write vectors as linear combinations of unit vectors.
10.1d Find direction angles of vectors.
10.2a Find and use the dot product of two vectors.
10.2b Find the angle between two vectors.
10.2c Write a vector as the sum of two vector components.
10.2d Use vectors to find force and work done by a force.
10.3a Plot complex number in the complex plane.
10.3b Find absolute values of complex numbers.
10.3c Write complex numbers in trigonometric/polar form.
10.3d Multiply and divide complex numbers in trigonometric form.
10.3e Use DeMoivre’s Theorem to find powers of complex numbers.
10.3f Find the nth root of complex numbers.
20 multiple-choice questions
N/A
Final Exam
Grades
Your final grade will be based on the number of points you earn on submitted work and exams. The available points are distributed as follows:
Source
Available Points
Lesson Assignments
72
Lesson Quizzes
200
Midterm Exam
205
Final Exam
205
Total
682
Textbook & Technology Requirements
To participate successfully, you will need:
- A computer that meets our Mizzou Academy technology requirements
- A microphone and webcam for recording audio and video assignments
- Any other required textbooks or materials for the course
To ensure you have everything you need, please review the additional requirements listed in the expandable sections below.
Accessibility
If you anticipate barriers related to the format or requirements of this course, please let Mizzou Academy know as soon as possible. If disability-related accommodations are necessary (for example, a scribe, reader, extended time on exams, captioning), please contact Mizzou Academy.Canvas Technical Support
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