Course Syllabus

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Syllabus Calculus FHU

Welcome

Welcome to Calculus FHU! 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

Calculus, First Half Unit, is designed to provide an overview of mathematical analysis through the study of functions. Functions have been introduced in your algebra classes. Graphing and functions are reviewed in the first lesson of this course. The course continues with the study of limits, a fundamental concept for calculus. Limits are then used to define a fundamental operation of calculus, differentiation. Several topics are covered that apply the use of differentiation. The Fundamental Theorem of Calculus is used for integration, the inverse operation of differentiation. The course ends with differentiation and integration of the natural logarithmic function.

This course is designed to provide an overview of mathematical analysis through the study of functions, which were introduced in the algebra courses. Beginning with a review of graphing and functions, the course continues with the study of limits and differentiation. The Fundamental Theorem of Calculus is used for integration, the inverse operation of differentiation. The course also covers differentiation and integration of the natural logarithmic function.

Course Essential Questions

 

 Essential Question

How can we use limits to connect the rate of change at a single point to the total accumulation of a function over an interval?

Course Overview

Lesson

Objectives

Quiz

Assignment

1: Preparation for Calculus
  1. Sketch the graph of an equation using intercepts, slope, and symmetry.
  2. Find the points of intersection of two graphs.
  3. Interpret mathematical models for real-life data.
  4. Write the equation of a line.
  5. Interpret slope as a ratio or rate.
  6. Use calculus symbols and function terminology.
  7. Use function notation to represent and evaluate a function.
  8. Find the domain, range, and graph of a function.
  9. Identify transformations of functions.
  10. Classify functions and recognize combinations of functions.
  11. Fit a linear or quadratic or trigonometric model to a real-life data set.

20 multiple-choice questions 

No Assignment

2: Limits and Their Properties
  1. Determine whether precalculus or calculus is required to solve a problem.
  2. Estimate a limit using a numerical or graphical approach.
  3. Determine whether a limit exists and use the formal definition of a limit.
  4. Evaluate a limit using properties of limits and strategies, cancellation and rationalization techniques, and the Squeeze Theorem.
  5. Identify transformations of functions.
  6. Determine continuity at a point, on an open interval, and on a closed interval.
  7. Use properties of continuity.
  8. Use the Intermediate Value Theorem.
  9. Determine infinite limits.
  10. Find and sketch the vertical asymptotes of the graph of a function.

20 multiple-choice questions 

No Assignment

3: The Derivatives and Differentiation Rules
  1. Find the slope of the tangent line to a curve at a point.
  2. Use the limit definition to find the derivative of a function.
  3. Summarize the relationship between differentiability and continuity.
  4. Use the formal definition of a limit.
  5. Find the derivative of a function using the Constant Rule, the Power Rule, the Constant Multiple Rule, and Sum/Difference Rules.
  6. Find rates of change.
  7. Find the derivative of a function using the Product and Quotient Rules.
  8. Find the derivative of a trigonometric function.
  9. Find the higher-order derivative of a function.

20 multiple-choice questions 

No Assignment

4: The Chain Rule, Implicit Differentiation, and Related Rates
  1. Find the derivative of a composite function or trigonometric function using the Chain Rule.
  2. Find the derivative of a function using the General Power Rule.
  3. Simplify the derivative of a function using algebra.
  4. Distinguish between functions written in implicit form and explicit form.
  5. Use implicit differentiation to find the derivative of a function.
  6. Find a related rate.
  7. Use related rates to solve real-life problems.

20 multiple-choice questions 

No Assignment

5: Finding Extrema on an Interval and the First Derivative Test
  1. Find extrema on a closed interval.
  2. Use Rolle's Theorem.
  3. Use the Mean Value Theorem.
  4. Determine intervals on which a function is increasing or decreasing.
  5. Apply the first derivative test to find relative extrema of a function.

20 multiple-choice questions 

No Assignment

Midterm Exam

6: Second Derivative Test
  1. Determine intervals on which a function is concave upward or concave downward.
  2. Find the points of inflection of the graph of a function.
  3. Apply the second derivative test to find relative extrema of a function.
  4. Determine the finite and infinite limits at infinity.
  5. Determine the horizontal asymptotes of the graph of a function.
  6. Determine the vertical asymptotes of the graph of a function.

20 multiple-choice questions 

No Assignment

7: Applications of Differentiation
  1. Solve applied minimum and maximum problems.
  2. Use Newton's Method to approximate the zero of a function.
  3. Compare the value of the differential, dy, with the actual change in y, Δy.
  4. Estimate a propagated error and percent error using a differential.
  5. Find the differential of a function using differentiation formulas.

20 multiple-choice questions 

No Assignment

8: Integration
  1. Write the general solution of a differential equation.
  2. Use indefinite integral notation for antiderivatives.
  3. Use basic integration rules to find antiderivatives.
  4. Find a particular solution of a differential equation.
  5. Use sigma notation to write and evaluate a sum.
  6. Approximate the area of a plane region.
  7. Find the area of a plane region using limits.
  8. Evaluate a definite integral using limits and properties of definite integrals.

20 multiple-choice questions 

No Assignment

9: Fundamental Theorem of Calculus
  1. Evaluate a definite integral using the Fundamental Theorem of Calculus.
  2. Use the Mean Value Theorem for integrals.
  3. Find the average value of a function over a closed interval.
  4. Use the Second Fundamental Theorem of Calculus.
  5. Evaluate an indefinite integral through integration by substitution, a change of variables, and the General Power Rule for Integration.
  6. Use a change of variables to evaluate a definite integral.
  7. Evaluate a definite integral involving an even or an odd function.
  8. Approximate a definite integral using the Trapezoidal Rule and Simpson's Rule.
  9. Analyze the approximate error in the Trapezoidal Rule and Simpson's Rule.

20 multiple-choice questions 

No Assignment

10: Logarithmic Functions
  1. Use properties of the natural logarithmic function.
  2. Find derivatives of functions involving the natural logarithmic function.
  3. Use the Log Rule for integration to integrate a rational function.
  4. Integrate trigonometric functions.
  5. Find the inverse function of another function.
  6. Determine whether a function has an inverse function.
  7. Find the derivative of an inverse function.

20 multiple-choice questions 

No Assignment

Final Exam

Quizzes and Assignments

The work you will submit for this course consists of 10 computer-evaluated quizzes that are scored instantaneously. They appear in each lesson. Quizzes are open-book assignments that test your knowledge and understanding of the course material presented in a particular lesson's commentary or textbook reading assignment. You may use any assigned readings, your notes, and other course-related materials to complete these assignments. The points you earn on your submitted work count toward your final course grade. Each quiz consists of 20 multiple-choice and true/false questions worth 1 point each for a total of 20 points.

Quizzes are taken online. After you submit them, you’ll quickly receive a report on how you did. Unlike exams, you may use any assigned readings, your notes, and other course-related materials to complete graded quizzes and assignments. 

Exam Matrix

You are required to take two proctored exams for this course.

Exam Matrix
Midterm Exam (through Lessons 5) Final Exam (through Lesson 10)
When to request an exam after you receive your feedback for Lesson 5 after you receive your feedback for Lesson 10
Questions and Type 35 multiple-choice 35 multiple-choice
Points Possible 175 points 175 points
Time Limit 150 minutes 150 minutes
Allowed Materials Pencil, Scratch/Graph Paper, Calculator, Formula Packet Pencil, Scratch/Graph Paper, Calculator, Formula Packet

See the "About Exams" in the policies section for additional information on exams at Mizzou Academy.

 

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 Quizzes 200
Midterm Exam 175
Final Exam 175
Total 550

 

Textbook & Technology Requirements

To fully participate, make sure you have:

  • 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

Textbook

Larson, Ron, Robert P. Hostetler, Bruce H. Edwards, and David E. Heyd. Calculus of a Single Variable. (7th Edition). Boston: Houghton-Mifflin, 2002.

Materials

  • You will need a graphing calculator (preferably a Ti-83 or Ti-84).
  • SUGGESTED: Microsoft Word to render MathType/equations.

Technology

The most up-to-date requirements can be found here: 

Additional requirements for the course are below: 

  • audio and video recording capabilities (e.g., smartphone, camera)

If you ever have trouble accessing course materials or recording tools, reach out to your teacher for support. We are here to help!

Course Credits

Developer
Brennan Ransdell with Mizzou Academy
Instructional Editor
Kimberly Small
Copyeditor
Adrian Corman

Image and Multimedia Attributions

Title graphic
The image in the background of the title graphic is © iStockphoto/rubenhi.
Calculator images
All images of calculators and calculator windows are courtesy of Texas Instruments.
Check Your Understanding icon
Image is © Microsoft Office Online Clip Art and Media.
Lesson 1: Preparation for Calculus
Figure 1.1, the dollar sign, was obtained from Wikimedia Commons courtesy of Anonymoususer and was released into the public domain by its author.
Lesson 2: Limits and Their Properties
Figure 2.1, the speed limit sign, was obtained from Wikimedia Commons courtesy of Ltljltlj and was released into the public domain by its author.
Lesson 3: The Derivative and Differentiation Rules
Figure 3.1, the bouncing basketball, was obtained from Wikimedia Commons courtesy of Richard Bartz and is licensed under the Creative Commons Attribution ShareAlike 3.0 Unported license.
Lesson 4: The Chain Rule, Implicit Differentiation, and Related Rates
Figure 4.1, the hourglass, was obtained from Wikimedia Commons courtesy of S Sepp and is licensed under the GNU Free Documentation license.
Lesson 5: Finding Extrema on an Interval and the First Derivative Test
Figure 5.1, the speedometer, was obtained from Wikimedia Commons courtesy of FlickreviewR and is licensed under the Creative Commons Attribution 2.0 Generic license.
Lesson 8: Integration
Figure 8.1, the theme park, was obtained from Wikimedia Commons courtesy of Angcr and is licensed under the Creative Commons Attribution 3.0 Unported license.

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

Canvas will be used as the primary platform for accessing course materials and assignments for this class.

Course Summary:

Course Summary
Date Details Due