College Algebra — Syllabus
College Algebra is a 3-unit, lower-division undergraduate course offered at [Institution] in [Term]. The class meets in person twice a week for about 75 minutes each time: [Meeting days/times].
This syllabus is the governing document for the course. It tells you what the course is, how your grade is built, what happens each week, and the policies you can count on. Weeks are numbered from Week 1 to Week 16; your instructor's course site gives the due date for each item.
Instructor and Contact
- Instructor: [Instructor name]
- Contact: [Contact info]
- Office hours: [Office hours]
Bring a specific problem you are stuck on to office hours, along with the line where your work stopped making sense, and reach out early: a question asked in the week it comes up is far easier to answer than one saved for exam week. Check the course announcements at the start of each week.
Course Description
This is the algebra course that a nursing, business, biology, or computer-science student takes once and then leans on for years. It teaches procedures you can always check: simplify, solve, graph, factor, and model, and then confirm every answer by substituting it back into the problem you started with. An answer without its check is unfinished, and by the end of the term checking will be a habit.
The course moves in a clear arc. It starts with the language of algebra (real numbers, the order of operations, exponents, and solving linear equations and inequalities). It then turns to functions and lines, systems of equations, polynomials and factoring, and quadratic equations, with the midterm as a checkpoint in Week 8. The second half builds a larger toolkit: quadratic functions and their graphs, polynomial and rational functions, rational expressions, radicals, and finally exponential and logarithmic functions and the growth, decay, and compound-interest models they describe.
Every idea starts with a situation you know, such as splitting a bill, comparing two phone plans, a ball tossed into the air, or a savings balance that grows, and every procedure is shown one step at a time. Graphs and formulas are taught together, so anything the course says about a graph is something you can confirm yourself in a free graphing calculator. This is not a proof course and not a precalculus course: there is no trigonometry, no matrices, and no limits, and complex numbers appear only as the reason a quadratic equation can have no real solution.
Required Materials
You buy no textbook and pay nothing for course materials. Every reading and video is a link to an external resource, opened from the week's page so you always reach the version the course teaches from. Beyond a web browser, you need:
- A free graphing calculator: Desmos (free) or GeoGebra, both of which run in a browser, for the weekly Model/Build Studio.
- A free account with one approved AI chatbot, from the list in the AI-Use Policy below. A free tier is enough for everything in this course, and every AI-based activity also has a route that needs no AI at all.
Learning Outcomes
By the end of this course you will be able to:
- Outcome A — Work accurately. Apply algebraic procedures accurately to simplify expressions and solve equations, showing correct steps and arriving at correct, checked results.
- Outcome B — Connect and interpret. Connect symbolic, numerical, and graphical representations of relationships and interpret algebraic results in context.
The eight course objectives below build toward those two outcomes. Each week's Start Here page turns the week's objective into a short checklist of skills you should have by the end of the week.
- Classify real numbers, and simplify and evaluate algebraic expressions using the properties of real numbers, the order of operations, and the rules of integer exponents.
- Solve linear equations and linear inequalities in one variable, including absolute-value equations and inequalities, and express solution sets in interval notation.
- Use function notation; determine the domain and range of a function; evaluate functions at numeric and algebraic inputs; and form sums, differences, products, quotients, and compositions of functions.
- Analyze linear functions (slope, intercepts, and the forms of a line, including parallel and perpendicular lines) and solve systems of linear equations and inequalities in two variables.
- Add, subtract, and multiply polynomials, apply the special products, and factor polynomial expressions by the greatest common factor, trinomial patterns, the difference of squares, and grouping.
- Solve quadratic equations by factoring, the square root property, completing the square, and the quadratic formula; use the discriminant to predict the number of real solutions; and analyze quadratic functions and their graphs, including the vertex, intercepts, and maximum or minimum value.
- Analyze polynomial and rational functions (end behavior, zeros and multiplicity, domain, and asymptotes), and simplify and solve rational and radical expressions and equations, including expressions with rational exponents, checking for extraneous solutions.
- Analyze exponential and logarithmic functions and their graphs, apply the properties of logarithms, and solve exponential and logarithmic equations and applied growth, decay, and compound-interest problems.
How this course works
Every module presents the same content in three ways — a chapter to read, a slide deck with speaker notes, and captioned videos — so you can choose how to take it in. Each module's lecture page carries the week's explanation as one spoken-style walk-through as well.
A typical week runs in this order:
- Start Here. Open the week's module overview. It lists the week's items in order with time estimates and names the week's checkpoint, the one thing you should be able to do by the end of the week.
- Chapter (about 35 to 50 minutes). The week's primary reading, with every worked example written out step by step and checked. Read it first.
- Lecture page and slide deck (about 15 to 20 minutes for the lecture, plus time with the deck). The same ideas, explained aloud and in slides.
- Readings and videos. An optional go-deeper menu; every video has captions.
- Lecture tutorial (60 to 90 minutes). A one-on-one session with your chatbot that teaches, gives practice, and ends with a summary you submit.
- Practice set (about 20 minutes). Ungraded practice with a coach, at your own pace.
- Model/Build Studio (about 90 minutes). A hands-on build in Desmos or GeoGebra: you write a model from real numbers, work the algebra step by step, verify your answers by substitution, and then catch and correct your chatbot's algebra slips on the same problem.
- Discussion (about 45 minutes) and assignment (60 to 90 minutes). Where you put the week's ideas to work: analyzing an error, choosing a method, or modeling a real situation.
- Quiz. A short auto-graded check of what you now know, taken on your own.
Week 8 is lighter: the chapter, lecture, slides, readings, practice set, and discussion, then the study guide, exam-prep tutorial, practice exam, and midterm. Week 16 has no new module; it holds the final exam and its study guide, practice exam, and exam-prep tutorial.
Grading
Your course grade is the weighted average of the six groups below. The weights sum to 100%.
| Component | Weight |
|---|---|
| Tutorials & Practice | 10% |
| Quizzes | 10% |
| Workshops | 20% |
| Assignments | 25% |
| Discussions | 15% |
| Exams | 20% |
| Total | 100% |
What each group holds
- Tutorials & Practice: the 14 weekly lecture tutorials, 5 points each. The practice sets sit beside them and are ungraded.
- Quizzes: 14 weekly quizzes, 10 points each, in every module except Week 8.
- Workshops: the 14 weekly Model/Build Studios, 50 points each, in every module except Week 8.
- Assignments: 14 weekly assignments, 100 points each, in every module except Week 8.
- Discussions: 15 weekly discussions, 10 points each, one in every module from Week 1 to Week 15.
- Exams: the midterm in Week 8 (50 points) and the cumulative final in Week 16 (100 points).
Each week's discussion and assignment ship in two versions. The adaptive version is published and graded by default. A traditional version that uses no AI is also in the module, unpublished; your instructor may publish it instead. An unpublished version does not appear to you and does not count. A published traditional version takes the adaptive one's place in the same group, for the same points.
Letter grades follow the standard scheme:
| Letter | Percentage range |
|---|---|
| A | 90–100 |
| B | 80–89 |
| C | 70–79 |
| D | 60–69 |
| F | below 60 |
Weekly Schedule
The course runs for sixteen weeks: fifteen weeks of modules and a finals week. Every module from Week 1 to Week 15 holds the same materials: the Start Here page, the chapter, the lecture page (titled "Lecture:" followed by the week's focus, such as "Lecture: Real Numbers, Exponents & Algebraic Expressions"), the slide deck, the readings and videos page, and the practice set. Every module also ships both an adaptive discussion and a traditional no-AI alternative, and every module except Week 8 ships both an adaptive assignment and a traditional no-AI alternative. The adaptive versions are graded and published; the traditional alternatives are unpublished by default and count only if your instructor publishes them instead.
| Week | Focus | Graded and published | Traditional alternative (unpublished) |
|---|---|---|---|
| 1 | Real Numbers, Exponents & Algebraic Expressions | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 2 | Linear Equations & Inequalities | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 3 | Functions: Notation, Domain & Range | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 4 | Linear Functions & Their Graphs | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 5 | Systems of Linear Equations & Inequalities | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 6 | Polynomials & Factoring | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 7 | Quadratic Equations | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 8 | Midterm Review & Exam | Discussion, midterm exam | Discussion |
| 9 | Quadratic Functions & Their Graphs | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 10 | Polynomial & Rational Functions | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 11 | Rational Expressions & Equations | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 12 | Radicals, Rational Exponents & Radical Equations | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 13 | Exponential Functions | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 14 | Logarithmic Functions | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 15 | Exponential & Logarithmic Equations & Applications | Tutorial, Model/Build Studio, discussion, assignment, quiz | Discussion, assignment |
| 16 | Finals week (no module) | Final exam | None |
The midterm in Week 8 covers Weeks 1 to 7, which is Objectives 1 to 6 as far as quadratic equations. The final in Week 16 is cumulative and draws on every course objective. Both exams come with a study guide, a practice exam, and an exam-prep tutorial you work with your chatbot.
Attendance and Participation
This course meets in person twice a week. Come to class having opened the week's Start Here page and read the chapter, because class time builds on that reading with worked problems and questions. Your participation also shows in your weekly work: the tutorial, the Model/Build Studio, the discussion, the assignment, and the quiz. Algebra builds week on week, so falling a week behind is the most common reason a grade slips; keep to the weekly rhythm and talk to your instructor the moment a step stops making sense. If you must miss class, follow the week's module from its Start Here page so you stay on pace.
Late Work
Late work loses 10% of the item's points for each day it is late. If something serious comes up, such as an illness or a family emergency, contact your instructor before the due date whenever you can so the two of you can agree on a fair plan. The penalty exists to keep the course moving, not to punish genuine hardship.
Academic Integrity
The work you submit must be your own, and you are bound by your institution's academic integrity standard. Do not copy another student's work, do not submit work you did not do, and do not misrepresent how a piece of work was produced. Two violations matter most in this course: fabricating or doctoring a chatbot conversation or its share link, and using AI on the quizzes, the midterm, or the final. Violations are handled under your institution's academic integrity process and may result in no credit for the item.
Accessibility and Disability
This course is designed to reflect universal-design principles and offers multiple means of representation, engagement, and expression. If you have a disability and need an accommodation, contact your institution's disability services office to arrange it, and let your instructor know so it can be put in place promptly. If any material is hard to use with your assistive technology, tell your instructor and an equivalent version will be provided; every graph the course refers to is also described in words. This course is not yet accessibility-certified, and your feedback helps improve it. The course page Accessibility & Inclusion in Module 0 explains how the course offers multiple modes, how to turn on captions, and how to request an accommodation.
AI-Use Policy
This course uses an AI chatbot as a study partner, and then asks you to check its work by hand. Use any one of the approved chatbots: Claude, Gemini, ChatGPT, Grok, or Microsoft Copilot. Your instructor may edit this list. Free tiers are fine, and Copilot is often included with a campus Microsoft 365 account.
AI may be used on these activities:
- Lecture tutorials (completed with a chatbot). Each week you work the tutorial in a conversation with an approved chatbot, then submit the conversation share link and your completion summary.
- Practice sets (ungraded). You work the practice problems with a chatbot coach.
- Adaptive discussions (completed with a chatbot). You hold a real-time dialogue with an approved chatbot, then post the AI's summary with the conversation share link. This version does not require replies to classmates.
- Adaptive assignments (AI-coached). You work the problems with a chatbot coach that scores your work against the assignment's rubric, then submit the self-scored report and the conversation share link.
- Model/Build Studios (a required AI-critique step). After your own build, you ask your chatbot to work the same problem, then verify its work by hand and correct a mistake in it, such as squaring a negative sign that sits outside the parentheses, adding exponents it should multiply, cancelling a term instead of a factor, skipping the check for an extraneous solution, or splitting the log of a sum.
- Exam-prep tutorials and studying. Use AI freely to review, to check your understanding, and to prepare for the exams.
AI may not be used on the quizzes, the midterm, and the final. These are closed to AI and must be entirely your own work, because they confirm that you personally can carry out the procedures and interpret the results.
A chatbot's algebra needs checking. A chatbot can explain a rule well and still drop a sign or swap two rules in the middle of a solution. Treat every answer it gives you the way this course teaches you to treat your own: substitute it back in and see whether it works.
If your instructor publishes a traditional alternative. A traditional discussion is your own post and your own replies to classmates; a traditional assignment is your own submitted work, graded by your instructor. AI may help you think, but you write and submit the work yourself.
Disclosure. The share link documents your AI use on the AI-based activities, so they need no separate note. For any other graded work where AI help is allowed, add one line naming the tool and how you used it.
Bring your own AI: access, cost, and privacy
- Equity and a non-AI route. You never have to create an account with a chatbot company to complete this course or to reach any grade in it. Every AI-based activity in this course carries an Equivalent route (no AI required) on its own page. It assesses the same objectives, for the same points, against the same rubric. Take it whenever you like, for any reason or none; you do not have to ask permission, explain, or arrange it in advance.
- Cost. A free tier of any approved chatbot covers everything in this course. No graded work depends on a paid subscription.
- Privacy. Before you start, read what your chosen chatbot keeps of your conversations and how it uses them. Never paste personal information you would not want stored, and remember that a share link lets anyone who has it read that conversation.
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