Sample course · full build

College Algebra

15 instructional weeks + finals week (Week 1–Week 16) Free sample edition

Built with The Course Maker · samples.thecoursemaker.com

This is a complete course: fifteen instructional weeks and a finals week, every student component, built with The Course Maker and ready to import. Weeks are relative (Week 1 to Week 16); you set the dates when you import it. Browse the whole thing below. Click any piece to read it in full, then click back to return here.

Nothing here is locked behind a signup. The course is the proof.

Free sample edition. No instructor, institution, or term identity appears anywhere in this edition, by design. The syllabus carries fill-in slots (instructor name, contact, office hours, institution policies) for the adopting instructor to make it their own. (Original objectives written from the standard College Algebra body of knowledge; not copied from any school's course outline.)

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This course is free, complete, and evergreen, and it is yours to keep; free downloads run through June 30, 2028. Students pay $0 for course materials: the readings and videos are links to freely available resources.

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What the paid build adds

This sample is complete and yours to keep. A paid build is the same course made yours in the ways a download cannot be:

Every date set to your term and your breaks, and re-paced to a second campus calendar at no extra charge.
Your syllabus, your policies, and your outline of record in the build, with an alignment report that shows which component addresses each objective and SLO, and a Universal design for learning section drawn from the course's own data.
Your name on every page as the course's creator.
Kept current every term: fresh assessment variants, every link re-checked and the dead ones replaced, and the subject brought up to date where it has moved.
The full instructor pack: answer keys and worked solutions, the alignment report, and the UDL map.
A record for your college's file: the design attestation, a disclosure statement for every edition, and what changed at the end of each term.

How a paid build works and what it costs →

Included in every course

ChapterRequired
Required in every course. Every module presents the same content in three ways — a chapter to read, a slide deck with speaker notes, and captioned videos — so each student can choose how to take it in. The course is designed to reflect UDL's multiple means of representation, and the alignment report describes this to your curriculum committee.
Slide deck with speaker notesRequired
Required in every course. Every module presents the same content in three ways — a slide deck with speaker notes, a chapter to read, and captioned videos — so each student can choose how to take it in. The course is designed to reflect UDL's multiple means of representation, and the alignment report describes this to your curriculum committee.
Captioned video linksRequired
Required in every course. Every module presents the same content in three ways — captioned videos, a chapter to read, and a slide deck with speaker notes — so each student can choose how to take it in. The course is designed to reflect UDL's multiple means of representation, and the alignment report describes this to your curriculum committee. We link videos only when a caption track exists (from the creator or generated automatically), and we never host them.

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The syllabus

Policies, schedule, and grading

Read the full course syllabusPolicies, the week-by-week schedule, grading, and the bring-your-own-AI rules, with fill-in slots for the adopting instructor.→

Weighted gradebook

Assignment groups & weights

Configured in the export — the gradebook is set the moment the course is imported.

Assignment group	Weight	Notes
Tutorials & Practice	10%
Quizzes	10%
Workshops	20%
Assignments	25%
Discussions	15%
Exams	20%
Total	100%	Letter Standard

Objectives & outcomes

What students will be able to do

Objective 1

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.

Objective 2

Solve linear equations and linear inequalities in one variable, including absolute-value equations and inequalities, and express solution sets in interval notation.

Objective 3

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.

Objective 4

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.

Objective 5

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.

Objective 6

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.

Objective 7

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.

Objective 8

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.

SLO A

Apply algebraic procedures accurately to simplify expressions and solve equations, showing correct steps and arriving at correct, checked results.

SLO B

Connect symbolic, numerical, and graphical representations of relationships and interpret algebraic results in context.

How this course is built — read this first

Every teaching module carries the same set, in the order a student meets it: a Start Here overview, the chapter (the primary reading), the lecture (titled “Lecture: <module title>”), the slide deck with speaker notes, readings & resources (links only), the lecture tutorial and practice exercises worked with an AI tutor, the quiz, the discussion and the assignment, and the weekly Model/Build Studio. Exams: the midterm in Week 8 and the final in Week 16, a finals week with no module.

The discussion and the assignment each ship in both formats: the adaptive version is the published, graded item, and its traditional alternative (no AI) is a separate item that ships unpublished beside it. An instructor who prefers the traditional format publishes it and unpublishes or deletes the adaptive one.

What you see here is every student page. The instructor pack (answer keys and worked solutions, rubric calibration, image prompts, audio-brief scripts, and the alignment report) ships only in the download, never on this site.

Adaptive and traditional

Discussions & assignments: both formats in every module

Same learning objective either way; what changes is how the work happens.

Adaptive · published

Work it through with an approved chatbot

The student does the work in a guided conversation with an approved chatbot, using a copy-paste prompt the course provides. For a discussion, the AI is a Socratic partner that challenges their thinking and never writes the post. For an assignment, the AI is a coach: it asks questions, checks the reasoning shown, and waits for the student to revise. The student submits the chat link with the required summary or report.

Traditional alternative (no AI) · unpublished

The familiar way, one click away

The student does the work themselves and submits it, and the instructor grades it against the rubric. No AI required. It ships unpublished, opening with a one-line note to the instructor; publish it instead of the adaptive version if you prefer.

All 16 weeks

Every week, every component

Each week is a heading; every component under it links to the full student page. Week 8 is a teaching module that also carries the midterm bundle; Week 16 is the finals week, with the final exam bundle and no module.

Week 1

Real Numbers, Exponents & Algebraic Expressions

the real-number system: natural, whole, integer, rational, and irrational numbers, and how the sets nestthe order of operations, including the -4^2 vs. (-4)^2 trapthe properties of real numbers: commutative, associative, distributive, identity, inversethe integer-exponent rules (product, quotient, power, power of a product, zero, negative) and simplifying algebraic expressions by distributing and combining like terms

Week 2

Linear Equations & Inequalities

solving linear equations in one variable: distribute, clear fractions, collect, divide, check; identities and contradictionslinear inequalities, the sign flip on a negative divisor, and interval notationabsolute-value equations: the split rule and the no-solution caseabsolute-value inequalities: less-than is a bounded interval (and), greater-than is two rays (or)

Week 3

Functions: Notation, Domain & Range

what a function is: one output per input, mappings, tables, and the vertical line testfunction notation and evaluating at numeric and algebraic inputs, including f(a + 2) and f(-x)domain and range: polynomials, rational functions (exclude denominator zeros), even-root radicals (radicand at least zero)operations on functions and composition, (f o g)(x) = f(g(x)), inside first and not commutative

Week 4

Linear Functions & Their Graphs

slope as rise over run and as a rate of change; horizontal (slope 0) and vertical (undefined) linesslope-intercept form y = mx + b and point-slope form y - y1 = m(x - x1)x- and y-intercepts, graphing a line, and standard formparallel lines (equal slopes) and perpendicular lines (negative reciprocal slopes, product -1)

Week 5

Systems of Linear Equations & Inequalities

solving a 2 x 2 system by substitutionsolving by elimination, including when a multiply is neededclassifying a system: consistent independent (one solution), inconsistent (none), dependent (infinitely many), and what each looks like on a graphsystems of linear inequalities: half-planes, dashed vs. solid boundaries, test points, the overlap region

Week 6

Polynomials & Factoring

polynomial vocabulary and operations: adding, subtracting (distribute the minus to every term), multiplying, FOILthe three special products and the missing-middle-term trap in (a + b)^2factoring: greatest common factor first, trinomials with leading coefficient 1 and with a leading coefficient (the ac method)the difference of squares, why a sum of squares does not factor over the reals, and factoring by grouping

Week 7

Quadratic Equations

solving by factoring and the zero-product property; never divide by the variablethe square root property for x^2 = c and (x - h)^2 = kcompleting the squarethe quadratic formula, the discriminant, and choosing the right method

Week 8 Midterm

Midterm Review & Exam

cumulative review of Weeks 1 to 7: simplify, solve, functions, lines and systems, factor, quadratic equationschoosing a method: reading a problem and naming the one core move it asks for (light new material that bridges to the second half)the midterm exam

The midterm exam bundle

Week 9

Quadratic Functions & Their Graphs

the parabola and vertex form f(x) = a(x - h)^2 + k: vertex, axis of symmetry, opening directionstandard form and the vertex formula h = -b / (2a), k = f(h)intercepts and the discriminant: how many x-intercepts a parabola has; converting between formsmaximum and minimum applications, including a launched object's height

Week 10

Polynomial & Rational Functions

end behavior from the leading term: degree even or odd, leading coefficient positive or negativezeros and multiplicity: crossing at odd multiplicity, touching at evenrational functions: domain, vertical asymptotes vs. holeshorizontal asymptotes by comparing degrees; sketching the key features

Week 11

Rational Expressions & Equations

simplifying rational expressions: factor first, cancel factors (never terms), carry the restrictionmultiplying and dividing rational expressionsadding and subtracting with a least common denominator built from factored denominatorssolving rational equations by clearing the LCD, excluded values and extraneous solutions, and work-rate applications

Week 12

Radicals, Rational Exponents & Radical Equations

simplifying radicals with the product and quotient rules; why sqrt(a + b) is not sqrt(a) + sqrt(b)rational exponents: a^(m/n) as the nth root raised to the m, converting in both directions, root firstsimplifying expressions with rational exponents using the exponent rulessolving radical equations: isolate, raise to the power, and check every candidate for extraneous solutions

Week 13

Exponential Functions

the exponential function f(x) = a * b^x: evaluating, initial value vs. growth factor, growth vs. decaygraph features: y-intercept (0, a), horizontal asymptote y = 0, always increasing or always decreasingthe natural base ecompound interest A = P(1 + r/n)^(nt), continuous compounding A = P * e^(rt), and growth and decay applications

Week 14

Logarithmic Functions

the logarithm as the inverse of an exponential: log_b(x) = y means b^y = x; converting between formsevaluating common, natural, and other-base logarithms mentallydomain and vertical asymptote of a logarithmic functionthe product, quotient, and power properties; expanding and condensing; no rule for the log of a sum

Week 15

Exponential & Logarithmic Equations & Applications

solving exponential equations by matching basessolving exponential equations by taking a logarithm of both sidessolving logarithmic equations by condensing and converting, with the domain check for extraneous solutionsapplications: doubling time, tripling time, half-life, and solving compound-interest models for the time; where the course has taken you

Week 16 · finals week Final

Finals week

No module this week: the final exam bundle