UW–Madison MATH 221: Calculus and Analytic Geometry 1
MATH 221 is UW–Madison's five-credit Calculus I — limits, derivatives, applications of differentiation, and the beginnings of integration — required across engineering, the sciences, and quantitative majors, taught in large lectures with TA-led discussion sections and common evening exams.
Fennie is independent and not affiliated with University of Wisconsin–Madison. This is an unofficial study guide.
Build my MATH 221 study planWhat makes it hard
The five-credit pace and evening-exam format expose the classic gap: algebra and trig weaknesses inside correct calculus setups cost more points than the calculus itself ever does. Homework with resources builds false confidence that timed, no-notes exams are designed to break, and the curve grades you against a room full of engineering students.
What you'll cover
- • Limits and continuity
- • Derivatives and differentiation rules
- • Implicit differentiation and related rates
- • Optimization and curve sketching
- • The Mean Value Theorem
- • Antiderivatives and intro to integration
The MATH 221 study guide
How to study for UW–Madison MATH 221, step by step.
- 1
Audit algebra and trig in the first two weeks
Most MATH 221 exam losses are precalculus errors inside correct setups. Find your gaps — factoring, exponents, trig identities — and fix them before the derivative units assume them.
- 2
Solve problems daily, cold
The five-credit pace makes weekend-only study a losing strategy. A daily problem set without solutions open builds the fluency timed evening exams measure.
- 3
Use discussion sections as a weekly diagnostic
TA section problems calibrate you to the department's difficulty bar. Attempt them before section and treat anything you couldn't start as that week's priority.
- 4
Drill the setup-heavy word problems
Related rates and optimization fail at translation, not differentiation. Practice converting scenarios into equations from scratch until starting cold feels routine.
- 5
Work past exams timed before each evening exam
The math department's old exams are the most faithful practice available. Timed, no notes — the format is designed to break untimed-homework confidence, so train under it.
- 6
Pace it to exam night with Fennie
Upload your MATH 221 syllabus and Fennie's Daily Plan schedules daily problem reps and algebra/trig refreshers around the evening exam dates, with practice quizzes built from your actual course material. Free to start.
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How Fennie helps with MATH 221
Fennie's Daily Plans match MATH 221's five-credit pace with daily problem reps and built-in algebra/trig refreshers — the gaps that actually fail people — synced to the evening exam dates. Chat walks related-rates and optimization setups step by step until starting an unfamiliar problem cold is routine.
FAQ
Is MATH 221 at UW–Madison hard?
It's a classic flagship weed-out: five-credit pace, timed evening exams, curved against an engineering-heavy room. The failure mode is nearly always precalculus gaps plus falling behind — students with solid algebra doing daily problems pass reliably.
How do I pass MATH 221?
Fix algebra and trig in the first two weeks, do problems daily rather than homework-night-only, and practice old exams under time pressure. The pace punishes catching up, so never let yourself fall a unit behind.
Should I take MATH 221 or MATH 211?
MATH 221 is the main calculus sequence for engineering, science, and math-track majors, including trigonometry. MATH 211 is the survey calculus for business and other programs — applied and terminal. Check which one your major actually requires before registering.
Pass MATH 221 with a plan, not a cram
Upload your MATH 221 materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.
Get started freeMore UW–Madison courses
MATH 222 — Calculus and Analytic Geometry 2
MATH 222 continues UW–Madison's main calculus sequence: techniques of integration, applications, sequences and series, Taylor series, and an introduction to vectors and parametric topics. Students widely consider it the harder half of the first-year sequence.
MATH 234 — Calculus—Functions of Several Variables
MATH 234 is UW–Madison's multivariable calculus: vectors, partial derivatives, gradients, multiple integrals, and vector calculus through Green's and Stokes' theorems — the third course of the main calculus sequence, required across engineering and the physical sciences.
MATH 340 — Elementary Matrix and Linear Algebra
MATH 340 is UW–Madison's standard linear algebra course — systems of equations, matrix algebra, determinants, vector spaces, linear independence, eigenvalues, and diagonalization — the computational track taken by most engineering, CS, and science students (MATH 341 is the proof-based alternative).