CMU 21-120: Differential and Integral Calculus
21-120 is CMU's first calculus course — limits, derivatives, applications of differentiation, and the integral through the fundamental theorem — the standard entry point for students not placing into 21-122 via AP credit. It feeds every quantitative major on campus.
Fennie is independent and not affiliated with Carnegie Mellon University. This is an unofficial study guide.
Build my 21-120 study planWhat makes it hard
It's a known quantity taught at CMU pace: the calculus is standard, but exams are time-pressured and most lost points are algebra and trig errors inside correct setups. Students whose high-school calculus was calculator-leaning or memorization-based find the bar for symbolic fluency higher than expected.
What you'll cover
- • Limits and continuity
- • Derivatives and differentiation rules
- • Related rates and optimization
- • Curve sketching
- • The definite integral
- • The fundamental theorem of calculus
The 21-120 study guide
How to study for CMU 21-120, step by step.
- 1
Audit your algebra and trig in week one
Most exam losses in 21-120 are precalculus errors inside correct calculus. Find and fix the gaps immediately — the derivative units assume them gone.
- 2
Work problems daily without a calculator crutch
CMU exams test symbolic fluency, and high-school habits of calculator-first work don't transfer. Daily by-hand problem sets build the speed the exams assume.
- 3
Drill the setup-heavy applications
Related rates and optimization fail at the translation from scenario to equation. Practice the setup from scratch until starting cold feels routine — the derivative itself is the easy part.
- 4
Understand the fundamental theorem conceptually
Questions probing what integration means and how it connects to differentiation are reliable exam material. Practice explaining the theorem in plain words alongside using it.
- 5
Rehearse under exam time pressure
Timed mixed problem sets without notes before each exam. Homework comfort with unlimited time is a misleading readiness signal for time-pressured tests.
- 6
Keep the dailiness honest with Fennie
Upload your 21-120 syllabus and Fennie's Daily Plan schedules daily problems with algebra and trig refreshers built in, paced to the exam dates, with quizzes from the actual course material. Free to start.
Start my 21-120 plan free
How Fennie helps with 21-120
Fennie's Daily Plans keep 21-120 practice daily and exam-synced, with the algebra and trig rehab that actually decides grades built into the schedule. Chat works setup-heavy problems — related rates, optimization — from scenario to equation step by step until cold starts are routine.
FAQ
Is 21-120 hard?
It's standard Calculus I at CMU pace: the concepts are familiar, but time-pressured exams expose algebra gaps and calculator dependence fast. Students who work daily by-hand problems find it very manageable; coasting on high-school memories is the standard mistake.
Should I take 21-120 or skip to 21-122 with AP credit?
Strong AP Calculus credit typically places you into 21-122. Be honest about your integration and symbolic fluency though — 122 assumes 120 cold, and a shaky foundation there costs more than a semester of review would have.
How many units is 21-120?
10 units — roughly ten hours of total weekly work in CMU's unit system. Budget real problem-set time within that: the exams reward by-hand fluency that lecture attendance alone doesn't build.
Pass 21-120 with a plan, not a cram
Upload your 21-120 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 CMU courses
21-122 — Integration and Approximation
21-122 is CMU's second calculus course — integration techniques, applications, improper integrals, then sequences, series, and Taylor approximation — where most AP-credit students enter the math sequence. It's widely considered the harder half of first-year calculus.
21-127 — Concepts of Mathematics
21-127 is CMU's introduction to mathematical proof — logic, sets, functions, induction, number theory, and combinatorics — required early for CS and math majors as the gateway to everything proof-based, including 15-251. For most students it's the first course where the answer is an argument.
21-241 — Matrices and Linear Transformations
21-241 is CMU's first linear algebra course — systems and matrices, vector spaces, linear transformations, determinants, eigenvalues, and orthogonality — serving CS, science, and engineering students. It blends computation with proof more than most schools' equivalents.
21-259 — Calculus in Three Dimensions
21-259 is CMU's multivariable calculus course — vectors and surfaces, partial derivatives, multiple integrals, and the vector calculus capstone of line integrals, Green's, Stokes', and the divergence theorem — required across engineering and the sciences.