Recommended First Week of Calculus Topics

Calculus Readiness · Axiom Academy

LESSON Your First Week of Calculus A realistic, day-by-day preview of what a standard Calculus 1 course covers in Week 1 — and why you're walking in already prepared. Here's the whole first week at a glance. Days 1 and 2 are review with fresh notation — material you've already seen. The genuinely new idea, the limit , arrives on Day 3, and Days 4 and 5 build directly on it. Play it through to watch the week assemble. Welcome, Review, and "What Is Calculus?" Most instructors spend Day 1 on syllabus logistics and a high-level motivation for calculus: what questions it answers (rates of change, areas, accumulated quantities) and why earlier math couldn't quite get there. You may also see a quick prerequisite review. Why this matters: the instructor is building shared vocabulary. Absorb the framing — it sets up everything that follows. Your prep: everything in Units 2–4 of this course. You're already caught up. Functions and Graph Fluency (A Fast Tour) Day 2 is usually a blitz through function concepts: definition, domain, range, composition, transformations, piecewise functions, even vs. odd, and so on. The pace is fast because the instructor assumes you've seen this — notation like f(x) , , and f^ -1 (x) shows up without much ceremony. Why this matters: calculus treats functions as the primary objects of study. If function fluency is shaky, you'll feel behind immediately. Your prep: Unit 3 of this course covered exactly this, in more depth than your calculus class will.

This is the written version of the interactive lesson above. See the full Calculus Readiness course.