How to use this guide
Where this guide comes from. It follows the course's published description (a first course on calculus with one variable: working with limits, differentiating and integrating polynomial, exponential, log and trig functions, then using derivatives to analyse and optimize, followed by the Fundamental Theorem, improper integrals and uses of the integral) and the standard topics for a first calculus course. Instructors' emphasis and notation vary: check your own course outline.
The order. 01 reviews the precalculus you need. 02 covers limits and continuity. 03 and 04 build the derivative: the definition and the rules, then exponentials, logarithms, trig, the chain rule and implicit differentiation. 05 and 06 use derivatives: tangent lines, approximation, related rates, marginal analysis, curve sketching and optimization. 07 to 09 turn to integrals: antiderivatives and Riemann sums, the fundamental theorem with substitution (and a taste of integration by parts), then improper integrals and applications. Sections differ on how much of each topic they teach: check your outline.
Business flavour, general maths. Many examples use costs, revenue and profit because that is where a business student meets calculus. The methods are completely general: nothing here depends on the context.
Inside a topic: read the idea, look at the formula boxes, then open each worked example and follow every step. Close it and redo it on paper. Then change the numbers in the lab until the answer stops surprising you, and finish with the traps.
Notation used here: f′(x) or dy/dx for the derivative, f″(x) for the second derivative, ∫ for the integral, Δx for a step, lim for a limit, ln for the natural logarithm, e ≈ 2.71828. Trig functions use radians. Powers are written x², roots as √x, and fractions in a line as a ÷ b, with brackets where the order matters.
Then practise. The Drill, the multiple-choice bank and the flashcards are all levelled:
| Level | What it asks | Example |
|---|---|---|
| Beginner | A definition, or one step: apply one rule once | Differentiate 5x4, or add up a simple left sum |
| Intermediate | A standard problem in a few steps | Use the quotient rule at a point, or a definite integral of a polynomial |
| Exam level | A full exam-style question that strings several steps together | Maximize a profit, or find a related rate |
| Hard | Twists: choosing the method, combining rules, and the traps that cost the most marks | An improper integral, or the absolute maximum on an interval |
The question generator starts on Auto: it begins at Beginner and moves up a level after three correct answers in a row. You can pick a level yourself at any time. The multiple-choice bank and flashcards are ordered from easy to hard, so working through them in order builds each idea from the ground up.
Answers are accepted within the stated rounding. Keep full precision in your calculator until the last step. Check which calculator rules your course allows.
Exam format, weight and allowed aids differ between sections and terms. Check your own course outline.
Sign in to open the full guide
This is the first section. The full guide has every topic, the labs and the practice questions.
Create an account · Forgot password, or no password yet? Got a code link from your class? Open it and it will ask you to sign in.