McGill MATH 140 Calculus 1: Topics, Study Guide and Practice
A study guide for McGill MATH 140 (Calculus 1): limits, derivatives, antiderivatives and applications, compared with MATH 139 and 150, with practice.
McGill University Updated 3 min read
At a glance
- Course code
- MATH 140
- Credits
- 3 (3 lecture hours and 1 tutorial hour per week)
- Offered
- Summer 2026, Fall 2026 and Winter 2027
- Prerequisites
- High school calculus
- Restrictions
- Not open to students who have taken MATH 139, MATH 150, CEGEP objective 00UN or equivalent, or (except by permission) MATH 122
- Covers
- Functions and graphs, limits, continuity, derivatives, differentiation of elementary functions, antidifferentiation and applications
- Next course
- MATH 141 (Calculus 2)
- Practice here
- Calculus 1
On this page
MATH 140 is Calculus 1 at McGill University and the standard first calculus course for students who took calculus in high school. It covers differential calculus and finishes with antiderivatives, setting up integration for the next course. This guide maps each MATH 140 topic to free practice so you can learn every idea by solving problems with instant feedback.
What McGill MATH 140 covers
McGill's Department of Mathematics and Statistics lists the topics as functions and graphs, limits, continuity, derivatives, differentiation of elementary functions, antidifferentiation and applications. It is worth 3 credits, with three hours of lectures and one hour of tutorial a week, and it runs in summer, fall and winter.
That is a standard Calculus 1 course up to antiderivatives. The definite integral and the Fundamental Theorem of Calculus come next, in MATH 141.
MATH 140 topic map
| MATH 140 topic | Practice | Read |
|---|---|---|
| Functions and graphs | Functions and notation | Polynomial functions, exponential functions |
| Limits | What is a limit? | How to evaluate limits, limit laws |
| Limits at infinity | Limits at infinity | Limits at infinity |
| Continuity | Continuity | Continuity, Intermediate Value Theorem |
| The derivative | The limit definition | Limit definition of the derivative |
| Differentiation of elementary functions | Exponentials and logarithms | Derivatives of trig functions, exponential and log derivatives |
| Product, quotient and chain rules | Chain rule: any function | Chain rule, product and quotient rules |
| Applications of derivatives | Optimization | Optimization problems, related rates, curve sketching |
| Antidifferentiation | Undoing derivatives | Antiderivatives, reverse power rule |
MATH 139 vs MATH 140 vs MATH 150
| Course | Title | Credits | Who it is for |
|---|---|---|---|
| MATH 139 | Calculus 1 with Precalculus | 4 | Students with no previous calculus (not offered this catalogue year) |
| MATH 140 | Calculus 1 | 3 | Students with high school calculus |
| MATH 150 | Calculus A | 4 | Stronger students aiming at Honours Mathematics (not offered this catalogue year) |
The department notes that MATH 150 and 151 together cover the material of MATH 139 or 140, 141 and 222. Most students take MATH 140, then MATH 141, then MATH 222, often alongside MATH 133 for linear algebra.
Example problems at the MATH 140 level
1. A factor-and-cancel limit.
2. A chain rule derivative. Differentiate y = \ln(x^2 + 1):
3. An antiderivative with a condition. Find f if f'(x) = 6x^2 - 4 and f(1) = 3. Then f(x) = 2x^3 - 4x + C, and f(1) = 2 - 4 + C = 3 gives C = 5, so
How to do well in McGill MATH 140
- Practice a little every day. Derivative rules only become automatic with repetition; short daily sets in practice work better than long weekend sessions.
- Show your algebra. Most lost marks come from algebra and sign slips. Our common calculus mistakes guide covers the big ones.
- Keep the formulas in front of you. The calculus formula sheet puts every derivative and basic antiderivative on one page.
- Prepare early for the final. Follow the plan in how to prepare for a calculus exam and test yourself under time pressure.
Tip: check every antiderivative by differentiating it. If you get back the original function, your answer is right.
Practice it now
What is a limit?
Solve real problems on this topic with instant feedback, hints and a step-by-step walkthrough for every answer. Free, no sign-up needed to start.
Practice this lesson