# 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.

Source: https://practicecalculus.com/courses/mcgill-math-140
Updated: 2026-11-03

## 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](/learn/calculus-1)

## Key takeaways

- McGill MATH 140 is a 3-credit Calculus 1 course for students who have taken high school calculus.
- It covers functions, limits, continuity, derivatives of elementary functions, antiderivatives and applications.
- MATH 139 adds precalculus for students without calculus, and MATH 150 is the faster option for strong students.
- MATH 140 is offered in summer, fall and winter, and leads to MATH 141.

**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](/courses/mcgill-math-141).

## MATH 140 topic map

| MATH 140 topic | Practice | Read |
| --- | --- | --- |
| Functions and graphs | [Functions and notation](/learn/calculus-1/functions-warmup/function-notation) | [Polynomial functions](/functions/polynomial-functions), [exponential functions](/functions/exponential-functions) |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits), [limit laws](/rules/limit-laws) |
| Limits at infinity | [Limits at infinity](/learn/calculus-1/limits/limits-at-infinity) | [Limits at infinity](/blog/limits-at-infinity) |
| Continuity | [Continuity](/learn/calculus-1/limits/continuity) | [Continuity](/blog/continuity), [Intermediate Value Theorem](/theorems/intermediate-value-theorem) |
| The derivative | [The limit definition](/learn/calculus-1/the-derivative/limit-definition) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Differentiation of elementary functions | [Exponentials and logarithms](/learn/calculus-1/derivative-rules/exponential-and-log-derivatives) | [Derivatives of trig functions](/blog/derivatives-of-trig-functions), [exponential and log derivatives](/blog/derivatives-of-exponential-and-logarithmic-functions) |
| Product, quotient and chain rules | [Chain rule: any function](/learn/calculus-1/derivative-rules/chain-rule-general) | [Chain rule](/rules/chain-rule), [product and quotient rules](/blog/product-and-quotient-rules) |
| Applications of derivatives | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems), [related rates](/blog/related-rates), [curve sketching](/blog/curve-sketching-with-derivatives) |
| Antidifferentiation | [Undoing derivatives](/learn/calculus-1/integrals/undoing-derivatives) | [Antiderivatives](/blog/antiderivatives), [reverse power rule](/rules/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](/courses/mcgill-math-141), then [MATH 222](/courses/mcgill-math-222), often alongside MATH 133 for linear algebra.

## Example problems at the MATH 140 level

**1. A factor-and-cancel limit.**

$$\lim_{x \to 3} \frac{x^2 - 9}{x - 3} = \lim_{x \to 3} (x + 3) = 6$$

**2. A chain rule derivative.** Differentiate $y = \ln(x^2 + 1)$:

$$\frac{dy}{dx} = \frac{2x}{x^2 + 1}$$

**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

$$f(x) = 2x^3 - 4x + 5$$

## 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](/practice) work better than long weekend sessions.
- **Show your algebra.** Most lost marks come from algebra and sign slips. Our [common calculus mistakes](/blog/common-calculus-mistakes) guide covers the big ones.
- **Keep the formulas in front of you.** The [calculus formula sheet](/formulas) 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](/blog/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.

## Frequently asked questions

### What is McGill MATH 140?

MATH 140 is Calculus 1 in McGill's Department of Mathematics and Statistics. It covers functions and graphs, limits, continuity, derivatives, differentiation of elementary functions, antidifferentiation and applications.

### What comes after MATH 140?

MATH 141, Calculus 2, which covers the definite integral, integration techniques, applications, and an introduction to sequences and series.

### MATH 139 vs MATH 140 vs MATH 150?

MATH 139 includes precalculus and is meant for students with no previous calculus. MATH 140 is the standard entry course for students with high school calculus. MATH 150, Calculus A, is recommended for stronger students aiming at Honours Mathematics; MATH 150 and 151 together cover MATH 140, 141 and 222.

### Is McGill MATH 140 hard?

It assumes you have seen calculus before, so the pace is quick from the start. Students who practice derivatives and limits regularly, rather than only before the midterm and final, usually do well.

### How should I prepare for MATH 140?

Review functions, exponent and logarithm rules, and trigonometry, then refresh limits and derivative rules. The free Calculus 1 path on PracticeCalculus covers these in short lessons.