Boston University MA 123 Calculus 1: Topics and Practice
A study guide for Boston University CAS MA 123 Calculus 1: limits, derivatives, maxima and minima, convexity, the definite integral and the Fundamental Theorem.
Boston University Updated 3 min read
At a glance
- Course code
- CAS MA 123
- Units
- 4
- Offered
- Fall and spring (sections listed for Fall 2026 and Spring 2027)
- Prerequisites
- None listed; students may receive credit for only one of CAS MA 121 or MA 123
- Covers
- Limits, derivatives, differentiation of algebraic and transcendental functions, maxima, minima and convexity, the definite integral and the Fundamental Theorem of integral calculus
- Next course
- CAS MA 124 (Calculus 2)
- Practice here
- Calculus 1
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On this page
Boston University CAS MA 123, Calculus 1, is the first calculus course in BU's College of Arts and Sciences. It covers the essentials of differential calculus and finishes with the definite integral and the Fundamental Theorem. This guide lists what the course covers and links each topic to free practice with instant feedback.
What MA 123 covers
The BU course page lists: limits; derivatives; differentiation of algebraic and transcendental functions; applications to maxima, minima and convexity of functions; the definite integral; and the fundamental theorem of integral calculus. The course carries 4 units, counts for MCS divisional credit in CAS, and fulfills one BU Hub unit each in Quantitative Reasoning II and Critical Thinking.
Students may receive credit for only one of CAS MA 121 or MA 123. The page lists sections for both Fall 2026 and Spring 2027. The Fall 2026 notes ask students to reserve Thursday evenings, 6:30 to 8:30 pm, for exams throughout the term and to register for a discussion section.
MA 123 topic map
| MA 123 topic | Practice | Read |
|---|---|---|
| Limits | What is a limit? | How to evaluate limits |
| Limit techniques | Factoring zero over zero | Limit laws |
| Derivatives | The limit definition | Limit definition of the derivative |
| Algebraic functions | Power rule | Power rule guide |
| Product, quotient and chain rules | Quotient rule | Product and quotient rules, chain rule |
| Transcendental functions | Exponential and log derivatives | Derivative of ln x, derivative of sin x |
| Maxima and minima | Absolute extrema | Extreme Value Theorem |
| Convexity | Second derivative | Curve sketching with derivatives |
| Optimization | Optimization | Optimization problems |
| The definite integral | Riemann sums | Riemann sums guide |
| Fundamental Theorem | Fundamental Theorem, part 2 | Fundamental Theorem of Calculus |
What "convexity" means here
"Convexity" on the BU course page is what many textbooks call concavity. A function is convex (concave up) where its second derivative is positive and concave (concave down) where it is negative. Exams usually combine this with first-derivative information to sketch graphs and classify extrema, so practice the second derivative lesson alongside critical points.
How MA 123 compares to other Calculus 1 courses
MA 123 is a standard Calculus 1 course. Like most, it moves from limits to derivatives to their applications, then closes with the definite integral and the Fundamental Theorem. The BU description does not list related rates, linear approximation or u-substitution by name, so check your syllabus for those. Two phrases are worth noticing: "transcendental functions" means you need exponential, logarithmic and trig derivatives early, and "convexity" tells you that second-derivative reasoning is a named goal of the course, not an afterthought.
Example problems at the MA 123 level
1. A transcendental derivative. \frac{d}{dx}\left(e^x \sin x\right) = e^x \sin x + e^x \cos x.
2. Convexity. For f(x) = x^3 - 3x, f''(x) = 6x, so f is concave down for x < 0 and concave up for x > 0, with an inflection point at 0.
3. The Fundamental Theorem.
How to do well in MA 123
- Protect your exam evenings. With evening exams through the term, plan your study around them, finishing review the day before.
- Practice derivatives every day. Short daily sets with the derivative rules practice build exam speed.
- Use your discussion section. Bring the problems you got wrong, not the ones you got right.
- Watch for algebra errors. Our list of common calculus mistakes shows where points usually go.
Next, see the MA 124 guide for Calculus 2.
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What is a limit?
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