# UF MAC 2233 Survey of Calculus 1: Study Guide and Practice

> A study guide for UF MAC 2233 Survey of Calculus 1: derivatives and integrals of algebraic and exponential functions, marginal analysis and optimization.

Source: https://practicecalculus.com/courses/university-of-florida-mac-2233
Updated: 2026-11-03

## At a glance

- **Course code:** MAC 2233
- **Credits:** 3
- **Prerequisites:** A minimum score on the online math placement exam, or a C in (or test credit for) MAC 1140 or higher
- **Covers:** A geometric and heuristic approach to calculus: derivatives and integrals of simple algebraic and exponential functions, graphing, marginal analysis, optimization, areas and volumes
- **Next course:** MAC 2234 Survey of Calculus 2
- **Credit note:** If both MAC 2233 and MAC 2311 are taken, credit is given only for MAC 2311
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MAC 2233 Survey of Calculus 1 is a 3-credit applied calculus course at UF that counts toward General Education mathematics.
- It takes a geometric and heuristic approach to derivatives and integrals of simple algebraic and exponential functions.
- Applications include graphing, marginal analysis, optimization, areas and volumes.
- It is followed by MAC 2234, and it does not stack with MAC 2311 for credit.

**UF MAC 2233** (Survey of Calculus 1) is the University of Florida's applied calculus course. It is a 3-credit General Education mathematics course for students who need calculus as a tool, built around graphs, rates of change and business-style applications such as marginal analysis and optimization. This guide maps each MAC 2233 topic to a lesson you can practice with instant feedback.

## What UF MAC 2233 covers

The UF catalog describes MAC 2233 as a geometric and heuristic approach to calculus: differentiation and integration of simple algebraic and exponential functions, with applications to graphing, marginal analysis, optimization, areas and volumes.

So it covers the main ideas of **Calculus 1** (derivatives, their applications and basic integrals) with fewer function types than MAC 2311. Trigonometric functions are not named in the description. On PracticeCalculus the most relevant lessons are in the derivative, derivative rules, applications and integrals units of Calculus 1.

## MAC 2233 topic map

| MAC 2233 topic | Practice | Read |
| --- | --- | --- |
| Linear functions and slope | [Slope and rate of change](/learn/calculus-1/functions-warmup/slope-and-rate-of-change) | [Linear function](/functions/linear-function) |
| Exponential functions | [Exponentials and logarithms](/learn/calculus-1/functions-warmup/exponentials-and-logs) | [Exponential functions](/functions/exponential-functions) |
| Limits (intuitive) | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [What is a limit?](/blog/what-is-a-limit) |
| The derivative as a rate | [Average rate of change](/learn/calculus-1/the-derivative/average-rate-of-change) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Derivatives of algebraic functions | [The power rule](/learn/calculus-1/derivative-rules/power-rule) | [Power rule](/blog/power-rule), [sum and difference rule](/rules/sum-and-difference-rule) |
| Derivatives of exponentials | [Chain rule: e and ln](/learn/calculus-1/derivative-rules/chain-rule-exponentials) | [Natural exponential function](/functions/natural-exponential-function) |
| Graphing | [Increasing and decreasing](/learn/calculus-1/applications-of-derivatives/increasing-and-decreasing) | [Curve sketching](/blog/curve-sketching-with-derivatives) |
| Marginal analysis | [Instantaneous rate of change](/learn/calculus-1/the-derivative/instantaneous-rate-of-change) | [Linear approximation](/blog/linear-approximation) |
| Optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| Integration | [The reverse power rule](/learn/calculus-1/integrals/reverse-power-rule) | [Antiderivatives](/blog/antiderivatives), [reverse power rule](/rules/reverse-power-rule) |
| Areas and volumes | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Area between curves](/blog/area-between-curves), [volumes of revolution](/blog/volumes-of-revolution) |

## MAC 2233 vs MAC 2311

| Question | MAC 2233 Survey of Calculus 1 | [MAC 2311 Calculus 1](/courses/university-of-florida-mac-2311) |
| --- | --- | --- |
| Credits | 3 | 4 |
| Functions studied | Simple algebraic and exponential | Algebraic, exponential, logarithmic and trigonometric |
| Placement | Placement exam, or C in MAC 1140 or higher | Placement exam, or C in MAC 1147 or higher |
| Next course | MAC 2234 Survey of Calculus 2 | [MAC 2312 Calculus 2](/courses/university-of-florida-mac-2312) |

MAC 2234 continues with sequences and Taylor series, matrices and linear systems, partial derivatives, multiple integrals, least squares and Lagrange multipliers. If your major may later require the full sequence, MAC 2311 is the safer start, since credit is given only for MAC 2311 if you take both.

## Example problems at the MAC 2233 level

**1. Maximum profit.** If $P(x) = -2x^2 + 80x - 300$, then $P'(x) = -4x + 80 = 0$ at $x = 20$. Since $P''(x) = -4 < 0$, this is a maximum, and $P(20) = -800 + 1600 - 300 = 500$.

**2. Marginal revenue.** For $R(x) = 50x - 0.5x^2$, the marginal revenue is $R'(x) = 50 - x$. At $x = 10$, $R'(10) = 40$, so the 11th unit adds about 40 dollars in revenue.

**3. Area under an exponential curve.**

$$\int_0^{\ln 3} e^x\,dx = e^{\ln 3} - e^0 = 3 - 1 = 2$$

## How to do well in MAC 2233

- **Think in pictures.** The course is geometric, so connect every derivative to a slope and every integral to an area. The [slope and rate of change](/learn/calculus-1/functions-warmup/slope-and-rate-of-change) lesson is a good anchor.
- **Learn the business vocabulary.** Marginal cost, revenue and profit are derivatives of cost, revenue and profit functions.
- **Practice optimization word problems** until setting up the function feels routine. Our [optimization guide](/blog/optimization-problems) shows the steps.
- **Keep the [formula sheet](/formulas) nearby**, read [common calculus mistakes](/blog/common-calculus-mistakes), and use timed [practice exams](/practice) before tests.

> **Tip:** in optimization, always confirm you found a maximum or minimum with the second derivative or a sign chart. A critical point alone is not an answer.

## Frequently asked questions

### What is MAC 2233 at UF?

MAC 2233 Survey of Calculus 1 is a 3-credit applied calculus course. The UF catalog describes a geometric and heuristic approach to calculus, covering differentiation and integration of simple algebraic and exponential functions with applications to graphing, marginal analysis, optimization, areas and volumes.

### Is MAC 2233 business calculus?

It is UF's survey course in applied calculus, and its applications, such as marginal analysis and optimization, are the ones business and social science students use. Check your major's requirements to see whether it accepts MAC 2233 or requires MAC 2311.

### What is the difference between MAC 2233 and MAC 2311?

MAC 2233 is 3 credits and focuses on simple algebraic and exponential functions with a geometric, applied approach. MAC 2311 is 4 credits, includes trigonometric and logarithmic functions, and starts the full calculus sequence. If you take both, the catalog gives credit only for MAC 2311.

### What comes after MAC 2233?

MAC 2234 Survey of Calculus 2, which requires MAC 2233 with a C. It covers sequences and series, linear systems and matrices, partial derivatives, multiple integrals, least squares and Lagrange multipliers.

### How do I prepare for MAC 2233?

Review linear and quadratic functions, exponent rules and exponential functions, since the course is built on them. Then practice reading slopes and rates of change from graphs.