# ASU MAT 210 Brief Calculus: Topics, Study Guide and Practice

> A study guide for ASU MAT 210 Brief Calculus: derivatives and integrals of elementary functions with applications, and practice for every topic.

Source: https://practicecalculus.com/courses/arizona-state-mat-210
Updated: 2026-11-03

## At a glance

- **Course code:** MAT 210
- **Credit hours:** 3
- **General studies:** Mathematical Studies (MATH / MA)
- **Covers:** Differential and integral calculus of elementary functions, with applications
- **Offered by:** School of Mathematical and Statistical Sciences
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MAT 210 Brief Calculus is a 3-credit-hour applied calculus course at ASU that counts toward Mathematical Studies.
- The catalog describes it as differential and integral calculus of elementary functions, with applications.
- It covers the core ideas of Calculus 1 in one semester, with an emphasis on using them.
- Students who need a full calculus sequence take MAT 265 or MAT 270 instead.

**ASU MAT 210**, Brief Calculus, is Arizona State University's one-semester applied calculus course. It is a 3-credit-hour Mathematical Studies course for students who need calculus as a working tool rather than as the start of a long sequence. This guide maps every MAT 210 topic to a lesson you can practice with instant feedback.

## What ASU MAT 210 covers

The ASU catalog describes MAT 210 as differential and integral calculus of elementary functions, with applications.

In practice that covers the main ideas of **Calculus 1**: rates of change, derivative rules for polynomial, exponential and logarithmic functions, using derivatives to graph and optimize, and the definite integral as accumulated change and area. Applied courses like this usually spend less time on limit theory and trigonometry and more on interpreting results. On PracticeCalculus the most relevant lessons are in the derivative, derivative rules, applications and integrals units of Calculus 1.

## MAT 210 topic map

| MAT 210 topic | Practice | Read |
| --- | --- | --- |
| Functions review | [Functions and notation](/learn/calculus-1/functions-warmup/function-notation) | [Linear function](/functions/linear-function), [quadratic function](/functions/quadratic-function) |
| Exponential and log functions | [Exponentials and logarithms](/learn/calculus-1/functions-warmup/exponentials-and-logs) | [Exponential functions](/functions/exponential-functions), [natural logarithm](/functions/natural-logarithm) |
| Rates of change | [Average rate of change](/learn/calculus-1/the-derivative/average-rate-of-change) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| The derivative | [Notation and meaning](/learn/calculus-1/the-derivative/derivative-notation-and-meaning) | [Power rule](/blog/power-rule) |
| Derivative rules | [The power rule](/learn/calculus-1/derivative-rules/power-rule) | [Sum and difference rule](/rules/sum-and-difference-rule), [constant multiple rule](/rules/constant-multiple-rule) |
| Product, quotient and chain rules | [Product rule](/learn/calculus-1/derivative-rules/product-rule) | [Product and quotient rules](/blog/product-and-quotient-rules), [chain rule](/blog/chain-rule) |
| Exponential and log derivatives | [Exponentials and logarithms](/learn/calculus-1/derivative-rules/exponential-and-log-derivatives) | [Derivatives of exponential and log functions](/blog/derivatives-of-exponential-and-logarithmic-functions) |
| Graphing with derivatives | [Critical points](/learn/calculus-1/applications-of-derivatives/critical-points) | [Curve sketching](/blog/curve-sketching-with-derivatives) |
| Optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| Antiderivatives | [The reverse power rule](/learn/calculus-1/integrals/reverse-power-rule) | [Antiderivatives](/blog/antiderivatives) |
| Definite integrals and net change | [Net change and displacement](/learn/calculus-1/applications-of-integrals/net-change) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus) |

## MAT 210 vs the ASU calculus sequences

| Course | Credit hours | Catalog topics |
| --- | --- | --- |
| MAT 210 Brief Calculus | 3 | Differential and integral calculus of elementary functions, with applications |
| [MAT 265 Calculus for Engineers I](/courses/arizona-state-mat-265) | 3 | Limits, continuity, differential calculus, intro to integration |
| MAT 270 Calculus with Analytic Geometry I | 4 | Real numbers, limits, continuity, differential and integral calculus |

MAT 210 is a stand-alone applied course. If your major might later require Calculus 2 or multivariable calculus, start with MAT 265 or MAT 270, which lead to [MAT 266](/courses/arizona-state-mat-266) and beyond.

## Example problems at the MAT 210 level

**1. A power rule derivative.**

$$\frac{d}{dx}\left(5x^3 - 4x + 7\right) = 15x^2 - 4$$

**2. Maximum revenue.** If $R(x) = 120x - 2x^2$, then $R'(x) = 120 - 4x = 0$ at $x = 30$. Since $R''(x) = -4 < 0$, this is a maximum, and $R(30) = 3600 - 1800 = 1800$.

**3. A definite integral.**

$$\int_0^2 (3x^2 + 4)\,dx = \left[x^3 + 4x\right]_0^2 = 8 + 8 = 16$$

## How to do well in MAT 210

- **Connect every derivative to a rate.** Ask what the units are: dollars per item, people per year. The [notation and meaning](/learn/calculus-1/the-derivative/derivative-notation-and-meaning) lesson builds this habit.
- **Learn the rules in order.** Start with the [power rule](/rules/power-rule) and [sum and difference rule](/rules/sum-and-difference-rule), then add the product and chain rules.
- **Set up optimization problems the same way every time:** write the quantity as a function of one variable, differentiate, set it to zero and check that you found a maximum or minimum.
- **Keep the [formula sheet](/formulas) close**, review [common calculus mistakes](/blog/common-calculus-mistakes), and practice with timed [practice exams](/practice).

> **Tip:** a definite integral of a rate gives the total change. If $r(t)$ is a rate in units per hour, $\int_a^b r(t)\,dt$ is the total number of units added between hours $a$ and $b$.

## Frequently asked questions

### What is ASU MAT 210?

MAT 210 Brief Calculus is a 3-credit-hour course from ASU's School of Mathematical and Statistical Sciences. The catalog describes it as differential and integral calculus of elementary functions, with applications.

### Is MAT 210 business calculus?

It is ASU's brief, applied calculus course, the kind of course business and social science programs often require. Applications such as marginal cost and revenue and optimization are typical. Check your degree map to confirm which calculus course your major accepts.

### What is the difference between MAT 210 and MAT 265?

MAT 210 is a single applied course in derivatives and integrals of elementary functions. MAT 265 Calculus for Engineers I starts the three-course engineering sequence, covering limits and continuity, differential calculus and an introduction to integration, and leads to MAT 266 and MAT 267.

### Is MAT 210 hard?

It is usually considered the most approachable calculus course, but it still moves quickly through derivatives and integrals. Comfort with algebra, exponents and functions is the biggest factor in how smooth it feels.

### How do I prepare for MAT 210?

Review linear, quadratic, exponential and logarithmic functions and practice reading slopes from graphs. The functions warm-up on PracticeCalculus covers these quickly.