# Texas A&M MATH 142 Business Calculus: Study Guide and Practice

> A study guide for Texas A&M MATH 142 (Business Calculus): limits, derivatives, optimization and integrals with business applications, plus free practice.

Source: https://practicecalculus.com/courses/texas-am-math-142
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 142 (Texas common course number MATH 1325)
- **Credits:** 3 (3 lecture hours)
- **Prerequisites:** C or better in MATH 140 or MATH 150, or equivalent, or an acceptable placement score; not open to seniors
- **Covers:** Limits and continuity, derivative techniques and applications including curve sketching and optimization, integrals and their applications
- **Focus:** Applications in business, economics and the social sciences
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 142 is a 3-credit business calculus course at Texas A&M, applied to business, economics and the social sciences.
- It covers limits and continuity, derivatives with curve sketching and optimization, and integrals with applications.
- It needs a C or better in MATH 140 or MATH 150, or a qualifying placement score.
- Only one of MATH 142, 147, 151 or 171 can count toward a degree.

**Texas A&M MATH 142**, Business Calculus, is the calculus course designed for business, economics and social science students. It teaches the core ideas of Calculus 1, limits, derivatives and integrals, through problems about cost, revenue, profit and growth. This guide lists every MATH 142 topic and links each to practice with instant feedback.

## What Texas A&M MATH 142 covers

The catalog describes MATH 142 as limits and continuity, then techniques and applications of derivatives, with curve sketching and optimization named specifically, followed by techniques and applications of integrals. The emphasis throughout is on business, economics and the social sciences.

Compared with a standard **Calculus 1** course, MATH 142 keeps the main ideas but sets them in applied contexts. The applications are economic: marginal cost is a derivative, maximizing profit is optimization, and total change from a rate is an integral.

## MATH 142 topic map

| MATH 142 topic | Practice | Read |
| --- | --- | --- |
| Functions and rates of change | [Slope and rate of change](/learn/calculus-1/functions-warmup/slope-and-rate-of-change) | [Linear functions](/functions/linear-function) |
| Exponentials and logarithms | [Exponentials and logarithms](/learn/calculus-1/functions-warmup/exponentials-and-logs) | [Exponential functions](/functions/exponential-functions), [natural logarithm](/functions/natural-logarithm) |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits) |
| Continuity | [Continuity](/learn/calculus-1/limits/continuity) | [Continuity](/blog/continuity) |
| Derivative techniques | [The power rule](/learn/calculus-1/derivative-rules/power-rule) | [Power rule](/blog/power-rule), [product and quotient rules](/blog/product-and-quotient-rules) |
| Exponential derivatives | [Chain rule: e and ln](/learn/calculus-1/derivative-rules/chain-rule-exponentials) | [Derivatives of exponential and log functions](/blog/derivatives-of-exponential-and-logarithmic-functions) |
| Curve sketching | [Concavity and the second derivative](/learn/calculus-1/applications-of-derivatives/second-derivative) | [Curve sketching with derivatives](/blog/curve-sketching-with-derivatives) |
| Optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| Integration techniques | [The reverse power rule](/learn/calculus-1/integrals/reverse-power-rule) | [Antiderivatives](/blog/antiderivatives), [u-substitution](/blog/u-substitution) |
| Applications of integrals | [Net change and displacement](/learn/calculus-1/applications-of-integrals/net-change) | [Area between curves](/blog/area-between-curves) |

## MATH 142 vs the other Texas A&M Calculus I courses

| Course | Title | Credits | Who takes it |
| --- | --- | --- | --- |
| MATH 142 | Business Calculus | 3 | Business, economics and social science majors |
| MATH 147 | Calculus I for Biological Sciences | 4 | Life science majors |
| MATH 151 | Engineering Mathematics I | 4 | Engineering and physical science majors |
| MATH 171 | Calculus I | 4 | Students wanting a more demanding course |

Only one of these four can count toward a degree. If your plan changes toward engineering or science, see the [MATH 151 guide](/courses/texas-am-math-151) or the [MATH 171 guide](/courses/texas-am-math-171).

## Example problems at the MATH 142 level

**1. Marginal cost.** If $C(x) = 500 + 20x - 0.01x^2$ dollars for $x$ units, the marginal cost is $C'(x) = 20 - 0.02x$. At $x = 100$ units, $C'(100) = 18$, so the next unit costs about 18 dollars.

**2. Maximizing profit.** Profit is $P(x) = -2x^2 + 120x - 1000$. Set $P'(x) = -4x + 120 = 0$, so $x = 30$. Since $P''(x) = -4 < 0$, this is a maximum, with

$$P(30) = -1800 + 3600 - 1000 = 800$$

**3. Total change from a rate.** Revenue grows at $R'(t) = 6t$ thousand dollars per month. The increase from month 0 to month 4 is

$$\int_0^4 6t\,dt = \left[3t^2\right]_0^4 = 48 \text{ thousand dollars}$$

## How to do well in MATH 142

- **Translate before you calculate.** Write the profit, cost or revenue function first. Most mistakes in business calculus happen in the setup.
- **Always check that a critical point is a maximum.** Use the second derivative or compare endpoint values, as in the [critical points lesson](/learn/calculus-1/applications-of-derivatives/critical-points).
- **Drill exponential growth.** Interest and growth models rely on [derivatives of exponentials](/blog/derivatives-of-exponential-and-logarithmic-functions).
- **Keep the [formula sheet](/formulas) handy**, practice with timed [practice exams](/practice), and skim [common calculus mistakes](/blog/common-calculus-mistakes) before each test.

> **Tip:** units are your friend. A derivative of cost in dollars with respect to units is in dollars per unit, which tells you what the answer means.

## Frequently asked questions

### What is MATH 142 at Texas A&M?

MATH 142, Business Calculus, is a one-semester calculus course for business, economics and social science students. It covers limits, continuity, derivatives with curve sketching and optimization, and integrals, all with an applied focus.

### What do I need before MATH 142?

A C or better in MATH 140 or MATH 150, an equivalent course, or an acceptable score on the Texas A&M math placement exam. The course is not open to seniors.

### Is MATH 142 easier than MATH 151?

MATH 142 has fewer credits and skips the vectors and analytic geometry in MATH 151, with problems set in business contexts. It still requires solid algebra, and only one of the two can count toward a degree, so check your degree plan.

### How do I study for MATH 142?

Focus on derivative rules and on translating word problems, such as profit or cost, into functions. Then practice optimization until finding and checking critical points feels routine.