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

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 vs the other Texas A&M Calculus I courses

Only one of these four can count toward a degree. If your plan changes toward engineering or science, see the MATH 151 guide or the MATH 171 guide.

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

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

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.
• Drill exponential growth. Interest and growth models rely on derivatives of exponentials.
• Keep the formula sheet handy, practice with timed practice exams, and skim 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.