Penn State MATH 110 Business Calculus: Study Guide and Practice

Penn State MATH 110, Techniques of Calculus I, is the business calculus course at Penn State. It is a 4-credit course aimed at students in business, finance and economics who need calculus as a tool for analyzing change. This guide maps each MATH 110 topic to practice with instant feedback, so you can learn by doing.

What Penn State MATH 110 covers

According to the bulletin, MATH 110 starts with limits, including their geometric and analytic meaning and their role in defining the derivative. Differential calculus follows, with rates of change, related rates, optimization and graphing. The applications are mainly economic: supply and demand models, elasticity, logistic growth, and marginal analysis of cost, revenue and profit.

The integral half begins with the Fundamental Theorem of Calculus. Antidifferentiation is then used to find areas, consumer and producer surplus, present and future values of income streams, annuities and perpetuities, and to solve initial value problems in business settings.

This covers the core of a Calculus 1 course, plus finance applications that most STEM calculus courses never mention.

MATH 110 topic map

MATH 110 vs MATH 140

Only one of MATH 110, 140, 140A, 140B and 140H earns credit. If you may switch into a STEM major, see the MATH 140 guide.

Example problems at the MATH 110 level

1. Marginal revenue. If R(x) = 40x - 0.5x^2, then R'(x) = 40 - x. At x = 10, marginal revenue is 30 dollars per unit.

2. Price elasticity. For demand q = 100 - 2p, elasticity is E = \frac{p}{q}\cdot\left|\frac{dq}{dp}\right| = \frac{2p}{100 - 2p}. At p = 20, E = \frac{40}{60} = \frac{2}{3} < 1, so demand is inelastic and raising the price slightly increases revenue.

3. Consumer surplus. With demand p = 50 - x and market price p = 30, the quantity is x = 20 and

How to do well in Penn State MATH 110

• Write the function before differentiating. In business problems the setup is most of the work. Name your variable and units first.
• Know what each derivative means. Marginal cost, marginal revenue and elasticity are derivatives with an economic reading. The optimization guide shows how to check a maximum.
• Get fluent with e^x. Logistic growth and continuous interest depend on exponential functions.
• Use the formula sheet for derivative rules, take timed practice exams, and review common calculus mistakes.

Tip: consumer surplus is the area between the demand curve and the price line. Sketching it makes the integral bounds obvious.