# Penn State MATH 110 Business Calculus: Study Guide and Practice

> A study guide for Penn State MATH 110 (Techniques of Calculus I): limits, derivatives, marginal analysis, optimization and integrals for business.

Source: https://practicecalculus.com/courses/penn-state-math-110
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 110
- **Credits:** 4
- **Prerequisites:** MATH 22, MATH 40 or MATH 41, or satisfactory placement exam performance
- **Covers:** Limits, derivatives, rates of change, related rates, optimization, graphing, the Fundamental Theorem, antidifferentiation and initial value problems
- **Applications:** Supply and demand, elasticity, logistic growth, marginal analysis, consumer and producer surplus, income streams
- **Next course:** MATH 111 (Techniques of Calculus II, 2 credits)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 110 is Penn State's 4-credit business calculus course, aimed at business, finance and economics students.
- It covers limits, derivatives and their applications, and integral calculus through the Fundamental Theorem.
- Applications are business focused: marginal analysis, elasticity, surplus, and present and future value of income streams.
- Students can earn credit for only one of MATH 110, 140, 140A, 140B and 140H.

**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 topic | Practice | Read |
| --- | --- | --- |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [What is a limit?](/blog/what-is-a-limit) |
| The derivative from a limit | [The limit definition](/learn/calculus-1/the-derivative/limit-definition) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Rates of change | [Average rate of change](/learn/calculus-1/the-derivative/average-rate-of-change) | [Linear functions](/functions/linear-function) |
| Derivative rules | [The power rule](/learn/calculus-1/derivative-rules/power-rule) | [Power rule](/rules/power-rule), [product rule](/rules/product-rule) |
| Exponential growth models | [Chain rule: e and ln](/learn/calculus-1/derivative-rules/chain-rule-exponentials) | [Natural exponential function](/functions/natural-exponential-function) |
| Related rates | [Related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates](/blog/related-rates) |
| Optimization and marginal analysis | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| Graphing | [Critical points](/learn/calculus-1/applications-of-derivatives/critical-points) | [Curve sketching with derivatives](/blog/curve-sketching-with-derivatives) |
| Fundamental Theorem of Calculus | [Evaluating definite integrals](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus) |
| Areas and surplus | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Area between curves](/blog/area-between-curves) |
| Initial value problems | [Undoing derivatives](/learn/calculus-1/integrals/undoing-derivatives) | [Antiderivatives](/blog/antiderivatives) |

## MATH 110 vs MATH 140

| | MATH 110 | MATH 140 |
| --- | --- | --- |
| Title | Techniques of Calculus I | Calculus With Analytic Geometry I |
| Credits | 4 | 4 |
| Audience | Business, finance, economics | Science, engineering and related fields |
| Applications | Marginal analysis, elasticity, surplus, income streams | Related rates, linearization, volumes of revolution |
| Next course | MATH 111 (2 credits) | MATH 141 (4 credits) |

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](/courses/penn-state-math-140).

## 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

$$\text{CS} = \int_0^{20} \big((50 - x) - 30\big)\,dx = \left[20x - \frac{x^2}{2}\right]_0^{20} = 200$$

## 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](/blog/optimization-problems) shows how to check a maximum.
- **Get fluent with $e^x$.** Logistic growth and continuous interest depend on [exponential functions](/functions/exponential-functions).
- **Use the [formula sheet](/formulas)** for derivative rules, take timed [practice exams](/practice), and review [common calculus mistakes](/blog/common-calculus-mistakes).

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

## Frequently asked questions

### What is MATH 110 at Penn State?

MATH 110, Techniques of Calculus I, is Penn State's business calculus course. It covers limits, the derivative and its applications to rates of change, related rates, optimization and graphing, then integral calculus with applications such as consumer and producer surplus and income streams.

### What is the difference between MATH 110 and MATH 140?

MATH 110 is designed for business and economics, with applications like elasticity and marginal analysis. MATH 140 is the STEM Calculus I course with trigonometric functions in every topic. Students can receive credit for only one of them.

### What comes after MATH 110?

MATH 111, Techniques of Calculus II, a 2-credit second course tailored to first-year business students, with applications in economics, business, social science and ecology.

### Is MATH 110 hard?

It is a real calculus course, but the problems are set in familiar business settings. The hardest part for most students is turning a word problem into a function, so practicing setups pays off.

### How do I prepare for MATH 110?

Review algebra, exponent rules and exponential functions, since growth and interest models appear often. Then work through limits and derivative rules.