# Ohio State MATH 1131 Calculus for Business: Study Guide, Practice

> A study guide for Ohio State MATH 1131 (Calculus for Business): derivatives, optimization, integrals, surplus and partial derivatives, with free practice.

Source: https://practicecalculus.com/courses/ohio-state-math-1131
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 1131
- **Credit hours:** 5
- **Offered:** Autumn and spring
- **Prerequisites:** C- or above in MATH 1130, 1144, 1148 or 1150, or credit for 130, 148 or 150, or Math Placement Level L
- **Covers:** A survey of calculus of one and several variables with business applications: derivatives, extrema, integrals, surplus, differential equations, partial derivatives
- **Restrictions:** Not open to students with credit for MATH 1151 (151) or above, or 1134 (132)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 1131 is Ohio State's 5-credit Calculus for Business course, offered in autumn and spring.
- It surveys calculus of one and several variables with business applications.
- The department's topic list runs from limits to integration, consumer and producer surplus, differential equations and partial derivatives.
- It is not open to students who already have credit for MATH 1151 or above.

**Ohio State MATH 1131**, Calculus for Business, is Ohio State's calculus course with applications to business. It is a 5-credit course offered in autumn and spring, and it surveys calculus of one and several variables with applications to business. This guide maps each MATH 1131 topic to practice with instant feedback.

## What Ohio State MATH 1131 covers

The catalog description is a single line: a survey of calculus of one and several variables, applied to business. The department's course description document lists the topics in order.

The first part covers limits and continuity, the derivative and its rules, rates of change, the product, quotient and chain rules, and derivatives of exponential and logarithmic functions. Then come implicit and logarithmic differentiation, higher-order derivatives, differentials, local and absolute extrema, concavity, the second-derivative test, asymptotes, graphing and applied max/min problems.

The integral part covers indefinite integrals, initial conditions, approximating area, the definite integral, the Fundamental Theorem, substitution, area between curves, and consumers' and producers' surplus. It ends with differential equations and partial derivatives, including applications and higher-order partials.

So MATH 1131 covers the core of **Calculus 1** plus a short taste of **Calculus 3** (partial derivatives).

## MATH 1131 topic map

| MATH 1131 topic | Practice | Read |
| --- | --- | --- |
| Limits and continuity | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits), [continuity](/blog/continuity) |
| The derivative and rates of change | [Instantaneous rate of change](/learn/calculus-1/the-derivative/instantaneous-rate-of-change) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Rules of differentiation | [Sums and constants](/learn/calculus-1/derivative-rules/sum-and-constant-rules) | [Power rule](/blog/power-rule), [product and quotient rules](/blog/product-and-quotient-rules) |
| Chain rule | [Chain rule: powers](/learn/calculus-1/derivative-rules/chain-rule-powers) | [Chain rule](/rules/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) |
| Implicit and logarithmic differentiation | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation) | [Logarithmic differentiation](/rules/logarithmic-differentiation) |
| Differentials | [Tangent lines at work](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Linear approximation](/blog/linear-approximation) |
| Extrema, concavity and graphing | [Absolute extrema on an interval](/learn/calculus-1/applications-of-derivatives/absolute-extrema) | [Curve sketching](/blog/curve-sketching-with-derivatives) |
| Applied max/min | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| Indefinite integrals and initial conditions | [Undoing derivatives](/learn/calculus-1/integrals/undoing-derivatives) | [Antiderivatives](/blog/antiderivatives) |
| Definite integrals and the FTC | [Evaluating definite integrals](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus) |
| Substitution | [U-substitution](/learn/calculus-1/integrals/u-substitution) | [U-substitution](/blog/u-substitution) |
| Area and surplus | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Area between curves](/blog/area-between-curves) |
| Differential equations | [Separable differential equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | [Antiderivatives](/blog/antiderivatives) |
| Partial derivatives | [Partial derivatives](/learn/calculus-3/partial-derivatives/partial-derivatives) | [Partial derivatives](/blog/partial-derivatives) |

## MATH 1131 vs MATH 1151

| | MATH 1131 | MATH 1151 |
| --- | --- | --- |
| Title | Calculus for Business | Calculus I |
| Credit hours | 5 | 5 |
| Offered | Autumn, spring | Autumn, spring, summer |
| Several variables | Yes, partial derivatives | No |
| Next calculus course | None in the main sequence | MATH 1152 or MATH 1172 |

MATH 1131 is not open to students with credit for MATH 1151 or above. If you may switch to a science or engineering major, see the [MATH 1151 guide](/courses/ohio-state-math-1151).

## Example problems at the MATH 1131 level

**1. Continuous growth.** If $A(t) = 1000e^{0.05t}$ dollars, then $A'(t) = 50e^{0.05t}$. At $t = 0$ the balance grows at 50 dollars per year.

**2. Minimizing average cost.** With $C(x) = 2x^2 + 50$, the average cost is $\bar{C}(x) = 2x + \frac{50}{x}$. Then $\bar{C}'(x) = 2 - \frac{50}{x^2} = 0$ gives $x = 5$, and $\bar{C}''(x) = \frac{100}{x^3} > 0$, so $x = 5$ is a minimum with $\bar{C}(5) = 20$.

**3. Partial derivatives of a production function.** For $P(L, K) = 10L^{0.5}K^{0.5}$,

$$P_L = 5L^{-0.5}K^{0.5}, \qquad P_K = 5L^{0.5}K^{-0.5}$$

At $L = 4$, $K = 9$: $P_L = 5 \cdot \frac{3}{2} = 7.5$, the marginal product of labor.

## How to do well in Ohio State MATH 1131

- **Master exponential and log derivatives.** Growth, interest and logarithmic differentiation all depend on them. Start with [exponential functions](/functions/exponential-functions).
- **Always confirm a max or min.** Use the second-derivative test or check endpoints, as in the [critical points lesson](/learn/calculus-1/applications-of-derivatives/critical-points).
- **Do not leave partial derivatives for last.** They come at the end of the term, right before the final. The idea is simple: treat the other variable as a constant.
- **Use the sample exams** on the course page, timed [practice exams](/practice), and the [formula sheet](/formulas). Review [common calculus mistakes](/blog/common-calculus-mistakes) before each test.

> **Tip:** consumers' surplus is the area between the demand curve and the price line, from zero to the market quantity. Draw it before you integrate.

## Frequently asked questions

### What is MATH 1131 at Ohio State?

MATH 1131, Calculus for Business, is a one-semester survey of calculus of one and several variables applied to business. It covers limits, derivatives, extrema and graphing, integrals and substitution, consumer and producer surplus, differential equations and partial derivatives.

### What are the prerequisites for MATH 1131?

A C- or above in MATH 1130, 1144, 1148 or 1150, credit for 130, 148 or 150, or Math Placement Level L.

### What is the difference between MATH 1131 and MATH 1151?

MATH 1151 is the Calculus I course for science, engineering and math majors and leads to Calculus II. MATH 1131 is a self-contained business course that adds partial derivatives of several variables. It is not open to students with credit for MATH 1151 or above.

### Is MATH 1131 hard?

It covers a lot in one semester, including a short unit on functions of several variables. Students who keep their algebra sharp and practice derivatives regularly usually do well.

### How should I study for MATH 1131?

Focus on derivative rules, especially for exponential and log functions, then practice setting up optimization word problems. The sample exams on the course page are a good final check.