# Ohio State MATH 1151 Calculus I: Topics, Study Guide, Practice

> A study guide for Ohio State MATH 1151 (Calculus I): limits, derivatives, related rates, optimization, integrals and substitution, with free practice.

Source: https://practicecalculus.com/courses/ohio-state-math-1151
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 1151
- **Credit hours:** 5
- **Offered:** Autumn, spring and summer
- **Prerequisites:** C- or above in MATH 1148 and 1149, or in 1144, 1150 or 150, or Math Placement Level L
- **Covers:** Differential and integral calculus of one variable: limits, continuity, derivatives, related rates, graphing, the Mean Value Theorem, optimization, L'Hôpital's rule, definite integrals, substitution
- **Next course:** MATH 1152 (Calculus II) or MATH 1172 (Engineering Mathematics A)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 1151 is Ohio State's 5-credit Calculus I course, offered in autumn, spring and summer.
- It covers differential and integral calculus of one variable, from the first limit to integration by substitution.
- The department's topic list includes logarithmic differentiation, derivatives of inverse functions, the Mean Value Theorem and L'Hôpital's rule.
- After 1151, students take either MATH 1152 (Calculus II) or MATH 1172 (Engineering Mathematics A).

**Ohio State MATH 1151**, Calculus I, is the first course in Ohio State's main calculus sequence. It is a 5-credit course offered every autumn, spring and summer, and it covers differential and integral calculus of one real variable. This guide maps every MATH 1151 topic to practice with instant feedback.

## What Ohio State MATH 1151 covers

The catalog description is brief: differential and integral calculus of one real variable. The department's course description document gives the full topic list. It begins with understanding functions and a review of common functions, then limits, limit laws, indeterminate forms, asymptotes and continuity with the Intermediate Value Theorem.

The derivative section covers the definition, differentiation rules, the product, quotient and chain rules, higher-order derivatives, implicit and logarithmic differentiation, and derivatives of inverse functions. Applications follow: related rates, maxima and minima, graphing, the Mean Value Theorem, linear approximation, optimization and L'Hôpital's rule. The course ends with antiderivatives, area approximation, definite integrals, both Fundamental Theorems and substitution.

That is a complete **Calculus 1** course, matching our Calculus 1 path unit for unit.

## MATH 1151 topic map

| MATH 1151 topic | Practice | Read |
| --- | --- | --- |
| Functions review | [Functions and notation](/learn/calculus-1/functions-warmup/function-notation) | [Exponential functions](/functions/exponential-functions), [logarithmic functions](/functions/logarithmic-functions) |
| Limits and limit laws | [Direct substitution](/learn/calculus-1/limits/direct-substitution) | [Limit laws](/rules/limit-laws), [how to evaluate limits](/blog/how-to-evaluate-limits) |
| Indeterminate forms | [Factor and cancel](/learn/calculus-1/limits/factoring-zero-over-zero) | [What is a limit?](/blog/what-is-a-limit) |
| Asymptotes | [Limits at infinity](/learn/calculus-1/limits/limits-at-infinity) | [Limits at infinity](/blog/limits-at-infinity), [rational functions](/functions/rational-functions) |
| Continuity and the IVT | [Continuity](/learn/calculus-1/limits/continuity) | [Intermediate Value Theorem](/theorems/intermediate-value-theorem) |
| Definition of the derivative | [The limit definition](/learn/calculus-1/the-derivative/limit-definition) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Rules of differentiation | [The product rule](/learn/calculus-1/derivative-rules/product-rule) | [Product and quotient rules](/blog/product-and-quotient-rules), [chain rule](/blog/chain-rule) |
| Implicit and logarithmic differentiation | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation) | [Logarithmic differentiation](/rules/logarithmic-differentiation), [inverse function rule](/rules/inverse-function-rule) |
| Related rates | [Related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates](/blog/related-rates) |
| Graphing and extrema | [Concavity and the second derivative](/learn/calculus-1/applications-of-derivatives/second-derivative) | [Curve sketching](/blog/curve-sketching-with-derivatives) |
| Mean Value Theorem and linear approximation | [Tangent lines at work](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Mean Value Theorem](/blog/mean-value-theorem), [linear approximation](/blog/linear-approximation) |
| Optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| L'Hôpital's rule | [L'Hôpital's rule](/learn/calculus-1/applications-of-derivatives/lhopitals-rule) | [L'Hôpital's rule](/rules/lhopitals-rule) |
| Definite integrals and the FTC | [Derivatives of integrals](/learn/calculus-1/integrals/fundamental-theorem-part-1) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus) |
| Substitution | [U-substitution](/learn/calculus-1/integrals/u-substitution) | [U-substitution](/blog/u-substitution) |

## The Ohio State calculus sequence

| Course | Title | Credit hours | Main topics |
| --- | --- | --- | --- |
| MATH 1151 | Calculus I | 5 | One-variable differential and integral calculus |
| MATH 1152 | Calculus II | 5 | Integration, series, parametric and polar |
| MATH 1172 | Engineering Mathematics A | 5 | Integration, Taylor series, start of several variables |
| MATH 2153 | Calculus III | 4 | Multivariable calculus |

After 1151, continue with the [MATH 1152 guide](/courses/ohio-state-math-1152) or the engineering alternative in the [MATH 1172 guide](/courses/ohio-state-math-1172). Both lead to [MATH 2153](/courses/ohio-state-math-2153). For business applications, Ohio State also offers [MATH 1131](/courses/ohio-state-math-1131), Calculus for Business.

## Example problems at the MATH 1151 level

**1. Logarithmic differentiation.** Differentiate $y = x^x$ for $x > 0$. Take logs: $\ln y = x\ln x$. Differentiate both sides: $\frac{y'}{y} = \ln x + 1$, so

$$y' = x^x(\ln x + 1)$$

**2. A horizontal asymptote.** Divide by the highest power of $x$:

$$\lim_{x \to \infty} \frac{3x^2 + 1}{2x^2 - x} = \lim_{x \to \infty} \frac{3 + \frac{1}{x^2}}{2 - \frac{1}{x}} = \frac{3}{2}$$

so $y = \frac{3}{2}$ is a horizontal asymptote.

**3. Substitution in a definite integral.** With $u = x^2 + 1$, $du = 2x\,dx$:

$$\int_0^1 2x(x^2 + 1)^3\,dx = \int_1^2 u^3\,du = \left[\frac{u^4}{4}\right]_1^2 = \frac{16 - 1}{4} = \frac{15}{4}$$

## How to do well in Ohio State MATH 1151

- **Practice without a calculator.** The course page states that calculators are not permitted on exams, so build hand computation skill with daily [mixed derivative practice](/learn/calculus-1/derivative-rules/derivative-rules-practice).
- **Use the posted sample exams.** The MATH 1151 course page links sample midterms. Pair them with timed [practice exams](/practice) here.
- **Watch the algebra.** Our list of [common calculus mistakes](/blog/common-calculus-mistakes) covers the slips that cost the most points.
- **Keep the [formula sheet](/formulas) nearby** while learning the rules, then wean yourself off it before exams.
- **Plan your exam prep** with [how to prepare for a calculus exam](/blog/how-to-prepare-for-a-calculus-exam).

> **Tip:** logarithmic differentiation turns any variable-to-a-variable power into a product rule problem. Take the log first, then differentiate.

## Frequently asked questions

### What is MATH 1151 at Ohio State?

MATH 1151, Calculus I, is Ohio State's first-semester calculus course covering differential and integral calculus of one variable. Topics run from limits and continuity through derivatives and their applications to definite integrals, the Fundamental Theorem of Calculus and substitution.

### What are the prerequisites for MATH 1151?

A grade of C- or above in MATH 1148 and 1149, or in 1144, 1150 or 150, or Math Placement Level L. The course is not open to students with credit for 1152 or above.

### What comes after MATH 1151?

MATH 1152, Calculus II, is the next course in the main sequence. MATH 1172, Engineering Mathematics A, also accepts 1151 as a prerequisite and is an alternative for students outside the math and actuarial science majors.

### Is MATH 1151 hard?

It is a 5-credit course that covers all of Calculus 1 in one semester, so the pace is steady. The course page notes that calculators are not permitted on exams, so practicing algebra and derivatives by hand matters.

### How do I prepare for MATH 1151?

Review functions, exponent and log rules and key trig values, then practice limits. The Ohio State math department also posts sample midterms on the MATH 1151 course page.