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

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

The Ohio State calculus sequence

After 1151, continue with the MATH 1152 guide or the engineering alternative in the MATH 1172 guide. Both lead to MATH 2153. For business applications, Ohio State also offers 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

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

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

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

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.
• Use the posted sample exams. The MATH 1151 course page links sample midterms. Pair them with timed practice exams here.
• Watch the algebra. Our list of common calculus mistakes covers the slips that cost the most points.
• Keep the formula sheet nearby while learning the rules, then wean yourself off it before exams.
• Plan your exam prep with 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.