Cornell MATH 1110 Calculus I: Topics, Study Guide and Practice

A study guide for Cornell MATH 1110 Calculus I: limits, derivatives, the mean value theorem and the Fundamental Theorem, with practice for every topic.

Cornell University Updated November 3, 2026 3 min read

Key takeaways

MATH 1110 is Cornell's Calculus I, a 4-credit course that works as a one-semester introduction or as the first half of a sequence with MATH 1120.

It covers limits, derivatives of all the elementary functions, applications such as max-min problems and tangent line approximation, the mean value theorem, and integration up to the Fundamental Theorem.

Students cannot get credit for both MATH 1110 and MATH 1106, the applied life-sciences course.

Engineering students continue to MATH 1910 instead of MATH 1120.

Cornell MATH 1110 is Calculus I at Cornell University, taken by students across Arts and Sciences, the life sciences and other colleges who need a first course in calculus. It can stand alone as a one-semester introduction or start a two-semester sequence with MATH 1120. This guide maps each MATH 1110 topic to a lesson you can practice with instant feedback.

What Cornell MATH 1110 covers

The Cornell class roster lists the topics as functions and graphs, limits and continuity, and differentiation and integration of algebraic, trigonometric, inverse trigonometric, logarithmic and exponential functions. Applications of the derivative include graphing, max-min problems, tangent line approximation, implicit differentiation and science applications. The course also covers the mean value theorem, antiderivatives, definite and indefinite integrals, the Fundamental Theorem of Calculus and area under a curve.

That is a complete Calculus 1, and it matches the PracticeCalculus Calculus 1 path from the warm-up through the integrals unit.

MATH 1110 topic map

MATH 1110 topic	Practice	Read
Functions and graphs	Functions and notation	Polynomial functions, exponential functions
Limits and continuity	What is a limit?	How to evaluate limits, continuity
Differentiation rules	Chain rule: any function	Chain rule, product and quotient rules
Trig and inverse trig derivatives	Sine, cosine and tangent	Derivatives of trig functions, arctangent
Log and exponential derivatives	Exponentials and logarithms	Derivatives of exponential and log functions
Implicit differentiation	Implicit differentiation	Implicit differentiation guide
Graphing and max-min problems	Absolute extrema	Curve sketching, optimization problems
Tangent line approximation	Tangent lines at work	Linear approximation
Mean value theorem	Tangent lines at work	Mean value theorem, Rolle's theorem
Antiderivatives and integrals	The reverse power rule	Antiderivatives
Fundamental Theorem and area	Evaluating definite integrals	Fundamental Theorem of Calculus

MATH 1110 and the Cornell calculus tracks

Course	Who takes it	What it covers
MATH 1106	Life and social science students who need one semester	Applied derivatives, integrals and intro differential equations
MATH 1110 Calculus I	Most first-time calculus students	Full Calculus 1
MATH 1120 Calculus II	Students continuing after MATH 1110	Integration techniques, differential equations, series
MATH 1910 Calculus for Engineers	Engineering students after MATH 1110 level calculus	Integration techniques, series, power series

MATH 1120 and MATH 1910 exclude credit for each other, so engineers and non-engineers split after MATH 1110. Multivariable calculus comes later in MATH 1920 or MATH 2220.

Example problems at the MATH 1110 level

1. Implicit differentiation. Find the slope of $inline$ at $inline$ .

Differentiate both sides: $inline$ , so $inline$ .

2. Tangent line approximation. Estimate $inline$ using the tangent line to $inline$ at $inline$ . Since $inline$ and $inline$ :

display

3. A log integral.

display

How to do well in MATH 1110

Drill the derivative rules until they are automatic. The chain rule appears in nearly every problem after week four.
Do not skip inverse trig. Many students forget the derivatives of arcsine and arctangent. Put them on your own summary sheet next to the formula sheet.
Learn the mean value theorem by picture. A secant slope equals some tangent slope. Our mean value theorem guide shows why.
Fix the common slips early with common calculus mistakes, then rehearse with timed practice exams.

Tip: in max-min problems on a closed interval, always check the endpoints as well as the critical points. The Extreme Value Theorem guarantees the answer is one of them.

Frequently asked questions

What is Cornell MATH 1110?

MATH 1110 is Calculus I at Cornell. It covers functions and graphs, limits and continuity, differentiation and integration of algebraic, trigonometric, inverse trig, logarithmic and exponential functions, applications of the derivative, the mean value theorem, and integrals up to the Fundamental Theorem of Calculus.

What comes after MATH 1110?

Most students continue to MATH 1120 Calculus II. Engineering students take MATH 1910 Calculus for Engineers, which assumes differential calculus at the level of MATH 1110.

Should I take MATH 1110 or MATH 1106?

MATH 1106 teaches derivatives, integrals and simple differential equations through life-science models and is more applied. The roster says students who plan to take more than one semester of calculus should take MATH 1110. You cannot get credit for both.

Is MATH 1110 hard?

It covers the whole of a standard Calculus 1, including inverse trig functions and the mean value theorem, in one semester. It is very manageable with steady practice, and most lost points come from algebra slips rather than new calculus ideas.

How can I prepare for MATH 1110?

Review functions, exponent and log rules and the unit circle, then start working limit problems. The free functions warm-up and limits units on PracticeCalculus are a good first week.