# 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.

Source: https://practicecalculus.com/courses/cornell-math-1110
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 1110
- **Credits:** 4
- **Recently offered:** Fall, spring and summer
- **Covers:** Functions and graphs, limits and continuity, derivatives and integrals of algebraic, trig, inverse trig, log and exponential functions, applications of the derivative, the mean value theorem, the Fundamental Theorem
- **Forbidden overlap:** MATH 1106 (Modeling with Calculus for the Life Sciences)
- **Next course:** MATH 1120 Calculus II
- **Practice here:** [Calculus 1](/learn/calculus-1)

## 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](/learn/calculus-1/functions-warmup/function-notation) | [Polynomial functions](/functions/polynomial-functions), [exponential functions](/functions/exponential-functions) |
| 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) |
| Differentiation rules | [Chain rule: any function](/learn/calculus-1/derivative-rules/chain-rule-general) | [Chain rule](/blog/chain-rule), [product and quotient rules](/blog/product-and-quotient-rules) |
| Trig and inverse trig derivatives | [Sine, cosine and tangent](/learn/calculus-1/derivative-rules/trig-derivatives) | [Derivatives of trig functions](/blog/derivatives-of-trig-functions), [arctangent](/functions/arctangent) |
| Log and exponential 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 differentiation | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation) | [Implicit differentiation guide](/blog/implicit-differentiation) |
| Graphing and max-min problems | [Absolute extrema](/learn/calculus-1/applications-of-derivatives/absolute-extrema) | [Curve sketching](/blog/curve-sketching-with-derivatives), [optimization problems](/blog/optimization-problems) |
| Tangent line approximation | [Tangent lines at work](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Linear approximation](/blog/linear-approximation) |
| Mean value theorem | [Tangent lines at work](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Mean value theorem](/theorems/mean-value-theorem), [Rolle's theorem](/theorems/rolles-theorem) |
| Antiderivatives and integrals | [The reverse power rule](/learn/calculus-1/integrals/reverse-power-rule) | [Antiderivatives](/blog/antiderivatives) |
| Fundamental Theorem and area | [Evaluating definite integrals](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem of Calculus](/blog/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](/courses/cornell-math-1120) | Students continuing after MATH 1110 | Integration techniques, differential equations, series |
| [MATH 1910 Calculus for Engineers](/courses/cornell-math-1910) | 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](/courses/cornell-math-1920) or [MATH 2220](/courses/cornell-math-2220).

## Example problems at the MATH 1110 level

**1. Implicit differentiation.** Find the slope of $x^2 + y^2 = 25$ at $(3, 4)$.

Differentiate both sides: $2x + 2y\frac{dy}{dx} = 0$, so $\frac{dy}{dx} = -\frac{x}{y} = -\frac{3}{4}$.

**2. Tangent line approximation.** Estimate $\sqrt{4.1}$ using the tangent line to $f(x) = \sqrt{x}$ at $x = 4$. Since $f(4) = 2$ and $f'(4) = \frac{1}{2\sqrt{4}} = \frac{1}{4}$:

$$\sqrt{4.1} \approx 2 + \frac{1}{4}(0.1) = 2.025$$

**3. A log integral.**

$$\int_1^e \frac{1}{x}\,dx = \left[\ln x\right]_1^e = 1 - 0 = 1$$

## How to do well in MATH 1110

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

> **Tip:** in max-min problems on a closed interval, always check the endpoints as well as the critical points. The [Extreme Value Theorem](/theorems/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.