# Yale MATH 1120 Differential Calculus: Topics and Practice > A study guide for Yale MATH 1120, the differential calculus course: limits, derivatives, applications and antiderivatives, plus placement and practice. Source: https://practicecalculus.com/courses/yale-math-1120 Updated: 2026-11-08 ## At a glance - **Course code:** MATH 1120 (formerly MATH 112) - **Credits:** Not stated on the department guide - **Offered:** Not stated on the department guide - **Prerequisites:** The calculus placement exam; students typically take it after pre-calculus - **Covers:** Limits, the derivative and its rules, using derivatives to understand functions and optimize, and antiderivatives with applications such as area and population growth - **Next course:** MATH 1150 or MATH 1160 (integral calculus) - **Practice here:** [Calculus 1](/learn/calculus-1) ## Key takeaways - MATH 1120 is Yale's differential calculus course, the first step in its introductory calculus sequence. - It covers limits, derivatives and their rules, applications of the derivative, and antiderivatives. - Students need the calculus placement exam to enroll, and usually take it after pre-calculus. - The two-semester MATH 1100 and 1110 sequence covers the same calculus with pre-calculus woven in, and counts as equivalent to MATH 1120. **Yale MATH 1120** is the differential calculus course in Yale's introductory sequence, the course long known as MATH 112. The math department's guide says its goal is to measure a function's instantaneous rate of change, the derivative, and to use that idea to understand how functions behave. This guide lists what MATH 1120 covers and links each topic to free practice with instant feedback. ## What MATH 1120 covers The Yale math department's introductory course guide describes MATH 1120 in four steps. First, the course defines limits, which make it possible to talk rigorously about instantaneous change. Next, it defines the derivative and develops rules that simplify computing it. Then it applies the derivative to understand function behavior, with examples such as minimizing cost or maximizing profit in economic models. Finally, it develops strategies for reversing differentiation to find antiderivatives, which have applications such as computing areas and modeling population growth. That makes MATH 1120 a close match for a standard **Calculus 1** course. It stops before the full treatment of integration, which belongs to MATH 1150. ## MATH 1120 topic map | MATH 1120 topic | Practice | Read | | --- | --- | --- | | Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [What is a limit?](/blog/what-is-a-limit) | | Evaluating limits | [Factoring zero over zero](/learn/calculus-1/limits/factoring-zero-over-zero) | [How to evaluate limits](/blog/how-to-evaluate-limits) | | Instantaneous rate 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) | | Defining the derivative | [The limit definition](/learn/calculus-1/the-derivative/limit-definition) | [Limit definition practice](/practice-problems/limit-definition-of-the-derivative) | | Rules for derivatives | [Power rule](/learn/calculus-1/derivative-rules/power-rule) | [Power rule](/rules/power-rule), [product rule](/rules/product-rule) | | Chain rule | [Chain rule in general](/learn/calculus-1/derivative-rules/chain-rule-general) | [Chain rule guide](/blog/chain-rule) | | Function behavior | [Increasing and decreasing](/learn/calculus-1/applications-of-derivatives/increasing-and-decreasing) | [Curve sketching with derivatives](/blog/curve-sketching-with-derivatives) | | Minimizing and maximizing | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) | | Antiderivatives | [Undoing derivatives](/learn/calculus-1/integrals/undoing-derivatives) | [Antiderivatives](/blog/antiderivatives) | | Area | [Signed area](/learn/calculus-1/integrals/signed-area) | [Riemann sums](/blog/riemann-sums) | | Population growth | [Exponentials and logs](/learn/calculus-1/functions-warmup/exponentials-and-logs) | [Exponential functions](/functions/exponential-functions) | ## Placement and the MATH 1100/1110 option MATH 1120 requires Yale's calculus placement exam, and the department says students typically take it after finishing pre-calculus. If your pre-calculus is shaky, the department offers MATH 1100 and 1110, a two-semester sequence that integrates pre-calculus and differential calculus. Completing both counts the same as MATH 1120 for majors and professional school requirements such as pre-med, and earns two course credits instead of one course. If you already have strong differential calculus, for example from AP Calculus AB, the placement exam may place you directly into MATH 1150. ## Example problems at the MATH 1120 level **1. A derivative from the rules.** For $f(x) = x^3 - 6x^2 + 9x$, $f'(x) = 3x^2 - 12x + 9 = 3(x - 1)(x - 3)$. **2. Function behavior.** From that factorization, $f$ increases on $(-\infty, 1)$, decreases on $(1, 3)$ and increases again on $(3, \infty)$, so it has a local maximum at $x = 1$ and a local minimum at $x = 3$. **3. An antiderivative.** $$\int (4x^3 + 2x)\,dx = x^4 + x^2 + C$$ ## How to do well in MATH 1120 - **Make the limit idea concrete.** Work through [average](/learn/calculus-1/the-derivative/average-rate-of-change) and [instantaneous rate of change](/learn/calculus-1/the-derivative/instantaneous-rate-of-change) until the derivative feels like a speedometer reading. - **Drill the derivative rules daily.** Short sessions with the [derivative rules practice](/learn/calculus-1/derivative-rules/derivative-rules-practice) build speed for exams. - **Connect graphs and derivatives.** Many questions ask what a derivative tells you about a graph, so practice reading both directions. - **Keep formulas close.** The [formula sheet](/formulas) puts every basic derivative on one page. When you are ready for integration, read the [MATH 1150 guide](/courses/yale-math-1150). ## Frequently asked questions ### What is Yale MATH 1120? MATH 1120 is Yale's differential calculus course. The math department says it defines limits, defines the derivative, develops rules for computing it, applies it to understand functions, and finishes with antiderivatives. ### Is MATH 1120 the same as MATH 112? Yale moved to four-digit course numbers, and MATH 1120 is the current number for the differential calculus course long known as MATH 112. ### Do I need the placement exam for MATH 1120? Yes. The department says MATH 1120 requires the placement exam, and students typically take the course after completing pre-calculus. ### What is the difference between MATH 1120 and MATH 1100/1110? MATH 1100 and 1110 are a two-semester sequence that combines pre-calculus with differential calculus. Completing both is equivalent to MATH 1120 for majors and pre-med requirements, and earns two course credits. ### What comes after MATH 1120? Integral calculus: MATH 1150, or MATH 1160, which emphasizes biology applications. Completing MATH 1120 at Yale qualifies you for either.