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UF MAC 2311 Calculus 1: Topics, Study Guide and Practice

A study guide for UF MAC 2311 Analytic Geometry and Calculus 1: limits, derivatives, optimization, curve sketching and integration, with practice.

University of Florida Updated 3 min read

At a glance

Course code
MAC 2311
Credits
4
Prerequisites
A minimum score on the online math placement exam, or a C in (or test credit for) MAC 1147 or higher
Covers
Limits, continuity, differentiation and rates of change, optimization, curve sketching, an introduction to integration and area, for algebraic, exponential, logarithmic and trig functions
Honors version
MAC 3472 Honors Calculus 1
Next course
MAC 2312 Analytic Geometry and Calculus 2
Practice here
Calculus 1
On this page
  1. What UF MAC 2311 covers
  2. MAC 2311 topic map
  3. MAC 2311 and the UF calculus options
  4. Example problems at the MAC 2311 level
  5. How to do well in MAC 2311

UF MAC 2311 (Analytic Geometry and Calculus 1) is the first calculus course at the University of Florida and the start of the three-semester MAC 2311, 2312, 2313 sequence. It also counts toward the General Education mathematics requirement. This guide maps every MAC 2311 topic to a lesson you can practice with instant feedback.

What UF MAC 2311 covers

The UF catalog describes MAC 2311 as the study of limits, derivatives, and definite and indefinite integrals of functions of one variable, including algebraic, exponential, logarithmic and trigonometric functions, with applications. Named topics include limits, continuity, differentiation and rates of change, optimization, curve sketching, and an introduction to integration and area. The catalog also frames the course around building problem solving, critical thinking and computational skills.

That is a standard Calculus 1 course, matching the PracticeCalculus Calculus 1 path from limits through the integrals unit.

MAC 2311 topic map

MAC 2311 topic Practice Read
Limits What is a limit? How to evaluate limits
Limits at infinity Limits at infinity Limits at infinity
Continuity Continuity Continuity, Intermediate Value Theorem
Differentiation and rates of change Instantaneous rate of change Limit definition of the derivative
Derivative rules Mixed rules practice Power rule, chain rule
Exponential, log and trig derivatives Chain rule: e and ln Derivatives of trig functions
Related rates Related rates Related rates
Curve sketching Concavity and the second derivative Curve sketching
Optimization Optimization Optimization problems
Indefinite integrals Antiderivative practice Antiderivatives
Definite integrals and area The definite integral as area Riemann sums, Fundamental Theorem

MAC 2311 and the UF calculus options

Course Credits Who it suits
MAC 2233 Survey of Calculus 1 3 Majors needing applied calculus (marginal analysis, optimization)
MAC 2311 Analytic Geometry and Calculus 1 4 Students starting the full calculus sequence
MAC 3472 Honors Calculus 1 4 Students with a strong precalculus background who want more depth

The catalog says the honors sequence (MAC 3472, 3473, 3474) closely parallels MAC 2311, 2312, 2313 but in greater depth, and credit is given for only one of MAC 2311 and MAC 3472. Next up is MAC 2312, then MAC 2313.

Example problems at the MAC 2311 level

1. A limit at infinity. Divide the top and bottom by x^2:

\lim_{x \to \infty} \frac{3x^2 + 1}{x^2 - 5} = \lim_{x \to \infty} \frac{3 + \frac{1}{x^2}}{1 - \frac{5}{x^2}} = 3

2. A chain rule derivative with a log.

\frac{d}{dx}\ln(x^2 + 1) = \frac{2x}{x^2 + 1}

3. Optimization. A rectangle has perimeter 40. With side x, the other side is 20 - x, so A(x) = x(20 - x) = 20x - x^2. Then A'(x) = 20 - 2x = 0 gives x = 10, and the largest area is 10 \cdot 10 = 100.

How to do well in MAC 2311

  • Close precalculus gaps right away. If your placement was borderline, the functions warm-up covers exponents, logs and trig values in a few short lessons.
  • Aim for the C, then beyond. MAC 2312 requires a C or better in MAC 2311, so treat every exam as a gate.
  • Practice curve sketching as a routine: domain, intercepts, f' sign chart, f'' sign chart, asymptotes. Our curve sketching guide walks through it.
  • Keep the formula sheet handy, read common calculus mistakes, and test yourself with timed practice exams.

Tip: in related rates, differentiate the equation before you plug in numbers. Plugging in first turns a changing quantity into a constant.

Practice it now

What is a limit?

Solve real problems on this topic with instant feedback, hints and a step-by-step walkthrough for every answer. Free, no sign-up needed to start.

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Frequently asked questions

What is MAC 2311 at UF?
MAC 2311 Analytic Geometry and Calculus 1 is UF's first-semester calculus course. It covers limits, derivatives and definite and indefinite integrals of algebraic, exponential, logarithmic and trigonometric functions, with topics such as continuity, rates of change, optimization, curve sketching and area.

What is the prerequisite for MAC 2311?
The UF catalog lists a minimum acceptable score on the online math placement exam, or a grade of C in (or test credit for) MAC 1147 or higher. Grades and AP or IB scores used for the prerequisite must be on file at UF by registration.

What is the difference between MAC 2311 and MAC 2233?
MAC 2233 Survey of Calculus 1 is a 3-credit, more applied course built around simple algebraic and exponential functions, with business-style applications. MAC 2311 is the 4-credit calculus course that starts the full sequence. If both are taken, the catalog gives credit only for MAC 2311.

Is MAC 2311 hard?
It is a full Calculus 1 course, and the main difficulty is the pace and the amount of algebra involved. Students who practice short sets of problems daily and keep precalculus skills sharp usually do well.

What comes after MAC 2311?
MAC 2312 Analytic Geometry and Calculus 2, which requires MAC 2311 (or MAC 3472) with a C or better. After that comes MAC 2313 Calculus 3.

Written by the PracticeCalculus team

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Related university courses

UF MAC 2312 Calculus 2 Analytic Geometry and Calculus 2 A study guide for UF MAC 2312 Analytic Geometry and Calculus 2: integration techniques, applications, inverse trig functions and series, with practice. UF MAC 2313 Calculus 3 Analytic Geometry and Calculus 3 A study guide for UF MAC 2313 Analytic Geometry and Calculus 3: solid analytic geometry, vectors, partial derivatives and multiple integrals, with practice. UF MAC 2233 Calculus 1 Survey of Calculus 1 A study guide for UF MAC 2233 Survey of Calculus 1: derivatives and integrals of algebraic and exponential functions, marginal analysis and optimization.