Arizona MATH 122B First-Semester Calculus: Topics and Practice

Arizona MATH 122B (First-Semester Calculus) is the main Calculus 1 course at the University of Arizona for engineering, science and math students. It is a 4-unit course, usually paired with the 1-unit MATH 122A Functions for Calculus at the start of the term. This guide maps the MATH 122B objectives to lessons you can practice with instant feedback.

What Arizona MATH 122B covers

The Department of Mathematics describes MATH 122B as an introduction to first-semester calculus with an emphasis on understanding, problem solving and modeling. Its course objectives are to:

• use derivatives to analyze and graph algebraic and transcendental functions,
• select and apply models and differentiation techniques to applications such as optimization and related rates,
• apply the Fundamental Theorem of Calculus to evaluate integrals,
• use estimation techniques to approximate rates of change, area and total change.

The course page says MATH 122B covers Chapters 2 to 5.5 and selections from 6.1 of Calculus: Concepts and Contexts (5th edition, Stewart and Kokoska), with homework on WebAssign and a common final exam for all sections. A graphing calculator is required, but CAS models are not allowed on exams and quizzes.

MATH 122B topic map

MATH 122B and the other Arizona calculus options

Next in the sequence is MATH 129 Calculus II, then MATH 223 Vector Calculus. For exact eligibility, the department points students to its Math Course Placement Chart.

Example problems at the MATH 122B level

1. Estimating a rate of change. If f(2) = 5 and f(2.1) = 5.4, then

2. A related rate. A circle's radius grows at 3 cm/s. When r = 10, the area grows at

3. Total change from a rate. If water flows in at r(t) = 4t liters per minute, then in the first 3 minutes

How to do well in MATH 122B

• Take MATH 122A seriously. You need a C or higher in it to stay in MATH 122B. Review with the functions warm-up.
• Read graphs and tables, not just formulas. The course stresses estimation and modeling, so practice reading slopes and areas from data.
• Use the calculator as a check, not a crutch. You still need to set up the derivative or integral yourself.
• Practice word problems weekly, especially optimization and related rates.
• Prepare for the common final with the department's study guide and our timed practice exams.

Tip: in an optimization problem, write the quantity to maximize as a function of one variable before you differentiate. Use the constraint to remove the extra variable.