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

> A study guide for University of Arizona MATH 122B First-Semester Calculus: derivatives, graphing, optimization, related rates and integrals.

Source: https://practicecalculus.com/courses/university-of-arizona-math-122b
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 122B
- **Units:** 4
- **Prerequisites:** MATH 122A Functions for Calculus with a C or higher, or eligibility on the department's Math Course Placement Chart
- **Covers:** Using derivatives to analyze and graph algebraic and transcendental functions, optimization, related rates, the Fundamental Theorem of Calculus, estimating rates of change, area and total change
- **Textbook:** Calculus: Concepts and Contexts, 5th edition (Stewart and Kokoska), Chapters 2 to 5.5 and parts of 6.1
- **Calculator:** Graphing calculator required (TI-83 or TI-84 recommended); CAS models not allowed on exams
- **Next course:** MATH 129 Calculus II
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 122B First-Semester Calculus is a 4-unit Calculus 1 course at the University of Arizona for engineering, science and math students.
- It focuses on derivatives, graphing, optimization, related rates, the Fundamental Theorem of Calculus and estimation of rates, area and total change.
- Students usually take the 1-unit MATH 122A Functions for Calculus first in the same term and need a C or higher in it to continue.
- All sections share a common final exam, and a non-CAS graphing calculator is required.

**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 topic | Practice | Read |
| --- | --- | --- |
| Limits and continuity | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits) |
| Rates of change | [Average rate of change](/learn/calculus-1/the-derivative/average-rate-of-change) | [Instantaneous rate of change](/learn/calculus-1/the-derivative/instantaneous-rate-of-change) |
| The derivative | [Derivative notation and meaning](/learn/calculus-1/the-derivative/derivative-notation-and-meaning) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Derivatives of transcendental functions | [Exponential and log derivatives](/learn/calculus-1/derivative-rules/exponential-and-log-derivatives) | [Derivatives of exponential and log functions](/blog/derivatives-of-exponential-and-logarithmic-functions) |
| Chain rule | [Chain rule in general](/learn/calculus-1/derivative-rules/chain-rule-general) | [Chain rule](/blog/chain-rule) |
| Graphing with derivatives | [Increasing and decreasing](/learn/calculus-1/applications-of-derivatives/increasing-and-decreasing) | [Curve sketching](/blog/curve-sketching-with-derivatives) |
| Optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| Related rates | [Related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates](/blog/related-rates) |
| Estimating area and total change | [Riemann sums](/learn/calculus-1/integrals/riemann-sums) | [Riemann sums](/blog/riemann-sums) |
| Fundamental Theorem of Calculus | [Fundamental Theorem, part 2](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem](/blog/fundamental-theorem-of-calculus) |
| Total change | [Net change](/learn/calculus-1/applications-of-integrals/net-change) | [Accumulation functions](/learn/calculus-1/integrals/accumulation-functions) |

## MATH 122B and the other Arizona calculus options

| Course | Units | Notes |
| --- | --- | --- |
| MATH 122A Functions for Calculus | 1 | Taken at the start of the term; a C or higher leads into 122B |
| MATH 122B First-Semester Calculus | 4 | Calculus 1 for engineering, science and math |
| MATH 196M | 1 | Optional supplemental instruction for 122B |

Next in the sequence is [MATH 129 Calculus II](/courses/university-of-arizona-math-129), then [MATH 223 Vector Calculus](/courses/university-of-arizona-math-223). 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

$$f'(2) \approx \frac{5.4 - 5}{0.1} = 4$$

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

$$\frac{dA}{dt} = 2\pi r \frac{dr}{dt} = 2\pi(10)(3) = 60\pi \text{ cm}^2/\text{s}$$

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

$$\int_0^3 4t\,dt = 2t^2 \Big|_0^3 = 18 \text{ liters}$$

## 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](/learn/calculus-1/functions-warmup/function-notation).
- **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](/practice-problems/optimization) and [related rates](/practice-problems/related-rates).
- **Prepare for the common final** with the department's study guide and our timed [practice exams](/practice).

> **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.

## Frequently asked questions

### What is MATH 122B at the University of Arizona?

MATH 122B First-Semester Calculus is an introduction to calculus for engineering, science and math students, with an emphasis on understanding, problem solving and modeling. The department lists objectives such as analyzing and graphing functions with derivatives, optimization and related rates, applying the Fundamental Theorem of Calculus, and estimating rates of change, area and total change.

### How do MATH 122A and MATH 122B fit together?

MATH 122A Functions for Calculus is a 1-unit course taught at the start of the term. Students who finish it with a C or higher continue into MATH 122B. Students who do not are switched out of MATH 122B and into MATH 120R Calculus Preparation.

### What calculator do I need for MATH 122B?

A graphing calculator is required, and the department recommends the TI-83 or TI-84 series. Calculators with symbolic algebra (CAS), such as the TI-89 or TI-Nspire CAS, are not allowed on exams and quizzes.

### Is there extra help for MATH 122B?

Yes. Students can add MATH 196M, a 1-unit supplemental instruction course, and the department runs the free Think Tank tutoring service.

### What comes after MATH 122B?

MATH 129 Calculus II, which the University of Arizona catalog describes as a continuation of MATH 122B or MATH 125.