# UW MATH 124 Calculus I: Topics, Study Guide and Practice

> A study guide for University of Washington MATH 124 (Calculus with Analytic Geometry I): limits, derivatives and their applications, with free practice.

Source: https://practicecalculus.com/courses/university-of-washington-math-124
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 124
- **Credits:** 5 (one quarter)
- **Offered:** Autumn, winter, spring and summer
- **Prerequisites:** None listed; completing the math department's Guided Self-Placement is recommended
- **Covers:** First quarter of single-variable calculus, emphasizing differential calculus, applications and problem solving
- **Next course:** MATH 125 (Calculus with Analytic Geometry II)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 124 is the first quarter of the University of Washington calculus sequence, worth 5 credits.
- It emphasizes differential calculus: limits, derivatives and their applications to problem solving.
- Because UW is on quarters, integrals mostly wait for MATH 125.
- MATH 124, 125 and 126 form the standard sequence, with MATH 134-136 as the accelerated honors alternative.

**UW MATH 124**, Calculus with Analytic Geometry I, is the first quarter of calculus at the University of Washington. It is a 5-credit course offered every quarter, including summer, and it focuses on differential calculus. This guide maps every MATH 124 topic to practice with instant feedback, so you can learn by solving problems.

## What UW MATH 124 covers

The UW course catalog describes MATH 124 as the first quarter of calculus of functions of a single variable. It emphasizes differential calculus, and it emphasizes applications and problem solving using the tools of calculus. There is no formal prerequisite, but the catalog recommends completing the math department's Guided Self-Placement.

The catalog does not list subtopics. A course on differential calculus covers the first half of a standard **Calculus 1** course: limits and continuity, the derivative, differentiation rules and applications such as optimization and related rates. Integration is the focus of the next quarter, MATH 125.

## MATH 124 topic map

| MATH 124 topic | Practice | Read |
| --- | --- | --- |
| Functions and rates of change | [Slope and rate of change](/learn/calculus-1/functions-warmup/slope-and-rate-of-change) | [Linear functions](/functions/linear-function) |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [What is a limit?](/blog/what-is-a-limit), [how to evaluate limits](/blog/how-to-evaluate-limits) |
| Continuity | [Continuity](/learn/calculus-1/limits/continuity) | [Continuity](/blog/continuity) |
| The derivative | [Instantaneous rate of change](/learn/calculus-1/the-derivative/instantaneous-rate-of-change) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Tangent lines | [Tangent lines](/learn/calculus-1/the-derivative/tangent-lines) | [Linear approximation](/blog/linear-approximation) |
| Power, product and quotient rules | [The product rule](/learn/calculus-1/derivative-rules/product-rule) | [Power rule](/blog/power-rule), [product and quotient rules](/blog/product-and-quotient-rules) |
| Chain rule | [Chain rule: any function](/learn/calculus-1/derivative-rules/chain-rule-general) | [Chain rule](/blog/chain-rule) |
| Trig, exponential and log derivatives | [Exponentials and logarithms](/learn/calculus-1/derivative-rules/exponential-and-log-derivatives) | [Derivatives of trig functions](/blog/derivatives-of-trig-functions) |
| Implicit differentiation | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation) | [Implicit differentiation](/blog/implicit-differentiation) |
| Related rates | [Related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates](/blog/related-rates) |
| Optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| Graphs and the Mean Value Theorem | [Increasing and decreasing](/learn/calculus-1/applications-of-derivatives/increasing-and-decreasing) | [Curve sketching](/blog/curve-sketching-with-derivatives), [Mean Value Theorem](/blog/mean-value-theorem) |

## The UW calculus sequence

| Course | Title | Credits | Emphasis |
| --- | --- | --- | --- |
| MATH 124 | Calculus with Analytic Geometry I | 5 | Differential calculus |
| MATH 125 | Calculus with Analytic Geometry II | 5 | Integral calculus |
| MATH 126 | Calculus with Analytic Geometry III | 5 | Vectors, multivariable derivatives, Taylor series |
| MATH 224 | Advanced Multivariable Calculus | 4 | Multiple integrals and vector calculus |
| MATH 134-136 | Accelerated [Honors] Calculus | 5 each | Honors alternative |

Continue with the [MATH 125 guide](/courses/university-of-washington-math-125) and the [MATH 126 guide](/courses/university-of-washington-math-126). For business and economics, see the [MATH 112 guide](/courses/university-of-washington-math-112), which overlaps with MATH 124.

## Example problems at the MATH 124 level

**1. A derivative from the definition.** For $f(x) = x^2$,

$$f'(x) = \lim_{h \to 0} \frac{(x + h)^2 - x^2}{h} = \lim_{h \to 0} (2x + h) = 2x$$

**2. Implicit differentiation.** For the circle $x^2 + y^2 = 25$, differentiate both sides: $2x + 2y\,y' = 0$, so $y' = -\frac{x}{y}$. At $(3, 4)$ the slope is $-\frac{3}{4}$.

**3. Related rates.** A 10 ft ladder slides down a wall with its base moving out at 1 ft/s. When the base is 6 ft out, the top is 8 ft up. From $x^2 + y^2 = 100$, $2x x' + 2y y' = 0$, so

$$y' = -\frac{x x'}{y} = -\frac{6 \cdot 1}{8} = -\frac{3}{4} \text{ ft/s}$$

## How to do well in UW MATH 124

- **Keep pace with the quarter.** Ten weeks goes fast. Practice a little every day with [mixed derivative practice](/learn/calculus-1/derivative-rules/derivative-rules-practice).
- **Focus on applications.** The catalog stresses problem solving, so spend time on [related rates](/blog/related-rates) and [optimization](/blog/optimization-problems) setups, not just rules.
- **Fix algebra slips early.** See [common calculus mistakes](/blog/common-calculus-mistakes) for the ones that cost the most points.
- **Use the [formula sheet](/formulas)** while learning, then take timed [practice exams](/practice) before midterms and the final.
- **Plan your study** with [how to study calculus](/blog/how-to-study-calculus).

> **Tip:** in related rates, plug in numbers only after you differentiate. Substituting too early turns changing quantities into constants.

## Frequently asked questions

### What is MATH 124 at the University of Washington?

MATH 124, Calculus with Analytic Geometry I, is the first quarter of UW's single-variable calculus sequence. It emphasizes differential calculus and its use in applications and problem solving.

### What do I need before MATH 124?

The catalog lists no formal prerequisite, but it recommends completing the Department of Mathematics' Guided Self-Placement first. Solid algebra and trigonometry are what the course builds on.

### What comes after MATH 124?

MATH 125, Calculus with Analytic Geometry II, which emphasizes integral calculus. It requires a minimum grade of 2.0 in MATH 124 or a qualifying AP score.

### Is UW MATH 124 hard?

A quarter is only about ten weeks, so a full unit of differential calculus moves quickly. Keeping up with practice every week matters more than in a semester course.

### What is the difference between MATH 124 and MATH 134?

MATH 134 is the first quarter of a two-year accelerated honors sequence that covers the material of MATH 124, 125, 126, 207 and 208. It is meant for students with above-average preparation and interest in mathematics.