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![Preview of What is a Derivative? [Activities for Exploration]](https://ecdn.teacherspayteachers.com/cdn-cgi/image/format=avif,quality=70,width=525,height=525,onerror=redirect/thumbitem/What-is-a-Derivative-Activities-for-Exploration--15187111-1767619323/750f-15187111-1.jpg)
What is a Derivative? [Activities for Exploration]
Do you just jump in to calculating the derivative without giving your students a chance to think about what a derivative really is? This collection of activities are great, short ways to get them to pause and think about what a rate of change really is. And what's the difference between an average rate of change and an instantaneous rate of change? These are excellent, classroom tested, ready-to-print activities that will fit naturally in your PreCalculus, Honors Calculus, AP Calculus, or Underg
11th - 12th, Higher Education
Applied Math, Calculus, PreCalculus
Infinite Series Unit Bundle for AP Calculus BC or Calculus 2
This Infinite Series Unit bundle of lessons and activities for the Calculus 2 / BC will challenge your students and help them succeed in this rigorous chapter. Key topics include convergence tests (Integral, Alternating, Comparison, Ratio, Root, Alternating), geometric series, Taylor/Maclaurin series, power series, and error bound approximations. Included are notes, homework, assessments, graphic organizers, foldables, study guides, posters, INB pages, and more. This a bundle for the entire
11th - 12th, Higher Education
Calculus
Solving for Theta | Trigonometry Functions | Answer Key
Help students conquer solving for θ θ with this engaging and comprehensive trigonometric equations worksheet! Designed for precalculus and trigonometry classes, this resource covers a variety of equation types involving sine, cosine, and tangent—linear equations, multiple angles, and equations transformed via identities. Students will master finding solutions within specified intervals, applying periodicity for general solutions, and interpreting solutions graphically. Perfect for classroom prac
9th - 12th, Higher Education
Calculus, PreCalculus
Introduction to Extreme Value Theorem (EVT) for AP Calculus AB
This introductory activity helps AP Calculus AB students explore the Extreme Value Theorem (EVT) in an intuitive way before taking formal notes on the topic. Students begin with a real-world analogy — hiking a trail — to understand the concept of absolute maxima and minima. Students will: ✔ Analyze continuous functions on closed intervals ✔ Predict extrema and verify their findings through graphing ✔ Graph two functions by hand and two using a graphing calculator The activity emphasizes why c
10th - 12th
Calculus
Limits and Continuity Review: Interactive Around the Room Circuit for Calculus
Limits, Continuity & IVT Review | AP Calculus AB & BC Interactive Around-the-Room Circuit Activity End your AP Calculus AB or BC limits unit with this engaging Around-the-Room circuit activity that gets students moving, thinking, and collaborating while reviewing essential calculus concepts. This interactive scavenger hunt is a fun, low-prep alternative to traditional worksheets and keeps students actively involved in their learning. Students complete 12 self-checking, AP-style problems focu
10th - 12th
Calculus, Math, Other (Math)
Also included in: BUNDLE! Comprehensive Limits and Continuity Review for Calculus Students
Product and Quotient Rules for Derivatives Notes
These notes cover where the product and quotient rules for finding derivatives come from. Students will be taking derivatives analytically (algebraically) and numerically. It's important to not that students should know the chain rule before attempting these problems. In my classroom, we learn the chain rule first and then practice it with the product and quotient rules. This note sheet formatted to be a 1/2 sheet of paper. It is intended to hand out to the students so that they do not have to
9th - 12th, Higher Education
Calculus
Also included in: Calculus Part 3 Notes (Derivative and Antiderivative Methods)
Product and Quotient Rules for Derivatives Assignment
This assignment covers finding derivatives using the product and quotient rules (analytically/algebraically and numerically). This assignment is also for students to practice the chain rule - some of the problems are complex and I had students complete them in small groups and compare/check. There is a note sheet that precedes this assignment found in the Texmathlete TPT store. Videos for the notes can be found on the FREE Calculus Slides and Videos for You and Your Students slides in the Tex
9th - 12th, Higher Education
Calculus
Also included in: Calculus Part 3 Assignments (Derivative and Antiderivative Methods)
Chain Rule / u-Substitution for Derivatives Notes and Bookmark
These notes cover finding derivatives using the chain rule (u-Substitution for derivatives). There is also a "cheat sheet" that you can print 2 pages to 1, then copy front to back. It will make 4 bookmarks (for the interactive journal) for your students. I used cardstock and my students found it helpful to just pull that out when they needed it. There is another product in the Texmathlete store that includes the bookmark and 7 "formula quizzes" to give the students. Mine did not need to know 10
9th - 12th, Higher Education
Calculus
Also included in: Calculus Part 3 Notes (Derivative and Antiderivative Methods)
Chain Rule / u-Substitution for Derivatives Assignment
This assignment covers the chain rule/u-Substitution for derivatives. There is a note sheet that precedes this assignment found in the Texmathlete TPT store. With that note sheet, there is a pdf that can be copied to make bookmarks for your students - it has all of the derivative and integral rules for AP Calculus AB and Calculus BC. Videos for the notes can be found on the FREE Calculus Slides and Videos for You and Your Students slides in the Texmathlete TPT store.
9th - 12th, Higher Education
Calculus
Also included in: Calculus Part 3 Assignments (Derivative and Antiderivative Methods)
The Final Countdown: 10 Things to Remember for AP Calculus
This resource is designed as a high-leverage, one-page "cheat sheet" that distills the most critical concepts for the AP Calculus AB exam into a student-friendly reference guide. It serves as a visual anchor for students during their final review phase, focusing on the "Top 10" topics that frequently appear on the test. Product OverviewThe guide covers the heavy hitters of the curriculum, including: Fundamental Theorem of Calculus (FTC): Provides a clear shortcut for the derivative of an accumu
12th
Calculus
Visualizing Calculus: A Visual Reference for Students and Teachers
Bring core calculus concepts to life with this classroom-ready visual resource. Designed by a PhD in mathematics with years of teaching experience, this packet uses clear diagrams and targeted prompts to build conceptual understanding from the ground up. Whether you’re teaching AP Calculus or Calculus I, these visuals help students see the math behind the rules. ✅ What’s Included7 core concepts visualized (25+ pages total)Teacher copies with labeled diagrams and instructional notesStudent copi
11th - 12th, Higher Education
Calculus
Vector Method Match
For this activity/card sort, students sort out what action they should take depending on what they are looking for. My students glued/taped their matches in their interactive notebook.
9th - 12th, Higher Education
Calculus, Physics
Differential Calculus Quick Study Guide
Quick study guide for Differential Calculus. Includes formulas for derivatives, definitions of theorems, and hints for curve sketching, related rates, tangent lines, linearization, optimization, implicit differentiation, derivative of an inverse, error approximation, and velocity/acceleration.
10th - 12th, Adult Education, Higher Education
Calculus
Calculus Integration Bundle of Fun Activities
This Integration Fun Bundle for Calculus plus Bonus includes resources which are engaging and fun, but are also rigorous and comprehensive. Use for end of unit, end of year, Subs, extra credit, or a fun assessment. All answer keys included. Some resources include Homework and quizzes. Please look at the individual previews. __________________________________________________________________ You may also like: ★ Bigger Bundle of Integration Activities ★ Definite Integration FUN Notes and Pract
11th - 12th, Higher Education
Calculus
Euler's Method Assignment
This assignment covers Euler's Method for estimating solutions to differential equations. There is a note sheet that precedes this assignment found in the Texmathlete TPT store. Videos for the notes can be found on the FREE Calculus Slides and Videos for You and Your Students slides in the Texmathlete TPT store.
9th - 12th, Higher Education
Calculus
AP CALCULUS AB - UNIT 2 DERIVATIVES REVIEW WORKSHEET (#4)
This Calculus worksheet is intended for students after they have learned the following Unit 2 topics: 2.6 - Derivative rules: constant multiple 2.7 - Derivatives of cosx, sinx, e^x 2.8 - The product rule 2.9 - The quotient rule 2.10 - Finding the derivatives of tangent, cotangent, secant, and cosecant functions Use this worksheet as homework, a class activity, or as a warm-up to lead into preparing for a Unit 2 test on derivatives. I have also included a key in the PDF, to use for reference. Y
10th - 12th, Higher Education
Calculus, Math
AP CALCULUS AB - 5.9 CONNECTING F(X) WITH ITS 1ST & 2ND DERIVATIVES WORKSHEET
This Calculus worksheet is intended for students after they have learned the 5.9 AP Calculus AB Topic: "Connecting a Function, Its First Derivative, and Its Second Derivative." When given the graph of f', often times my students struggle with identifying where the graph of f has a local minimum or maximum, where f is increasing/decreasing, or identifying where the graph of f is concave up/down, or has a point of inflection. Similarly, when given the graph of f'', they tend to struggle with ide
10th - 12th, Higher Education
Applied Math, Calculus, Math
Introduction to Implicit Differentiation Matching Puzzle
This matching/domino/puzzle activity is for an introduction to implicit differentiation - BEFORE the students have taken notes, etc. Students only need to know the power and product rules to complete the activity (the question on each card matches to an answer on another card). There are easier problems that should help them figure out the harder problems. dx/dx is left in the problems to help them understand what they are doing - hopefully, they will ask about it needing to be there when they f
9th - 12th, Higher Education
Calculus, PreCalculus
Derivative Formulas Foldable Mini Book Calculus
This Calculus Derivatives Mini Book is perfect for all Calculus students and includes the 24 derivative formulas that students must learn to succeed in Calculus, all in a small pocket sized format. What's included? Two versions of the mini book, one with the formulas typed in and the other for the students to fill in themselves.Illustrated directions. The booklet is easy to make and requires just one sheet of paper per book. (One sided printing). Finished size 4” by 2 3/4”. No glue, no tape.
11th - 12th
Calculus
AP Calculus AB Cheatsheet | Full course review | 2026 aligned
A two-page formula and concept reference for the entire AP Calculus AB course - every unit, every key formula, every theorem your students need for exam prep. All 8 Units Covered: 🌅 Unit 1: Limits & Continuity – limit definitions, one-sided limits, limit properties, growth rates, horizontal asymptotes, continuity types (removable, jump, asymptote), IVT 🧒 Unit 2: Fundamentals of Differentiation – definition of derivative, AROC, power rule, product rule, quotient rule, trig derivatives, ex
9th - 12th
Calculus
Also included in: AP Calculus AB + BC Cheatsheets | Full course review | Bundle
Power Rule Worksheet
This Power Rule worksheet provides straightforward, independent practice for students learning how to differentiate functions using the Power Rule. Unlike a guided worksheet, this resource is designed for students who are ready to apply the rule on their own without structured steps or prompts. The problems increase in complexity to help build fluency and confidence while reinforcing foundational derivative skills. Perfect for classwork, homework, bell-ringers, or quick review before quizzes and
11th - 12th, Higher Education
Calculus, PreCalculus
Implicit Differentiation, Geometry, Related Rates Matching
This card sort/domino/matching activity is intended for the end of an implicit differentiation or ideally at the very, very beginning of related rates. This is an easy process of elimination task, but it is made for the questions that come after - questions you ask about structure, patterns, coefficients, etc. It lets them see what their derivatives should look like in the middle of the problems (and a reminder about the need for the product rule). It was the opening activity on the first day of
9th - 12th, Higher Education
Calculus
Calculus Circuit Practice Training AP Calculus AB / BC
Students will love these Self- checking Calculus Circuits for practice. Teachers will love these, too, as they include fully typed solutions. No Prep! Circuits are from AP Units 1 - 9*. If you have never used circuits, then the best way to describe them is a combination of a scavenger hunt and worksheet with the answers embedded. Students start at the first problem, and after solving it, search the circuit for the correct answer, completing the problem in that section. This continues until
11th - 12th, Higher Education
Calculus
Horizontal and Oblique/Slant Asymptotes Assignment
This assignment covers using limits to determine the equations for horizontal, vertical, and oblique asymptotes. There is a note sheet that precedes this assignment found in the Texmathlete TPT store. Videos for the notes can be found on the FREE Calculus Slides and Videos for You and Your Students slides in the Texmathlete TPT store.
9th - 12th, Higher Education
Calculus, PreCalculus
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