Function and Not a Function
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Programs & methods
Limit of Functions
Chapter: LimitsThis chapter introduces the concept of limits, which form the foundation of calculus. Limits describe how a function behaves as the input approaches a particular value, even if the function is not defined at that value. Understanding limits is essential for studying continuity, derivatives, and integrals. Students will learn to evaluate limits using graphs, tables, algebraic techniques, and analytical reasoning. The chapter covers one-sided limits, limits at infinity, and infin
10th - 12th, Higher Education
Calculus, Math Test Prep, PreCalculus
Calculus Integration with Inverse Trig Functions Circuit Training
Challenge your Calculus students' skills solving problems involving Integration with Inverse Trig Functions with this self-checking circuit style worksheet. This practice is designed to build your students' skills and proficiency. Included are 12 problems involving Inverse Trig functions including inverse sine, cosine, tangent, secant, and cotangent. Some problems include trig functions, exponentials and/or basic rules in which Inverse trig functions as components. Students should not need a
11th - 12th, Higher Education
Calculus
Also included in: Calculus 2 Circuit Training Bundle
Polar Parametric Vector Valued Functions Editable Unit Test | Calc BC | Calc 2
Use this Editable Unit Assessment for Polar, Parametric, and Vector Valued Functions as a Test or Review. You can also use the questions as a Test Bank for quizzes or Exit Slips in Calculus 2 and AP Calculus BC. This is NO PREP for you as all solutions are included and are typed for your convenience. Time saver and classroom tested. The assessment is editable in MS word. You may need an equation editor such edit some of the equations. There is a mix of multiple choice (3) and free response
11th - 12th, Higher Education
Calculus
AP® PreCalculus - Unit 4: Functions and Modelling
Unit 4: Functions & ModelingTopic 1: Function Characteristics4.1 Function notation & structure 4.2 Average rate of change 4.3 Domain & range 4.4 Composition of functions 4.5 Inverse functions 4.6 Even & odd functions Topic 2: Transformations of Functions4.7 Vertical & horizontal shifts 4.8 Reflections 4.9 Stretching & compressing 4.10 Combined transformations 4.11 Piecewise functions Topic 3: Function Families & Modeling4.12 Linear vs nonlinear models 4.13 Polynomial models 4.14 Rational models
12th, Higher Education
PreCalculus
Also included in: AP® PreCalculus - Full Course Curriculum
Limits of Trig Functions for Calculus with optional QR
Your Calculus students find the limits of 16 trigonometric functions, some of which use basic identities, and others use the “special Limits", sin x /x, 1 - cos x / x, and variations of them. Use as Task Cards, Station cards, or as a worksheet. A second self-checking set with QR included. This practice will build your students' skills and proficiency on this topic. What's Included?Two sets of 16 Task cards, one with QR and one without. Students do not need to be on the internet to get the an
11th - 12th, Higher Education
Calculus, Math
Also included in: Limits and Continuity Calculus Unit 1 Bundle
Hyperbolic Functions and Calculus
Hyperbolic Functions are part of the Calculus Curriculum at colleges and universities. Though not necessarily on the AP Calculus exams, the topic is necessary for transition for those students who have earned college credit through the AP program and are continuing their education and pursuing a STEM career. This is a great topic for after the AP Calculus exams. Included:20 Task cards # 1 - 9 Students determine the derivatives of hyperbolic functions and hyperbolic inverse functions using the c
11th - 12th, Higher Education
Calculus
Derivatives of Exponential Functions Notes and Flash Cards
These notes cover finding derivatives of expressions involving exponential functions (using the chain rule). It also includes a set of flashcards for just that and another set that has an exponential expression on one side and both the derivative and integral on the other for students to quiz each other (the one answering just sees the function). 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 write everything down - n
9th - 12th, Higher Education
Calculus
Also included in: Calculus Part 3 Notes (Derivative and Antiderivative Methods)
Integrals Involving Exponential and Logarithmic Functions Notes and Flashcards
These notes cover finding antiderivatives/indefinite integrals of functions that result in exponential or logarithmic expressions (using u-Substitution). It also includes a set of flashcards that has an exponential expression on one side and both the derivative and integral on the other for students to quiz each other (the one answering just sees the function). 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 write ever
9th - 12th, Higher Education
Calculus
Also included in: Calculus Part 3 Notes (Derivative and Antiderivative Methods)
Function Derivative Rules Coloring Activity | Calculus Review | Low Stress
Function Derivative Rules Coloring Pages | Calculus ReviewLooking for an engaging, low-prep way to help students memorize function derivative rules in your Calculus class?This set of coloring pages helps students review key derivative rules while staying focused, engaged, and relaxed. Perfect for AP Calculus review and test prep, these activities provide a low-stress review, helping students remember these differentiation rules. What’s Included:11 total coloring pages covering essential derivat
10th - 12th, Higher Education
Calculus, Coloring Pages
Calculus Worksheet - Derivatives of Trig Functions (Matching)
Need a worksheet to help your Calculus or AP Calculus students practice finding the derivatives of trigonometric functions? This matching worksheet will give students practice finding the first and second derivatives and using the first derivative to find the slope. Trig functions use only the basic derivative rules (product rule, quotient rule and chain rule) so it is wonderful for students who may or may not have learned the derivatives of exponentials, logarithms, etc. An answer key is inc
10th - 12th, Higher Education
Calculus, Math Test Prep
Also included in: Calculus Derivative Worksheet Bundle
Derivatives Involving Logarithmic Functions Notes
These notes cover finding derivatives of logarithmic functions - using the chain rule. 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 write everything down - not for them to cram everything on the note page. They can use it as part of their interactive notebook OR they can staple/tape/glue it to wherever they are taking notes. My students kept it out during the lecture and labeled their notes to reference it and it wa
9th - 12th, Higher Education
Calculus
Also included in: Calculus Part 3 Notes (Derivative and Antiderivative Methods)
Precalculus Exam Reviews/Calculus Prerequisite Reviews
This is a set of three review sheets that are designed to be used at the beginning of Calculus course or as exam reviews for Algebra 2 or Precalculus. They could also be used for SAT or ACT prep, college entrance exam review or for any purpose you wish. Included are reviews for: Exponents, radicals and functionsPolynomial functions and manipulationsThe unit circle and trigonometric functionsThe first two have optional answer banks that you can give students to use as they work out the review p
10th - 12th, Higher Education
Calculus, Math Test Prep, PreCalculus
CCSS
HSA-SSE.B.3a
, HSA-SSE.B.3c
, HSA-APR.A.1
+9
Graphing the Sine and Cosine and Properties Notes Organizers
Graphing the Sine and Cosine Functions using their key properties could not be easier for your students to learn to do by hand than with this versatile and engaging resource with notes and step by step graphic organizers. Included in the Lesson: Illustrated Guided Notes on graphing the Sine and Cosine by hand using the 5 Point Method for both the Sine and the Cosine. The notes also include formulas for the properties, including Amplitude, Phase Shift, Vertical Shift, and Period. 16 graphic
10th - 12th, Higher Education
Math, PreCalculus
CCSS
HSF-IF.B.4
, HSF-IF.C.7
, HSF-TF.B.5
Also included in: AP PreCalculus Unit 3 Trig Functions Activity Bundle
Integration U substitution Activity for Calculus
This Integration of Transcendental Functions with u-Substitution Dominoes matching activity will challenge your Calculus students while giving them a fun outlet to learn along with the ability to self check their work. Included are 11 definite integrals with Transcendental functions including the 6 trig functions, logarithmic, exponential, and inverse trig functions. It is suggested that students not use a graphing calculator. All answers are in exact form and many answers are similar. Stude
11th - 12th, Higher Education
Calculus
Derivative Basics (Power Rule/Basic Trig) Notes
These notes cover simple and complex power rule and the six basic trig function problems. There is also a look at the continuity and differentiability of piece-wise functions. 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 write everything down - not for them to cram everything on the note page. They can use it as part of their interactive notebook OR they can staple/tape/glue it to wherever they are taking notes. My
9th - 12th, Higher Education
Calculus, PreCalculus
Graphs of First & Second Derivatives Identify and Match f, f', f''
In this activity students practice identifying the Graphs of a function and its first and second derivative, f, f ', and f ''. They analyze 3 graphs, one blue, one black, and one red, superimposed on the same coordinate grid, to determine which is the graph of original function, the graph of first derivative, and the graph of the second derivative. The activity does not require differentiation, but requires students to understand increasing, decreasing, relative extrema, and concavity. Man
11th - 12th, Higher Education
Calculus, Graphing
Also included in: Calculus Applications of Differentiation Unit Bundle
Calculus Part 3 Notes (Derivative and Antiderivative Methods)
These notes cover introductions to the following topics: Chain Rule (including a bookmark of all derivative and integral rules and 7 formula quizzes)Product and Quotient Rulesu-Substitution for IntegralsDerivatives and integrals of exponential functions (including 2 sets of flashcards)Derivatives and Integrals involving logarithmic functionsThese note sheets are formatted to be on 1/2 sheets of paper. They are intended to be handed out to the students so that they do not have to write everything
9th - 12th, Higher Education
Calculus
Finding Limits Analytically Digital Maze plus Printable and Digital HW
This rigorous and fun digital practice for Finding Limits Analytically (Algebraically) before Transcendentals is NO PREP and paperless. Students find the limits analytically for a variety of functions as they work through a fun maze. Each solution leads to the next problem. The Limits do not include trig functions or other transcendentals or limits as x approaches infinity. Problems include polynomials, rational functions, and piecewise defined functions with 20 possible questions of which 15
11th - 12th, Higher Education
Calculus, PreCalculus
Also included in: Limits Bundle of Fun Activities for Calculus
Chain Rule Activity Bundle | Guided Notes, Practice, Exit Tickets & Games
Help your calculus students understand the Chain Rule by thinking in layers! This resource uses a memorable inside-out “pretzel” approach to help students identify the inside function, track each layer of a composite function, and build the derivative one piece at a time. This is especially helpful for students who struggle with composition of functions, forget the inside derivative, or need a stronger foundation before future topics like u-substitution. What’s Included Guided notes Scaffol
11th - 12th, Higher Education
Calculus
Precalculus Prioritized Standards | AI-Ready | Curriculum Guide (PDF)
Precalculus prioritized standards aligned to Common Core (+). Designed from a calculus teacher’s perspective to prepare students for AP Calculus AB/BC and advanced STEM coursework. Focus on algebraic fluency, function analysis, trigonometric reasoning, and modeling.Are you trying to figure out what actually matters in Precalculus—and what truly prepares students for Calculus? This resource is built with a clear goal: 👉 Prepare students for the pace, rigor, and abstraction of AP CalculusNot j
9th - 12th, Adult Education, Higher Education
Calculus, Math Test Prep, PreCalculus
CCSS
HSN-CN.A.3
, HSN-VM.A.1
, HSN-VM.A.3
+15
Also included in: Precalculus Prioritized Standards Bundle | PDF + Editable Google Doc
Limits on Tables Practice Worksheet
Strengthen your students’ understanding of limits with this focused Calculus worksheet on evaluating limits from tables. In this activity, students analyze numerical data presented in table form to determine the limit of a function as xxx approaches a given value. Students must express each answer using proper limit notation, reinforcing both conceptual understanding and mathematical communication. Skills Reinforced: Interpreting function behavior from a table Identifying one-sided and two-si
11th - 12th, Higher Education
Calculus, Math Test Prep, PreCalculus
CCSS
MP6
Circuit AP Calculus AB or BC Volume with known cross sections with SOLUTIONS
This circuit contains 11 problems requiring students to understand and apply the concept of volume by slicing. It even includes a problem that provides the area of a cross sectional slice as a function, requiring students to accumulate that area and not create a function for it. A done out solution key is attached as well. Circuits are designed where students start with the very first cell labeled #1 and solve the problem. Find the cell that has the answer to #1 in the corner and that problem b
9th - 12th, Higher Education
Calculus
Also included in: AP Calculus BC Bundle
Derivative of Composite, Implicite , Inverse and Related rates
Key Differentiation Techniques Composite Functions (Chain Rule): Used when one function is nested inside another, such as H(x) = G(F(x)). The derivative is found by taking the derivative of the outside function and multiplying it by the derivative of the inside function: H'(x) = G'(F(x)) * F'(x).Implicit Differentiation: Applied when a function is not isolated for one variable (e.g., y^2 - 3xy + x^2 = 7). You differentiate both sides of the equation with respect to x, treating y as a function of
10th - 12th, Higher Education
Calculus, Math Test Prep, PreCalculus
Also included in: Derivative of Functions review
AP Precalculus Mock Free Response FRQ Set (Unit 3)
Are you looking for AP-style Free Response questions to add to your formal assessment days in AP Precalculus? Look no further. This is a set of five Free Response prompts designed for your use in Unit 3: Trigonometric and Polar Functions. ☑️ What types of questions are included in the set?This task model will present a real-life context modeled by either a sine or cosine function. Both parts will require students to construct the sinusoidal model by using the context to determine the ampli
10th - 12th, Higher Education
Math, PreCalculus
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