Curated OER
Average Value of Functions
In this integrals and average value instructional activity, learners problem solve thirty equations or word problems involving average value of functions, volume and integrals.
Curated OER
Challenge Sheet 3: Average Value of a Function
In this average value worksheet, students determine the average value of functions, sketch graphs of continuous intervals, evaluate integrals, find the average value of a function and convert limits to a definite integral. This one-page...
Curated OER
Instantaneous Rate of Change of a Function
Pupils draw the graph of a door opening and closing over time. They graph a given function on their calculators, create a table of values and interpret the results by telling if the door is opening or closing and evaluate the average...
Balanced Assessment
On Averages and Curves
Determine the average on a curve. The class finds graphical representations of averages and expresses them both symbolically and on the graph. The assessment requires class members to justify using average to describe graphs.
Curated OER
Average Value of a Function
In this calculus worksheet, 12th graders calculate the line tangent to a curve and find the average value of a function. There are 12 questions.
Curated OER
Find the Average Value of a Function
In this calculus worksheet, 11th graders calculate the average value of a function. They find the line tangent to a curve and graph the equation. There are 15 questions.
Curated OER
Worksheet 2: Graphs, Functions and Derivatives
In this math worksheet, students answer 7 questions having to do with graphing derivatives of functions, rectilinear motion, speed and distance.
West Contra Costa Unified School District
Average Rate of Change
The concept of slope gets an approachable, yet theoretical, treatment in a comprehensive algebra lesson. The use of functional notation and problem-solving techniques keep the material rigorous, but detailed teaching notes and lots of...
EngageNY
Graphs of Simple Nonlinear Functions
Time to move on to nonlinear functions. Scholars create input/output tables and use these to graph simple nonlinear functions. They calculate rates of change to distinguish between linear and nonlinear functions.
Curated OER
Average Value of a Function
In this value learning exercise, students determine the average amount of money in an account at various period of time. This one-page learning exercise contains one multi-step problem. An example and explanation is provided.
Flipped Math
Calculus AB/BC - Using the Mean Value Theorem
At some point the rate of change must be the average. Pupils first see the definition of the Mean Value Theorem and hear an explanation of it in simple terms. The helpful video then compares the Mean Value Theorem with the Intermediate...
Curated OER
Average Value of a Function
Students investigate the average value of a function given different interval values. For this calculus lesson, students explore word problems and apply their knowledge of average value to find the answer. They apply previous knowledge...
Howard Hughes Medical Institute
Spreadsheet Tutorial 1: Formulae, Functions, and Averages
Spread your knowledge of spreadsheets. The first of five tutorials in the Spreadsheet Data Analysis unit introduces the basics of spreadsheets. It shows future data analysts how to organize and format tables, and how to use functions to...
Curated OER
Exploration 1: Instantaneous Rate of Change Function
In this function worksheet, students read word problems and write functions. They determine the instantaneous rate of change and identify intervals. This three-page worksheet contains approximately 20 problems.
West Contra Costa Unified School District
Average Rate of Change
Learners investigate average rates of change for linear functions and connect the concept to slope. They then determine average rates of change in quadratic and exponential functions.
EngageNY
Interpreting Quadratic Functions from Graphs and Tables
Seeing functions in nature is a beautiful part of mathematics by analyzing the motion of a dolphin over time. Then take a look at the value of a stock and maximize the profit of a new toy. Explore the application of quadratics by...
Mt. San Antonio Collage
Quiz 1: Functions, Domain and Range
Take the work out of worksheets and use these problems and worked-out answer key as a resource. The problems reinforce skills in domain and range, identifying graphs, and even and odd functions.
EngageNY
The Concept of a Function
Explore functions with non-constant rates of change. The first installment of a 12-part module teaches young mathematicians about the concept of a function. They investigate instances where functions do not have a constant rate of change.
EngageNY
Modeling with Exponential Functions
These aren't models made of clay. Young mathematicians model given population data using exponential functions. They consider different models and choose the best one.
Curated OER
Functions
In this functions worksheet, students solve and complete 5 different sets of problems that include determining functions on intervals. First, they define a definite integral and the Fundamental Theorem of Calculus. Then, students draw a...
Curated OER
Lesson 25 - Applications of Logarithmic Functions
in this applications of logarithmic functions activity, students solve 11 short answer problems. Students use logarithms to find half lives, compound interest, and population growth given a word problem.
Curated OER
Graphing of Functions Using First and Second Derivatives
In this calculus worksheet, students solve problems using the first and second derivatives. They define the behavior of the function based on the derivative. There are 11 questions with an answer key.
Flipped Math
Calculus AB/BC - Estimating Derivatives of a Function at a Point
It seems like it should be about three. Pupils learn to get an estimate of the derivative of a function at a point by using the derivative functionality of their graphing calculators. They take that information to determine the equation...
College Board
Reasoning from Tabular Data
Don't table the resource—use it now. An AP® Calculus curriculum module encourages the use of tabular data throughout the course. It provides some example topics, such as rate of change, net change, and average value of a function, where...