Flipped Math
Calculus AB/BC - Determining Concavity of Functions over Their Domains
Time to take a second look at derivatives finding concavity. While watching the video, learners find out the definition of concavity. Individuals see how to determine whether an interval is concave up or concave down using graphs and the...
West Contra Costa Unified School District
Families of Functions Sort
Have some fun with functions with a short activity that asks learners to first sort scatter plot in terms of their correlation. They then sort graphs of different types of functions in terms of key features, such as slope.
Flipped Math
Calculus AB/BC - Connecting a Function, Its First Derivative, and Its Second Derivative
Uncover what the first and second derivatives reveal about the function. Pupils move beyond sketching graphs to determine what derivatives tell about the function itself. The video reminds learners about particle motion and how to...
Curated OER
Senior Analysis: Graphing Rational Functions
Budding mathematicians graph given functions, identify the asymptotes, graph absolute values, and write a table of points. This three-page instructional activity contains 23 problems.
Illustrative Mathematics
Identifying Quadratic Functions
Put your high schoolers to the test and see how well they know their quadratic functions. With excellent thought-provoking questions, learners use what they know about creating quadratic equations based off different pieces of...
Curated OER
Worksheet 13: Slope and Concavity
In this function worksheet, students determine the equation of a line, compute slope and concavity of a graph, and find the maximum volume of three-dimensional figures. This one-page worksheet contains six multi-step problems.
Flipped Math
Calculus AB/BC - Interpreting the Behavior of Accumulation Functions Involving Area
Accumulation functions should behave like other functions. Using content from Unit 5, pupils analyze the first and second derivative to determine the behavior of an accumulation function. Learners find out how to calculate the relative...
Flipped Math
Calculus AB/BC - Approximating a Function's Value Using Local Linearity
No need to be exact every time. Pupils watch an engaging video on approximating function values. They see how to write the equation of a tangent line, use it to calculate approximations, and then determine whether it is an overestimate...
Curated OER
Concavity of a Graph
Learners explore the graph of a function. For this calculus lesson, students identify when and where the graph is increasing or decreasing. They identify if it concave up or down by moving the cursor.
Curated OER
Functions and Differentiation
In this calculus worksheet, students identify functions based on different Theorems as it relates to calculus and the Fundamental Theorem. There are 13 questions dealing with differentiation and trigonometric graphs.
West Contra Costa Unified School District
Using Derivatives to Graph Polynomials
You can learn to graph as well as a calculator using calculus. The lesson introduces using derivatives to find critical points needed to graph polynomials. Pupils learn to find local maximums and minimums and intervals of increase and...
Curated OER
Applications of Derivatives: Concavity and Optimization
For this derivatives worksheet, students sketch the graph of a function by determining the local maxima, minima and inflection points. They graph a second function when given the interval. Students solve two word problems involving...
Curated OER
Rate Equations, Slope Functions and Concavity
In this rate equation worksheet, students identify an inflection value for given functions. They determine an expression that stultifies a given rate equation. This three-page worksheet contains definitions, explanations and examples. ...
Curated OER
Exploring Functions and Their Derivatives
Students explore and derive functions. In this calculus lesson, students graphs a function and find the derivative of each function as they compare exponential graphs. They relate and compare each function to its derivative.
Curated OER
Teen Pregnancy: Investigating Cubic Functions
For this teen pregnancy worksheet, students use a scatter plot and cubic functions to solve word problems about teen pregnancy. Students complete 7 problems.
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.
Illustrative Mathematics
Identifying Quadratic Functions (Vertex Form)
Pupils calculate the equation of a quadratic in vertex form from a specific graph and determine an equation that would fit the description of a parabola. The final question determines the individuals' understanding of the signs of the...
West Contra Costa Unified School District
Matching Quadratic Functions
Ever sigh when learners ask why they have to know so many different forms of the quadratic equation? Here is a lesson that comes in handy! Using hands-on matching activities, quadratic equations are explored through their graphical...
Curated OER
Analyze This Function
In this derivatives worksheet, students solve 11 short answer and graphing problems. Students find inflection points, increasing and decreasing intervals, maximums and minimums, and graph an exponential derivative. Students use the...
Curated OER
Average Value of a Function
For 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
From F to F
In this derivatives activity, students solve 16 short answer problems. Students use a graph of a derivative to determine local maximums and minimums, concavity, inflection points, etc.
Curated OER
Graphs and Derivatives
In this graphs and derivatives worksheet, students graph the derivative of a function. They find the intervals and identify the maximum and minimum. This one page worksheet contains three multi-step problems.
Curated OER
AP Calculus Practice Exam 2008
In this calculus practice exam instructional activity, students solve 16 multiple choice problems. Students find derivatives, points of continuity, area, rates, etc.
Curated OER
Increasing and Decreasing Functions
Students discuss the process involved in increasing and decreasing functions. In this calculus lesson, students analyze functions based on increasing, decreasing, constant, concave up, concave down and point of inflection. They base...