College Board
2003 AP® Calculus AB Free-Response Questions
Take a free look. Released free-response questions from the 2003 AP® Calculus AB exam show how questions cover different topics. Pupils and teachers review the topics of bounded regions, particle movement, rates, relationships between...
College Board
Approximation
Sometimes close enough is appropriate. A curriculum document for AP® Calculus examines the importance of providing approximation questions throughout the course. It looks at approximating derivative values, approximating definite...
College Board
2008 AP® Calculus AB Free-Response Questions Form B
How would those items score? The resource provides pupils an opportunity to answer actual free-response questions and determine their scores. Items from the AP® Calculus AB exam from the 2008 administration demonstrate how topics appear...
Flipped Math
Calculus AB/BC Mid-Unit 5 Review: Analytical Applications of Differentiation
It's time to put analytical applications to work. Learners use the eight questions of the mid-Unit 5 review to refresh their memories of the key points. Pupils apply what they have learned to use the Mean Value Theorem, find extrema...
Flipped Math
Calculus AB/BC Mid-Unit 6 Review: Integration and Accumulation of Change
Accumulate the content so far. Learners review the content from the first five lessons dealing with accumulation functions. The eight problems go over finding maximums, minimums, concavity, points of inflection, and intervals of increase...
Curated OER
Highs and Lows
Solve problems using integration and derivatives. By using calculus, learners will analyze graphs to find the extrema and change in behavior. They then will identify the end behavior using the derivatives. Activities and handouts are...
Curated OER
Product Rule
In this calculus instructional activity, students find the derivative of a function. They use the product rule to to differentiate each problem. There are 21 problems with an answer key.
Curated OER
Higher Order Derivatives
In this math worksheet, students explore the concept of higher order derivatives. They also use the example to find the fourth order Taylor expansion.
Curated OER
Derivatives and Maximum or Minimum
For this calculus worksheet, students calculate the maximum, minimum, and determine if the graph is concave up or down. There are 2 questions.
Curated OER
Applications of Derivatives: Optimization
In this optimization worksheet, students write a short essay listing the criterion for global minimum. They write directions for finding the global minimum on a closed or open interval.
Curated OER
Integration by Substitution
Looking for help in introducing integration by substitution to your calculus students? Here is a lesson that walks a learner through a review of the change rule, and then by starting with more recognizable derivatives, it helps...
Curated OER
Home Spelling Practice: Words From French
This activity asks middle schoolers to copy words derived from French. While rigor is absent from this assignment, it could be altered slightly to require more thought. Instead, ask that class members look up each English word in a...
EngageNY
Deriving the Quadratic Formula
Where did that formula come from? Lead pupils on a journey through completing the square to discover the creation of the quadratic formula. Individuals use the quadratic formula to solve quadratic equations and compare the method to...
West Contra Costa Unified School District
Law of Sines
One must obey the sine laws. A lesson introduces and derives the Law of Sines for non-right triangles. With examples that use the Law of Sines to determine unknown measures in triangles, the lesson checks to see if the Law...
Curated OER
Differentiation Quiz
In this differentiation quiz worksheet, students solve 10 short answer problems. Students differentiate rational equations, trig functions, exponential models, higher order polynomials, etc.
Curated OER
Differentiation Quiz Form B
In this differentiation worksheet, students differentiate 10 functions in short answer format. Students differentiate trig, logarithmic, cubic, exponential, rational, and higher order functions.
Virginia Department of Education
Circles in the Coordinate Plane
Make the connection between the distance formula and the equation of a circle. The teacher presents a instructional activity on how to use the distance formula to derive the equation of the circle. Pupils transform circles on the...
Curated OER
Derivatives Rules
For this calculus worksheet, 12th graders use the derivative rules to determine the derivative of a function. The one page worksheet has twenty-six problems. Solutions are not provided.
Curated OER
Application of Differentiation: Optimization
In this optimization worksheet, students complete a table identifying the characteristics of a function and it's derivative and provide an illustration of each type of function. Afterward, they use the first derivative test for finding...
Curated OER
Motion of a Bouncing Ball
Twelfth graders complete a unit of lessons on derivatives as they are applied to motion. They observe and discuss demonstrations, conduct an experiment involving a motion sensor, graph and analyze the results, and summarize their findings.
Curated OER
Differentiability and Linear Approximation
In this linear approximation worksheet, students determine the derivative of a function and explore properties of the error when using a tangent line to approximate a function graph. This two-page worksheet contains four problems.
Curated OER
AP Calculus Practice Exam
In this Calculus worksheet, students are provided with practice problems for their exam. Topics covered include derivatives, area bounded by a curve, local maximum, instantaneous rate of change, and the volume of a solid of...
Curated OER
Implicit Differentiation
Students implicitly differentiate functions . For this implicitly differentiating functions lesson, students take the derivative of functions that cannot be solved for a variable. Students find the derivative of an equation...
Curated OER
The Product and Quotient Rules
In this derivatives worksheet, students solve nine short answer problems by multiplying or dividing with derivatives. They answer one true/false question. Students solve five short answer questions.
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