Flipped Math
Calculus AB/BC - Derivative Rules: Constant, Sum, Difference, and Constant Multiple
Use derivatives to find equations of lines. Pupils learn more rules to use as shortcuts to find derivatives. Using the rules, they find the equations of the tangent line and the normal line at a given point. Scholars then apply the new...
Flipped Math
Calculus AB/BC - Defining the Derivative of a Function and Using Derivative Notation
Pupils learn how to find the derivative of a function by applying the definition using limits. Learners understand that the derivative provides the slope of the tangent line and use that information to find the equation of the tangent...
College Board
2009 AP® Calculus BC Free-Response Questions
Dive into the exam review. Pupils use questions, including one about diving into a pool, to prepare for the AP® Calculus BC exam. Items include contextual and non-contextual questions with contextual examples requiring a calculator....
College Board
2007 AP® Calculus BC Free-Response Questions
Provide a review for the exam so individuals don't tank. AP® provides the free-response questions for teachers to use to help their pupils prepare for the exam. The six BC questions from 2007 include regions bounded by functions, water...
College Board
2009 AP® Calculus AB Free-Response Questions
What was one of the big takeaways from 2009? By reviewing the released AP® Calculus free-response questions, pupils and teachers realize that performing mathematics is not all there is to doing well on the exam. Several items require...
Mt. San Antonio Collage
Circles
Don't circle around the topic, but get right to the center with tons of practice regarding circles in geometry. The note-incorporated learning exercise provides guided practice through many topics such as central angles, inscribed...
Flipped Math
Unit 11 Review: Circles
Solve problems around a circle. Pupils watch a video that shows how to apply concepts about circles and related angles and segments to find solutions to word problems. Learners then review the different concepts from the unit in...
Flipped Math
Secants and Tangents
Put the vertex in, put the vertex out. Pupils explore theorems about the relationships of lengths of segments and angles of line segments that intersect inside or outside the circle. Learners use the theorems to solve problems involving...
Flipped Math
Tangents to Circles
Touch a circle once. Individuals watch a video and learn two theorems related to tangents and circles. The pupils then apply the theorems to find missing angle measures and lengths in figures. At the end, they practice their skills on...
Flipped Math
Calculus AB/BC - Unit 7 Review: Differential Equations
Differentiate everyone's knowledge. Pupils work through nine review questions to highlight key concepts from Unit 7. Items range from finding slope fields and reasoning with them to finding general and particular solutions of...
Flipped Math
Calculus AB/BC - Reasoning Using Slope Fields
Find a solution in the field. An informative video presentation shows pupils how to use the information from a slope field to sketch the graph of a particular solution to a differential equation. Individuals learn how to determine the...
Flipped Math
Calculus AB/BC - Sketching Slope Fields
Frolic through a field of slopes. Learners watch a video describing slope fields and how to create one. Scholars use given slope fields to determine the equation of a tangent line and the possible differential equation. Pupils continue...
Flipped Math
Calculus AB/BC Unit 4 Review: Analytical Applications of Differentiation
It's nice to know that there are actual real-world uses of derivatives. Scholars review their knowledge of the applications of derivatives from the unit. They work on a set of practice problems to test their understanding.
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...
Flipped Math
Calculus AB/BC - Selecting Procedures for Derivatives
Don't get lost trying to memorize all those derivative rules. Scholars review the different methods at their disposal to determine derivatives from Units 2 and 3. They fill out a graphic organizer and then complete a set of practice...
Flipped Math
Calculus AB/BC Unit 3 Review: Differentiation
It's time to take stock of the class's knowledge of derivatives. Individuals review how to take the derivatives of composite, implicit, and inverse functions. They complete some problems involving the Chain Rule, implicit...
Flipped Math
Calculus AB/BC - Differentiating Inverse Functions
Reverse any loss of knowledge on inverse functions. Individuals watch a video to learn about differentiating inverse functions. They memorize the rule, then see how to apply it in finding derivatives and determining equations of tangent...
Flipped Math
Calculus AB/BC - Implicit Differentiation
It's implied that implicit differentiation is important. Viewers of an engaging video learn the process of implicit differentiation. After watching several examples, they see how to apply implicit differentiation to find the vertical and...
Flipped Math
Calculus AB/BC - Unit 2 Review: Differentiation
Tie up everything in one differentiable bow. Pupils work through 20 problems to review the concepts from the unit. The problems range from finding the average rate of change to finding the derivatives of various functions that require...
Flipped Math
Calculus AB/BC - Can Change Occur at an Instant?
Be instantly transfixed by the idea of instantaneous rates of change. Scholars watch an informative video that introduces the fathers of calculus, Newton and Leibniz. They then learn about instantaneous rates of change by first...
College Board
2010 AP® Calculus BC Free-Response Questions Form B
Keep moving along a curve. Two items in the set of released free-response questions from the 2010 AP® Calculus BC exam involve movement along a graph. One involves particle motion along a polar curve while the other uses a squirrel...
College Board
2009 AP® Calculus BC Free-Response Questions Form B
Let them eat cake. The free-response questions from an AP® Calculus BC exam cover several topics that include finding the area under a curve within the context of creating a birthday cake. Calculus concepts include finding rates of...
College Board
2007 AP® Calculus BC Free-Response Questions Form B
There is just a single real-world problem. Released free-response items from the 2007 AP® Calculus BC Form B contains only one real-world question. The question involves rate of change of wind chill scenario. The mathematical problems...
College Board
2005 AP® Calculus BC Free-Response Questions Form B
Let's put it in context. Pupils use the AP® Calculus BC free-response questions to practice for the exam. Five of the six released items deal with mathematical problems, with one using a real-world situation. Learners use differentiation...