Graph Analysis and Interpretation (AP Calculus)

Description

Graphical Analysis & Interpretations- A Graph Trifecta Activity.

As you progress through the year in AP Calculus, it is helpful to revisit concepts and big ideas to help students prepare for the rigor of the AP Exam.

This activity is designed to using the same graph that will be used in three different settings students could possibly see on the exam. This resource uses only one graph to create three question sets in an effort to create planned sequencing, scaffolding

& repetition for AP Calculus students.

***(5/5/2022) Revised Key for More Integration #4 POI at x=1 on question 4.

Activity #1: GRAPHICAL ANALYSIS & INTERPRETATION

Students analyze and interpret characteristics of a derivative function that include extrema, intervals of increase/decrease, derivatives, concavity, and mean value theorem.

Activity #2: PARTICLE MOTION and VELOCITY

Students use the graph as a velocity function to answer questions related to the language used with particle motion, including topics for displacement, total distance, average speed, distance traveled, position of a particle given initial conditions, location of a particle and more.

Activity #3: INTEGRATION and ACCUMULATION

This activity will have students use the graph to evaluate concepts and topics related to integration, properties of limits, properties of integrals, and the fundamental theorem of calculus.

Activity #4: BONUS GRAPHS

There are 3 more graphical interpretations where students review key concepts and topics from early units. The prompts discuss horizontal tangent lines, intervals of increase, decrease, critical numbers, extrema, inflection points, and methods of justification. There is a final graphing interpretation for a derivative function to provide an overall review for year-end exam preparation.

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