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AP Calculus Project: Roller Coaster with Piecewise Functions & Derivatives
Engage your AP Calculus students after the exam with this hands-on and creative project! Students design a mathematically valid roller coaster using piecewise functions that are continuous and differentiable at each transition point. They must graph the coaster, build a 3D model, and provide formal mathematical proofs of continuity and differentiability. Perfect for: AP Exam wrap-up weeks Summative assessments Honors Calculus projects Includes: Full student instructions Grading rubric Proof
10th - 12th
Calculus
Finding g and Moment of Inertia Using a Physical Pendulum using a meter stick
This engaging Compound (Physical) Pendulum Lab allows students to explore rotational motion by using a meter stick suspended from different pivot points. Students will measure the period of oscillation at multiple pivot locations, analyze how the distance to the center of mass affects motion, and use their data to determine gravitational acceleration (g) and the moment of inertia (I). This hands-on investigation strengthens understanding of key physics concepts including torque, rotational
11th - 12th, Higher Education
Calculus, Engineering
DERIVATIVES HIDING IN THE LIMIT FORMULA
Description: Derivative Detectives 🕵️♂️In this activity, students become Derivative Detectives and solve the mystery of hidden derivatives! Each problem is written as a limit, but secretly represents a derivative using the definition: f′(a)= Lim h→0(f(x+h)-f(x))/h Students must analyze each expression, identify the function and the point, and determine the derivative. Then, they match their answers to the correct choices. This activity helps students: Recognize derivatives from limits (fir
11th - 12th, Higher Education
Calculus, Engineering, PreCalculus
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