Calculation of area between curves and volumes of solids using disk, washer, and shell methods. Connects integral calculus to physical applications like work, arc length, and centroids.
Guide de correction détaillé pour les exercices d'intégrales appliquées à l'économie (IPP, Gini, Surplus).
Feuille d'exercices sur les intégrales appliquées à l'économie pour L1 Éco-Gestion (IPP, Gini, Surplus).
Présentation visuelle pour le cours de calcul intégral appliqué à l'économie (IPP, Surplus, Gini).
Answer key and instructional notes for Lesson 5, focusing on arc length calculations and the distinction between displacement and distance.
A comprehensive grading rubric for the Synthesis Assessment. Includes a 4-point proficiency scale for path analysis, vector kinematics, and structural geometry, along with a rapid evaluation key for teachers.
Presentation for Lesson 5 on arc length and total distance traveled in parametric form.
The final synthesis performance task for the sequence. Students perform a full analysis of a 4-petal rose curve, including area integration, vector differentiation for speed, and arc length setup.
Worksheet for Lesson 5 on calculating arc length and distinguishing between net displacement and total distance.
Final slide deck for Lesson 5 introducing the "Particle Report" synthesis assessment. Provides the raw kinematic data for a 4-petal rose curve and outlines the multi-step analysis requirements for the final performance task.
Presentation for Lesson 4 covering kinematics in parametric form, including position, velocity, acceleration, and speed.
Teacher resource for the Logic Lock activity. Contains a deep dive into the specific logical flaws provided in the "compromised" student work and the correct multi-step calculus resolutions.
Worksheet for Lesson 4 applying derivatives to particle motion, including velocity vectors, acceleration vectors, and speed.
A comprehensive unit on parametric equations and their applications in modeling motion. Students move from the basics of parametric curves to advanced calculus concepts like derivatives, concavity, vectors, and arc length.
An advanced 11th-grade Calculus unit focusing on the integration of parametric and polar coordinate systems. Students analyze motion, calculate complex areas, perform error analysis, and complete a final synthesis project based on particle kinematics.
This sequence covers the calculus of parametric curves, including first and second derivatives, tangent lines, concavity, arc length, and surface area of revolution. Designed for undergraduate calculus students, it emphasizes direct parametric differentiation and integration techniques.
This sequence explores the intersection of calculus and geometry through infinite series and fractals. Students investigate convergence and divergence using visual area models, fractal dimensions, and physical simulations like block stacking.
A comprehensive 11th Grade Calculus sequence covering applications of integration including arc length, surface area of revolution, centroids, and the theorems of Pappus. Students explore the geometric properties of curves and regions using analytical methods.
This sequence connects calculus to physics by applying integration to calculate Work and Force in variable systems. Students explore Hooke's Law, tank pumping, and lifting variable-mass objects, culminating in a mastery assessment of physical engineering applications.
This sequence introduces advanced volume techniques in calculus, including the Shell Method and solids with known cross-sections. Students move from theoretical derivation to a project-based application where they model and calculate the volume of real-world objects.
This sequence guides 11th-grade students through the transition from 2D area calculations to 3D volume determinations using integral calculus. Students will master vertical and horizontal slicing techniques for area, and progress to the Disk and Washer methods for rotational volumes.
A comprehensive Calculus unit focused on calculating areas and volumes using integration. Students move from 2D area analysis to 3D geometric modeling using disks, washers, and cross-sections, culminating in a real-world modeling project.
A comprehensive 11th-grade calculus unit focused on strategic method selection for complex integration. Students transition from basic procedural fluency to high-level diagnostic thinking and real-world applications in physics and engineering.
A 12th-grade calculus unit focusing on advanced integration techniques, including improper integrals, partial fractions, and trigonometric substitution, applied to real-world modeling scenarios like population growth and physics.
This sequence explores trigonometric integration techniques, from power reduction and identity manipulation to the geometric power of trigonometric substitution. Students learn to bridge the gap between algebraic radicals and right-triangle geometry.
Une leçon complète sur le calcul intégral appliqué à l'économie, couvrant l'intégration par parties, l'indice de Gini et les surplus du consommateur et du producteur.
Calculates the total distance traveled and arc length of parametric curves by integrating speed.
Applies derivatives to physics, interpreting parametric equations as position vectors and calculating velocity, speed, and acceleration.
Explores finding second derivatives in parametric form to determine concavity and analyze curve behavior.
Focuses on calculating dy/dx for parametric curves and finding tangent lines, distinguishing between coordinate rates of change and geometric slope.
Students explore the definition of parametric equations, learning to sketch curves by plotting points and eliminating the parameter to find Cartesian equivalents.
A comprehensive performance task where students analyze a raw data set from a simulated particle accelerator to generate a full kinematic report.
Students critique sample calculus work to identify and correct common misconceptions in limits of integration, derivative rules, and coordinate conversions.
A workshop focused on finding areas of overlapping polar curves and managing regions with multiple intersections or negative r-values.
An investigation into motion along polar curves, converting polar paths into parametric velocity and acceleration vectors to analyze particle movement.
Students evaluate the efficiency of rectangular, parametric, and polar methods for various geometric problems, emphasizing when to switch systems for algebraic simplicity.
A cumulative review and application session where students solve complex parametric problems in a workshop setting, culminating in a mastery assessment.
