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Curve Sketching and Analysis

Analysis of function behavior using first and second derivatives to identify extrema, concavity, and points of inflection. Integrates limits, asymptotes, and intercepts to accurately visualize complex algebraic expressions graphically.

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Videos

Mastering Math with the Desmos Online Graphing Calculator

Mastering Math with the Desmos Online Graphing Calculator

This comprehensive tutorial introduces students and educators to the Desmos online graphing calculator, a powerful and free tool for visualizing mathematics. The video begins with the basics of accessing the site and graphing simple functions like lines and parabolas, then progressively moves to more advanced topics including trigonometry, polar coordinates, and calculus operations. The narrator demonstrates not just how to plot graphs, but how to use the tool to solve equations, factor quadratics, and visualize systems of inequalities. Key mathematical themes include function families (linear, quadratic, cubic, absolute value, exponential, logarithmic), systems of equations and inequalities, trigonometry (degrees vs. radians), and statistical analysis (mean, standard deviation). The video also highlights the calculator's computational abilities, such as evaluating definite integrals, summations, and permutations, making it a versatile utility for various levels of math. For the classroom, this video serves as an excellent training resource for students transitioning from handheld calculators to computer-based tools. It allows teachers to show students how to verify their algebraic work visually, such as checking factors by looking at x-intercepts or solving systems by finding intersection points. The visual nature of the tool helps bridge the gap between abstract algebraic manipulation and concrete graphical understanding.

The Organic Chemistry TutorThe Organic Chemistry Tutor

13mins 58s

Materials

Curve Quest Worksheet

Curve Quest Worksheet

A two-page print-ready calculus and algebra worksheet guiding students through systematic curve sketching. Features analysis frameworks, polynomial and rational functions, property-based curve puzzles, and precise coordinate grids.

R

Robinson

Sequences

Growth Dynamics Slides

System Dynamics and Chaos

A graduate-level exploration of discrete dynamical systems, moving from linear growth models to the complex, chaotic behavior of the logistic map. Students apply recursive sequences to model biological and economic phenomena, emphasizing stability analysis and bifurcation theory.

10
Radial Slope Slides

Radial Calculus

A comprehensive unit for 12th Grade Calculus students focusing on the derivation and application of derivatives in polar coordinates. Students transition from Cartesian slope to polar slope, analyze horizontal and vertical tangency, investigate behavior at the pole, and solve optimization problems involving polar curves.

15
Coordinate Chronicles Worksheet

Vector Voyages

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.

12
Polar Slope Slides

Polar Differentiation Techniques

This sequence explores the calculus of polar functions, focusing on differentiation techniques. Students will learn to calculate slopes of tangent lines, identify horizontal and vertical tangents, analyze behavior at the pole, and apply optimization to find maximum and minimum distances from the origin.

10
Cusps and Curves Slides

Rational Exponents Blueprint

A sequence for undergraduate students bridging pre-calculus and calculus by focusing on the analytical properties of functions with rational exponents. Students explore graphing, algebraic rewriting, rationalizing for limits, and growth comparison.

11
Tangent Slopes Worksheet

Curve Calculus

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.

10

Lessons

Polynomial Power Review Packet

Polynomial Power Review

A comprehensive AP Precalculus Unit 1 review covering Topics 1.1 through 1.6, featuring student practice problems with AP-style reasoning and a full teacher scoring guide.

2
Zoom Pente Slides

Zoom sur la Pente

Une leçon interactive de niveau Première générale sur la notion de nombre dérivé, s'appuyant sur des visualisations graphiques du passage de la sécante à la tangente, la lecture et le tracé de coefficients directeurs, et le lien avec le sens de variation.

3
Blueprint for Limits Lesson Plan

Blueprint for Limits

This AP Calculus review lesson bridges the gap between algebraic rational function rules and formal limit notation, using visual sketching as a framework for understanding asymptotic behavior and continuity. Students translate pre-calculus 'rules' into calculus 'logic' to prepare for the formal definition of limits.

4
Roller Coaster Design Worksheet

Roller Coaster Calculus

Students will learn to identify and describe intervals of increase, decrease, and constant behavior in functions using interval notation through a roller coaster design challenge. The lesson emphasizes using x-values to define these intervals and distinguishing between location and value.

4
Asymptote Limits Lesson Plan

Asymptote Blueprints

A 12th-grade Pre-Calculus lesson connecting the algebraic evaluation of infinite limits and limits at infinity to the visual behavior of vertical and horizontal asymptotes. Students analyze reciprocal functions from a video to bridge the gap between algebra and calculus.

5
Asymptote Analysis Lesson Plan

Asymptote Analysis

A comprehensive lesson plan and student activity connecting algebraic graphing rules to rigorous calculus limit definitions, centered around a detailed rational functions tutorial.

4