Derivative Rules and Techniques

A comprehensive prep sequence for the most challenging questions on the ACT Math and Science sections. It focuses on high-level conceptual blueprints for math topics like complex numbers and matrices, alongside speed-reading and data-interpretation strategies for the Science section.

A diverse collection of resources spanning high-level mathematics and early literacy, providing targeted practice for trigonometric derivatives and foundational letter formation.

This sequence explores numerical analysis through the lens of sequences, focusing on iterative methods to approximate solutions to complex equations. Students investigate fixed-point iteration, Newton's method, convergence rates, and the transition into chaotic behavior.

This sequence bridges the gap between discrete mathematics and quantitative finance, focusing on the application of geometric series to asset valuation, loan amortization, and risk management. Graduate students will develop the mathematical foundations for pricing complex financial instruments and understanding market dynamics.

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.

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 bridges the gap between radical notation and exponential notation, establishing a unified system for algebraic manipulation. Students begin by defining rational exponents through the lens of roots and powers, then systematically apply the laws of exponents to simplify expressions containing fractional powers.

This calculus sequence guides 11th-grade students through the integration techniques required to calculate area and arc length within polar coordinate systems. From the geometric derivation of the polar sector formula to complex multi-curve regions and boundary measurements, students apply integral calculus to circular geometries.

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.

This sequence introduces students to parametric equations through the lens of particle motion and physics simulations. Students progress from basic plotting and parameter elimination to advanced calculus applications involving derivatives, vectors, and arc length.

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.

A specialized AP Calculus lesson exploring the unique geometric and analytical properties of Euler's number. Students use graphing software to discover why e is the unique base where the function's height, slope, and area under the curve are identical.

A high-speed review of logarithmic expansion properties designed to build the algebraic fluency required for Calculus. Students learn to recognize patterns in complex rational expressions to expand logs instantly, facilitating easier differentiation and integration.

This lesson focuses on calculating the difference quotient for radical functions using the conjugate method. It includes a conjugate warm-up, guided video notes for a complex radical example, a collaborative group relay activity, and a conceptual preview of derivatives.

An 11th-grade honors lesson connecting the limit definition of the derivative to instantaneous velocity through rocket launch simulations. Students will analyze height functions to determine peak altitude and impact force.