Study Guides

Interactive, theorem-based lessons with diagrams, worked examples, and practice problems.

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Geometry

Chapter 10: Circles

Master inscribed angles, angle & segment relationships, coordinate-plane equations, arc length, and sector area.

5 lessons·20 problems
Lesson 10.4: Inscribed Angles
Lesson 10.5: Angle Relationships in Circles
Lesson 10.6: Segment Relationships in Circles
Lesson 10.7: Circles in the Coordinate Plane
Lesson 10.8: Arc Length & Sector Area
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Physics

Physics: Mechanics

Master one-dimensional kinematics, Newton's laws of motion, work & energy, impulse & momentum, and rotational motion with step-by-step examples and practice problems.

5 lessons·20 problems
Lesson 1: One-Dimensional Kinematics
Lesson 2: Newton's Laws of Motion
Lesson 3: Work, Energy & Power
Lesson 4: Impulse & Momentum
Lesson 5: Rotational Motion & Torque
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Mathematics

Calculus

Master limits and continuity, the definition and rules of differentiation, applications of derivatives, and the Fundamental Theorem of Calculus with step-by-step examples and practice problems.

5 lessons·20 problems
Lesson 1: Limits & Continuity
Lesson 2: The Derivative
Lesson 3: Differentiation Rules
Lesson 4: Applications of Derivatives
Lesson 5: Integration
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Mathematics

College Number Theory

Explore divisibility and primes, modular arithmetic, the Euclidean algorithm, the Fundamental Theorem of Arithmetic, Euler's and Fermat's theorems, and their applications to cryptography.

5 lessons·20 problems
Lesson 1: Divisibility & Prime Numbers
Lesson 2: Modular Arithmetic & Congruences
Lesson 3: GCD, LCM & The Euclidean Algorithm
Lesson 4: The Fundamental Theorem of Arithmetic
Lesson 5: Euler's & Fermat's Theorems
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Physics

Physics: Electricity & Magnetism

A comprehensive 10-unit course covering electric charge, fields, Gauss's law, potential, capacitors, DC circuits, magnetic forces and sources, electromagnetic induction, and Maxwell's equations. Advanced level, aligned with Griffiths and OpenStax University Physics Vol. 2.

10 lessons·61 problems
Unit 1: Electric Charge & Coulomb's Law
Unit 2: Electric Fields
Unit 3: Gauss's Law
Unit 4: Electric Potential
Unit 5: Capacitance & Dielectrics
Unit 6: Current, Resistance & DC Circuits
Unit 7: Magnetic Fields & Forces
Unit 8: Sources of Magnetic Fields
Unit 9: Electromagnetic Induction
Unit 10: Maxwell's Equations & Electromagnetic Waves
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