Unit route
Complete lessons in sequence, use diagnostic evidence to select a pathway, conduct the investigation, submit corrected work, and demonstrate mastery at 80% or above.
Weeks 1, 2 · 7 college lessons
Calculus I Bridge & Integration Fluency
How can the Fundamental Theorem, substitution, algebraic structure, units, and verification restore fluent integration reasoning?
Pathways
Lesson 01 · Week 1
Antiderivative Families, Constants & Initial Conditions
Reconstructing antiderivative families and using initial conditions to determine constants.
Lesson 02 · Week 1The Fundamental Theorem as an Evaluation and Accumulation Principle
Connecting derivative and integral forms of the fundamental theorem.
Lesson 03 · Week 1Net Change, Total Change & Units
Distinguishing signed accumulation from total accumulation and preserving units.
Lesson 04 · Week 1Substitution with Algebraic Structure
Identifying inner-function and differential structure before integrating.
Lesson 05 · Week 2Substitution with Exponential, Logarithmic & Trigonometric Forms
Recognizing reverse-chain patterns in transcendental integrals.
Lesson 06 · Week 2Integration Strategy Triage
Selecting simplification, substitution, direct integration, or a later calculus ii technique.
Lesson 07 · Week 2Readiness Synthesis, Error Analysis & Technology Verification
Coordinating exact work, numerical checks, graph evidence, and written justification.