WORLD 01
L
limits, continuity, and asymptotic behavior
← Grade 11 Pathfinder Forge
PREVIEW PATHWAY · CHANGE, ACCUMULATION, AND MATHEMATICAL MODELS
Calculus & Modeling Preview
Approach the limit. Measure the change. Explain what accumulates.
The Change Engine is racing ahead without explaining where it is going. Super Gio needs a mathematical pathfinder to study limits, rates, accumulation, and infinite processes until every moving part tells a coherent story.
FIELD NOTE FROM GIO“When the graph starts moving, calculus brings the compass.”
0 / 24case missions complete
CALC
GRADE 11 ARTIFACTLimit Beacon
PATHFINDER FORGE · PREVIEW MAP
Eight mapped worlds to investigate
Selected Challenge missions test transfer; progress here is practice evidence, not course mastery.
WORLD 02
R
derivatives from definitions and efficient rules
Derivative Definition and Rules
A derivative measures instantaneous change and can be computed, interpreted, and connected across representations.WORLD 03
O
motion, extrema, related rates, and optimization
Applications of Derivatives
Derivative information supports decisions about growth, motion, approximation, and optimal conditions.WORLD 04
A
definite integrals and the Fundamental Theorem
Integrals and the Fundamental Theorem
Integrals measure accumulation, while the Fundamental Theorem links accumulation with rates of change.1
LearnAccumulation from a rate
→2PracticeFTC at a moving upper limit
→3ChallengeNet change versus total distance
→SUPER GIO CHALLENGE · WORLDS 1–4
WORLD 05
D
differential equations, slope fields, and growth models
Differential Equations and Slope Fields
Differential equations model systems by relating a quantity to the way it changes.WORLD 06
T
area, volume, average value, and net change
Applications of Integration
Integration solves geometric and contextual problems by accumulating infinitely small contributions.WORLD 07
M
parametric, polar, and vector representations
Parametric, Polar, and Vector Functions
Alternative coordinate systems reveal motion, direction, curvature, and shapes hidden by standard function notation.WORLD 08
C
sequences, series, convergence, and approximation
Infinite Series and Modeling
Infinite processes can converge to finite values and support powerful approximations when their conditions are justified.SUPER GIO CHALLENGE · WORLDS 5–8