A mastery path into advanced mathematics
Advanced students may reach COTA’s Calculus IV (Integration) by senior year. The mastery-based Math report card makes progress visible.
The standard course path
A boy’s demonstrated mastery governs his pace.
Precalculus
Polynomial and rational functions, exponentials, logarithms and sequences build the tool kit. Advanced logic and right-triangle / unit-circle work connect computation to proof.
Trigonometry, then limits
The unit circle, graphs, identities, general triangles and polar coordinates deepen function knowledge. Limits and continuity introduce the central idea behind calculus.
Differential calculus
Derivative rules, the chain rule and applications develop into related rates and optimization. Integration and the Fundamental Theorem connect change with accumulation.
Integral calculus and beyond
Applications of integration and differential equations connect to Physics. Series, parametric/polar/vector work and an introduction to double integrals open the college door.
Advanced opportunity. For advanced students, the senior-year destination is COTA’s Calculus IV (Integration). The Math mastery report card tracks actual progress. AP options include Precalculus, Calculus AB, Calculus BC and Statistics; exam preparation is individualized.
Different starting points. Real mathematical growth.
Illustrative pathways, not predictions for a particular boy. Placement and pace respond to what he actually knows.
View the full Math mastery paths chart
Mastery—not simply the passage of a school year.
The strong student can move into calculus and advanced work. The typical student builds secure knowledge and calculus readiness. The boy with major gaps deserves a foundation before he is asked to build higher.
The best gift: a foundation he can trust.
For a ninth-grader with major holes in his Math knowledge, this is the work that matters. Moving to the next course each year can leave the same foundational gaps unresolved.
The portal mastery report card identifies exactly which foundational skills are missing.
Targeted worksheets give him work on the skills he actually needs.
Individual skills tests and mastery checks establish what he truly knows.
He advances when the skills are secure—not merely when the year changes.
Real, fundamental Math knowledge—not merely credits on a transcript.
He works until the skills are truly his, then moves up on a solid foundation.
Precalculus • Calculus AB • Calculus BC • Statistics