Unit 7 — differential equations (Weeks 17–18)
- Slope fields: sketch from dy/dx, match solution through a point (2015 AB/BC 4a)
- Separable equations + particular solutions (2011 AB #5c, 2017 AB/BC 4c); exponential models dy/dt=ky, growth/decay
- Logistic model (BC): dP/dt=kP(1−P/M), carrying capacity, inflection at M/2, field shape
- Euler's method (BC): step-by-step table; Unit 7 quiz + unit test
Unit 8 — applications of integration (Weeks 19–20)
- Area between curves (dx vs dy choice; 2015 AB 2a); average value (2011 AB #6c)
- Volumes: disk/washer around x/y lines (2011 AB #3c); cross-sections — square/triangle/semicircle (2015 AB 2b)
- Arc length (BC); distance vs displacement; density/work; Unit 8 quiz + unit test
- FRQ pair: area + volume — always sketch + write setup integral before evaluating
Unit 9 — parametric, polar, vector-valued functions, BC only (Week 21)
- Parametric differentiation dy/dx=(dy/dt)/(dx/dt); second derivatives (parametric); parametric arc length; quiz
- Vector-valued differentiation + second derivatives (vector); planar motion (differential calculus); motion along a curve — rate of change + velocity magnitude; planar motion with integrals; quiz
- Polar: differentiate polar functions; tangents to polar curves; area bounded by polar curves (intro + full); area between two polar curves; calculator-active polar area (cardioid worked example); quiz + unit test
- FULL AB MOCK over 2 days + AB subscore analysis — require ≥55% before Series month
CED: FUN-7, CHA-5–CHA-6, LIM-5. Vector speed = |v|; total distance = ∫|v|dt — test every lesson.