Model change itself. Write and verify differential equations, visualize their solutions with slope fields, solve them by separation of variables, apply initial conditions, and build exponential (and, for BC, logistic) growth models.
Six ways to master Unit 7 — pick whichever fits how you like to study.
All 9 topics from the College Board CED, in order. Topics 7.5 and 7.9 are BC only.
Unit 7 studies differential equations — equations that relate a function to its own derivatives, describing how a quantity changes. You’ll model situations by translating “the rate is proportional to…” into an equation like dy/dt = ky, and verify that a proposed function is a solution by substituting it back.
Slope fields give a visual picture: at each point you draw a short segment with slope dy/dx, and solution curves follow the flow. To solve analytically, you use separation of variables — gathering y-terms on one side and x-terms on the other, then integrating — and apply an initial condition to find the particular solution. The unit’s big application is exponential growth and decay (y = y₀eᵏᵗ), and BC students add Euler’s method for numerical approximation and logistic models for bounded growth toward a carrying capacity.
On the exam this unit is 6–12% for AB and 6–9% for BC, and takes about 8 class periods (AB). The four mathematical practices below run through every topic: