AP Calculus BC FRQs cover all of AB content plus BC-only topics: series (Taylor/Maclaurin, convergence tests), parametric equations, polar curves, and Euler's method. The 6 FRQs are 50% of your score.
BC-Specific FRQ Topics
- Series: Most common BC FRQ topic. Finding Taylor/Maclaurin series from scratch, determining interval of convergence with endpoint analysis, using the Lagrange error bound. Know the series for sin x, cos x, eˣ, and 1/(1-x) from memory.
- Parametric curves: Finding dy/dx and d²y/dx² for parametric equations, arc length, and speed at a point. dy/dx = (dy/dt)/(dx/dt) — never forget the chain rule.
- Polar curves: Area enclosed by a polar curve (A = ½∫r² dθ), area between two polar curves, and finding x/y-coordinates from r and θ.
- Differential equations (Euler's method): Approximating y-values step by step using Euler's method. Show each step; partial credit is available for correct process with arithmetic errors.
Scoring Tips
On series problems, state which test you're using before applying it — the name earns a point. For convergence, always check endpoints separately since the ratio test is inconclusive at endpoints.
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