AP Calculus BC 70% Sectional Test: Through Differential Equations (Units 1–7)
Take the AP Calculus BC 70% sectional test covering Units 1–7 through differential equations. Confirm BC integration and DE mastery before tackling Units 9 and 10.
Pre-BC Exclusive Content Checkpoint: Units 1–7
The 70% sectional test covers all AP Calculus BC content through Unit 7, including differential equations. This is the most comprehensive sectional checkpoint and serves as the gateway assessment before BC-exclusive content in Units 9 and 10. Students who perform well here have demonstrated mastery of derivatives, all BC integration techniques, and differential equations — the complete foundational toolkit for the advanced BC topics ahead.
What This Sectional Tests
Units 1–5: Cumulative Derivative Content
All derivative topics from the previous sectionals are tested in integrated, multi-step problems. At the 70% level, derivative skills appear as embedded components within integration and differential equation problems rather than as isolated questions. Chain rule, implicit differentiation, and analytical applications are expected to be automatic.
Unit 6: Integration and Accumulation of Change
BC-specific integration techniques are assessed at this level. Questions cover Riemann sum approximation and analysis, FTC Part 1 and Part 2 including chain rule variants, u-substitution for definite and indefinite integrals, integration by parts with single and repeated application, and partial fraction decomposition. Students who have not fully internalized these techniques will find Unit 7 content difficult to execute.
Unit 7: Differential Equations
This sectional adds separable differential equations with initial conditions, slope field matching and solution curve analysis, Euler's method step calculations, and logistic growth analysis including carrying capacity and inflection point interpretation. These BC topics are tested in the multi-part FRQ format that appears on the actual AP exam.
Why This Checkpoint Matters Before Units 9–10
Units 9 and 10 require students to apply integration, differential calculus, and limit techniques within unfamiliar coordinate systems and series frameworks. A student who is not fluent with integration by parts, for example, will struggle with arc length of parametric curves and certain Taylor series derivations. The 70% sectional confirms that the foundational toolkit is complete and reliable before you advance into the most demanding portion of the BC curriculum.
After the 70% Sectional
Use your results to identify any remaining gaps in Units 6 and 7 before beginning Unit 9 and 10 content. Once those gaps are addressed, proceed with unit-wise tests for Units 9 and 10 individually before moving into full mock exams that integrate all 10 units.