BC Calculus — Why and How

Every formula derived, not just stated. The goal is that if you blank on something at 9pm, you can rebuild it in thirty seconds from something you do remember.

This is a reference for one AP Calculus BC course. It follows the College Board's official ten-unit framework, in its order and with its numbering, so “we're starting Unit 6” means the same thing here as in class.

Who wrote this, and who it's for

A parent wrote this, for himself — so that there would be a second voice in the house on the same material, thirty years after last seeing any of it. Much of it is addressed to him, and it talks about the student in the third person.

She is welcome to every word. Nothing here is meant to be kept from her, and it is better that she knows what it says than that she finds out. It is not an authority: it is a second explanation, and where it disagrees with her teacher, her teacher is the one grading.

The five documents

All of them work offline and print.

The guideTen units and an appendix. Derivations, worked examples in two columns, the traps that actually cost points, and a formula sheet per unit. Practice generatorForty problem templates with randomised numbers, worked solutions and answer checking — plus a rederivation drill against a thirty-second clock. Sanity checksEight ways to tell that an answer is wrong without doing the problem again. Triage, not proof. Reference cardThe whole course on one sheet, three columns. Built to print landscape on letter. The parent's toolkitA rederivation map, questions worth asking, a pacing calendar, and what to do when it goes wrong.

Jump to a unit

1 Limits and Continuity
2 Differentiation: Definition and Fundamental Properties
3 Differentiation: Composite, Implicit, and Inverse Functions
4 Contextual Applications of Differentiation
5 Analytical Applications of Differentiation
6 Integration and Accumulation of Change
7 Differential Equations
8 Applications of Integration
9 Parametric Equations, Polar Coordinates, and Vector-Valued Functions
10 Infinite Sequences and Series
A How BC compares to other programs

How to use it

The guide's sidebar has a set of Show checkboxes — Why / history, Reminders, Worked examples, Traps, Beyond BC, Ahead of syllabus, Formula sheets, Sanity checks. Turning categories off is the fastest way to make the document match what you need right now, and the setting follows you from unit to unit. For revision, leave only Formula sheets and Sanity checks on.

Press / anywhere to search all five documents. Each unit ends with a link into the practice generator filtered to that unit.

Everything at once, for printing or a PDF: print all.

Nothing here talks to a server. There are no accounts, no tracking, and no network calls — save the pages and they keep working on a plane.