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AP Calculus AB In the AP Calculus AB bundle

AP Calculus AB Rates of Change and Related Rates — Unit Notes

Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 10 definitions and 4 theorems, 5 worked examples, 3 diagrams, in 12 printable pages. This page lists what the notes cover. The notes themselves come with the AP Calculus AB bundle.

Unit notes — in the bundle

12 pages 14 definitions & theorems 5 worked examples 33 key words 6 Try-it pairs, answered 14-row at-a-glance table 33-entry glossary Fill-in-the-blank guided twin 3 diagrams Letter size, print-ready

Not sold separately. The practice worksheet for this unit is free, with no email and no account.

Rates of Change and Related Rates — what the notes cover

7 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.

What you need

Also in this section: 1 note on method and common errors.

What a derivative says in context

  • Definition — Derivative as a rate of change
  • Definition — Interpretation in context

Also in this section: 1 worked example, 1 note on method and common errors.

Straight-line motion

  • Definition — Position, velocity and acceleration
  • Definition — Speed
  • Theorem — Speeding up and slowing down
  • Definition — Displacement and total distance

Also in this section: 1 worked example, 1 diagram.

Rates in applied contexts other than motion

  • Theorem — The chain rule in Leibniz notation

Related rates

  • Definition — Related rates
  • Definition — Constant quantities and instantaneous values

Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.

Local linearity and linearization

  • Definition — Local linearity
  • Definition — Linearization
  • Theorem — Concavity and the direction of the error

Also in this section: 1 worked example, 1 diagram.

L'Hospital's rule

  • Definition — Indeterminate form
  • Theorem — L'Hospital's rule

Also in this section: 1 worked example, 1 note on method and common errors.

Where the notes are

The notes are one of the documents in the AP Calculus AB Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Rates of Change and Related Rates practice worksheet is free and stays free.

Best value for the whole year

Every AP Calculus AB topic — the complete Solutions Bundle

One download, one payment, the whole program. For all 8 AP Calculus AB units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.

8 units · 64 PDFs · 527 pages$19.99
  • Worked solutions, not answer lists — every step written out
  • Covers the whole year's program at this level
  • Less than the price of one hour of tutoring — for the entire year's solutions
Everything paid, in one file $19.99CAD · one payment AP Calculus AB bundle — coming soon Not on sale yet

Practise it, then test yourself

Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.

Rates of Change and Related Rates practice worksheet   About the Rates of Change and Related Rates unit test

← All 8 AP Calculus AB unit notes

Free practice worksheet

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