Quizzes, exams, and flashcards about Calculus AB: No calculator 1 — limits, derivatives, integrals.
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Limits, derivatives, integrals and the Fundamental Theorem — and an exam that is deliberately half with a calculator and half without.
Four parts, and the calculator rule changes between each pair:
Note the weighting carefully: the two no-calculator parts are 35% and 33.3%, which is more than two thirds of the whole exam. Fluency by hand is not optional and cannot be replaced by technique on a device.
Answers, on this exam, are the smaller half of the mark. Most free-response points are awarded for the work and the justification, and a correct number with no supporting line earns almost nothing.
Three habits carry most of those points:
Say which theorem you are using, by name. If a question asks you to justify that a value is attained, the words Intermediate Value Theorem and the check that the function is continuous on the closed interval are what the rubric is looking for. The same goes for the Mean Value Theorem and for the conditions each one requires.
Justify in sentences, with reasons. "f has a local minimum at x = 2 because f′ changes from negative to positive there" is a point. "Local min at x = 2" is not.
Keep the units and the context. Rate-of-change problems are usually set in a real situation, and the question asks what the integral means as well as what it equals. An answer with no units, or one that reports a rate where a total was asked for, gives back marks already earned.
And the calculator sections have their own convention: on those you are expected to set up the integral or the equation and report a decimal answer to three places, without showing the intermediate algebra — the setup is the work.
The by-hand fluency the two no-calculator parts test, and the conceptual distinctions the whole exam turns on: a derivative as a rate against a derivative as a slope, the chain rule where it is easy to miss the inner function, the difference between the average value of a function and the average rate of change, what the Fundamental Theorem actually says in both of its forms, and the standard interpretation questions that require no computation at all.
They do not set a multi-part free-response problem, and no multiple-choice bank can. For those, use College Board's released questions, which come with scoring guidelines that show exactly where each point is awarded — reading two of those is worth more than a week of extra practice problems.
