AP Calculus AB Optimization Quiz: 10 Questions with Explanations

AP Calculus AB math quiz: Optimization – Maths PDF

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This optimization quiz for AP Calculus AB covers optimization (Common Core AP CALC AB 5.10, AP CALC AB 5.11), with a free PDF to print.

Test yourself on optimization problems with fences, boxes, cans, closest points and revenue, including justifying a maximum or minimum with 10 multiple-choice questions. Pick one answer for each question, then read the explanation to see why it is right and which common mistake the other choices represent.

AP Calculus AB · Common Core State Standards: AP CALC AB 5.10, AP CALC AB 5.11

Optimization quiz: 10 questions

Question 1

What is the first step in an optimization problem?

Question 2

What is the constraint in “maximize area with 100 ft of fence”?

Question 3

Area A(x) = x(100 − x).

Two sides of a rectangle with perimeter 200 are \(x\) and \(100-x\). At what \(x\) is the area greatest?

Question 4

Two positive numbers have a sum of 12. What is the largest possible product?

Question 5

The box net.

For the open box, which formula gives the volume?

Question 6

To show a critical number gives a maximum, you can use

Question 7

A closed can.

A can has volume \(V=\pi r^{2}h\). Which expression is its total surface area?

Question 8

A price model gives revenue \(R(p)=200p-4p^{2}\). Which price maximizes revenue?

Question 9

The distance to a point is minimized when

Question 10

Values of A at the candidates.

Using the table for \(A(x)=x(60-2x)\) on \([0,30]\), what is the maximum area?

Remember

Name the variables, write an objective function, and use a constraint to reduce it to one variable.
Find critical numbers by solving f′ = 0 on the allowed domain.
Justify the extreme with a sign change of f′, the sign of f″, or by comparing endpoint values.
Check the domain and give the final answer in context with units.

How to use this optimization quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

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