AP Calc AB Review

Optimization

100

You solve optimization problems by finding what values?

Absolute Extrema

200

What equations do you need to solve these problems?

Primary and Secondary (if applicable)

300

What is the primary equation of:

A manufacturer needs to make a cylindrical can that will hold 1.5 liters of liquid. Determine the dimensions of the can that will minimize the amount of material used in its construction.

V=(pi)r²h

400

Find two positive numbers whose sum is 300 and whose product is a maximum.

x=150 y=150

500

Let x and y be two positive numbers such that x+2y=50 and (x+1)(y+2) is a maximum.

x=53/2 y=47/4

Related Rates

100

What is the first step to completing a related rates problem?

Knowns and Unknowns

200

What other calculus concept should you use when solving related rates?

Implicit Differentiation

300

When solving a lamp post problem, what equation is most commonly used?

Pythagorean Theorem

400

A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at a rate of 2 cm³/sec. How fast is the water level dropping when the height of the water is 3 cm?

-2/(pi) cm/sec

500

A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at a rate of 0.5 m²/sec at what rate is the radius decreasing when the area of the sheet is 12 m²?

r'=-0.04m/sec

Derivatives/Antiderivatives

100

What must you ALWAYS include with the answer of an indefinite integral?

+C

200

What is quotient rule?

BDT-TDB/B²

300

d/dx of e⁵⁰⁰(ln(56))+1200

0

400

integral of x²/sqrt(x³)dx

2/3[(x³)^1/2]+C

500

d/dx arctan(x)

1/1+x²

Volumes of Revolution

100

What are the two methods of solving?

Washer and Disk

200

What is R and r?

R = outer radius, r = inner radius

300

What is the equation for a washer around the x-axis?

(pi)(integral from a to b) of R²-r² dx

400

Rotate the region bounded by y=2x² and y=x³ about the x-axis.

256(pi)/35

500

Rotate the region bounded by y=2x+1, x=4 and y=3 about the line x=−4.

126(pi)

Brooke and Mahathi's Interests

100

What club does Brooke spend an ungodly amount of time with?

Robotics

200

What middle school did Brooke and Mahathi both go to?

Sterling Montessori Academy and Charter School

300

What is Brooke and Mahathi's favorite band? Extra points for the song? (Yes they are the same for both of us)

Paramore (Fences)

400

What is Mahathi's Chipotle order? (It's in the yearbook)

white rice, black beans, mild salsa, corn, sour cream, cheese, guac, and lettuce

500

What was the name of the show choir Brooke and Mahathi were both in?

Sterling Stars (no you may not see videos they were burned)