AP Calc BC Test Review Jeopardy Template

Integration

Differentiation

Optimization or Related Rates

Area Between Curves

Approximations

100

∫2xe^xdx

e^x^{^2}+C

100

Find y':

y=(sin(x²+3))^1/2

y'=1/2(sin(x²+3)^-1/2)cos(x²+3)(2x)

100

What steps do you take to solve a related rates problem?

1. Label variables (x,y,r,h,l,w)

2. Write the basic Volume/Area Equation

3. Differentiate (usually implicit)

4. Substitute: Plug in known rates and values (only after differentiating)

5. Solve for the final unknown rate (include units!!)

100

What are the steps to finding the area between two curves?

1. Identify Points of Intersection

2. Identify top/bottom section

3. Integrate (top-bottom) between points of intersection

100

List the first 4 terms of the Taylor Polynomial for e^x

1+x+x²/2!+x³/3!

200

∫cos(3x+5)dx

1/3 sin(3x+5)+C

200

x³+y³=6xy

dy/dx=(6y-3x²)/(3y²-6x)=(2y-x²)/(y²-2x)

200

A spherical balloon is being inflated. The volume increases at a constant rate of 100 cm³/s. How fast is the radius of the balloon increasing when the diameter is 50cm?

dr/dt=1/(25pi) cm/s

200

Set up the integral for finding the area between the following two curves:

y=x² and y=√𝑥.

𝐴=∫(√𝑥)−𝑥²⁢𝑑⁢𝑥

(w/ bounds [0,1])

200

Tangent Line Approximation:

f is concave up on its domain and f(4)=5 and f'(4)=3.

a. What is the estimate for f(3.8) using the local linear approximation for f at x=4.

y=4.4

(y-5=3(x-4) and plug in 3.8 to that)

300

∫((4x³)/(x⁴+7))dx

ln|x⁴+7|+C

300

solve for y:

dy/dx=2xy²

y=(-1)/(x²+C)

300

A farmer has 100 meters of fencing to create a rectangular pen against a straight wall (no fencing needed against the wall). What dimensions maximize the area? [1, 2]

2W+L=100

W=25m

L=100-2(25)=50m

A=1250m²

300

Find the area between y=x² and y=x.

Area=1/6

300

The function f(x)=5x-2x²-2 is concave down at x=1.

a. Find the tangent line of f at x=1.

y-1=-1(x-1)

400

∫x²e^xdx

(Hint: Integration by Parts)

x²e^x-2xe^x+2e^x+C

400

Find y'':

x²+y²=16

y"=-16/y³

400

DOUBLE JEOPARDY:

The team to name the most digits of pi (correctly) in 20 seconds gets the 500 points.

3.1415926535897932384626...

400

Find the VOLUME of the solid formed by revolving the region bounded by y=x^1/2 and y=x² around the x-axis from x=0 to x=1.

V=3pi/10

400

DOUBLE JEOPARDY:

How many minutes per question do you get for each of the four sections on the AP Calculus BC Exam?

(Hint: MCQ calc and MCQ non-calc, FRQ calc and FRQ non-calc)

MCQs:
Part A - no calculator - 2 mins per

Part B - calculator - 3 mins per

FRQs:

Part A - calculator - 15 mins per

Part B - no calculator - 15 mins per