AP Calculus Jeopardy! by Michael Edwards

Limits

100

Evaluate the limit, if it exists

What is 50?

200

What is 1/2?

300

Find the Limit: 

What is x=1

400

Evaluate the limit, if it exists: 

What is ?

500

What is 384?

Differentiation

100

Find dy/dx. 3xy=4x+y² 

What is (3y-4)/(2y+3x)?

200

Find the derivative of f(x)=ln(x³+3x²+7).

What is (3x²+6x)/(x³+3x²+7)?

300

Find dy/dx for y=e^x+y

What is (e^x+y)/(1-e^x+y)?

400

Find the derivative of f(x)=cos(3x).

What is -3sin(3x)?

500

Find dy/dx for y = 4sin²(3x)

What is 24sin(3x)cos(3x)?

Integration

100

Integrate F'(x)=sec²x-2.

What is tan(x)-2x+C?

200

If F(x) =  , what is F'(x)?

What is ?

300

Let R be the region between the function f(x) = x³+6x²+10x+4, the x-axis, and the lines x=0 and x=4. Using the Trapezodial Rule, compute the area when there are 4 equal subdivisions.

What is 296?

400

If =k and =-4, what is the value of ?

What is -16+k?

500

what is f(x) if f'(x) = (2x)/(x²-1)

What is f(x) = ln|x²-1|-ln3?

Theorems

100

Complete the Fundamental Theorem of Calculus. ∫_a^bF(x)dx=?

What is F(b)-F(a)?

200

What does the Mean Value Theorem state?

What is there exists a point c in the interval (a,b) such that f'(c)=f(b)-f(a)/b-a, if a function is continuous on the closed interval [a,b] and differentiable on the open interval (a,b)?

300

What does Rolle's Theorum state

What is Rolle's theorem states that for any continuous, differentiable function that has two equal values at two distinct points, the function must have a point on the function where the first derivative is zero?

400

Use the second Fundamental Theorem of Calculus to find F'(x). F(x)=∫₂^x(256x+128)dx.

What is 256x+128?

500

Use the second Fundamental Theorem of Calculus to find F'(x). F(x)=∫_-3^x(16t+8)dt.

What is 16x+8?

Applications

100

Find the area of the region bounded by f(x)=x²-3x-10 and g(x)=-x²+5x+14.

What is 170.667?

200

Find the average acceleration of a particle over the interval (0,50) given v(50)=80ft/sec and an initial velocity of 10 ft/sec. Include units in your answer.

What is 7/5 ft/sec²?

300

The rate of change of radius r of a circle is 7 cm/s. Find the rate of change of Area A when r=12cm.

What is 168π?

400

The acceleration of a particle is given by the function a(t)==3t²+7. Find the position function of the particle given that its initial velocity is 10 m/sec and an initial height of 80m.

What is s(t)=(t⁴/4)+3.5t²+10t+80?

500

Find the volume of the solid generated by revolving the region bounded by y= √ x, x=0, and x=8 around the x-axis.

What is 15.08?