AP Calculus AB Jeopardy!

AP QS (TI Active)

100

https://docs.google.com/document/d/1C-NWzuwELA68dLQyKIR90P5evNj2qXND/edit?usp=sharing&ouid=116032141790180690468&rtpof=true&sd=true

What is ANSWER D?

200

https://docs.google.com/document/d/1ioiSn5MgkQTKdavr7BsOzb3Zr_ImXo9wb6K5JRz0Phk/edit?usp=sharing

What is ANSWER E?

300

https://docs.google.com/document/d/1ig7rWL9Qm-1UEXfMWs1PY3cZm6Hmq8EXaurk8m2TwgM/edit?usp=sharing

What is ANSWER C?

400

https://docs.google.com/document/d/1G0ahXpMrVlHcDoyPtD_DzAn48pvAYZWkwbyCJ-oZzKQ/edit?usp=sharing

What is ANSWER A?

500

https://docs.google.com/document/d/1eEN5TWK3m07GID1StIZfDbBGwe7TzMaootjehjSqwR4/edit?usp=sharing

What is ANSWER E?

Differentiation

100

Differentiate: y = e^sinx

What is y' = cosx e^sinx?

200

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

What is (3x²+6x)/(x³+3x²+7)?

300

Find dy/dx for the following function: x²y³+3x=y.

What is (3+2xy³)/(1-3x²)?

400

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

What is 3sec²(3x)

500

Solve for dy/dx when 1=3x²+xy+y at the point (2,5).

What is -17/3?

Anti-differentiation

100

Integrate F'(x)=3x²+6x.

What is F(x) = x³+3x²+C?

200

Integrate F'(x) = 3/(x-4)

What is F(x) = 3ln|x-4| +C

300

Find the equation of F given F'(x)=x³-3x²+7x+8 and F(0)=5

What is F(x)=(x⁴/4)-x³+3.5x²+8x+5

400

Solve for y=f(x) when f(2)=1. dy/dx=(3x²+x)/(2y)

What is (x³+.5x²-9)^.5?

500

Integrate x/(4+x²)^.5.

What is (4+x²)^.5+C?

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

Find a value c such that the conclusion of the mean value theorem is satisfied for f(x)=2x²+6x-2 on the interval [-1,2].

What is c = 0.5?

400

Use the second Fundamental Theorem of Calculus to find F'(x). F(x)=∫₂^sinx(9t+9)dt.

What is (9sinx+9)cosx?

500

Use the second Fundamental Theorem of Calculus to find F'(x). F(x)=∫₂^ln(cosx)(7t³+9)dt.

What is [7(ln(cosx))³+9](-tanx)?

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 4 cm/s. Find the rate of change of Area A when r=2cm.

What is 16π?

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 (at t =0) 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=x², the x-axis, and x=2 around the y-axis.

What is 8π?