AB Calculus Jeopardy Game!

Derivatives

100

4x³-2x²+5

What is 12x²-4x

200

(5x²+2)(3x³-2x)

What is (10x)(3x³-2x)+(9x²-2)(5x²+2)

300

(5x-2x²)/(x³-2)

What is (2x⁴-10x³+8x+10)/(x⁶-4x³+4)

400

tan(cosx)

What is sec²(cosx)(-sinx)

500

e^x sinx

What is e^x cosπ+ (sinx) e^x

Integrals

100

∫x³+5 dx

What is (x⁴/4)+5x+c

200

∫sinx+cosx dx

What is -cosx+sinx+c

300

Find the area of the region bounded above by y = x² + 1, bounded below by y = x, and bounded on the sides by x = 0 and x = 1.

What is 5/6

400

∫2x(x²-1)⁴ dx

What is ((x²-1)⁵)/(5)+c

500

∫sin(2x)cos(2x)dx

What is (1)/(4) sin²(2x)+c

Trig Functions

100

Sin π/4

What is √2/2

200

Tan π/6

What is √3/3

300

Cos 3π/2

What is 0

400

Sin 4π/3

What is -√3/2

500

Cot π/3

What is √3/3

Differentiating Trig Functions

100

y=2sinx

What is y'=2cosx

200

f(t)= t(cost)

What is f'(t)=-tsint+cost

300

y=6(cos²x)²

What is y'=-24(cos²x)(sin²x)

400

y=tan√x

What is y'=sec²√x/2√x

500

y=4sec3xtan3x

What is y'=12sec(3x)(sec²(3x)+tan²(3x))

Identifying Formulas

100

UV' + VU'

What is the Product Rule

200

(VU'-UV')/V²

What is the Quotient Rule

300

d/dx[f(g(x)]=f'(g(x))*g'(x)

What is Chain Rule

400

(Final Position- Initial Position)/ total time

What is Average Velocity

500

f'(c)= (f(b)-f(a))/b-a

What is Mean Value Theorem