Precalculus Jeopardy

Factoring

100

x⁴+12x²+27

What is (x²+9)(x²+3)?

200

-2x+x³+x⁵

What is x(x+1)(x-1)(x²+2)?

300

64+125a³

What is (4+5a)(16-20a+25a²)?

400

(x²+3x)²-22(x²+3x)+72

What is (x+6)(x-3)(x+4)(x-1)?

500

(5x²-14x)²-22(5x²-14x)+57

What is (5x+1)(x-3)(5x-19)(x+1)?

Asymptotes

100

Find the vertical asymptotes of: f(x) = (x+2)/(2x-10)

What is x = 5?

200

Find all horizontal asymptotes of: f(x) = (2x²-162)/(3x²-27x)

What is y = 2/3?

300

Find all vertical asymptotes of: f(x) = (3x²-27x)/(2x-18)

What is "No Vertical Asymptotes"?

400

Find all horizontal asymptotes of: f(x) = [3(5x-4)(x+7)]/[2(5x-4)]

What is "No Horizontal Asymptote"?

500

Find all vertical asymptote of: f(x) = (2x²-50)/(3x²+11x-20)

What is x = 4/3?

Logarithms

100

Change this log equation into an exponential equation: log_2x(4x+8) = 2x+2

What is (2x)^2x+2 = 4x+8?

200

Evaluate: log₁₆(1/32)

What is 

-(5/4)?

300

Find all values of x: log_x(2x²-7x+12) = 2

What is x = 4 and x = 3?

400

Solve for x. log₃(x-1)+log₃(4x+5) = 2

What is x = 7/4?

500

Find x: 5ln(4x+9)-1 = 14

What is x = (e³-9)/4?

Trig Identities

100

Given: sinθ = 12/13. Find: sin2θ 

What is 120/169?

200

Find the maximum and minimum of the trig function. f(x)=-4cos5x-8

What is maximum of -4 and minimum of -12?

300

Simplify: cscθ/sinθ

What is csc²θ?

400

Simplify: csc²x-1

What is cot²x?

500

Simplify: sec²x-1

What is tan²x?

Derivatives

100

Find dy/dx: y = x/(3-5x³) 

What is (10x³+3)/(3-5x³)²?

200

Find dy/dx: y = 4(x²+9)^3/2

What is 6(x²+9)^1/2(2x)?

300

Find dy/dx: y = 3sin(2-3x³)

What is -27x²cos(2-3x³)?

400

Find dy/dx: y = cos[(5x³+5)⁴]

What is -60x²(5x³+5)³sin[(5x³+5)⁴]?

500

Find dy/dx: y = cos(2x³)sin⁴(x)

What is -6x²sin(2x³)sin⁴(x)+4sin³(x)cos(x)cos(2x³)?