Mu Alpha Theta Jeopardy!

SolvingLogarithmic Functions

100

log₃(x) = 2

9

200

Solve: e^3x=12

x ≈ 0.828

300

Solve: 5e^0.12t=10e^0.08t

t≈ 17.329

400

ln(x+2)+ln(x+1)=ln(4x+14)

x = 4

x = -3 is NOT a solution!

500

If $1000 is invested in an account earning 2% interest compounded quarterly, how long will it take the account to grow in value to $1300?

t ≈ 13.15 years

Integration and u-substitution

100

Find the integral of e^3x

1/3 e^3x+c

200

Evaluate the integral: ∫ ³₂(x+1)2x

7/2

300

Find the integral of tan(x)

sec x+c

400

Find the integral of: u=xe^xdx

xe^x-e^x+c

500

Find the integral of u=ln(x²+5)

d_u=(-2x/x²+5)dx

Polynomial Long Division

100

4x³+5x²+5x+1 / 4x+1

x²+x+1

200

6x³+17x²+18x+8 / 3x+4

2x²+3x+2

300

16x³-16x²-21x+20 / 4x-5

4x²+x-4

400

4x³-20x²-27x+19 / x-6

4x²+4x-3 + 1/x-6

500

9x⁴-6x³-2x²-7 / 3x²-4x+1

3x²+2x+1+ 2x-8/3x²-4x+1

Factoring Polynomials

100

Factor out the GCF: a³b⁸−7a¹⁰b⁴+2a⁵b² 

a³b²(b⁶-7a⁷b²+2a²)

200

Factor: 4w²-25

(2w+5)(2w-5)

300

Factor: x⁶+3x³-4

(x³+4)(x-1)(x²+x+1)

400

Solve for t: 6t²-19t-7

(2t-7)(3t+1)

t = 7/2 AND -1/3

500

Solve for x: x²+2x-2

x = -1+√ 3 AND -1-√ 3

Domain and Range

100

What is the domain of the absolute value parent function? (|x|)

(-∞ ,∞ ) OR all real numbers

200

What is the domain and range of the reciprocal squared function? (1/x²)

Domain: (-∞ ,0)U(0,∞)

Range: (0,∞)

300

Find the domain: 2√-x+5

x ≤ 5

Domain: (-∞, 5]

400

Find the domain: 1-4x/x²-2x-15

(-∞,-3)U(-3,5)U(5,∞) 

500

Find the domain and range: ln(x+2)

Domain: (-2,∞)

Range: (-∞,∞)