Mu Alpha Theta Jeopardy - 3/13

Algebra I & II

100

Solve for x:

2x + 3 = 9

x = 3

200

Solve for the quadratic equation:

x² - 5x + 6

x = 2 and x = 3

300

Divide 2x³ - 3x² + 4x - 5 by x - 2

2x² + x + 2 + 3/x-2

400

Given the geometric sequence where the first term is 3 and the fourth term is 24, find the common ratio.

Common ratio: 2

500

Solve for x:

log₂(x-1) + log₂(x+1) = 3

x = 3

Extraneous: x = -3

Pre-Calculus

100

Evaluate:

sin(45)

sqrt(2)/2

200

Find the equation of the line that passes through the points (2,3) and (4,7).

y = 2x - 1

300

Simplify the complex number: 

(3 + 2i)(4 - 5i)

22 - 7i

400

Find the domain:

f(x) = sqrt(5-x)

x is less than or equal to 5

500

Determine the polar coordinates of the point with Cartesian coordinates (-4, 4/sqrt(3)) where r is positive and 0 ≤ θ < 2pi.

(8, 2pi/3)

Random

100

What room number are we currently in?

5-310

200

I am the product of six times four minus six. My digits add to nine. What number am I?

18

300

Which anime is featured on Mr. Navarro's lanyard?

Jujutsu Kaisen

400

If we are given the graph of a(t), how do we find v(t)?

Take the integral/Find area under the curve

500

I am always coming, but never here, never arriving, but always near. What am I?

Tomorrow

Calculus AB

100

Find the limit as x approches 0:

sin(x)/x

limit = 1

200

Evaluate the integral from 0 to 3:

(2x + 1)dx

12

300

Use implicit differentiation to find dy/dx:

x² + xy + y² = 7

dy/dx = (-2x-y)/(x+2y)

400

Find the derivative:

f(x) = e^2xsin(x)

f'(x) = 2e^2xsin(x) + e^2xcos(x)

500

Determine the area of the region bounded by y = x² and y = 4x - x².

8/3

Calculus BC

100

Find the derivative of the vector valued function:

r(t) = <t², sin(t), e^t>

r'(t) = <2t, cos(t), e^t>

200

Find the integral of the vector valued function with the initial condition <1,2,1>:

r(t) = <2t, cos(t), e^t>

r'(t) = <t² + 1, sin(t) + 2, e^t + 1>

300

Solve the integral using integration by parts:

(xe^x)dx

xe^x - e^x + C

400

Find the arc length of the curve given the parametric equations x = 3t² and y = 2t³ from t = 0 to t = 1.

7sqrt(14) - 4

500

Evaluate the improper integral with bounds from 1 to infinity:

(ln(x)/x²)dx

-1