Math Jeopardy

Geometry

100

The sum of the interior angles of any triangle

What is 180 degrees?

200

A regular polygon has an interior angle of 150∘. How many sides does it have?

12

300

A circle has radius r. A chord is drawn at a distance r/2 from the center. Find the chord length.

r√3

400

In a right triangle, the altitude to the hypotenuse is 6, and one segment of the hypotenuse is 4. Find the other segment.

9

Algebra

100

Solve for x:

3^x+1 = 27

x = 2

200

Simplify: (x² - 4) / (x² - x - 6)

(x + 2) / (x - 3)

300

1/x-2 + 1/x+2 = 1/3

Solve.

x = 8 or x = -8

400

f(x) = √2x -3, find f^-1(x)

f^-1(x) = (x² + 3)/2

Pre-Calculus

100

Convert 225 degrees to radians.

5pi/4

200

Solve for θ: sin⁡(2θ)= √3/2 on [0,2pi).

θ=pi/6,5pi/6,7pi/6,11pi/6

300

Write cos⁡(x)+cos⁡(3x) as a product.

2cos⁡(2x)cos⁡(x)

400

Given f(x)=2^x+1−3, find the exact value of f^-1(5).

2

Calculus

100

Find d/dx(ln(x²+1))

2x/(x²+1)

200

Evaluate ∫ 1/xln⁡x dx.

ln⁡|ln⁡x|+C

300

The derivative of e^3x

3e^3x

400

Given y=x^x, find dy/dx.

x^x(lnx+1)