Mu Alpha Theta Ceremony Jeopardy

History

100

This person created the theorem we use to find the hypotenuse of a right triangle. 

Who is Pythagoras?

200

This person created a method to find binomial coefficients. 

Who is Pascal? 

Bonus question: what was his first name and what is the method called?

300

These civilizations created major contributions to the world of algebra. 

Who are the ancient Babylonians and the ancient Egyptians?

400

This person created the prime counting function at the ripe age of 15. 

Who is Carl Friedrich Gauss?

500

This number, later named the “taxicab number”, was called by Ramanujan “the smallest number expressible as the sum of two cubes in two different ways,” after he mentioned it while ill in a London hospital.

what is 1729?

Addition

100

25+5

30

200

326+247

573

300

1265+349

1614

400

1978+3423+5496

10897

500

e^i*pi+1

0

Multiplication

100

5*10

50

200

30*20

600

300

27*19

513

400

342*27

9234

500

The product, taken over all prime numbers, of one divided by (1 minus p to the negative 2)

pi²/6

Calculus

100

limit of (sin(x)-x+x³/6)/(x⁵) as x approaches 0

1/120

200

d/dx [((x²+1)^sin(x)e^x)/((lnx)²)]

((x²+1)^sin(x)e^x)/(ln²(x))*(cos(x)ln(x²+1)+(2xsin(x)/(x²+1))+1-(2/(xln(x))))

300

integral of x*cos(sqrt(1+x²)) with respect to x

(sqrt(1+x²))*sin(sqrt(1+x²))+cos(sqrt(1+x²)+C

400

Sand is poured on a beach creating a cone whose radius is always equal to twice its height. If the sand is poured

at the rate of 20 in³/sec, how fast is the height of the conical pile changing at the time the height is 2 inches?

5/(4pi)

Bonus question (100): what are the units?

500

integral of e^{-x^2} from negative infinity to positive infinity with respect to x.

sqrt(pi)

Algebra

100

Find x if 2x+3=9. 

what is 3?

200

find the non-trivial zeros of x²+9x+30.

what is -4.5+/-(sqrt(39)*i)/2

300

create a function that has a horizontal asymptote at 5, a vertical asymptote at 0, a removable discontinuity at 3, and a y-intercept of 2

impossible. 

Bonus question: if you didn't have to make a y-intercept of 2, what would the function be then?

400

This is the largest integer of the sum of the three consecutive integers that add up to 63. 

What is 22?

500

if 2x-3y=6 and 4x+ky=10, find the value of k that makes the system have infinitely many solutions. 

What is -6?