Calc BC Jeopardy!

"Easy" Math

100

What is the sum of 5 + 5!

125 = 5 + (5 x 4 x 3 x 2 x 1)

200

∫ (1)/(1+x²) dx

tan^-1(x) + C

300

Convert the polar equation r=2cos⁡(θ) to its Cartesian form and identify the resulting shape.

Cartesian Form: (x-1)²+y²=1

Circle with a center of (1,0) and a radius of 1

400

What is the Taylor series for ln(1+x)?

x - x² + x³ - x⁴ + x^{5    ...}
---  ---  ---  ---
2      3    4     5

500

lim_n→∞ (n²+3n-1)/(2n²-n)

Evaluate the limit and determine whether it converges or diverges.

The limit converges at 1/2

HARD Math

100

Determine whether the following series converges or diverges:

sum_(n=1)^∞ (n!)/n^n

Limit is 0, converges by the ratio test.

200

Evaluate:

∫₀^π/2 sin²(x)cos²(x) dx

(π)/(16)

300

Find the area enclosed by one loop of the polar curve r=1+2cos⁡(θ)

π  

400

Evaluate the improper integral:

∫^∞₁ (1)/(x²+1) dx

pi/4

500

Find the Taylor series for the function f(x) = (1)/(1-x)² centered at x=0. Determine the radius of convergence for this series.

Radius of convergence is: 1

Taylor Series: 

sum_(n=0)^∞ (n+1)x^n

Lerohl's Extra Credit

100

How many hats does Perry have? 

6 (Agent Perry, Party Perry, Thinking cap, Graduation cap, Green hat, Chopper Hat)

200

The college the bear went to.

What is Washington University in St. Louis?

300

What the dog says in the comic

"Based on all the head tilts, maybe I'd better explain this again..."

400

The poster on the wall near the door (not on the closet).

EINSTEIN BALLING

500

The amount of stars in the bottle. +-3 for point.

56

Math History

100

Who are the two people who "invented" calculus?
Full names are needed

Sir Issac Newton and Gottfried Wilhelm Leibniz.

200

Where does the word calculus come from? Say the origin and guess its meaning

Calculus comes from Latin and means "small stone."

The reason is because you are trying to understand mathematical concepts by looking at small pieces.

- source: https://www.mathsisfun.com/calculus/

300

Who developed the method of finding the maxima and minima in a function by setting the derivative equal to 0?

Who is Pierre de Fermat?

Source: https://www.mscs.dal.ca/~kgardner/History.html

400

Who is one of the first people to begin to discover the concept of limits?

Who is the Greek mathematician Archimedes of Syracuse?

(He used it to try and find the volume of a sphere and other curved figures according to various sources like encyclopedia.com)

500

"If the statement is true, then it must be false, but if it is false, then it must be true." Which paradox challenges the binary nature of truth and falsity?

A). Russell's Paradox      C).Barber Paradox

B). Zeno's Paradox         D).Liar's Paradox

D). Liar's Paradox

Geography :)

100

Which is the largest country in the Balkans?

Romania

200

What country is Mount Kilimanjaro located in?

Tanzania

300

What country does this flag belong to and what year did that country form?

Luxembourg and it became a country in 1867.

400

What country is this?

Ivory Coast

500

What US state does this flag represent?

Maryland

World History

100

What month did World War II start on (Europe)?

4:45 AM, September 1, 1939

200

Which of the following is considered to be the bloodiest conflict (out of the 4)?

A) The Thirty Years' War (1618 - 1648)

B) An Lushan Rebellion (755 - 763)

C) Second Punic War (218 - 201 BC)

D) The Crusades (1096 - 1291)

B) The An Lushan Rebellion (13-36 million people)

30 Years': 4.5-8 million

Second Punic: 1.2-1.5 million

Crusades: 1-3 million

300

What is the name of the conflict between Finland and the Soviet Union from June 25, 1941 to September 19, 1944.

The Continuation War 

Considered to be a "continuation" of the earlier Winter War (1939-1940), this conflict saw the Finnish military attack Soviet forces on all fronts in an effort to regain lost territories while earning support from the German Luftwaffe during World War II.

400

In 1861, the Kingdom of Siam (modern-day Thailand) offered to send elephants to aid which country during a war?

A) France

B) The United States

C) Japan

D) Qing Empire

A) The United States

King Mongkut of Siam offered to send a herd of elephants to aid the Union Army in logistics during the American Civil War. Abraham Lincoln kindly rejected the offer, stating that the climate in the USA wasn't suitable for elephants.

500

Which European country had a plan in the 1960s to create an artificial island called "New Atlantis" in the Atlantic as a base for spaceship launches?

A) United Kingdom

B) Greece

C) Portugal

D) Belgium

D) Belgium

Project proposed by engineer Andre Benard, who sought to create an island base for space exploration, oceanography, and international cooperation. The project was cancelled due to budget constraints and weather-related issues.

Miscellaneous 1

100

The deadliest caltrops that doubles as a toy(an area denial weapon you throw on the ground)

What are Legos?

200

What is the name of the third chronologically released Star Wars movie in the Skywalker Saga?

What is "Revenge of the Sith"

300

Who should have won the Balon D'or in 2020?

Robert Lewandowski

400

This sequence is a series of numbers.
In this sequence, the next number is found by adding the previous two numbers. For example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.

What is the Fibonacci Sequence?

500

Some people say "I'll be there in a jiffy" in order to convey they'll be there soon. What is the actual number and units for a jiffy.

1 jiffy = the time it takes for light to travel one centimeter in a vacuum

1 jiffy = about 33.4 picoseconds

Miscellaneous 2

100

Starter brawler in Brawl Stars.

Who is Shelly?

200

The coding language taught in APCS.

What is Java?

300

The first day of school?

Thursday (09/07/2023)

400

Where Mrs. Lerohl went for college.

What is UVA? (I THINK)

500

The person who sends us the "Empty your locker" email.

Rebecca Barreras