Round 5 First Half

Transylvania University Academic Tournament

Feb. 12, 2000

1.

A circle with area 64 pi square inches is drawn. The right triangle is drawn inside the circle with largest area possible. What is the are of the triangle?
Answer: 64 square inches

2.

In group theory, how many elements does the symmetric group on five elements have?
Answer: 120

3.

This disorder is generally characterized as a parent's need to make a child ill, in order to gain attention.
Answer: Munchausen syndrome by proxy

4.

What was the unattainable lover's name who inspired Hector Berlioz's ``Symphonie Fantastique''?
Answer: Harriett Smithson

5.

Find the antiderivative of $24 \cos 6x + 24 \sin 4x$ (read: 24 times cosine of six x plus 24 times the sine of 4 x).
Answer: $4 \sin 6x - 6 \cos 4x + C$ (4 times sine of 6 x minus 6 times cosine of 4 x plus C)

6.

Name the regenerative electrical signal use by neuronal axons to carry information to the axon terminal region.
Answer: action potential

7.

What is the highest USA military decoration?
Answer: Congressional Medal of Honor

8.

Which organ is most severely affected by rheumatic fever?
Answer: heart

9.

On what Carribean Island did Toussaint l'Ouverture establish in 1801 the first black ruled nation in Americas?
Answer: Haiti

10.

A compound which has a non-superimposable mirror image is known as what?
Answer: an enantiomer

11.

What ancient philosopher and scientist has a species of fish named after him?
Answer: Aristotle

12.

Which ancient neo-Platonic philosopher and mathematician was assassinated by her Christian rivals in 415 CE in Alexandria?
Answer: Hypatia

13.

This Thracian gladiator Spartacus was responsible for leading what sort of event from 73-71 BCE?
Answer: a slave revolt against Rome

14.

Who invented the name, ``United States of America'' for this country?
Answer: Thomas Paine

15.

In what century was a doctorate in philosophy first conferred upon a woman?
Answer: the seventeenth century; or the 1600s

16.

Eighteen people are in a room. Each person shakes hands with everyone in the room once. How many handshakes occur?
Answer: 153

17.

Spell a B dominant-7th chord.
Answer: B-D#-F#-A (prounce B D-sharp F-sharp A)

18.

In 490 BCE one of the most important military engagements of all time took place on a plain approximately 26 miles outside of Athens. What is the name by which that battle is known today?
Answer: The Battle of Marathon

19.

The square of a number is seven more than six times the number. What two numbers satisfy this description?
Answer: -1 and 7

20.

What high-ranking German official secretly parachuted into Great Britain in an effort to negotiate a truce with that country and keep Great Britain out of WWII?
Answer: Herman Hess

21.

How many chromosomes are there in a typical cell in the human body?
Answer: 46 (23 pairs)

22.

In what German principality was Catherine the Great of Russia born?
Answer: Anhalt-Zerbst

23.

This Sinclair Lewis novel explores the issues of race and its effect on one white man who discovers he may have an African-American ancestor.
Answer: Kingsblood Royal

24.

What type of rock music begun in the seventies features long guitar solos, loud volume and elaborate stage shows?
Answer: Heavy metal or metal

25.

Four coins are tossed. What is the probability that the number of heads and tails appearing is the same?
Answer: 1/4 (one-fourth)

26.

How many calories are in one gram of fat?
Answer: 9 grams

27.

Name the title of a nineteen century fantasy novel by Edwin Abbott that features geometry prominantly in its theme.
Answer: Flatland

28.

What nineteenth-century German philosopher is famous for having said, ``God is dead, and we have killed him.''?
Answer: Nietzsche

29.

The pulsar in the Crab Nebula is an example of what type of star?
Answer: a neutron star

30.

What is the weakest of the four fundamental forces known to scientists?
Answer: Gravity

31.

What was Walt Disney's first animated full-length film?
Answer: Snow White and the Seven Dwarfs

32.

In what year was the Gulf of Tonkin incident, an event which drew the U.S. into the Vietnam conflict?
Answer: 1964

33.

What is the greatest common factor of x²-4 and x²+5x+6 (x squared minus four and x squared plus 5 x plus 6)?
Answer: x + 2 (x plus two)

34.

Which ancient Greek philosopher was abducted and sold into slavery on his way back to Greece from a trip to the Italian penninsula?
Answer: Plato

35.

Into which phylum of animals are snails and slugs placed?
Answer: mollusks

36.

What is the least common multiple of 24 and 22?
Answer: 264

37.

What religion did U.S. Presidents George Washington and Thomas Jefferson practice?
Answer: deism (neither were Christian)

38.

What structure is largely responsible for the formation of the osmotic gradient in the renal medulla?
Answer: loop of Henle

39.

What famous sports event happens in April in Augusta, Georgia?
Answer: The Masters Golf Tournament

40.

What two European countries began recognizing the same monarch in 1603 but were only formally joined through the Act of Union in 1707?
Answer: England and Scotland