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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

1. When Buffon, a French scientist, made a mirror following the description of Archimedes' mirrors, how far away could he set fire to wood?
(a) 50 feet.
(b) 100 feet.
(c) 75 feet.
(d) 150 feet.

2. What mathematics is needed to figure the cattle problem?
(a) Algebra.
(b) Arithmetic.
(c) Calculus.
(d) Trigonometry.

3. When did people first glimpse the idea of gravity and its effects?
(a) Some time during the 200s B.C.
(b) 12th century.
(c) 17th century.
(d) Some time during the 600s B.C.

4. Who was the Roman general who waged war against Syracuse?
(a) Marcellus.
(b) Bonifacius.
(c) Aureolus.
(d) Glabrio.

5. How did Marcellus' soldiers enter Syracuse?
(a) Through an unguarded gate.
(b) Over the wall.
(c) Through a hole in a wall.
(d) Under the wall.

Short Answer Questions

1. What is the ratio of the area of a circle to the circle's diameter squared?

2. What is a lemma?

3. How many banks of oars did the galleys have that a Roman general used to attack Syracuse?

4. What word means balance?

5. What books did Archimedes send to friends in Alexandria with deliberate errors?

Short Essay Questions

1. What agreement did the Romans and Carthaginians make to divide the Mediterranean between themselves?

2. What did Archimedes set out to prove in "The Sand Reckoner"?

3. What is the center of gravity?

4. What did Archimedes consider to be his most important work?

5. How did Archimedes figure the area of a circle?

6. Describe Marcellus' fleet that he sent to attack Syracuse.

7. How do people know that some of Archimedes' writing have been lost?

8. What happened when a soldier came to bring Archimedes to Marcellus?

9. What calculations did Archimedes use to show how numbers were infinite?

10. Why is Archimedes' "Method" so important to all mathematicians who followed him?

(see the answer keys)

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