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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. What did Archimedes call the largest number that he worked with?
(a) D100,000.
(b) P100,000,000.
(c) C100,000,000.
(d) B100,000.

2. What is the formula for the area of a circle?
(a) Multiply the radius times the circumference of a circle.
(b) Multiply the length of the circle from rim to rim times pi.
(c) Multiply pi times the radius of the circle times the radius again.
(d) Subtract the radius from the circumference of a circle.

3. How much larger did Archimedes believe that the Greek universe (our solar system) was larger than the earth?
(a) 10,000 times.
(b) 20,000 times.
(c) 50,000 times.
(d) 30,000 times.

4. Who succeeded Hiero when he died?
(a) Hieronymus.
(b) Herodotus.
(c) Pericles.
(d) Hesiod.

5. What did Marcellus do while Syracuse was in siege?
(a) Conquered Sparta.
(b) Overran much of Corinth.
(c) Conquered Athens.
(d) Overran much of Sicily.

Short Answer Questions

1. What would be the area of a circle that had a radius of 2 inches?

2. Where did Rome capture city states?

3. How many different sciences did Archimedes begin?

4. How do people know that some of Archimedes' writings have been lost?

5. When do most people believe that the first real understanding of the laws of gravitation began?

Short Essay Questions

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

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

3. What were the people of Syracuse doing when the Romans crept into their city?

4. Describe Carthage.

5. How did Archimedes estimate the number of grains that would fill the universe?

6. Why isn't the center of gravity always at the center of an object?

7. Why did Archimedes not want to help King Hiero make plans to defend Syracuse from a possible attack?

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

9. What is the center of gravity?

10. Before Archimedes, how did people find the area of a circle?

(see the answer keys)

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