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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 strait did Carthage control?
(a) Gibralter.
(b) Pentland.
(c) Cook.
(d) Messina.

2. How much larger did Archimedes believe that the universe (all the stars) was than the Greek universe?
(a) 100,000 times.
(b) 10,000 times.
(c) 75,000 times.
(d) 50,000 times.

3. What did Marcellus have his workmen build when he noticed a poorly guarded wall and tower in Syracuse?
(a) Step ladders.
(b) Climbing poles.
(c) Scaling ladders.
(d) Bridges.

4. What is the solid of a circle?
(a) Box.
(b) Cube.
(c) Sphere.
(d) Cone.

5. What would be the area of a circle that had a radius of 3 inches?
(a) 5.9986.
(b) 12.3454.
(c) 45.33813.
(d) 28.27431 inches.

Short Answer Questions

1. How many sides did the polygons have that Archimedes used to determine the area of a circle?

2. What did Archimedes want on his tomb?

3. What was the name of the largest number for which the Greeks had a name?

4. Where is earth's center of gravity in the solar system?

5. What calculation today does not use the unusual mathematical properties of a spiral?

Short Essay Questions

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

2. What happens when a pebble is dropped into a pond?

3. Why did Marcellus watch the battle for Syracuse with tears in his eyes?

4. Describe Carthage.

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

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

7. Where is the earth's center of gravity?

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

9. Why is it possible for a person to balance standing on one foot?

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

(see the answer keys)

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