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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) C100,000,000.
(b) P100,000,000.
(c) D100,000.
(d) B100,000.

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

3. How many galleys did the Roman general have who attacked Syracuse?
(a) 70.
(b) 50.
(c) 60.
(d) 40.

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

5. What is the ratio of the area of a circle to the circle's diameter squared?
(a) 5 to 9.
(b) 3 to 8.
(c) 11 to 14.
(d) 10 to 12.

Short Answer Questions

1. For which type of science were Archimedes' demonstrations of centers of gravity the foundation?

2. What did Marcellus do while Syracuse was in siege?

3. What scientist do most people believe was the first to understand the laws of gravitation?

4. What is the solid of a rectangle?

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

Short Essay Questions

1. What is the center of gravity?

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

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

4. How do modern scientists work with very large numbers?

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

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

7. What is a chain reaction in a nuclear explosion?

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

9. What interests mathematicians regarding Archimedes and square roots?

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

(see the answer keys)

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