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

2. 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) 10 to 12.
(d) 11 to 14.

3. What calculation today does not use the unusual mathematical properties of a spiral?
(a) Finding an unknown quantity.
(b) Speeds.
(c) Directions.
(d) Distances in space.

4. When Archimedes worked with a sphere and cylinder, he figured the ratio or relationship of the cylinder to the sphere was ___________.
(a) 6/5.
(b) 3/2.
(c) 7/6.
(d) 10/9.

5. What is the circumference of a circle?
(a) The distance from rim to rim of a circle.
(b) The ratio between the diameter and the radius.
(c) The distance from the center of a circle to the rim.
(d) The distance around the circle.

Short Answer Questions

1. What is a good project to learn about centers of gravity?

2. Which of these would be a lemma?

3. How long did Marcellus hold Syracuse in siege.

4. What can a giant radio telescope fill with broadcast signals?

5. What is pi?

Short Essay Questions

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

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

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

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

5. What did Marcellus do while he held Syracuse in siege?

6. What is the center of gravity?

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

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

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

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

(see the answer keys)

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