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

2. Which of these is not a plane figure that Archimedes discovered a method for finding the center of gravity?
(a) Triangle.
(b) Parallelogram.
(c) Cone.
(d) Parabola.

3. Which of these would be a lemma?
(a) 33(y)=66.
(b) a + b = 4c.
(c) 27 - x = 15.
(d) 1 + 1 = 2.

4. How do people know that some of Archimedes' writings have been lost?
(a) A list of his writings was engraved on his tomb.
(b) Oral tradition.
(c) A list of them survives.
(d) He refers to them or other mathematicians refer to them in other writings.

5. What festival was a favorite of the people in Syracuse?
(a) Greater Dionysia.
(b) Feast to Diana.
(c) Festival of the Vine Flower.
(d) Hieros Gamos.

Short Answer Questions

1. What word means balance?

2. What is always the same as the area of a circle if one side was the same as the radius of the circle?

3. Which area of scientific discovery was not part of Archimedes work?

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

5. What is the solid of a square?

Short Essay Questions

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

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

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

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

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

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

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

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

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

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

(see the answer keys)

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