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This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. Which of the following can not be solved using algebra?
(a) Triangulation.
(b) Geometric equation.
(c) Quadratic equation.
(d) Quintic equation.

2. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?
(a) Quadrature.
(b) Triangulation.
(c) Square root.
(d) Cubation.

3. Besides being a mathematician, what else other work was Archimedes famous for?
(a) Politician.
(b) Artist and musician.
(c) Doctor and writer,
(d) Inventor and scientist.

4. Heron devised which of the following methods?
(a) A way to apply mathematics to public health.
(b) A way to determine the volume in a sphere.
(c) A way to solve binomial equations.
(d) A way to determine the area of a triangle.

5. Which city was the center of thinking and learning in Third century BC?
(a) Rome.
(b) Athens.
(c) Alexandria.
(d) Olympia.

6. Which of the following is an example of a perfect number?
(a) 20.
(b) 6.
(c) 1.
(d) 10.

7. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?
(a) 180 degree angle.
(b) Intersection.
(c) Circle.
(d) Parallel lines.

8. Where was Neil's Abel from?
(a) Ireland.
(b) Norway.
(c) Finland.
(d) Great Britian,

9. As described by Archimedes, what is always true about he diameter of the circle?
(a) It's always proportional to its circumference.
(b) It's equal to the square of the radius.
(c) It's never proportional to its circumference.
(d) It's equal to pi.

10. Which mathematician was first to take the challenge to solve cubic equations?
(a) Luca Pacioli.
(b) Scipione del Ferro.
(c) Niccolo Fontana.
(d) Tartaglia.

11. How did Archimedes demonstrate his theory of pi?
(a) He demonstrated that the area of the circle is always greater than the area of the triangle.
(b) He demonstrated that the area of the circle is never less than the area of the triangle.
(c) He demonstrated that the area of the circle is never equal to the area of the triangle.
(d) He demonstrated that the area of the circle is neither greater than nor less than the area of the triangle and therefore must be equal to it.

12. Which of the following was NOT defined by Euclid?
(a) Even numbers.
(b) Nominal numbers.
(c) Odd numbers.
(d) Whole numbers.

13. How many sides did the pentadecagon have, as presented by Euclid?
(a) Ten.
(b) Five.
(c) Twenty.
(d) Fifteen.

14. How did Archimedes arrive at a number value for pi?
(a) By proving pi could not be equal to one.
(b) By constructing multi-sided polygons inside and outside a circle and determining their perimeters.
(c) By constructing successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal.
(d) By proving that pi could not be a negative number.

15. Who was Neil's Abel?
(a) He proved that to solve a quartic equation, one must use more than algebra.
(b) He proved that quintic equations cannot be solved using algebra.
(c) He demonstrated that Cardano's solution to the cubic was incorrect,
(d) He demonstrated the modern version of the Pythagorean Theorem.

Short Answer Questions

1. What did Plato use his inspiration from Euclid for?

2. What is a "depressed cubic"?

3. How do we know about Hippocrates proofs and theorems?

4. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

5. What was true about Heron's theorem as described by Dunham?

(see the answer keys)

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