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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 is true in modern math about twin primes?
(a) They are infinite.
(b) They are not considered whole numbers.
(c) Their sum is always another prime number.
(d) We don't know if they are finite or infinite.

2. In what time period did mathematicians find a solution to cubic equations?
(a) Twentieth century.
(b) Fifteen century.
(c) Seventeeth century.
(d) Thirteenth century.

3. Who was del Ferro's student?
(a) Gerolamo Cardano.
(b) Luca Pacioli.
(c) Antonio Fior.
(d) Niccolo Fontana.

4. What was most useful about finding the square of a shape, before Hippocrates?
(a) It was useful in finding the area of circles.
(b) It was useful in finding the area of oddly shaped pieces of land.
(c) It was useful in determining the distance between two points.
(d) It was useful in creating simple elevation maps,

5. Where was the modern number system developed?
(a) In ancient Rome.
(b) In the East.
(c) In the West.
(d) In ancient Alexanderia.

6. Where was Archimedes born?
(a) Athens.
(b) Olympia.
(c) Sicily.
(d) Rome.

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

8. Which of the following becomes an important definition in mathematics that was first presented in Elements?
(a) Parallel line.
(b) Intersection.
(c) 180 degree angle.
(d) Circle.

9. Heron's work referred to the work of what other famous scholar?
(a) Hippocrates.
(b) Thales.
(c) Euclid.
(d) Archimedes.

10. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number could have been better if he had understood Euclid's work better,
(b) Archimedes's number was perfectly correct.
(c) Archimedes's number was not very accurate, considering the technology of his time.
(d) Archimedes's number was very good, considering he did not have a way to calculate square roots.

11. What was known about pi, during Archimedes' time?
(a) Nothing, the concept of pi was unknown.
(b) That is was the relationship between the diameter and circumference of a circle.
(c) That it was never the same number value for a given circle.
(d) That it could not be assigned a relationship between measurements in a circle.

12. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?
(a) Since the circumference can also be expressed as twice the radius multiplied by π, the area is 2πr²/2, or πr².
(b) Since the diameter of a circle is equal to the hypotenuse of the right triangle, the area of the triangle in his proof is 1/2 the radius times the circumference.
(c) The area of a triangle is one half the base times the height.
(d) Since the base of the triangle is equal to the circumference and the height is the radius, the area of the triangle in his proof is 1/2 the radius times the circumference.

13. Who asked Tartaglia for his solution to cubic equations?
(a) Pacioli.
(b) Fontana.
(c) Fior,
(d) Cardano.

14. According to Euclid, when is a triangle a right triangle?
(a) When a triangle has a side whose square is the sum of the squares of the two legs.
(b) When a triangle can be constructed with three unequal sides.
(c) When a triangle has three sides whose squares are equal to the area of the triangle.
(d) When a triangle does not have a side which can be considered a hypotenuse.

15. What else, besides a solution to cubic equations, was in Cardano's book?
(a) A solution to quartic equations.
(b) A suggested method to depress all complex geometry.
(c) A proof of the Pythagorean Theorem.
(d) An alegrabic solution to quintic equations,

Short Answer Questions

1. Which of the following was an important proposition given by Euclid's number theory?

2. Who was Neil's Abel?

3. How many sides did the pentadecagon have, as presented by Euclid?

4. Where did Hippocrates come from?

5. Who was the author of the book Elements?

(see the answer keys)

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