View a FREE sample

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

Multiple Choice Questions

1. After Hippocrates, what shape did the Greeks attempt to square without success?
(a) Parallelogram.
(b) Pentagon.
(c) Circle.
(d) Hemisphere.

2. After working on pi, what did Archimedes continue with in his study of mathematics?
(a) He studied the relationship between ratios in triangles.
(b) He studied the volume and surface area of spheres, cones, and cylinders.
(c) He studied the volume to surface area ratios of cubes.
(d) He studied the relationship of sine to cosine.

3. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?
(a) Even numbers.
(b) Discrete numbers.
(c) Perfect numbers.
(d) Composite numbers.

4. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's proof on right triangles.
(b) Euclid's postulate on parallel lines.
(c) Euclid's postulate on right triangles.
(d) Euclid's postulate on creating an arc.

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

6. Who acted as the gate keepers of knowledge?
(a) Roman emporers.
(b) Greek tradesman.
(c) Greek philosophers.
(d) Arabian scholars.

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

8. How did Lindeman prove his conclusion?
(a) Lindeman proved that square roots are irrational numbers.
(b) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.
(c) Lindeman proved that some numbers are constructable without the use of a compass.
(d) Lindeman proved that all numbers are constructable with a compass and ruler.

9. What did Archimedes manage to prove using Euclid's ideas?
(a) That the relationship of area to circumference is really the same as the relationship of radius to diameter.
(b) That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.
(c) That the square of a diameter is equal to pi.
(d) That the value of pi is proportional to the area of the circle.

10. What did Heron's advances put into historical perspective for Dunham?
(a) A shift in learning across continents.
(b) A shift in information flow that ignored socioeconomic order.
(c) A change in learning foundations in the ancient scholarly universities.
(d) A change in political theory across the globe.

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

12. Which was true of Euclid's number theory?
(a) It has an impact on modern math.
(b) It was incorrect, as proved by Plato.
(c) It was proven to the true by Hippocrates.
(d) It has been proven too basic to be useful.

13. What did the Pythagorean Theorem accomplish for mathematics?
(a) The concept of providing a logical proof.
(b) The ability to measure angles.
(c) The concept of constructing useful mathematics.
(d) The ability to find square roots.

14. Which of the following is false about the modern implications of Euclid's number theory?
(a) Euclid's recipe for constructing even perfect numbers is incorrect.
(b) Euclid gave a good idea for how to construct even perfect numbers.
(c) Whether there are no odd perfect numbers is still not known.
(d) Great mathematicians continue to puzzle over some aspects of Euclid's number theory.

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

Short Answer Questions

1. What allowed Cardano to justify publishing his book?

2. In Elements, how many postulates must be accepted as given?

3. What is true about prime numbers?

4. What was Hippocrates's great advance to mathematics?

5. Which mathematician was first to take the challenge to solve cubic equations?

(see the answer keys)

This section contains 710 words (approx. 3 pages at 300 words per page) View a FREE sample