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Math 201 Final Exam Review: Fall '02, Exams of Elementary Mathematics

A review sheet for the final exam of math 201 in the fall semester of 2002. It includes various math problems covering topics such as ratios, decimals, polygons, inductive reasoning, number lines, multiplication, bases, primes, and geometry. Students are expected to explain concepts, draw diagrams, use patterns, and apply mathematical formulas.

Typology: Exams

2012/2013

Uploaded on 03/31/2013

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Fall ’02 Math 201 Final Exam Review Prof. Brick
1. Explain why a ratio of integers must have a repeating or terminating decimal and then
express 17
19 as a repeating or terminating decimal.
2. Draw a pentagon and a hexagon. Define the terms “concave”, “isosceles”, and “poly-
gon”.
3. Give an example where inductive reasoning doesn’t work.
4. Think of a number. Multiply it by 2. Add 2. Divide by 2. Subtract 1. Explain.
5. Explain how a numberline model with a car handles 5 −3 and 7 −(−2).
6. Explain why the commutative law of multiplication holds using areas of rectangles.
7. A student says that 39 + 51 = 40 + 50 and concludes that 39 ·51 = 40 ·50. How will
you handle that ?
8. Use a Venn diagram to determine if the following is valid:
College classes are always a lot of fun.
Math 201 is a college class.
Therefore, Math 201 is always a lot of fun.
9. Explain why we study the arithmetic of other bases in this class. Then show how to
add 2738+ 7658working only in base 8.
10. Use patterns to show how to compute 9 + (−2).
11. Explain why multiplication by 5 can be done by dividing by 2 and then moving the
decimal place.
12. For what values of the digit a is the integer 92145341679532a divisible by 3.
13. What is a prime number. Show how to use the Sieve of Eatosthenes to find all primes
less than 100. Suppose you just wanted to test whether or not 397 is prime by looking for
factors. At what point should you stop looking for factors ? Why are primes and factorings
and related concepts important to the average person (without them knowing usually) ?
14. Describe what you get if you take a rectangular piece of paper and glue two opposite
sides together with a twist. What is that object called. Describe some interesting and
perhaps surprising properties it has.
15. Suppose you are transported back in time and find yourself in a prisoner of war camp.
Explain how you would use similar triangles to estimate how far you would have to dig an
escape tunnel.
16. Use the Euclidean algorithm to find the g.c.d. of 8532 and 3876.
17. Xavier Roundhead wears a size 8 hat. Assuming that corresponds to his head’s
diameter (in inches), find the circumeference of his head.
18. A sale item is priced at $120 and is described as 25% off. What do you think the
original price was and why ? What should they have said ?
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Fall ’02 Math 201 Final Exam Review Prof. Brick

  1. Explain why a ratio of integers must have a repeating or terminating decimal and then express 1719 as a repeating or terminating decimal.
  2. Draw a pentagon and a hexagon. Define the terms “concave”, “isosceles”, and “poly- gon”.
  3. Give an example where inductive reasoning doesn’t work.
  4. Think of a number. Multiply it by 2. Add 2. Divide by 2. Subtract 1. Explain.
  5. Explain how a numberline model with a car handles 5 − 3 and 7 − (−2).
  6. Explain why the commutative law of multiplication holds using areas of rectangles.
  7. A student says that 39 + 51 = 40 + 50 and concludes that 39 · 51 = 40 · 50. How will you handle that?
  8. Use a Venn diagram to determine if the following is valid: College classes are always a lot of fun. Math 201 is a college class. Therefore, Math 201 is always a lot of fun.
  9. Explain why we study the arithmetic of other bases in this class. Then show how to add 273 8 + 765 8 working only in base 8.
  10. Use patterns to show how to compute 9 + (−2).
  11. Explain why multiplication by 5 can be done by dividing by 2 and then moving the decimal place.
  12. For what values of the digit a is the integer 92145341679532a divisible by 3.
  13. What is a prime number. Show how to use the Sieve of Eatosthenes to find all primes less than 100. Suppose you just wanted to test whether or not 397 is prime by looking for factors. At what point should you stop looking for factors? Why are primes and factorings and related concepts important to the average person (without them knowing usually)?
  14. Describe what you get if you take a rectangular piece of paper and glue two opposite sides together with a twist. What is that object called. Describe some interesting and perhaps surprising properties it has.
  15. Suppose you are transported back in time and find yourself in a prisoner of war camp. Explain how you would use similar triangles to estimate how far you would have to dig an escape tunnel.
  16. Use the Euclidean algorithm to find the g.c.d. of 8532 and 3876.
  17. Xavier Roundhead wears a size 8 hat. Assuming that corresponds to his head’s diameter (in inches), find the circumeference of his head.
  18. A sale item is priced at $120 and is described as 25% off. What do you think the original price was and why? What should they have said?
  1. Without using decimals, find a model that can be used to compare 15 and 17? What about 25 and 38?
  2. Find the l.c.m. of 12 and 32. Show it using lists of mulitples.
  3. Working modulo 12, compute 7 + 9 + 4 + 7 + 11 and 8 · 3. What common object can be used to understand these problems? Historically, ancient people ended up using base 12 for time (and 60 which is five 12’s). It is believed that counting with a certain part of the hand led to this. Explain.
  4. Explain some methods that can be used for quick arithemetic, such as for computing a tip, or multiplying by 4 or estimating a sum of numbers.
  5. Why can’t you divide by zero?
  6. Give a model that explains why 13 equals 26.
  7. What does it mean for two triangles to be congruent? to be similar?
  8. When we say that we can construct a perpendicular bisector in geometry, what two tools are we using? Give an example of something about angles that cannot be constructed using these tools.
  9. Using the sums of angles of a triangle, explain the difference between planar geometry (aka flat or zero curvature), spherical geometry (aka positively curved) and hyperbolic geometry (aka negatively curved).
  10. How many degrees is π 3 radians?
  11. Which of the following sets are countable: the integers, the rationals, the irrationals, the reals?
  12. Recall some interesting and unusual fact about Hotel Infinity (other than the fact that there are an infinite number of rooms).
  13. A coin is flipped three times. Find the probability that at least two tails results.
  14. List six rational numbers that lay between 1/2 and 2/3.
  15. Suppose that Professor B is teaching two classes. One has 23 students, of whom 8 get a B or higher. The other has 41 students, of whom 10 get a B or higher. Which class might be considered the better class and why? Explain without using decimals or common denominators.
  16. Suppose the probability of an A is 20%, that of a B is 30%, that of a C is 30%, that of a D is 10% and that of an F is 10%. Find the expected value of the GPA.
  17. Imelda has 12 blouses, 8 pairs of pants, and 305 pairs of shoes. How many possible outfits can she wear?
  18. Review all the homework, all the quizzes, the previous review sheets, the previous exams, and your notes from class. Then review everything else.