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Elementary Education Mathematics I Exams, Exams of Elementary Mathematics

Three exams for the elementary education mathematics i course, taught by prof. Brick in fall 99. The exams cover various mathematical concepts, including arithmetic, algebra, set theory, and geometry. Problems require students to solve calculations, explain reasoning, draw diagrams, and justify answers.

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Math 201 Prof. Brick
section 2 Fall 99
Elem. Ed. Math I — Exam 1
Do the problems in order in your bluebook. Show your work. Explain and
justify your answers.
1. Without adding all the terms up by hand, compute the sum 9 + 10 + 11 + ...+ 66.
2. The statement “the next term in the sequence 1,4,9,...is 25” is an example of what
type of reasoning ?
3. The set Xhas 63 nonempty subsets. Find the cardinality of X.
4. Consider the sets A={x|x=2k−1,where k is an integer and 1 ≤k≤3}and
B={k|kis an integer and 1 ≤k≤3}. Find A−B.
5. Draw a Venn diagram showing two nonempty sets Aand Bfor which A=Band
A∪B=A.
6. Suppose A={1,2,9}and B={0,2}. Find A×B.
7. Suppose f(x)=x2+ 1 and the domain is {−2,0,2}. Describe f(x) using two sets with
directed arrows.
8. Write the contrapositive of the statement “if I studied then I will pass”.
9. A snail climbs 4 inches up a wall each day, but slips down 2 inches each night. If the
wall is 3 feet high and the snail started at the halfway point, when will it reach the top ?
10. Use a Venn diagram to determine if the following is a valid syllogism:
College classes are always a lot of fun.
Math 201 is a college class.
Therefore, Math 201 is always a lot of fun.
11. Use a truth table to determine when if ever the formula (¬q)→pis true ?
12. Suppose f(x)=2x−3 and g(x)=x2+ 3. Draw a “black box” diagram for the
composite function (g◦f)(x) and compute its value when x=4.
pf3
pf4

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section 2 Fall 99

Elem. Ed. Math I — Exam 1

Do the problems in order in your bluebook. Show your work. Explain and justify your answers.

  1. Without adding all the terms up by hand,compute the sum 9 + 10 + 11 +... + 66.
  2. The statement “the next term in the sequence 1,4,9,... is 25” is an example of what type of reasoning?
  3. The set X has 63 nonempty subsets. Find the cardinality of X.
  4. Consider the sets A = {x | x = 2k − 1 , where k is an integer and 1 ≤ k ≤ 3 } and B = {k | k is an integer and 1 ≤ k ≤ 3 }. Find A − B.
  5. Draw a Venn diagram showing two nonempty sets A and B for which A = B and A ∪ B = A.
  6. Suppose A = { 1 , 2 , 9 } and B = { 0 , 2 }. Find A × B.
  7. Suppose f (x) = x^2 + 1 and the domain is {− 2 , 0 , 2 }. Describe f (x) using two sets with directed arrows.
  8. Write the contrapositive of the statement “if I studied then I will pass”.
  9. A snail climbs 4 inches up a wall each day,but slips down 2 inches each night. If the wall is 3 feet high and the snail started at the halfway point,when will it reach the top?
  10. Use a Venn diagram to determine if the following is a valid syllogism:

College classes are always a lot of fun. Math 201 is a college class. Therefore,Math 201 is always a lot of fun.

  1. Use a truth table to determine when if ever the formula (¬q) → p is true?
  2. Suppose f (x) = 2x − 3 and g(x) = x^2 + 3. Draw a “black box” diagram for the composite function (g ◦ f )(x) and compute its value when x = 4.

section 2 Fall 99

Elem. Ed. Math I — Exam 2

Do the problems in order in your bluebook. Show your work. Explain and justify your answers in details,labelling any figures you choose to use.

  1. Show how the comparison model illustrates 8 − 3
  2. Is the set of even positive integers closed under multiplication? Why or why not?
  3. Rainman likes to make addition problems as easy as possible. When faced with the problem of computing 27 + 16,he instead did the addition 30 + 13. Explain.
  4. Use the charged pattern model to illustrate 5 + (−8).
  5. Draw and label a geometric figure that models (X + 1)(Y + 1) = XY + X + Y + 1
  6. Working in base six,compute 3324 6 ÷ 46.
  7. Use patterns to illustrate 2 − 6.
  8. What method makes the addition problem 12 + 45 + 18 + 39 + 15 + 11 easier?
  9. What is the least whole number n for which 17n > 408.
  10. Let A 12 = 10 and B 12 = 11. Compute A 212 · 3 B 12 ,working in base twelve.
  11. Use a model of your choice to illustrate (−2) · (−3).
  12. Compute 3112 5 − 24145 in base five.

section 2 Elem. Ed. Math I — Final Exam Fall 99

Do the problems in order in your bluebook. Show your work. No calculators allowed. Explain and justify your answers in detail.

  1. A bike shop inspects 50 bikes and finds that 40 need new tires while 30 need new gears. Find the least possible number that needs both. Draw a Venn diagram.
  2. Find all subsets of the set B = { 3 , 5 , x}.
  3. Use a Venn diagram to determine if the following is valid (be sure to label it): Everyone taking a math class is happy. Socrates is not taking any math classes Therefore,Socrates is not happy.
  4. Let A = {x | x is an even integer} and B = {k | k is an integer and 1 ≤ k ≤ 9 }. Find B − A.
  5. Use the charged pattern model to illustrate 4 + (−6). Explain how it works.
  6. Draw and label a geometric figure that illustrates the distributive law. (Be sure to explain exactly how the figure illustrates the distibutive law.)
  7. Use patterns to illustrate 3 − 4. Explain how it works.
  8. Compute 34 5 · 145 and 2312 5 − 3445 working in base five.
  9. Professor Zer has saved 145 math articles and 120 statistics articles from assorted publications. He wants to file these in folders so that each folder contains only math articles or only statistics articles. And he wants each folder to contain exactly the same number of articles. What is the greatest number of articles he could place in each folder?
  10. Working modulo 7,find all a for which 1 + (4 · a) = 0.
  11. Two classes take the same exam. In the first class 18 out of 27 pass,while in the second class 17 out of 25 pass. Which class did better? (Do not use decimals.)
  12. Use the Euclidean algorithm to reduce the fraction 325/1612 to simplest form.
  13. Gauss won some money at a math contest. He decided to go on a shopping spree. He spent $63 on a new calculator and 3/5 of what then remained on a Math T-shirt. He used all of the remaining money to buy 1 13 pounds of special coffee beans which were on sale at $9 a pound (at a savings of 101 off). Determine how much money Gauss had won.