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Math Exam 1 - February 13, 2007, Exams of Advanced Calculus

Christian Brothers University (CBU)Advanced Calculus

A math exam from february 13, 2007, consisting of 14 multiple-choice and problem-solving questions. Topics covered include set theory, number systems, functions, and problem-solving techniques. Students are required to show their work and partial credit will be given.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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EXAM 1
Math 106
February 13, 2007
Name
You must show all your work. Partial credit will be given.
1. Let U={1, a, 2, b, 3, c, 4, d, 5,11,12,13,14},A={1,2,3,4,5, a},B={a, b, c, d, 12,13,14},
C={1, d, 11}.
(a) Find A∪B(5 pts)
(b) Find C∩B(5 pts)
(c) Find B(5 pts)
(d) Find A∪B(5 pts)
(e) Find A∪B(5 pts)
2. Draw a Venn Diagram and shade in the area which represents S∩T(5 pts)
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EXAM 1

Math 106 February 13, 2007

Name

You must show all your work. Partial credit will be given.

  1. Let U = { 1 , a, 2 , b, 3 , c, 4 , d, 5 , 11 , 12 , 13 , 14 }, A = { 1 , 2 , 3 , 4 , 5 , a}, B = {a, b, c, d, 12 , 13 , 14 }, C = { 1 , d, 11 }.

(a) Find A ∪ B (5 pts)

(b) Find C ∩ B (5 pts)

(c) Find B (5 pts)

(d) Find A ∪ B (5 pts)

(e) Find A ∪ B (5 pts)

  1. Draw a Venn Diagram and shade in the area which represents S ∩ T (5 pts)
  1. Change the numeral 12,354 into Egyptian, Mayan and Roman numerals. (9 pts)
  2. Use the set method (for defining counting numbers) to explain why 3 < 5. (5 pts)
  3. Write the numeral 567 in expanded form. Now write this numeral in base 6 form. (6 pts)
  1. A fitness club charges an initiation fee of $85 plus $35 per month. Write a formula for the function C(x) that gives the total cost for using the fitness club facilities for x months. Use your formula to calculate the cost for 18 months. (5 pts)
  2. A textbook is opened and the product of the page numbers of the two facing pages is 6162. What are the page numbers? (5 pts)
  3. What are the four steps in Polya’s problem solving technique? (4 pts)
  4. Find the largest 8-digit number made up of the digits 1, 1 , 2 , 2 , 3 , 3 , 4 , and 4 such that the 1s are separated by one digit, the 2s by two digits, the 3s by three digits and the 4s by four digits. (5 pts)
  1. Together a baseball and a football weigh 1.25 pounds, the baseball and a soccer ball weight 1.35 pounds and the football and the soccer ball weigh 1.9 pounds. What do each of these balls weigh? (7 pts)
  2. Rectangular numbers are numbers which can be represented by a rectangular array of dots where each array must have exactly one more column than it has rows. (So one is not a rect- angular number because its array would have one row and one column. Two is a rectangular number because its array has one row and two columns.) Find the sixth rectangular number. Write a formula for the nth rectangular number. (5 pts)