MATH 212 Midterm: MATH212_ALL-SECTIONS_FALL2012_0000_MID_EXAM

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turquoisegnu128

10 Jan 2019

School

University of Maryland

Department

Mathematics

Course

MATH 212

Professor

All

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Identify each statement below as true or false. If a number is divisible by 2 then the last two digits will also be divisible by 2. If the sum of the digits of a number is a multiple of 5 then the number is a multiple of 5. Extra credit: in base n, if the sum of the digits of a number is a multiple of 5 then the number is a multiple of 5. Give a value for n that would make this statement true. (there is more than one correct answer. ) Do not change the tenths to hundredths: use sketches of base 10 blocks to help explain, be sure to identify clearly what place values are represented by which blocks. In particular, be sure to identify which block represents one whole: be sure the relationship between the sizes of the blocks is believable.

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Problem: Divisibility and Divisibility Rules There are many rules to determine if a number is divisible by other smaller numbers. In basic arithmetic courses, you learned divisibility and discussed a few common divisibility rules. Your task is to determine if the given number is divisible by 9 but is not divisible by 11 Given number: 7,176,825,942,116,027,211 Note: You want to use divisibility rules. Do not attempt to use long division and do not just use your calculator 1. Research the topic of divisibility 2. Research the divisibility rules for 9 and 11. 3. Using the divisibility rules found, determine how the given number is divisible by 9 and is not divisible by 11. "Note:I am telling you that the number IS divisible by 9 and IS NOT divisible by 11. Do not try to show the opposite of this statement. 4. Include the following information in a report, in this order: a. Explain (in a few sentences) the topic of divisibility, including any correct terms that apply b. Explain in your own words the divisibility rule of 9. C. Give an example using another number to help the explanation. d. Show how the given number is divisible by 9. Work out all your steps. e. Explain in your own words the divisibility rule of 11 f. Give an example using another number to help the explanation. g. Show how the given number is not divisible by 11. Work out all your steps. 5. You must locate a minimum of 2 sources to help you complete this project. More than two sources, though not required, can be used if it helps to give detail to the project. a. You must use at least one book or E-book (other than your textbook). Do not use the dictionary for your definition. b. You must use at least one website. Do not use Wikipedia c. Your sources should explain the topics of the problem (divisibility and divisibility rules) and have examples that help you with the problem. Your sources should be relevant to the project and not just be a math source because it has math in the context d. 6. Correctly cite, in MLA format, the sources that you located to complete the assignment. If you need help for citations in MLA format, you can try using the website EasyBih Be sure to do the entire project typed neatly 7. Papers will be compared for similarity Plagiarism is against the academic honesty policy and will receive a zera. Note: A detailed Grading Rubric is provided on Canvas and on the assignment submission link The due date for the project is listed on Canvas. The Math/Analytical Project must be submitted through Canvas. Directions for submitting can be found in the Course Syllabus and on Canvas.

Show transcribed image text Problem: Divisibility and Divisibility Rules There are many rules to determine if a number is divisible by other smaller numbers. In basic arithmetic courses, you learned divisibility and discussed a few common divisibility rules. Your task is to determine if the given number is divisible by 9 but is not divisible by 11 Given number: 7,176,825,942,116,027,211 Note: You want to use divisibility rules. Do not attempt to use long division and do not just use your calculator 1. Research the topic of divisibility 2. Research the divisibility rules for 9 and 11. 3. Using the divisibility rules found, determine how the given number is divisible by 9 and is not divisible by 11. "Note:I am telling you that the number IS divisible by 9 and IS NOT divisible by 11. Do not try to show the opposite of this statement. 4. Include the following information in a report, in this order: a. Explain (in a few sentences) the topic of divisibility, including any correct terms that apply b. Explain in your own words the divisibility rule of 9. C. Give an example using another number to help the explanation. d. Show how the given number is divisible by 9. Work out all your steps. e. Explain in your own words the divisibility rule of 11 f. Give an example using another number to help the explanation. g. Show how the given number is not divisible by 11. Work out all your steps. 5. You must locate a minimum of 2 sources to help you complete this project. More than two sources, though not required, can be used if it helps to give detail to the project. a. You must use at least one book or E-book (other than your textbook). Do not use the dictionary for your definition. b. You must use at least one website. Do not use Wikipedia c. Your sources should explain the topics of the problem (divisibility and divisibility rules) and have examples that help you with the problem. Your sources should be relevant to the project and not just be a math source because it has math in the context d. 6. Correctly cite, in MLA format, the sources that you located to complete the assignment. If you need help for citations in MLA format, you can try using the website EasyBih Be sure to do the entire project typed neatly 7. Papers will be compared for similarity Plagiarism is against the academic honesty policy and will receive a zera. Note: A detailed Grading Rubric is provided on Canvas and on the assignment submission link The due date for the project is listed on Canvas. The Math/Analytical Project must be submitted through Canvas. Directions for submitting can be found in the Course Syllabus and on Canvas.

In this exercise you will use an algorithm, called the sieve of Eratosthenes,
that isolates prime numbers. (Eratosthenes lived from about 276 to 194
b.c. He was also known for his computation of the circumference of the
earth and for his treatises on the theater, moral philosophy, and history.)
Here is how it works. List the integers from 2 through n. Circle the
number 2, then cross off all the higher multiples of 2 (namely, 4, 6, 8,
10, etc.). Circle 3, which is the first remaining number after 2. Then
cross off all the multiples of 3 that have not yet been crossed off. Then
circle 5. Et cetera. When you are finished with the repeated sieving
operations, only the primes will remain on the list, and they will have been
circled for emphasis. The exercise: perform the sieve of Eratosthenes with
n = 120. As you do this, cross off the multiples of different primes by using
different kinds of slashes (slashing in different directions, or using different
colors), and provide a key for the reader. By this device the reader will
immediately know the smallest prime divisor of each composite number
on your list. (In view of Exercise 4, after the multiples of 7 have been
crossed off, the remaining numbers will all be prime and can be circled to
mark this fact.)

MATH 212 Midterm: MATH212_ALL-SECTIONS_FALL2012_0000_MID_EXAM

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