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Math5900 Midterm I Spring, 2006 Kelly MacArthurName____________________________ Date________________Instructions: Please show all your work, as partial credit will be given whereappropriate. If there is no work shown, you may not get any points for an answer,even if it’s correct. Please put answer in the designated place. 1. (10 points) Write a mathematically convincing argument to explain the formula123...n=n n12.2. (10 points) Find three irrational numbers between 4 and 5.Answer 2: ____________, ____________, ______________13. (20 points)Convert these numbers to a different base as indicated.(a) 4678to base 104678= ________________(b) 101110112to base 10101110112= ______________(c) 312 to base 4312 = ___________________(d) 555 to base 5555 = ___________________24. (15 points)Draw a Venn Diagram for all the number systems (including fractions) andplace these numbers in the proper place in the Venn Diagram.(a) -3.2(b) 7.03(c) -1.212112111...(d) 3(e) -5(f) −0. 9(g) 142(h) 14.96(i) 0(j) 4935. (20 points)Convert these numbers from one form to another to fill up the table.Decimal Percent Fraction42.00%992250.193.01 529646. (15 points)If the statement is true, write true in the blank. If it’s false, give anexample which shows that the statement is not true OR correct the statement (justnegating the statement is not allowed!).(a) The set of irrational numbers is closed under addition. T or F (circle one) _______________________________________________________________________(b) -x is a negative number. T or F (circle one)_______________________________________________________________________(c) The decimal 0.0031 is read “31 thousandths.” T or F (circle one)_______________________________________________________________________(d) The set of rational numbers is the union of the set of T or F (circle one) fractions with the set of integers._______________________________________________________________________(f) Addition is commutative. T or F (circle one)_______________________________________________________________________(g) The square root of any positive rational number is irrational. T or F (circle one)_______________________________________________________________________(h) The additive identity is 1. T or F (circle one)________________________________________________________________________5Choose 5 of the following 7 questions to do. Indicate clearly (by circling“Yes”)which problems you want graded. I will only grade 5 problems!! Each question is worth 10 points.A. (Grade: Yes or No ) A 40-row auditorium seats 18 people in the first row,19 in the second row, 20 in the third row and so on. Use short-cuts to find the totalnumber of seats in the auditorium.Answer A: _______________________B. (Grade: Yes or No ) The difference between two numbers is 11 and theirproduct is 476. What is the sum of the two numbers?Answer B: _______________________6C. (Grade: Yes or No ) For the sequence 6, 10, 14, 18, 22, ...(a) Find a formula to give the nth term in the sequence.(b) What is the 100th term?Answer C: (a) ______________ (b) _______________D. (Grade: Yes or No ) At a benefit concert, 600 tickets were sold and $1500was raised. If there were $2 and $5 tickets, how many of each were sold?Answer D: # $2 tickets= _________, # $5 tickets = _________7E. (Grade: Yes or No ) There are 26 children in a class, including exactly 12girls and 20 eight-year-olds. How many eight-year-old girls could there be? (Giveall possible answers.)Answer E: __________________________________F. (Grade: Yes or No ) Write a mathematically convincing argument toexplain why the sum of any seven consecutive integers is always divisible by 7.8G. (Grade: Yes or No ) Joe and Sue are the same age. Joe is youngerthan Paul. Paul is older than Jane. Is (i) Joe older than Jane, (ii) younger thanJane, or (iii) is it impossible to tell from the given information?Answer G:


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U of U MATH 5900 - Math 5900 Midterm 1

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