MATH 140 Final Exam Name____________

Instructions: Answer all questions on the paper provided and show all your work so that partial credit may be given.

1. Ratios, Proportion, and Percent (20)

a) Find x if 28 is to 42 as 1.12 is to x. a)____________

b) Find x if 56 is x% of 11,200. b)____________

c) Find x if x is 67 decreased by 15%. c)____________

d) Find x if 31 is 250% of x. d)____________

2. Rational Numbers and Decimals (20)

a) Write as a rational number in lowest terms. a)____________

b) Write as a repeating decimal expansion. b)____________

c) Write .504 as a rational number in lowest terms. c)____________

d) Give an example of an irrational number. d)____________

3. Numeration in other bases (15)

a) Express 563 as a base 12 numeral. a)____________

b) Express 255 as a base 5 numeral. b)____________

c) Express 3T7₁₂ as a base ten numeral. c)____________

4. Perform the indicated operations in the given bases: (10)

a) 102040₁₂ – T0107₁₂ a)____________

b) 21431₅ ¸ 43₅ b)____________

5. Prime Factorization (20)

a) Find the prime factorization of 4284. a)____________

b) Find d(4284). b)____________

c) Find GCD(4284, 4158). c)____________

d) Find LCM(4284,4158). d)____________

6. Elements of Sets (10)

Let A = {1,2,3}, B = {2,3,4}, and C = {1,a,x}. Give one example of an element of each of the following sets:

a) a)____________

b) b)____________

7. Examples of Subsets (25)

Let U = {1,2,3…,10} be the universal set and let A = {1, 3, 5, 7}. Find an example of a set B for each of the following conditions (if possible):

a) and n(A-B) = 1. a) B = {____________}

b) b) B = {____________}

c) c) B = {____________}

d) d) B = {____________}

e) n(A-B) = 1 and n(B-A) = 1 e) B = {____________}

8. Give an example of a function from A = {1,2,3,4,5} to B = {a,b,c} expressed in ordered pairs. (5)

9. Prove that . (5)

10. Explain why is undefined. (5)

11. Consider the progression 3, 7, 11, 15, … (15)

a) What is the 25^th term of this progression? a)____________

b) How many terms are there in the sequence 3, 7, 11, …,703?

b)____________

c) Find the sum c)____________