Sample Exam II
I. PROBLEM SOLVING.

1. A number of employees are enrolled in a fitness program. By March 2 4/5 of them were still participating. Of these 1/6 dropped out by May 2. Of the employees aprticipating on May 2 9/10 were still there on July 2. If 90 employees were participating on July 2 how many started? (8 points)

2. Monica has a daisy with 9 petals. She asks Jerry to play the following game. They take turns picking either 1 or 2 petals. The player who picks last wins. Does the first player always win if they play well? Does the first player always lose if the second player plays well? Explain. (8 points)

3. A pilot of a small plane must make a round trip from A to B a distance of 300 miles. His plane has a speed of 150 mph. Today there is a wind from B to A of 50 mph. Tomorrow is predicted to be calm. Which day will have a quicker trip? (8 points)

4. A bookstore has a summer sale. All items are reduced 25% in price. After the sale prices of unsold items are marked up 25% of the sale price. If a book cost $60.00 oriinally --

a) How much did it cost during the sale? (4 points)

b) How much would it cost after the sale if unsold? (4 points)

II. DEFINITIONS. Define each of the following terms. (4 points each)

1. x is a prime number.

2. a divides b or a|b.

3. Scientific Notation

III. MULTIPLE CHOICE. In each case, circle the letter of the best response. (4 points each)

 1. What do the following numbers have in common? 357 819 1001

a) They are all multiples of three

b) They are all prime numbers

c) They are all divisible by seven

d) They have a common factor greater than 10

2. Which of the following has a non-terminating decimal representation in base ten?

a)

b)

c)

d) None of these.

3. Which of these fractions is between and

a)

b)

c)

d)

4. If x is a positive integer then --

a) -x is positive

b) -(-x) = -x

c) |-x| = x

d) None of the above

5. If a is 50% of b then which of the following must be true?

a) ab = 2

b) a = 1 & b = 2

c) b = 2a

d) None of the above

6. In a class of 70 students 50% missed a certain question on a test. Of the students who missed the question 20% missed the same question on a retest. How many students missed the question twice?

a) 70

b) 35

c) 14

d) 7

7. If the 7 digit number 1, 336, 56_ is to be divisible by 6 then which of the following may be the missing digit?

a) 4

b) 5

c) 6

d) 7

IV. CONCEPTS.

1. Solve? (2 points each)

a)

b)

2. If A and B are negative integers, and C is a positive integer, then determine whether each of the following are positive, negative, or undetermined. (2 points each)

a) (-A) * (-B)

b) A * (B-C)

c) (C-B) * (C-A)

3. Arrange in order from smallest to largest. (5 points)

-1/3, 1/3, 0.333, 3%, -1/5

4. Illustrate on a unit square model. (4 points)

5. Find the character in the 199th position of 0.(34786543120987856743) (6 points)

6. Show that 1/3 and 2/6 are equivalent fractions using unit squares. (4 points)

7. Give an example of a fraction whose decimal expansion has a six cycle but which does not have a two or a three cycle. (4 points)

8. Answer the following measurement questions. (2 points each)

a) How many pints in a peck?

b) How many jiggers in a cup?

c) How many centimeters in a kilometer?

V. COMPUTATION. SHOW YOUR WORK WHENEVER POSSIBLE.

1. Determine if 10447 is prime or not. Explain your decision. (6 points)

2. Find the smallest n so that 8 cubed divides n!. (6 points)

3. Is 9,977,664,422 divisible by: (2 points each)

a) 3?

b) 4?

c) 6?

d) 9?

e) 11?

f) 12?

4. Write 3/7 as a repeating decimal. (5 points)

5. Write each of the following as fractions. (5 points each)

a) 0. 2 3 (2 3)

b) 0.342(42)

c) 0.342(525)

6. Write 3 5/7 as a fraction.(4 points)

7. 20% of 25% is what? (4 points)

8. Find a fraction between and . (4 points)

9. What is the reciprocal of ? (4 points)

10. Write as a mixed number. (4 points)

11. Complete the below table. Fractions do not have to be expressed in lowest terms. Decimals should be to 4 places. ( 3 points per blank.)

12. 2 percent of 106 is what? (3 points)

13. 48 is 120% of what? (3 points)