Sample Exam III I. PROBLEM SOLVING.

1. The directions on a juice can say to mix a can of concentrate with 2 cans of water.

a. What is the ratio of water to concentrate? (4 points)

b. How many 6oz. cans of concentrate will be needed to make 90 oz. of juice? (4 points)

2. A school has 240 students. The ratio of students to teachers is 20:1. If eight more teachers are hired, what will the ratio o students to teachers become? (8 points)

3. If the ratio of whale sightings to shark sightings is 4 : 7 and the total number of sightings is 66, how many whales were sighted? (8 points)

4. A bookstore had a spring sale. All items were reduced 25%. After the sale, prices were marked up 25% over the sale price. If a certain book cost $60.00 originally,

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

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

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

1. Clock Arithmetic

2. Scientific Notation

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

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

a) 70

b) 35

c) 14

d) 7

2. The expanded form of 2001.0043 is ?

a)

b)

c)

d) 2000 + 1 + 0.004 + 0.0003

3. 0.003604 + 0.00076 =

a) 3604 + 760

b)

c)

d) 0.003680

4. If a : b = 1 : 2, which of the following must be true?

a) ab = 2

b) a = 1 and b = 2

c) b = 2a

d) None of these

5. Which of the following fractions has a non-terminating decimal representation?

a)

b)

c)

d) None of these.

6. Which of these fractions is between and

a)

b)

c)

d)

7. Which of the following is irrational?

a)

b) 4.233233233 . . .

c) 7.121231234. . .

d) none is irrational

IV CONCEPTS.

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

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

2. Use a number line to illustrate the following problems. Indicate your answer to the right. (4 points each)

a) 5 + (-8) =

b) 3 * (-2) =

3. Show, using an area model, that and are equivalent fraction. (5 points)

4. Illustrate on a unit square model. (6 points)

5. Describe division on an eleven clock. ( 4 points)

6. If a 1 inch cube of metal costs $1000, what should a 2 inch cube of the same metal cost? ( 6 points)

V. COMPUTATION. SHOW YOUR WORK WHENEVER POSSIBLE.

1. Solve each problem below using the standard algorithms. You do not have to explain the steps, but show the proper method so that your 6th grade students will understand the solution. DO NOT use a calculator. (4 points each)

a) 1.3 x 0.024

b) 0.000608 0.02

2. Give an example of a fraction whose decimal expansion has a six cycle but does not have two or three cycles. (8 points)

3. 2 percent of 106 is what? (4 points)

4. 48 is 120% of what? (5 points)

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

6. Find the character in the 120th decimal place of . (5 points)

7. Solve each proportion for n: (4 points each)

a)

b)

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. Compute the following on the given clock. ( 4 points each)

a) 12 clock

b) 3 x 5 10 clock

12. Write as a repeating decimal. (5 points)

13. Write as a fraction. (5 points)

14. Write the equation of a line passing through ( -4, 3 ) & ( 1, -2 ). (5 points)

15. What is the slope of the line . (3 points)

16. Sketch the graph of the line . (4 points)