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PART I: EXERCISES

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Directions: Answer each of the following questions.  When appropriate, please show work.

1.      In a right triangle, find the length of the side not given.  Give an exact answer and an approximate to three decimal places.  Assume c represents the length of the hypotenuse.

2.      In a right triangle, find the length of the side not given.  Give an exact answer and an approximate to three decimal places.  Assume 14 represents the length of the hypotenuse.

3.      If the measures of an object are different, what should be the first step for finding the area of the object?

4.      Find the area of the shaded region (the figures are not drawn in perfect proportion).  Give the answer in square feet.  Round to the nearest thousandth.

5.      Find the area of the shaded region (the figures are not drawn in perfect proportion).  Give the answer in square feet.  Round to the nearest thousandth.

6.      Find the volume of the solid (the solid is not drawn in perfect proportion).  Give the answer in cubic feet.  Use 3.14 for π (pi) and round to the nearest thousandth.

7.      Simplify: |-11|

8.      Find the opposite or additive inverse: 3/5

9.      Compute and simplify: 3.7 + (-7.1)

10.    Compute and simplify: -6 + 3 + (-9) + 5

11.    Compute and simplify: -3/4 + 1/3

12.    Compute and simplify: 7- (-3)

13.    Compute and simplify: 3.1 – 6.5

14.    Compute and simplify: 1/6 – (-1/3)

15.    What are the sign rules for multiplying real numbers?

16.    Compute and simplify: 7 x (-3)

17.    Compute and simplify: -1/6 x (-2/5)

18.    In the course of one five-month period, the water level of a lake went down 8 in., up 10 in., down 4 in., down another 11 in., and up 5 in.  How much had the lake level changed at the end of the five months?

19.    The population of Charlton was 7200.  It decreased by 75 each year for 5 years.  What was the population of Charlton after 5 years?

PART II: PRACTICAL APPLICATION

Directions: Estimate the value of π.

Focus: Circles

Background: In Section 9.3 of your textbook, the circumference and diameter of a can are used to show that the constant, π, is equal to the ratio C/d. We will verify that this is true by calculating the values of C/d for circles of different sizes.

1. Use the string to measure the circumference of each circle on the next page. Place one end of the string anywhere on the circle, and carefully lay the string around the circle till you reach the starting point. Mark the ending point on the string, then use a ruler to measure the length of the string that is marked. Record this measurement in the table below.  In addition, you may measure the circumference and diameter of any cylindrical object, like a soda can or roll of paper towels.

2. Next, use a ruler to measure the diameter of each circle. Make sure you measure the diameter at the widest part of the circle. Record this measurement in the table also. Round to the nearest inch.

 Circle Circumference, C Diameter, d C/d A B C D E F

3. When you have completed all your measurements, use a calculator to compute the ratio C/d for each circle. Round your answers to 2 decimal places, and write the results in the table on the previous page.

4. Now, let’s analyze the ratios C/d. Compare the values of C/d for all the circles.  Be sure to use complete sentences to answer all the questions in this step.

Are the ratios the same?

If not, how much do they differ by?

What could be the reasons for any differences?

5. Calculate the average of the ratios, C/d, in your table, and write this value below.

Average value of C/d = __________

Conclusion: By measuring several circles, you have verified that the ratio of the circumference of a circle to its diameter is a constant. This ratio is called π, and is approximately equal to 3.14.

PART III: JOURNAL ACTIVITY

Directions: Write a page about the benefits of understanding perimeter, area, and volume.  Give examples of when you have needed to know or use any of these.  Think of or find uses of the Pythagorean Theorem.

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