# Basic Math - Geometry - Algebra

MAT115 - Checkpoint - Week 4

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Section of Basic Mathematical Skills with Geometry (6th ed.) Page Numbers Exercises

Section 4.1 pp. 287-291 2, 4, 24, 34, 72

Section 4.2 pp. 301-308 20, 36, 48, 58, 72

Section 4.3 pp. 317-320 32, 68, 70

Section 4.4 pp. 329-333 4, 10, 20, 26, 30, 38, 44

Section 4.5 pp. 345-348 24, 52, 74

Section 4.6 pp. 356-358 20, 36

Activity 12: Terminate or Repeat? p. 359 all

Section 4.7 pp. 362-363 28, 30, 34

Section Problem

Number Your Solution Final Answer (Restate Your Final Answer Here) Points Earned

4.1 2 For the decimal 8.57932, what is the place of the 5?

Your Solution

Recommended Learning Resources

• Watch Video Lecture for #3

• Work #1 and check your answer

4.1 4 For the decimal 8.57932, what is the place of the 2?

Your Solution

Recommended Learning Resources

• Watch Video Lecture for #3

• Work #1 and check your answer

4.1 24 Write the following number as a mixed number (be sure to reduce to lowest terms):

4.0171

Your Solution

Recommended Learning Resources

• Watch Video Lecture for #23

• Study Example 5 on page 283

• Work Check Yourself #5 and check your answer

4.1 34 Arrange the following numbers in order from smallest to largest:

Your Solution

Recommended Learning Resources

• Many students miss this; in order for you to rank order these numbers you have to express them all with the same common denominator, or all in decimal so that they can be compared

• Recommend working #33, and then checking your answer

4.1 72 Lulu wants to round 76.24491 to the nearest hundredth. She first rounds 76.24491 to 76.245, and then rounds 76.245 to 76.25 and claims that this is the final answer. What is wrong with this approach? What would the right answer be?

Your Solution

Recommended Learning Resources

• Be sure to give a word explanation of why Lulu is wrong, and show the correct way to round the number to the nearest hundredth.

4.2 20 Add:

27.4 + 213.321 + 39.38

Your Solution

Recommended Learning Resources

• Watch Video Lecture for #19

• Use a calculator to check your answer!

4.2 36 Subtract:

45.6 - 8.75

Your Solution

Recommended Learning Resources

• Watch Video Lecture for #37

• Work problem #35 and check your answer

• Use a calculator to check your answer!

4.2 48

Add thirty-eight and nine tenths, five and fifty-eight hundredths, seven, and fifteen and eight tenths.

Your Solution

Recommended Learning Resources

• Watch Video Lecture for #47

• There are 4 numbers to be added. I have underlined each of the different numbers.

4.2 58 Find the perimeter of the figure below:

Your Solution

Recommended Learning Resources

• Review from previous sections what "perimeter" is.

4.2 72 Alem's restaurant bill is pictured below. Estimate his total by rounding the items to the nearest dollar. The key to this problem is estimation - if the answer is calculated without estimating, no credit will be given.

Your Solution

Recommended Learning Resources

• Unless you use estimation and round each item to the nearest dollar, no credit is given.

• The price for the "2 chocolate cakes" is $7.40 (some students say it looks like $7.90, so I wanted to clarify that)

4.3 32 Claudia earns $6.40 per hour. For overtime (each hour over 40 hrs) she earns $9.60. If she works 48.5 hours in a week, what pay should she receive?

Your Solution

Recommended Learning Resources

• No recommended resources...just read problem very carefully and the method for solving it should be straight forward

4.3 68 To find the simple interest on a loan for 1 year at 12.5%, multiply the amount of the loan by 0.125. What simple interest will you pay on a loan of $1458 at 12.5% for 1 year?

Your Solution

Recommended Learning Resources

• Read very carefully the "Step by Step" on how to multiply decimals that is on page 311 in Section 4.3

• Use your calculator to check your answer

4.3 70 In a bottling company, a machine can fill a 2-liter bottle in 0.5 seconds and move the next bottle into place in 0.1 seconds. how many 2-liter bottles can be filled by the machine in 2 hours?

Your Solution

Recommended Learning Resources

• For this problem you want to determine the "cycle time" - that is how many TOTAL seconds does it take to fill ONE bottle (fill time plus the time to move the next bottle into place). Then use math to find out how many bottles can be done in 2 hours, given that particular cycle time.

4.4 4 Find the circumference of the figure below. Use 3.14 for π and round your answer to 1 decimal place.

Your Solution

Recommended Learning Resources

• Watch Video Lecture for #3

• When working these problems, your FIRST STEP should be to write down the formula that you are going to use.

• Work Problem #1 and check your answer

4.4 10 Find the perimeter of the figure below (the curve is a quarter-circle). Round answers to one decimal place

Your Solution

Recommended Learning Resources

• Perimeter means "distance around"...so you have to find the lengths of THREE blue sides.

• You have to use circumference formula, but that curved section is only a portion of the circumference.

• View Video Lecture for #7 and this might very well help you figure this one out.

4.4 20 Find the area of the figure below.

Your Solution

Recommended Learning Resources

• Watch Video Lecture for #19

• The FIRST STEP should be to write down the formula you are going to use.

• You are calculating area, not perimeter.

• Look at Example 5 on page 325

4.4 26 Find the area of the figure below.

Your Solution

Recommended Learning Resources

• As we learned in previous checkpoints involving areas, we have to some times break objects into separate pieces, calculate the area of the pieces, then ADD the areas together to get total area.

4.4 30 A circular coffee table has a diameter of 5 ft. What will it cost to have the top refinished if the company chares $3 per square foot for the refinishing

Your Solution

Recommended Learning Resources

• must calculate the area of the table top, then figure the cost to refinish based on the per square foot charge

• don't forget that there is a difference between the "radius" of the circle and the "diameter" of the circle. The diameter is twice the radius.

• Watch the Video Lecture for #31

4.4 38 An A-frame cabin has a triangular front with a base of 30 ft. and a height of 20 ft. If the front is to be class that costs $3 per square foot, what with the glass cost?

Your Solution

Recommended Learning Resources

• Conceptually the same problem as that above on the table top: find the area of the triangle, then you can calculate the cost based on how much each square foot costs

4.4 44 The distance from Philadelphia to Sea Isle is 100 mi. A car was driven this distance using tires with a radius of 14 in. How many revolutions of each tire occurred on the trip? (Hint: one revolution is equivalent to one circumference distance traveled. Thus, need to find how many ft is in 100 miles, and then need to find what the circumference of a 14 inch tire is)

Your Solution

Recommended Learning Resources

• one revolution is equivalent to one circumference distance traveled. Thus, need to find how many ft is in 100 miles (each mile is 5280 feet), and then need to find what the circumference in feet is of a 14 inch tire.

4.5 24 Divide the following:

Your Solution

Recommended Learning Resources

• Study the "Step by Step" on page 340 for dividing decimals

• Study Example 6 on page 340

• Watch Video Lecture for #15 and #25

• Check your answer with your calculator

4.5 52 Seven employees of an office donated a total of $172.06 during a charity drive. What was the average donation?

Your Solution

Recommended Learning Resources

• Watch Video Lecture for #53; be sure to watch this so you know what "average" means, if you don't already know what it means

• Check your answer with your calculator

4.5 74 Four brands of soap are available in a local store:

Calculate the unit price and decide with brand is the best buy. Your work should show the unit price of each of the four soaps, and your final answer should be the soap which is the best buy, and what its unit price is.

Your Solution

Brand Unit Price

Squeaky Clean

Smell Fresh

Feel Nice

Look Bright

Recommended Learning Resources

• About ½ of the students miss this, as they don't do the calculation for unit price correctly. Example 4 on page 339 shows an example of how to find the unit price.

• In unit pricing, you must ALWAYS divide the price by the quantity, NEVER the quantity by the price.

• Be sure to answer specifically the question asked

4.6 20 Find the decimal equivalent for the following mixed number:

Your Solution

Recommended Learning Resources

• Watch Video Lecture for #21

• Check your answer with your calculator

4.6 36 The following table gives the free throws attempted (FTA) and the free throws made (FTM) for the top five players in the NBA for a recent season. Calculate the free throw percentage for each player by writing the FTM over the FTA, and converting this fraction to a decimal. You may use your calculator and just show the decimal answers.

Your Solution

Player FTM FTA Fraction Decimal

Houston 363 395

Allen 316 345

Nash 308 339

Hudson 208 231

Miller 207 230

No answers required here...answers shown at left in table.

4.6

Page 359 Activity 12 See page 359 for the details of this activity, then complete the table below, and answer the question after the table is completed. I filled in the first two rows for you as an example.

Your Solution

Fraction Decimal Terminate? Prime Factorization of Denominator

1/2 0.5 Yes 2 x 1

1/3 0.333.... No 3 x 1

1/4

1/5

1/6

1/7

1/8

1/9

1/10

1/11

1/12

After you complete the table, compare the last two columns and state a general rule describing which fractions have decimal forms that terminate and which have decimal forms that repeat.

Recommended Learning Resources

• Be sure to review how to "prime factor" a number No answers go here...all answers are at left.

4.7 28 Write the following as a mixed number. Write your answer in lowest terms:

15.35

Your Solution

Recommended Learning Resources

• Watch Video Lecture for #25

• Be sure to reduce answer to lowest terms

4.7 30 Complete each of the following statements, using the symbol < or >

Your Solution

Recommended Learning Resources

• Watch Video Lecture for #31

4.7 34 The following table gives the winning percentage of the top five coaches in NFL history. What fractions of his games as each coach won? Hint: convert each decimal to a fraction, and reduce the fraction to lowest terms:

Your Solution

Coach Fraction Games Won

Shula

Halas

Landry

Lambeau

Brown

Recommended Learning Resources

• Watch Video Lecture for #33 No answers go here...put answers in table at left

End of Checkpoint

#### Solution Summary

Neat, step-by-step solutions for the problems is provided. Construction of figures is neatly done