Quiz review - Unit 2 Quiz A

Here are some review problems for anyone who wants them, for the quiz on Wednesday/Thursday. There are also many practice problems in your packet.

More Practice

*** Remember there will be a quiz on September 30 (B day) or October 1 (A day) on the (1) Venn diagrams, (2) tree diagrams, and (3) area diagrams.

Here are some of the examples we did in class. I strongly encourage you to look through them, make sure you understand them (ask questions in class or on group me if you need help!) and, especially for the area diagrams, try some of the other ones in the packet.

Venn Diagrams:

Tree diagrams:

Area diagrams:

  

  

Tree and area diagrams

Here are the examples from today (or Monday for A day people).

TREE DIAGRAMS:

AREA DIAGRAMS:

 

Venn Diagrams

New unit: We're on probability. Here are some graphics to help you out with the Venn diagrams. Remember to watch for those "magic" words!

"What's on the test?"

That's a very good question. Here you go. The test is Thursday September 10 (1A, 2A, 4A) and Friday September 11 (1B, 2B, and 3B).

What's on it:

• Crowd size (from quiz #1)
• Tennis balls (from quiz #1)
• Phone numbers / license plates (from quiz #1)
• TV's (from quiz #2)
• Tires (from quiz #2)
• Grade weighting (new; Wed/Thurs)
• Baseball (new; Wed/Thurs)
• Football (new; Wed/Thurs)
• UPC's (new; Fri/Tues/Wed)
• Credit Cards (new; Fri/Tues/Wed)
• You should also be prepared to write sentences to discuss 
• the real-world context of any of these problems, and
• assumptions made when trying to answer a big Fermi type question

Keep your eye on this blog; keep checking back.

I think I now have an example and a practice problem for each of these.
You can use this to study and practice.
 
Please ask me or Ms. Johnson for help - in class, after school, or on group me!

Also, I'm only human - if you think you've found a mistake, please let me know so I can fix it!

Examples:

Crowd size (from quiz #1)

There's a big party at the Square in Marietta, and it overflows into Marietta Pizza Company (they've removed the tables). The square is 500 feet on each side, and Marietta Pizza is 15 feet by 25 feet. If each person has about 3 square feet of space, estimate the total number of people.

           Step 1: Find the total area: 
                           square = 500 ft * 500 ft = 250,000 ft^2
                           MPC = 15 ft * 25ft = 375 ft^2
                   + _________________________________
                                                             250,375 ft^2

          Step 2: Set up the ratios and cross-multiply to solve for x, the total number of people

                         1 person  / 3 ft^2        =   X people / 250,375 ft^2

                         3 ft^2 * X people = 1 person * 250,375 ft^2

                            X people = 1 person *250,375 ft^2 / 3 ft^2 = 83458.333 people, which rounds to

                             83,458 people

You Try: 

The MHS homecoming parade comes down Polk St. People crowd both sides of the street for a length of 0.5 miles, 5 feet back. There are 5280 feet in a mile! If each person has about 2.2 square feet of space, estimate the total number of people. This one is like the one on the first quiz!
 

Tennis balls (from quiz #1)

Mr. Smith's room is 30 ft wide, 40 feet long, and 9.25 feet high. One softball has a diameter of 3.5 inches. How many softballs could the senior class fill his room with (assuming the balls stack straight up in rows, the walls are flat, and the room is empty)?

step 1: the volume of the room (in cubic INCHES - convert if and ONLY IF needed)
         
            length = 40 ft (12 inches/ft) = 480 inches
            width = 30 ft (12 inches/ft) = 360 inshes
            height = 9.25 ft (12 inches/ft) = 111 inches

            volume = length * width * height = 19180800 inches^3

step 2: the volume used by one ball (we basically assume a small cube holding one ball)

            length = width = height = 3.5 inches (the diameter of one ball)

            volume = 3.5 in * 3.5 in * 3.5 in = 42.875 inches^3

step 3: set up the ratio and cross-multiply:

            1 ball / 42.875 in^3 = X balls / 19,180,800 in^3

             42.875 in^3 * X balls = 1 ball * 19,180,800 in^3

             X balls = 1 ball * 19180800 in^3 / 42.875 in^3 = 447,365.59 balls, which rounds to

             447,366 balls.

You Try:

Sara's bedroom is 20 ft wide, 15 feet long, and 9.5 feet high. One balloon has a diameter of 10 inches. How many balloons could her annoying little sister fill her room with (assuming the balloons stack straight up in rows, the walls are flat, and the room is empty)?

Phone numbers / license plates (from quiz #1)

Driver's license numbers in Hawaii follow a pattern: HI 5 {} # # # # # [], where {} is any number 1-9 (not 0), # is any number 0-9, and [] is any letter. How many different combinations are there?

                     H is set, not changing. So we don't care.
                     I is set, not changing. So we don't care
                     5 is set, not changing. So we don't care.
                    { } has 9 possibilities (1,2,3,4,5,6,7,8,9)
                     #   has 10 possibilities (0,1,2,3,4,5,6,7,8,9), AND there are 5 of them!
                    [] has 26 possibilities (A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z)

                    total possibilities = 9*10*10*10*10*10*26 = 23,400,000

You Try:

Phone numbers in Switzerland follow a pattern: 78  () # # # # # @, where () is any number 2-9 (not 0 or 1), # is any number 0-9, and @ is a 4 or a 5. How many different combinations are there?

TV's (from quiz #2)

Find the area of a 60 inch TV with a 16:9 aspect ratio.

                 60 inches is the diagonal. The width is 16x and the height is 9x
                 (from the aspect ratio we know that they are 16 and 9 times some unknown amount : x) 

                 step 1: Set up Pythagorean Theorem and solve for x:

                                 (16x)^2 + (9x)^2 = (60in)^2

                                256 x^2 + 81 x^2 = 3600 in^2    (square EVERYTHING)

                                  377 x^2 = 3600 in^2 (combine like terms)

                                       x^2 = 9.549    (divide both sides by the 377)

                                      x = 3.090  (take the square root)

                     step 2: Plug back in and get the width and the height:

                                  width = 16(3.090) = 49.44 INCHES    (REMEMBER TO PUT UNITS!!!)
                                  height = 9(3.090) = 27.81 INCHES

                    step 3: Multiply to get the area (A = W*H)

                                 Area = 49.44 inches * 27.81 inches = 1374.926 inches^2

You Try:  Find the area of a 48 inch TV with an aspect ratio of 4:3.

Tires (from quiz #2)

 My car came with P250/70R17 tires. I decided to replace them with P270/73R19. If my odometer reads 14,000 miles (the total distance I think I have driven) and my speedometer reads 60 miles per hour (the speed I think I am driving), what are my ACTUAL miles driven and speed?

   REMEMBER: There are always 25.4 mm per inch.

                                        original tires:                                                new tires:
                     width:         250 mm                                                        270 mm
                aspect ratio:     70%=0.70                                                     73% = 0.73
       height of the rubber: 250*0.70/25.4 = 6.890 in                             270*0.73/25.4=7.760 in
        diameter of the rim: 17 in                                                             19 in
           total diameter:       17 + 6.890 + 6.890 = 30.780 in                   19 + 7.760 + 7.760 = 34.520 in
            circumference:     30.780*pi = 96.698 inches                          108.448 inches

                 ratio of the bigger to the smaller circumference:  108.448 in/ 96.698 in = 1.122
                     (NO UNITS for a ratio)

                 CORRECTED odometer reading = 14,000 miles * 1.122 = 15,708 miles
                 CORRECTED speedometer reading = 60 mph * 1.122 = 67.320 mph

You Try:

Your car came with P225/72R16 tires. You decide to replace them with P250/74R20. If your odometer reads 25,000 miles (the total distance you think you have driven) and your speedometer reads 75 miles per hour (the speed you think you are driving), what are your ACTUAL miles driven and speed?

Grade weighting (new; Wed/Thurs)

Coordinate Algebra grades are 60% for tests, 15% for quizzes, 5% for homework, and 20% for the final exam. Jose has 4 test grades: 70, 80, 82, 60. He has 2 quizzes: 54 and 80. He has a 75 average for his homework. What does he need on the final exam to get a C (73 average) ?

step 1: test average:  70+80+82+60 = 292. 292/4 = 73  (divide by 4 because there are 4 of them) 
(Any time you're given a list of scores, average them)

step 2: quiz average: 54+80 = 134  134/2 = 67

Step 3: multiply by the weights (as decimals, so divide by 100%!!), and add up the grade so far
                73(0.60) = 43.8
                67(0.15) = 10.05
                75(0.05) = 3.75
                +____________
                                    57.6

Step 4: Add in the Final Exam (x) times the weight for that, set equal to the goal grade, and then solve for x

                           57.6 + 0.20x =73
                          -57.6                  -57.6
                         ___________________
                                      0.20x = 15.4
divide both sides by 0.20:         x = 77

You Try: 
Geometry grades are 50% for tests, 20% for quizzes, 10% for homework, and 20% for the final exam. Kim has 3 test grades: 73, 85, 100. She has 4 quizzes: 88, 92, 99, 85. She has a 80 average for her homework. What does she need on the final exam to get a B (80 average) ?

Baseball (new; Wed/Thurs)

My nephew is in junior baseball. He has the following stats for this season:

     12 Doubles        4 Triples         53 Singles        8 Home runs         300 At bats
 

Find the Slugging Percentage.    

  

    SLG = (1*S) + (2*D) + (3*T) + (4*HR)

                                      AB

            =  (1*53) + (2*12) + (3*4) + (4*8)    =  121/300 = 0.40333333

                                      300

             To get in as a percent, multiply by 100%:   0.40333333 * 100% = 40.333%

You Try:  His older brother is in the same league. He has the following stats out for this season:

     12 Doubles        4 Triples         53 Singles        8 Home runs         300 At bats
 

            Find the Slugging Percentage.   

Football (new; Wed/Thurs)

Find the quarterback rating of a player with the following stats:

• 250 completed passes in 420 attempts
• Total of 2200 yards
• 18 touchdowns and 
• 15 interceptions

Percent of total completions (%COMP)= 250/420 * 100% = 59.524%

Percent of total touchdowns (%TD)= 18/420 * 100% = 4.286%

Percent of interceptions per attempt (%INT)= 15/420 * 100% = 3.571%

Average yards gained per attempt (YD)= 2200/420 = 5.238 (yds)

Quarterback rating:     (It's a long formula, but then you just plug in!)

                  QR = 25 + 10(%COMP) + 40(%TD) - 50(%INT) + 50(YD)
                                                          12

                       = 25 + 10(59.524) + 40(4.286) - 50(3.571) + 50(5.238) = 875.03/12 = 72.919
                                                          12

You Try: 
                 
Find the quarterback rating of a player with the following stats:

• 325 completed passes in 510 attempts
• Total of 2805 yards
• 22 touchdowns and 
• 17 interceptions

UPC's (new; Tues/Wed)

What does the check digit d have to be to make 8 32946 73208 [d] a valid UPC?

3(a1) + a2 + 3(a3) + a4 + 3(a5) + a6 + 3(a7) + a8 + 3(a9) + a10 + 3(a11) + d

         3(8) + 3 + 3(2) + 9 + 3(4) + 6 + 3(7) + 3 + 3(2) + 0 + 3(8) + d
       = 24 + 3 + 6 + 9 + 12 + 6 + 21 + 3 + 6 + 0 + 24 + d
       = 114 + d

         the total has to end in 0, so 114 + d = 120 (the next number that ends in 0)

                                   d = 120 - 114 = 6.

You Try:
         What is the last digit of the UPC   9 28363 45821 [d] ?

Credit Cards (new; Tues/Wed)

(This is kind of like the UPC, but the rule is different.)

Find the last digit (the check digit) of the Visa number below so that it is valid:
2314 2463 8536 225[d]

      step 1: add the digits in the ODD positions (1st, 3rd, 5th, 7th ... 15th)
              2 + 1 + 2 + 6 + 8 + 3 + 2 + 5 = 29
      step 2: double that number:
               29*2 = 58
      step 3: COUNT how many of those ODD positioned numbers are more than 4, and add that:
               There are 3 that are more than 4: 6, 8, and 5.  58 + 3 = 61
      step 4: add the digits in the EVEN positions (2nd, 4th, 6th, 8th ... 14th) to that total:
               61 + 3 + 4 + 4 + 3 + 5 + 6 + 2 = 88
      step 5: (just like UPC) find the digit you can add to make a total that ends in 0:
               88 + d = 90
              -88          -88
             ___________
                       d = 2

You Try:

Find the last digit (the check digit) of the Mastercard number below so that it is valid:
8234 3248 3255 324[d]

Calculating Grades - NEW ASSIGNMENT AFTER THIS WEEK'S QUIZ

The quiz grades were pretty good! On average, they were better than last time, which for most of you will bring up your average in the "quiz" category in the grade book.

Speaking of grades ... That's what we're doing next. It's pages 17, 18, and 18A in your packet. Please come prepared to go over that in class next time.

If you don't have those pages, here they are:

Here's another example, from my actual grade categories for this class:

Assessments (tests and major projects) : 60%  <<< These are the CATEGORY WEIGHTS
Daily assignments and quizzes: 20%
Final exam: 20%

To calculate a student's grade, (1) multiply their grade in each category by that category's weight, as a DECIMAL, then (2) add them all up.

So if a student has a 70 average on daily grades and quizzes, but an 80 average on tests, and they get a 78 on the final, their grade will be:

70*.60 = 42
80*.20 = 16
78*.20 = 15.6
+ __________
                73.6, which would round to a 74.

If a student has a 75 average on daily and quizzes, and a 78 average on tests, what do they need to get on the final to get a B?

75*.60 = 45
78*.20 = 15.6
[x]*.20 = 0.20X
+____________
              60.6 + 0.20X = 80 (a B)    <<< now we solve for X, the final exam grade needed.
             -60.6                  -60.6
___________________________
                         0.20X = 19.6
                              /0.2           /0.20

                              X = 98.
The student would need to get a 98 on the final exam to get a B for the class.