Name:________________________________________ JMJ Precalculus Honors Trimester 2 Exam April 11, 2014 10:35 AM - 12:05 PM Mr. Casalinuovo ___________________________________________________________________________________ Part 1: Answer 4 of the 5 problems in this part. Each problem is worth 20 points. Partial credit will be given if the work merits. 1) Baseball The number of home-runs during a season is one of the statistics recorded about baseball players. The following table has the number of home-runs (over many seasons) for several of the best hitters in baseball. Compare the home-run hitting performance of these exceptional baseball players. Mark McGwire
Babe Ruth
Barry Bonds
49
54
16
32
59
25
33
35
24
39
41
19
22
46
33
49
25
25
9
47
34
9
60
46
39
54
37
52
46
33
58
49
42
70
46
40
65
41
37
32
34
34
29
22
49 73 46
a) Calculate the following statistics for all 3 players. Round to the nearest integer. Total Home runs
Average HR per season
Most HR in a season
Fewest HR in a season
Standard deviation
McGwire
Ruth
Bonds
b) Find the fences and any outlier(s) if any, for all Babe Ruth and Barry Bonds using your calculator. Work need not be shown. PLAYERS
LOWER FENCE
UPPER FENCE
OUTLIERS (if any)
Ruth Bonds
c) Construct Box and Whisker Plot to scale for Babe Ruth’s homeruns.
____________________________________________________________________
d) Construct a Modified Box Plot to scale for Barry Bonds’ homeruns.
_____________________________________________________________________
2) Evaluations For a school in the mid-west the teachers are given evaluations in three different categories: Professionalism, Student Performance, and Time Available Outside of the Classroom. Below is a table for the ratings for each category for each teacher. Teachers are rated from 1 to 20 (with 20 being the highest). TEACHER
Professionalism
Miss Jones Mrs. Smith Mr. Curtis Miss Rodriques Mrs. Blue Mr. Fire Miss Marino
14 19 15 16 14 20 18
Student Performance 19 20 15 14 11 18 17
Time Available 16 5 15 19 19 19 15
a) Compute the mean, median, and mode for each category rounding to the nearest tenth. CATEGORY
Professionalism
Student Performance
Time Available
Mean Median Mode
b) Each teacher’s overall teacher rating is determined by giving a weight of 2 for Professionalism, 7 for Student Performance, and 4 for Time Available Outside of the Classroom. Compute Mrs. Smith’s, Mrs. Blue’s, and Mr. Curtis’s overall teacher ratings to the nearest tenth, and if you had to promote one of those three teacher’s to the role of supervisor, which teacher would you choose and why?
Mrs. Smith’s overall teacher rating:_________________________________
Mrs. Blue’s overall teacher rating:__________________________________
Mr. Curtis’s overall teacher rating:___________________________________
d) If you had to promote one of those three teachers to the role of supervisor, which teacher would you choose and why.
Your Choice:_______________________
Your reason:________________________________________________________________________
___________________________________________________________________________________
3) Gas Prices Below are the prices for regular gasoline at 20 Mobil Stations across Long Island last week. $ 3.79 $ 3.38 $ 3.25 $ 3.39
$ 3.95 $ 3.19 $ 3.39 $ 3.25
$ 3.15 $ 3.35 $ 3.29 $ 3.49
$ 3.09 $ 3.30 $ 3.29 $ 3.59
$ 3.23 $ 3.35 $ 3.29 $ 4.54
a) Create a Stem and Leaf Diagram for the data. b) Calculate a 5 % and a 10 % trimmed mean for the data. c) What percent of the data lies within 2 standard deviations of the mean? d) If the two stations with the highest price for regular gasoline are eliminated from the original set of data, by how much (to the nearest cent) does the mean decrease?
------------------------------------------------------------------------------------------------------------------------a) Create a Stem and Leaf Diagram for the data.
STEM
LEAF
b) Calculate a 5 % and a 10 % trimmed mean for the data to the nearest cent.
5 % trimmed mean = _________________ 10 % trimmed mean = _________________________ c) What percent of the data lies within 2 standard deviations of the mean?
_______________________________ d) If the two stations with the highest price for regular gasoline are eliminated from the original set of data, by how much (to the nearest cent) does the mean decrease?
____________________________
4) College Acceptance Rates Below is a table that displays the general acceptance rate for select colleges and universities for 20122013: Institution Acceptance Rate Acceptances / Applications _________________________________________________________________ Amherst College 13.7% 1,084 / 7,927 Bowdoin College 14.5% 1,021 / 7,052 Brown University 9.2% 2,649 / 28,919 Caltech 10.6% 584 / 5,535 Carleton College 21.0% 1,475 / 7,030 Colorado College 23.1% 1,286/ 5,568 Columbia University 6.9% 2,311 / 33,531 Dartmouth College 10.0% 2,252 / 22,416 Davidson College 24.8% 1,185 / 4,770 Emory University 26.0% 4,592 / 17,698 Grinnell College 36.3% 1,458 / 4,021 Haverford College 23.3% 835 / 3,590 MIT 8.9% 1,620 / 18,109 Northwestern University 13.9% 4,555 / 32,772 Oberlin College 33.8% 1,976 / 5,841 Pomona College 12.9% 922 / 7,153 Princeton University 7.3% 1,931 / 26,498 Rice University 16.6% 2,552 / 15,408 Scripps College 36.3% 785 / 2,163 Stanford University 5.7% 2,210 / 38,828 Swarthmore College 14.0% 929 / 6,614 Trinity College 31.1% 2,379 / 7,651 Tufts University 18.7% 3,445 / 18,420 University of Chicago 8.8% 2,676 / 30,369 University of Notre Dame 23.3% 3,947 / 16,957 University of Pennsylvania 12.1% 3,785 / 31,280 University of Virginia 28.4% 8,038 / 28,265 Vanderbilt University 12.0% 3,717 / 31,056 Vassar College 23.1% 1,752 / 7,597 a) Create a frequency distribution and a cumulative frequency distribution for the acceptance rates for the schools in intervals beginning with 5 % and using intervals of 5 %. b) Draw a histogram using your graphing calculator, and indicate the viewing window used. c) Find the percentile rank of the University of Notre Dame (Go Irish!) among the schools given. d) Create a cumulative histogram.
a) Create a frequency distribution and a cumulative frequency distribution for the acceptance rates for the schools in intervals beginning with 5 % and using intervals of 5 %. Frequency Distribution: Intervals
Frequency
Cumulative Frequency
b) Draw a histogram using your graphing calculator, and indicate the viewing window used.
Xmin = ____________
Xmax = ______________
Xscl = ____________
Ymin = ____________
Ymax = ______________
Yscl = ____________
c) Find the percentile rank of the University of Notre Dame (Go Irish!) among the schools given.
d) Create a cumulative histogram.
5) McDonalds Menu. You must answer this one problem. It is worth 20 points. The following is the nutrition information for 9 menu items from McDonalds. Menu Item
Serving Size
Total Calories
Calories from Fat
Cholesterol
Sodium
Big Mac
7.6 oz.
550
260
75 mg
970 mg
1/4 lb. with Cheese
7.1 oz.
520
240
95 mg
1,100 mg
1/4 lb. with bacon & cheese
8 oz.
610
260
105 mg
1,440 mg
Hamburger
3.5 oz.
250
80
25 mg
480 mg
4 oz.
300
110
40 mg.
680 mg
Crispy Chicken Sandwich
7.5 oz.
670
300
45 mg.
1,480 mg
Grilled Chicken Sandwich
8.3 oz.
510
180
105 mg.
1,250 mg
Filet-O-Fish
5 oz.
390
170
40 mg.
590 mg
McNuggets (6 piece)
3.5 oz.
300
170
40 mg.
540 mg
Cheeseburger
a) Construct a scatter plot which displays the servings size, x, and the sodium, y, for each of the 9 menu items. b) Perform a linear, quadratic, and exponential regression on the data from part C, and give their corresponding a, b, c, and r values. Round to the nearest 2 decimal places. c) Using the best-fit model, estimate the amount of sodium a menu item would contain if its serving size is 6 oz. d) Using the best-fit model, if a menu item had 1,000 mg. of sodium, what would be the serving size to the nearest tenth of an oz.?
a) Construct a scatter plot which displays the servings size, x, and the sodium, y, for each of the 9 menu items.
b) Perform a linear, quadratic, and exponential regression on the data from part C, and give their corresponding a, b, c, and r values. Round to the nearest 2 decimal places. LINEAR
QUADRATIC
EXPONENTIAL
a b c r
c) Using the strongest type of correlation from part D, estimate the amount of sodium a menu item would contain if its serving size is 6 oz.
_________________________ d) Using the best fit model, if a menu item had 1,000 mg. of sodium, what would be the serving size to the nearest tenth of an oz.?
_________________________
Part 2: Answer all parts of both questions in this part. Each question is worth 10 points. 6) Exponents and Logarithms a) Solve for x in all four equations. If necessary round to two decimal places. 1. log 3 356 = x
____________
3. log 5 4x = 6
_____________
2. log x 215 = 7
___________
b) Tyler invests $ 15,000 in an account which paid 2.5% interest compounded quarterly for five years. 1. What was the balance after the five years?
_________________ 2. How much interest did Tyler earn ?
_________________
c) What principle (to the nearest cent) will result in a balance of $ 20,000 if the interest is compounded continuously at 5.5 %?
_________________ c) An SUV that costs $ 45,675 new has a blue book value of $ 32,500 after 3 years. Using the exponential model Y = Cekt find the value of k to 4 decimal places and find the value of the SUV after 8 years.
k = ________________________
Value of the SUV = ____________________
7) MORTGAGE You are buying a home for $ 425,000. The Bank of America requires a 20 % down payment and is giving you an interest rate of 4.5 % that will run for 30 years. TD Bank requires a 15 % down payment is giving you a 4.75 % that will run for 30 years. a) Bank of America 1. What will the down payment be if you chose their offer? __________________
2. How much money will you be mortgaging through the bank? _____________________
3. What will the monthly payment be? _________________________
4. How much in interest will you pay over the course of the mortgage? _______________
over
b) TD Bank 1. What will the down payment be if you chose their offer? ____________________
2. How much money will you be mortgaging through the bank? ___________________
3. What will the monthly payment be? ________________________
4. How much in interest will you pay over the course of the mortgage? ___________________
-------------------------------------------------------------------------------------------------------------------------------c) Which bank offers you the better deal? ______________________________
d) Using the bank with the better deal for you, if the school taxes for your town are $ 900, how much would your monthly payment be to the bank?
________________________________
Name:________________________________________ JMJ Precalculus Honors Trimester 2 Exam April 11, 2014 10:35 AM - 12:05 PM Mr. Casalinuovo ___________________________________________________________________________________ Part 1: Answer 4 of the 5 problems in this part. Each problem is worth 20 points. Partial credit will be given if the work merits. 1) Baseball The number of home-runs during a season is one of the statistics recorded about baseball players. The following table has the number of home-runs (over many seasons) for several of the best hitters in baseball. Compare the home-run hitting performance of these exceptional baseball players. Mark McGwire
Babe Ruth
Barry Bonds
49
54
16
32
59
25
33
35
24
39
41
19
22
46
33
49
25
25
9
47
34
9
60
46
39
54
37
52
46
33
58
49
42
70
46
40
65
41
37
32
34
34
29
22
49 73 46
a) Calculate the following statistics for all 3 players: Total HRs, Most HR in a season, Fewest HR in a season, and standard deviation. Round to the nearest integer. b) Find the fences and any outlier(s) if any, for all Babe Ruth and Barry Bonds using your calculator. Work need not be shown. c) Construct Box and Whisker Plot to scale for Babe Ruth’s homeruns. d) Construct a Modified Box Plot to scale for Barry Bonds’ homeruns.
2) Evaluations For a school in the mid-west the teachers are given evaluations in three different categories: Professionalism, Student Performance, and Time Available Outside of the Classroom. Below is a table for the ratings for each category for each teacher. Teachers are rated from 1 to 20 (with 20 being the highest). TEACHER
Professionalism
Miss Jones Mrs. Smith Mr. Curtis Miss Rodriques Mrs. Blue Mr. Fire Miss Marino
14 19 15 16 14 20 18
Student Performance 19 20 15 14 11 18 17
Time Available 16 5 15 19 19 19 15
a) Compute the mean, median, and mode for each category rounding to the nearest tenth. b) Each teacher’s overall teacher rating is determined by giving a weight of 2 for Professionalism, 7 for Student Performance, and 4 for Time Available Outside of the Classroom. Compute Mrs. Smith’s, Mrs. Blue’s, and Mr. Curtis’s overall teacher ratings to the nearest tenth, and if you had to promote one of those three teacher’s to the role of supervisor, which teacher would you choose and why? d) If you had to promote one of those three teachers to the role of supervisor, which teacher would you choose and why.
3) Gas Prices Below are the prices for regular gasoline at 20 Mobil Stations across Long Island last week. $ 3.79 $ 3.38 $ 3.25 $ 3.39
$ 3.95 $ 3.19 $ 3.39 $ 3.25
$ 3.15 $ 3.35 $ 3.29 $ 3.49
$ 3.09 $ 3.30 $ 3.29 $ 3.59
$ 3.23 $ 3.35 $ 3.29 $ 4.54
a) Create a Stem and Leaf Diagram for the data. b) Calculate a 5 % and a 10 % trimmed mean for the data. c) What percent of the data lies within 2 standard deviations of the mean? d) If the two stations with the highest price for regular gasoline are eliminated from the original set of data, by how much (to the nearest cent) does the mean decrease?
4) College Acceptance Rates Below is a table that displays the general acceptance rate for select colleges and universities for 20122013: Institution Acceptance Rate Acceptances / Applications _________________________________________________________________ Amherst College 13.7% 1,084 / 7,927 Bowdoin College 14.5% 1,021 / 7,052 Brown University 9.2% 2,649 / 28,919 Caltech 10.6% 584 / 5,535 Carleton College 21.0% 1,475 / 7,030 Colorado College 23.1% 1,286/ 5,568 Columbia University 6.9% 2,311 / 33,531 Dartmouth College 10.0% 2,252 / 22,416 Davidson College 24.8% 1,185 / 4,770 Emory University 26.0% 4,592 / 17,698 Grinnell College 36.3% 1,458 / 4,021 Haverford College 23.3% 835 / 3,590 MIT 8.9% 1,620 / 18,109 Northwestern University 13.9% 4,555 / 32,772 Oberlin College 33.8% 1,976 / 5,841 Pomona College 12.9% 922 / 7,153 Princeton University 7.3% 1,931 / 26,498 Rice University 16.6% 2,552 / 15,408 Scripps College 36.3% 785 / 2,163 Stanford University 5.7% 2,210 / 38,828 Swarthmore College 14.0% 929 / 6,614 Trinity College 31.1% 2,379 / 7,651 Tufts University 18.7% 3,445 / 18,420 University of Chicago 8.8% 2,676 / 30,369 University of Notre Dame 23.3% 3,947 / 16,957 University of Pennsylvania 12.1% 3,785 / 31,280 University of Virginia 28.4% 8,038 / 28,265 Vanderbilt University 12.0% 3,717 / 31,056 Vassar College 23.1% 1,752 / 7,597 a) Create a frequency distribution and a cumulative frequency distribution for the acceptance rates for the schools in intervals beginning with 5 % and using intervals of 5 %. b) Draw a histogram using your graphing calculator, and indicate the viewing window used. c) Find the percentile rank of the University of Notre Dame (Go Irish!) among the schools given. d) Create a cumulative histogram.
5) McDonalds Menu. You must answer this one problem. It is worth 20 points. The following is the nutrition information for 9 menu items from McDonalds. Menu Item
Serving Size
Total Calories
Calories from Fat
Cholesterol
Sodium
Big Mac
7.6 oz.
550
260
75 mg
970 mg
1/4 lb. with Cheese
7.1 oz.
520
240
95 mg
1,100 mg
1/4 lb. with bacon & cheese
8 oz.
610
260
105 mg
1,440 mg
Hamburger
3.5 oz.
250
80
25 mg
480 mg
4 oz.
300
110
40 mg.
680 mg
Crispy Chicken Sandwich
7.5 oz.
670
300
45 mg.
1,480 mg
Grilled Chicken Sandwich
8.3 oz.
510
180
105 mg.
1,250 mg
Filet-O-Fish
5 oz.
390
170
40 mg.
590 mg
McNuggets (6 piece)
3.5 oz.
300
170
40 mg.
540 mg
Cheeseburger
a) Construct a scatter plot which displays the servings size, x, and the sodium, y, for each of the 9 menu items. b) Perform a linear, quadratic, and exponential regression on the data from part C, and give their corresponding a, b, c, and r values. Round to the nearest 2 decimal places. c) Using the best-fit model, estimate the amount of sodium a menu item would contain if its serving size is 6 oz. d) Using the best-fit model, if a menu item had 1,000 mg. of sodium, what would be the serving size to the nearest tenth of an oz.?
Part 2: Exponents and Logarithms – Answer all parts of both questions in this part. Each question is worth 10 points. 6) Exponents and Logarithms a) Solve for x in all three equations. If necessary round to two decimal places. 1. log 3 356 = x
2. log x 215 = 7
3. log 5 4x = 6
b) Tyler invests $ 15,000 in an account which paid 2.5% interest compounded quarterly for five years. 1. What was the balance after the five years? 2. How much interest did Tyler earn? c) What principle (to the nearest cent) will result in a balance of $ 20,000 if the interest is compounded continuously at 5.5 %? d) An SUV that costs $ 45,675 new has a blue book value of $ 32,500 after 3 years. Using the exponential model Y = Cekt find the value of k to 4 decimal places and find the value of the SUV after 8 years.
7) MORTGAGE You are buying a home for $ 425,000. The Bank of America requires a 20 % down payment and is giving you an interest rate of 4.5 % that will run for 30 years. TD Bank requires a 15 % down payment is giving you a 4.75 % that will run for 30 years. a) Bank of America 1. What will the down payment be if you chose their offer? 2. How much money will you be mortgaging through the bank? 3. What will the monthly payment be? 4. How much in interest will you pay over the course of the mortgage? b) TD Bank 1. What will the down payment be if you chose their offer? 2. How much money will you be mortgaging through the bank? 3. What will the monthly payment be? 4. How much in interest will you pay over the course of the mortgage? c) Which bank offers you the better deal? d) Using the bank with the better deal for you, if the school taxes for your town are $ 900, how much would your monthly payment be to the bank? Sales kd
