Name: JMJ April 10, 2017 Trigonometry A2 Trimester 2 Exam 8:40 AM 10:10 AM Mr. Casalinuovo
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1 Name: JMJ April 10, 2017 Trigonometry A2 Trimester 2 Exam 8:40 AM 10:10 AM Mr. Casalinuovo Part 1: You MUST answer this problem. It is worth 20 points. 1) Temperature vs. Cricket Chirps: Crickets make a chirping noise by sliding their wings over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (Fahrenheit) and the number of chips per second for the striped ground cricket. Temp (F) Chirps/Sec a) Use your graphing calculator to create a scatter plot of the data. Make a graph of the scatter plot in the accompanying viewing window. b) Use the regression feature of your graphing calculator to find a linear, quadratic, and an exponential model of the data. Graph it with the scatter plot, and round to three decimal places. c) Identify the best-fit model for the data. d) Using the best-fit model, find the outside temperature (to the nearest tenth of a degree) if a cricket makes 16 chirps a second. e) Using the best-fit model, find the number of chirps per second if the outside temperate is 90.1 degrees. Part 2: Answer FOUR of the following FIVE problems in this part. Each problem you answer is worth 20 points. 2) Frequency Distribution and Histograms Construct a frequency distribution (in ascending order) and a histogram, a cumulative frequency distribution and a cumulative frequency histogram using intervals beginning with 0 gallons and using intervals of size 4: Amount of gasoline purchased by 21 drivers:
2 3) Exercise The following are data on weekend exercise time for 20 females consistent with summary quantities in the paper, An Ecological Momentary Assessment of the Physical Activity and Sedentary Behavior Patterns of University Students (Health Education Journal [2010]) Weekend Exercise (minutes): a. Calculate the mean, median, and standard deviation for the data. b. Find the percent of the data that is within 2 standard deviations from the mean. c. Find the 5 % and the 10 % trimmed mean for the data. 4) Weather: In the table below, the average monthly temperatures for and Seattle is shown. Month Seattle January 14.7 February 40.1 March 53.4 April 59.4 a) Perform the five number summary. b) Draw a box & whisker graph from the data. c) Find the interquartile range, the lower and the upper fence values for Seattle s average monthly temperatures. d) Identify any outliers for the data e) Construct a modified box plot for Seattle s average monthly temperature. May 66.7 June 71.2 July 76.9 August 76.3 September 71.0 October 61.3 November 52.0 December 47.1
3 5) Test Scores Given the previous statistics exam grades for 20 statistics students, 97, 92, 88, 75, 83, 67, 89, 55, 72, 78, 81, 91, 57, 63, 67, 74, 87, 84, 98, 46 a) Create a stem and leaf plot for the data. b) Find the percentile ranking for a student who scored a 89. c) Find the score that is at the second decile. 6) Trade Winds Trade winds are one of the beautiful features of island life in Hawaii. The following data represent total air movement in miles each day over a weather station in Hawaii as determined by a continuous anemometer recorder. The period of observation was January 1 to January a) Calculate the Mean Absolute Deviation for the Data rounding to the nearest tenth. b) If the day in which the 113 mile reading was incorrect, and it should have measured as 13 mile, by how much (to the nearest tenth) does the average decrease and find the percent decrease. 7) Interpreting Charts and Tables: Answer A) and B). A) The accompanying box-and-whisker plot represents the cost, in dollars, of sixteen DVD s. 1) Which cost is the lower quartile? 2) What is the range of the costs of the DVD s? 3) What is the median? 4) How many DVD s cost between $14.50 and $29 5) I bought one of the DVD s that cost me $ How many DVD s cost more than the one I bought? The back-to-back stem-and-leaf plot below shows the average monthly temperatures for Seattle, Washington, and Helena, Montana. a. Which city has lower monthly temperatures? Explain. b. Which city has more varied temperatures? c. What is the median monthly temperature for Seattle? d. What is the median monthly temperature for Helena?
4 Name: JMJ April 10, 2017 Trigonometry A2 Trimester 2 Exam 8:40 AM 10:10 AM Mr. Casalinuovo Part 1: You MUST answer this problem. It is worth 20 points. 1) Temperature vs. Cricket Chirps: Crickets make a chirping noise by sliding their wings over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (Fahrenheit) and the number of chips per second for the striped ground cricket. Temp (F) Chirps/Sec a) Use your graphing calculator to create a scatter plot of the data. Make a graph of the scatter plot in the accompanying viewing window. b) Use the regression feature of your graphing calculator to find a linear, quadratic, and an exponential model of the data. Graph each with the scatter plot, and round to three decimal places. LINEAR QUADRATIC EXPONENTIAL a b c N/A N/A r c) Identify the best-fit model for the data. d) Using the best-fit model, find the outside temperature (to the nearest tenth of a degree) if a cricket makes 16 chirps a second. e) Using the best-fit model, find the number of chirps per second if the outside temperate is 90.1 degrees.
5 Part 2: Answer FOUR of the following FIVE problems in this part. Each problem you answer is worth 20 points. 2) Frequency Distribution and Histograms Construct a frequency distribution (in ascending order) and a histogram, a cumulative frequency distribution and a cumulative frequency histogram using 6 intervals. Amount of gasoline purchased by 21 drivers: a. Create a frequency distribution and a cumulative frequency distribution. Intervals Frequency Cumulative Frequency b. Draw a frequency histogram and a cumulative frequency histogram for the data. FREQUENCY HISTOGRAM CUMULATIVE FREQUENCY HISTOGRAM Xmin = Ymin = BE SURE TO LABEL THE Xmax = Ymax = X AND Y-AXIS FOR THE XScl = YScl = CUMULATIVE HISTOGRAM
6 3) Exercise The following are data on weekend exercise time for 20 females consistent with summary quantities in the paper, An Ecological Momentary Assessment of the Physical Activity and Sedentary Behavior Patterns of University Students (Health Education Journal [2010]) Weekend Exercise (minutes): a. Calculate the mean, median, and standard deviation for the data. Round to the nearest tenth. MEAN = MEDIAN = STANDARD DEVIATION = b. Find the percent of the data that is within 2 standard deviations from the mean. c. Find the 5 % and the 10 % trimmed mean for the data. 5 % Trimmed Means = 10 % Trimmed Means =
7 4) Weather: In the table below, the average monthly temperatures for and Seattle is shown. a) Perform the five number summary. Round to the nearest tenth. Month Seattle January 14.7 February 40.1 March 53.4 April 59.4 May 66.7 June 71.2 b) Draw a box & whisker graph to scale from the data on the number line. July 76.9 August 76.3 September 71.0 October 61.3 November 52.0 December 47.1 c) Find the interquartile range, the lower and the upper fence values for Seattle s average monthly temperatures. Interquartile Range = Lower Fence = Upper Fence = d) Identify any outliers for the data. e) Construct a modified box plot for Seattle s average monthly temperature.
8 5) Test Scores Given the previous statistics exam grades for 20 statistics students, 97, 92, 88, 75, 83, 67, 89, 55, 72, 78, 81, 91, 57, 63, 67, 74, 87, 84, 98, 46 a) Create a stem and leaf plot for the data. b) Find the percentile ranking for a student who scored a 89. c) Find the score that is at the second decile.
9 6) Trade Winds Trade winds are one of the beautiful features of island life in Hawaii. The following data represent total air movement in miles each day over a weather station in Hawaii as determined by a continuous anemometer recorder. The period of observation was January 1 to January a) Calculate the Mean Absolute Deviation for the Data rounding to the nearest tenth. X Mean Absolute Deviation = b) If the day in which the 113 mile reading was incorrect, and it should have measured as 13 mile, by how much (to the nearest tenth) does the average decrease and find the percent decrease. Decrease = Percent Decrease =
10 7) Interpreting Charts and Tables: Answer A) and B). A) The accompanying box-and-whisker plot represents the cost, in dollars, of sixteen DVD s. 1) Which cost is the lower quartile? 1) 2) What is the range of the costs of the DVD s? 2) 3) What is the median? 3) 4) How many DVD s cost between $14.50 and $29 4) 5) I bought one of the DVD s that cost me $ How many DVD s cost more than the one I bought? 5) B) The back-to-back stem-and-leaf plot below shows the average monthly temperatures for Seattle, Washington, and Helena, Montana. 1. Which city has lower monthly temperatures? 2. Which city has more varied temperatures? 3. What is the median monthly temperature for Seattle? 4. What is the median monthly temperature for Helena?
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