SAT MATH Cô Phạm Thảo SCATTERPLOTS AND LINES OF BEST FIT LEARNING OBJECTIVES 1 ) Determine the average rate of change; 2 ) Write an equation for a line of best fit; 3 ) Extrapolate values from the lin. học học học toán toán toán
SAT MATH Cô Phạm Thảo SCATTERPLOTS AND LINES OF BEST FIT LEARNING OBJECTIVES 1.) Determine the average rate of change; 2.) Write an equation for a line of best fit; 3.) Extrapolate values from the line of best fit; 4.) Determine whether a linear, a quadratic, or an exponential model describes the data presented in a scatterplot Best Fit Description Relationship Between Variables Upward-sloping straight line Linear and positive Downward-sloping straight line Linear and negative Upward-opening parabola Quadratic with a positive coefficient in front of the squared term Downward-opening parabola Quadratic with a negative coefficient in front of the squared term Upward-sloping curve with an in- Exponential and positive (e.g., compound interest) creasing slope Downward-sloping curve with a Exponential and negative (e.g., radioactive decay) flattening slope 5.) Correlation Strength/Positive and Negative Correlations A LINEAR MODELS Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo Question Which of the following is the most accurate statement about the scatterplot above? A The data in the scatterplot has a weak positive correlation B The data in the scatterplot has a strong positive correlation C The data in the scatterplot has a negative correlation D There is no correlation in the data set Question The Human Resources department of a company tracks employee sick day usage to see if there are patterns One of the HR representatives decides to check employee sick day usage against outside temperature He compiles the information for the employees’ sick day usage and temperature in the scatterplot below Which of the following conclusions can he draw based on this data? A There is no relationship between the number of sick days used by employees in general and outside temperature B There is no relationship between the number of sick days used by this company’s employees and outside temperature C No conclusions can be drawn about the number of sick days used by this company’s employees and outside temperature D There is a relationship, but not a causal link, between the number of sick days used by this company’s employees and outside temperature Question Suppose a scatterplot shows a weak negative linear correlation Which of the following statements is true? Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo A The slope of the line of best fit will be a number less than −1 B The slope of the line of best fit will be a number between −1 and C The data points will follow, but not closely, the line of best fit, which has a negative slope D The data points will be closely gathered around the line of best fit, which has a negative slope Question Wesley went to an amusement park with his family He paid for his own admission ticket and all of the rides he rode The scatterplot shows possible amounts that he could have paid If a line of best fit (not shown) is used to model the data, the equation of the line would be y = 3x + In this scenario, what does represent? A The cost of one ride B The number of rides Wesley rode C The cost of the admission ticket D The number of hours Wesley stayed at the park Question The graph below shows the amount that a new, high-tech video arcade charges its customers What could the y-intercept of this graph represent? A The cost of playing games B The cost per game, which is $5 C The entrance fee to enter the arcade D The number of games that are played Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo Question The scatterplot shows the prevalence of obesity plotted against the prevalence of diabetes in various areas of the United States Which of the following best estimates the average rate of change in the prevalence of diabetes as compared to the prevalence of obesity? A 0.3 B 0.9 C 1.1 D Question The figure below shows the number of emails sent per day plotted against the number of hours an adult works on a computer per day Which of the following best estimates the average rate of change in the number of emails sent compared to the number of hours working on a computer? A 0.12 B 1.5 C 8.5 D 12 Question The scatterplot below shows data collected each year after the British Parliament enacted a mandatory seat belt law and the line of best fit to the data Which of the following equations best represents the trend of the data shown in the figure? Tích kiến thức, trữ niềm vui SAT MATH A y = 0.4x + 25 Cô Phạm Thảo B y = 1.8x + 15 C y = 2.1x + 35 D y = 2.6x + 25 Question The scatterplot above shows the weight, in ounces, of the fruits on a certain truffula tree from days 55 to 85 after flowering According to the line of best fit in the scatterplot above, which of the following is the closest approximation of the number of days after flowering of a truffula fruit that weighs 5.75 ounces? A 63 B 65 C 77 D 81 Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo Question 10 The scatterplot above shows the relationship between gas mileage, in miles per gallon, and weight, in tons, for 10 cars selected at random The line of best fit models the gas mileage based on the weight of the car What is the weight, in tons, of the car for which the actual gas mileage was closest to the predicted value? A 2.5 B 4.5 C 15 D 27 Question 11 Wind chill, a measurement that reflects the temperature that one feels when outside based on the actual temperature and the wind speed, was first introduced in 1939, and the formula was revised in 2001 If the outside temperature is 0°F, what is the approximate wind chill at 40 miles per hour based on the 2001 formula? A −20o F B −30o F C −40o F D −50o F Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo Question 12 What wind speed would produce the same wind chill using the 1939 formula as the wind chill produced using the 2001 formula when the outside temperature is 0o F and the wind speed is 40 miles per hour? A 10 miles per hour B 15 miles per hour C 20 miles per hour D 40 miles per hour Question 13 The scatterplot above shows the number of minor muscle strain injuries sustained in a year by athletes, plotted against their selfreported amount of time spent stretching and doing other warm-up activities before engaging in rigorous physical activity Which of the following best estimates the average rate of change in the number of injuries compared with the number of minutes spent warming up? A −1.2 B −0.8 C D 20 B QUADRACTIC MODELS Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo Question 14 Given that a, b, and c are constants and that a > 0, which of the following is the equation for the line of best fit for the above scatterplot? B y = abx A y = ax + b C y = −ax2 + bx + c D y = ax2 + bx + c Question 15 Adriana used the data from a scatterplot she found on the U.S Census Bureau’s website to determine a regression model showing the relationship between the population in the area where she lived and the number of years, x, after she was born The result was an exponential growth equation of the form y = x0 (1 + r)x Which of the following does x0 most likely represent in the equation? A The population in the year that she was born B The rate of change of the population over time C The maximum population reached during her lifetime D The number of years after her birth when the population reached its maximum Question 16 The data in which of the following scatterplots would be best modeled by a quadratic function in which the x2 term has a negative coefficient? A B C D Question 17 The scatterplot above shows the average therms of natural gas used by residential customers over a 12 -month period Of the following equations, which best models the data in the scatterplot? A y = 1.061x + 312.9 B y = −1.061x − 312.9 C y = 6.1x2 − 85.1x + 312.9 D y = −6.1x2 + 85.1x − 312.9 Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo Question 18 Scientists measured the concentration of an experimental medication in blood samples over time If a quadratic function is used to model the data, which of the following best explains the meaning of the vertex? A The average maximum medicine concentration in the blood sample is 7.5 units B The average maximum medicine concentration is more than 20 units C The average maximum medicine concentration in the blood samples occurs around 2.5 minutes D The average maximum medicine concentration in the blood sample occurs between and 10 minutes Question 19 Nine data points were used to generate the scatterplot shown Assuming all whole number values for the data points, which list correctly gives the domain of the data? A {10, 35, 55, 70, 80, 85} B {100, 200, 300, 400, 500} C {0, 50, 100, 150, 200, 250, 300, 350, 400} D {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100} Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo Question 20 Following the catastrophic oil spill in the Gulf of Mexico in April of 2010, more than 900 bottlenose dolphins were found dead or stranded in the oil spill area The figure above shows the weight of a rescued dolphin during its recovery Based on the quadratic model fit to the data shown, which of the following is the closest to the average rate of change in the dolphin’s weight between week and week of its recovery? A pounds per week B 16 pounds per week C 20 pounds per week D 40 pounds per week C EXPONENTIAL MODELS Question 21 Which of the following best describes the type of association shown in the scatterplot above? A Linear, positive B Linear, negative C Exponential, positive D Exponential, negative Question 22 The blue whale is the largest creature in the world and has been found in every ocean in the world Tích kiến thức, trữ niềm vui SAT MATH Cơ Phạm Thảo A marine biologist surveyed the blue whale population in Monterey Bay, off the coast of California, every three years between 1995 and 2010 The figure above shows her results If w is the number of blue whales present in Monterey Bay and t is the number of years since the study began in 1995 , which of the following equations best represents the blue whale population of Monterey Bay? t t2 t C w = 100 × D w = 100 × A w = 100 + 2t B w = 100 + Question 23 When water is heated in a closed system, the vapor pressure increases slowly at first and then more rapidly As the water reaches the boiling point of 100o C, the vapor pressure reaches atm, known as standard atmosphere Which of the following models best describes the increase in vapor pressure as water is heated to its boiling point? A Linear B Quadratic C Polynomial D Exponential Question 24 Students in a finance class surveyed 20 percent of the account holders at Docen Bank to determine whether the bank’s "Stock Market Special" savings account actually paid account holders the promised 10 percent annual interest rate The scatterplot above shows the data the students collected from account holders about how long ago they opened their and their current balances The students calculated accounts 12x 08 a line of best fit with the equation y = 120 + , which means that the bank was actually paying 12 account holders only an percent annual interest rate Which of the following best explains how the number 120 in the equation relates to the scatterplot? A A "Stock Market Special" account with $120 initially will likely have less than $350 after 15 years B All "Stock Market Special" accounts started with a $120 initial investment C The difference between the promised 10 percent annual interest rate and the actual percent rate is $120 a year D A "Stock Market Special" account with $120 initially will likely have more than $350 after 15 years Question 25 A dietician working in the children’s ward at a hospital is monitoring the water intake of all the patients in the ward The total water intake for each patient is recorded throughout the day and then averaged over the 24-hour period The results are recorded in the scatterplot, where each dot represents the average hourly water intake for one child Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo Which of the following ages has the greatest range of values for the average hourly water intake? A Age B Age C Age D Age 11 Question 26 A dietician working in the children’s ward at a hospital is monitoring the water intake of all the patients in the ward The total water intake for each patient is recorded throughout the day and then averaged over the 24-hour period The results are recorded in the scatterplot, where each dot represents the average hourly water intake for one child A child between the ages of and should consume at least liter of water per day Based on the data presented in the scatterplot, what percent of the children, ages 5-8, in the ward consumed less than the daily-recommended amount? (Note: There are 24 hours in one day and approximately 33.814 ounces in liter.) A 35% B 60% C 70% D 85% Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo Question 27 Given the scatterplot graph above, ten students at Welton Academy were polled at random about their usage of the school’s new physics-centered social media app, E = MC Shared The app was developed to encourage students to discuss physics curricula and concepts in ways that mirrored social media trends in 2013 Students were asked how many times they logged into the app each day as well as how many posts they actually made using the app With the given data, what conclusions can be drawn about this group of students? A The majority of students polled logged in more times per day than they posted B The majority of students polled posted more times per day than they logged in C The majority of students polled logged in and posted an equal number of times D No relationship can be drawn between logins per day and posts per day Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo KEYS Tích kiến thức, trữ niềm vui ... approximation of the number of days after flowering of a truffula fruit that weighs 5 .75 ounces? A 63 B 65 C 77 D 81 Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo Question 10 The scatterplot... data in which of the following scatterplots would be best modeled by a quadratic function in which the x2 term has a negative coefficient? A B C D Question 17 The scatterplot above shows the... the domain of the data? A {10, 35, 55, 70 , 80, 85} B {100, 200, 300, 400, 500} C {0, 50, 100, 150, 200, 250, 300, 350, 400} D {0, 10, 20, 30, 40, 50, 60, 70 , 80, 90, 100} Tích kiến thức, trữ