Comparing and Modeling with Functions

Transcription

1 Name Date Class 13 Comparing and Modeling with Functions Quiz 1. Which of the following data sets is best described by a linear model? A {(5, 1), (4, 2), (3, 4), (2, 8)} B {(5, 1), (4, 1), (3, 3), (2, 5)} C {(5, 12), (4, 6), (3, 3), (2, 1.5)} D {(5, 1), (4, 0), (3, 1), (2, 4)} 2. $1200 is invested at 3% compounded quarterly. What is the total amount, to the nearest dollar, after 5 years? F $1236 H $1391 G $1245 J $ Chess club earnings are $40 per month and will increase at a rate of 2.5% each month. Which function describes this situation? A y 40(0.75) x C y 40(1.025) x B y 40(0.975) x D y 40(1.25) x 4. Iodine-131 has a half-life of about 8 days. About how much is left from a 50 gram sample after 24 days? F grams H grams G grams J grams 5. Which of the following data sets is best described by a quadratic model? A {(1, 2), (2, 4), (3, 6), (4, 8)} B {(1, 2), (2, 4), (3, 6), (4, 8)} C {(1, 1), (2, 2), (3, 4), (4, 8)} D {(1, 1), (2, 2), (3, 7), (4, 14)} 6. Which of the following data sets is best described by a linear model? F {(2, 4), (3, 9), (4, 16), (5, 25)} G {( 2, 1), ( 3, 0), ( 4, 1), ( 5, 0)} H {(2, 12), (3, 6), (4, 0), (5, 6)} J {(2, 1), (3, 0), (4, 1), (5, 4)} 7. Which of the following models best describes the data set? {( 1, 1), (0, 0), (1, 1), (2, 4)} A linear C exponential B quadratic D none 8. The table shows store sales by year. Which function models the data? Year Sales F y x H y 5000(0.8) x G y x J y 5000(1.2) x 9. Which kind of model best describes the data graphed below? A linear C exponential B quadratic D none of these 10. Argyle has $1000 in his savings account. He wants to save more money. He is looking at two investment plans. Under plan A, he will increase his account balance by $200 a year. Under plan B, he will increase his account balance by 15% each year. How much more will he save with Plan B after 10 years? F $1,046 H $131 G $459 J $ Which is the average rate of change over the interval [0, 4]? Equation A X Y Equation B f( x) 2x 1 A A: 4, B: 2 C A: 8, B: 16 B A: 4, B: 4 D A: 8, B: 4 49

2 Name Date Class 13 Comparing and Modeling with Functions Quiz continued 12. Determine which kind of model linear, quadratic, exponential, or square-root best describes this data set. {( 2, 0.75), ( 1, 1.5), (0, 3), (1, 6), (2, 12)} 13. Which kind of model best describes the graph? 14. Which kind of model best describes the data set? X Y _ 15. Alistair has $1000 in his savings account. He wants to save more money. He is looking at two investment plans. Under plan A, he will increase his account balance by $300 a year. Under plan B, he will increase his account balance by 25% each year. How much more will he save with Plan B after four years? Round your answer to the nearest whole. 16. What is the average rate of change over the interval [ 1, 2]? Equation A X Y Equation B f( x) 3x Which is the y-intercept of the equations? Equation A X Y Equation B f( x) 3x Emil has $500 in his savings account. He wants to save more money. He is looking at two investment plans. Under plan A, he will increase his account balance by $150 a year. Under plan B, he will increase his account balance by 25% each year. How much more will he save with Plan B after four years? Round your answer to the nearest whole. 19. What is the average rate of change over the interval [ 1, 1]? Equation A X Y Equation B f( x) 2x 3 50

3 Name Date Class 14 Data Distributions Quiz 1. Which type of graph would best display the change in the number of student absences over the school year? A circle C bar B line D double-bar Use the double-bar graph for How many people were enrolled in college courses in 1999? F 100 H 200 G 120 J In what year was the difference between men s and women s enrollment the greatest? A 2000 C 2002 B 2001 D 2003 Use the stem-and-leaf plot for Key: If you organized the data in a frequency table, which could be intervals? F and G and H and J and What is the median? A 72 C 82.5 B 80 D What is the mean? F 72 H 82.5 G 80 J A group of men and women were polled about whether they go to the gym regularly. The joint and marginal relative frequencies corresponding to the results are shown in the two-way table. Yes No Total Men 0.4 x 0.6 Women 0.3 y 0.4 Total Which of these is the value of x? F 1 H 0.2 G 0.5 J Use the two-way table from Question 7. Which of these is the value of y? A 1 C 0.2 B 0.5 D For the set {1, 1, 2, 4, 5, 6, 7, 8, 10,} which would NOT be affected if another value of 10 was included? A range C median B mean D mode 10. Look at the box-and-whisker plot below. Between what values does the middle half of the data fall? F 12 and 18 H 18 and 26 G 12 and 30 J 22 and 30 63

4 Name Date Class 14 Data Distributions Quiz continued 11. Use this bar graph to identify how many more candies are green than yellow. 14. Find the mean, median, and mode. mean: median: mode: 15. Use the data to make a box-andwhisker plot. 16. Men and Women at a shoe store were polled to see if they prefer comfort or fashion. The results of the poll are shown in the two-way table. _ The low temperatures for Nashville, TN, for October 1 15, 2005, are given below. Use this data for questions Low Temperatures (ºF) Complete this frequency table. Temperature (ºF) Frequency 13. Use your frequency table in question 4 to make a histogram. Comfort Fashion Men 20 3 Women How many people were polled? 17. Use the two-way table from Question 17. How many people prefer fashion? 18. Use the two-way table from Question 17. Did more people prefer comfort or fashion? 64

5 Name Date Class 15 Linear and Exponential Models Quiz 1. Which ordered pairs match the scatter plot below? 4. Based on the graph below, which is the best prediction for the cost of 9 items? A (1, 2), (4, 2), (5, 5), (7, 6) B (2, 1), (2, 4), (5, 5), (7, 6) C (1, 2), (2, 4), (5, 5), (6, 7) D (2, 1), (4, 2), (5, 5), (7, 6) 2. Which correlation best describes the scatter plot below? F Positive H Continuous G Negative J None 3. Which of the following best describes a negative correlation? A height of person over time B depth of swimming pool as it drains over time C number of drinks sold over the summer and air temperature D number of groceries purchased and total amount of bill F about 8 H about 21 G about 14 J about The table shows the relationship between the size of a painting by a particular artist, and the price they charge for the painting. Painting Size (in 2 ) Price (dollars) Which equation could represent a line of best fit for this data? A y 2.09x 1.95 B y 209x The table shows the age of several people and how many hours a day they spend playing computer and/or video games. Age (yrs) Playing (hrs/day) Which equation could represent a line of best fit for this data? F y 53x 7.9 G y 7.9x + 53 H y 5.3x J y 0.079x

6 Name Date Class 15 Linear and Exponential Models Quiz continued 7. The table shows the number of fish in a small pond over four years. Draw a scatter plot and trend line. Year Number of Fish The table shows the number of employees in a company over five years. Draw a scatter plot and trend line. Year Employees Based on the trend line, predict how many fish will be in the pond in _ 8. An artisan crochets blankets for a craft fair. The table shows the relationship between how many hours the artisan spent on a blanket and the price charged for the blanket. Hours Price (dollars) Find an equation for a line of best fit. _ Based on the trend line, predict how many employees the company will have in An artisan builds birdhouses out of pine for a craft fair. The table shows the relationship between the number of hours the artisan spends on a birdhouse, and how much she charges for it. Hours Price (dollars) Find an equation for a line of best fit. 66

7 Name Date Class 16 Transformations Quiz 1. Which best describes the transformation? A preimage B reflection C rotation D translation 2. A figure has vertices at K(5, 5), L(5, 3), M(1, 1), and N(3, 5). After a transformation, the image of the figure has vertices at K ( 5, 5), L ( 3, 5), M ( 1, 1), and N ( 5, 3). Which best describes the transformation? F preimage H rotation G reflection J translation 3. What is the image of ( 8, 1) when it is reflected across the line y x? A ( 1, 8) C (1, 8) B 1, 1 D 1 8 1, 8 4. Which of the following capital letters is a reflection image of itself across a horizontal line? F M H O G N J P 5. The vertices of PQR are P(10, 6), Q(6, 2), and R(4, 1). The triangle is translated along a vector. Which vector places the image of the triangle entirely in Quadrant II? A 6, 10 C 11, 6 B 10, 7 D 12, 8 6. The point (90, 0) is rotated 150 about the origin. What are the coordinates of its image? F (90, 150) H ( 45 3,45) G (90, 45) J ( 45,45 3) 7. Which shows the image of after a 180 rotation about the endpoint of the ray? A C B D Use the figure for Exercises 8 and 9. The coordinates of the vertices are integers. 8. JKL is rotated 90 about the origin and then translated along the vector 8, 5. What are the coordinates of the final image of point L under this composition of transformations? F ( 7, 10) H ( 9, 10) G ( 7, 0) J ( 9, 0) 9. JKL is translated along the vector 1, 3 after it is reflected across the x-axis. What are the coordinates of the final image of point J under this composition of transformations? A (6, 1) C (1, 6) B ( 6, 1) D ( 1, 6) 75

8 Name Date Class 16 Transformations Quiz continued 10. JKL is translated so that the image of vertex K is K (4, 12). A composition of reflections across the lines of which equations creates the same image? F first y 5, then y 9 G first y 5, then y 1 H first y 9, then y 1 J first y 1, then y The composition of two reflections across two intersecting lines is equivalent to which isometry? A rotation C translation B glide rotation D reflection 12. A triangle has vertices at A( 2, 3), B(2, 1), and C(1, 0). After a transformation, the image of the triangle has vertices at A ( 2, 3), B (2, 5), and C (1, 6). Identify the transformation. 15. Two cabins are on the same side of a river. Two trails are planned to connect the campsites to a planned boat dock on the river. On a grid, cabin A would be at (4, 2), cabin B would be at ( 2, 4), and the river would be located along the x-axis. Where should the dock be located to make the combined length of the trails as short as possible? 16. The point R(2, 3) is translated along a vector that is parallel to the line y 2x 1. The translation vector has a magnitude of 2 5. What are the coordinates of a possible image of point R? 17. Given the function y x 2, write a function that reflects the graph across the x-axis. _ 13. Identify the image of the point A( 6, 9) when A is reflected across the line y x. _ 14. ABC has vertices A( 4, 2), B( 1, 4), and C(0, 1). Draw ABC and its image A B C for translation along the vector 2, Use mapping notation to represent a 90 clockwise rotation about the origin of the point (x, y). 76