Mathematical Models with Applications Second Nine Weeks Exam

Transcription

1 Name: Period: Mathematical Models with Applications Second Nine Weeks Exam This exam will count as approximately 20% (one-fifth) of your second nine weeks average. This exam is not optional, and you may not exempt it (the exemption policy is for semester exams only). You must indicate your answers clearly on the answer sheet provided at the end of this test. There is a TAKS formula chart attached to this test, and also some blank graph paper for you to use if you need it. A graphing calculator is not required to complete this test. However, a four-function calculator will be very helpful. If you would like to use a graphing calculator, you may do so before school, during first homeroom, or after school. Calculators are not available to check out to take home. You may use your notes, textbook, the internet, or any other resource to complete this test. I will have access to my over the winter break to help answer questions. (Emily_Carlile@LagoVista.txed.net) This test is due no later than Friday, January 8 th at the start of your class period. If you choose not to turn your test in on time, the school-wide late work policy will apply. Turn it in on Monday January 11 th, for 80% value, turn it in on Tuesday January 12 th for 50% value, and after that, a zero will be recorded for the grade. Good luck!

2 Texas Assessment of Knowledge and Skills Mathematics Chart LENGTH Metric Customary 1 kilometer = 1000 meters 1 mile = 1760 yards 1 meter = 100 centimeters 1 mile = 5280 feet 1 centimeter = 10 millimeters 1 yard = 3 feet 1 foot = 12 inches CAPACITY AND VOLUME Metric Customary 1 liter = 1000 milliliters 1 gallon = 4 quarts 1 gallon = 128 fluid ounces 1 quart = 2 pints 1 pint = 2 cups 1 cup = 8 fluid ounces MASS AND WEIGHT Metric Customary 1 kilogram = 1000 grams 1 ton = 2000 pounds 1 gram = 1000 milligrams 1 pound = 16 ounces TIME 1 year = 365 days 1 year = 12 months 1 year = 52 weeks 1 week = 7 days 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds Metric and customary rulers can be found on the separate Mathematics Chart. Page 5 Continued on the next page

3 Page 6 Mathematics Chart Perimeter rectangle P = 2l + 2w or P = 2(l + w) Circumference circle C = 2πr or C = πd Area rectangle A = lw or A = bh triangle 1 bh A = bh or A = 2 2 trapezoid A = 1 (b 1 + b 2 )h 2 or A = regular polygon A = 1 ap 2 circle A = πr 2 P represents the Perimeter of the Base of a three-dimensional figure. B represents the Area of the Base of a three-dimensional figure. Surface Area cube (total) S = 6s 2 prism (lateral) S = Ph prism (total) S = Ph +2B pyramid (lateral) 1 S = Pl 2 pyramid (total) 1 S = Pl + B 2 cylinder (lateral) S = 2πrh cylinder (total) S = 2πrh +2πr 2 or S =2πr(h + r) cone (lateral) S = πrl cone (total) S = πrl + πr 2 or S = πr(l + r) sphere S = 4πr 2 Volume prism or cylinder V = Bh pyramid or cone 1 V = Bh 3 sphere 4 V = πr 3 3 Special Right Triangles 30, 60, 90 x, x 3, 2x 45, 45, 90 x, x, x 2 Pythagorean Theorem a 2 + b 2 = c 2 Distance Formula d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 Slope of a Line m = Midpoint Formula M = ( x 1 + x 2 y, 1 + y 2 ) Quadratic Formula x = b ± b 2 4ac 2a Slope-Intercept Form of an Equation y = mx + b Point-Slope Form of an Equation y y 1 = m(x x 1 ) Standard Form of an Equation Simple Interest Formula Ax + By = C I = prt y 2 y 1 x 2 x (b 1 + b 2 )h 2

4 1. Pearl's science scores for this grading period are shown in the line plot below. 3. Which scatterplot shows a positive relationship. What is Pearl's mean score for this grading period? 86 and Mr. Stewart plotted the scores on the last math models exam. What percentage of grades were 84 or higher? 42% 45% 47% 50% 4. In a scatterplot, a negative relationship exists if which of the following is generally true? As x increases, y increases and decreases As x decreases, y values increase As x increases, y values decrease As x increases, y values increase 5. According to this graph, what percentage of the grades are 78% or better? 60% 70% 73% 75% Page: 1

5 6. Determine which of the following graphs do not represent functions. 7. Alicia's Restaurant is trying to determine the relationship between the average prices of the entrees on its menu and daily profits? The maximum profit occurs when entrees are sold for approximately $5.50. The maximum profit is about $250. The maximum profit occurs when entrees are sold for approximately $6.50. The maximum profit occurs when entrees are sold for $4.00. iii and iv i and iii i and ii i, ii, and iv 8. Placing 500 names into a box and drawing the names of 50 people to ask them the name of their favorite TV show is an example of what type of sampling? Cluster Convenience Random Systematic Page: 2

6 9. Joey is conducting a survey for his math class. He selected a grocery store at random and asked all of the shoppers to name their favorite brand of bread. What type of sampling did he use? cluster convenience random systematic 10. Jeremy asked the 10 people sitting at his lunch table to name their favorite type of music. What type of sampling did he use? Cluster Convenience Random Systematic 11. Paula has a new job as a quality control engineer at a children's toy factory. She pulls every fifth spin toy off the production line and tests it. What type of sampling is Paula using? Cluster Convenience Random Systematic 12. The table below shows the salaries for the central office positions in a school district. Position Salary Superintendent $195,000 Associate Superintendent $160,000 Personnel Director $125,000 Curriculum Director $86,000 Business Director $109,000 Technology Director $75,000 Which measure of central tendency best describes the average central office salary? Range Mean Median Mode 13. Find the median salary for a central office person. Position Salary Superintendent $195,000 Associate Superintendent $160,000 Personnel Director $125,000 Curriculum Director $86,000 Business Director $109,000 Technology Director $75,000 $105,500 $109,000 $117,000 $125,000 Page: 3

7 14. The scatterplot above displays the heights and weights of members of the local basketball team. Which of the following statements is not true? The mean and median for this graph are both good indicators of the size of the team. The mode is 66. The mean is 69.7 The median is 70. Page: 4

8 15. Hunter earns $2,200 per month after taxes. The pie chart above shows his expenses. Use the legend below to answer the question: 1 = food 2 = gas 3 = utilities 4 = rent 5 = car note 6 = phone 7 = miscellaneous costs Which item represents the median for his monthly budget? rent car note gas food Page: 5

9 16. Look at the set of scatterplots below that were on Joshua's math test. Which of these answers should Joshua choose in order to get this problem correct? 19. Julio is practicing for a track meet. Here are his times in seconds: 9.1, 8.7, 9.2, 9.0, 8.7, 8.9, 15.0, and 9.2 Which of the following statements is true? The median is 9.5. The median is The mode is 9.2. The mean is 9.5. Given that a = positive correlation, b = negative correlation, and c = no correlation, which of the following pairings is correct? 1c, 3b, 4c 1b, 2a, 4c 1a, 2b, 3a 1a, 2b, 3c 17. Which of the following graphs has an axis of symmetry of x = -1? f(x) = x 2 + x + 3 f(x) = x 2 + 4x - 3 f(x) = x 2 + 2x - 8 f(x) = x x Which of the following graphs is wider than y = x 2 and turns downward? y = 3/5 x 2 y = 4 x 2 y = -4 x 2 y = -3/5 x Which of the central tendency measures would best represent the most frequently selected color of a car purchased? Standard deviation mode mean median 21. Bob has been tracking the price changes for the newest electronic game console. He recorded the price the day the newest game console was introduced and recently noted that the price of the console has varied by $ What measure of data did Bob use to make that determination? Range Mean Median Mode Page: 6

10 22. Jared was reviewing the salary chart to predict his salary if he worked for his current employer for 6 more years. If Jared has worked for the company for 3 years already, what would Jared's salary be if the current trend continues? $62,500 $65,000 $67,500 $70,000 Page: 7

11 23. Which scatterplot below best represents a positive correlation? 24. Ashton, Anywhere, U.S.A has a population of 541,000 in The population is increasing at a constant rate of 2.8%. Based upon this data, predict the population for , , ,480 Cannot be determined using the given data. 25. Amy works for a bridal store. She makes a base salary of $500 plus 4% commission. Write an equation to compute Amy's salary per week..04x = y 500x +.04 = y 500(.04)x = y.04(x + 500) = y 26. Jessica earns a base salary of $500 plus 4% commission per week. Her goal is to sell $3000 worth of inventory next week. Find her salary for the week if she meets her goal. $120 $620 $500 $3000 Page: 8

12 27. Jason earns $500 per week plus 8% commission on his sales of luggage. How much luggage must Jason sell in a week to make at least $1000? $500 $1000 $5000 $ Jared is paid a weekly salary of $700 and receives a 3% commission on all sales over $8000. Find his gross salary if he sold $12,000 worth of merchandise ast week. $381 $1060 $820 none of the above 29. Linnea is paid a weekly salary of $650 and receives a 4% commission on all sales over $9,250. Find her gross salary if she sold $12, 285 worth of merchandise last week. $ $ $ $ The soccer booster club is ordering miniature soccer balls to sell as a fundraiser. They paid $550 for the soccer balls and will sell them for $10 each. Which of the following equations represents the relationship between the number of balls they sell and the profit they will make? 31. The church preschool is selling candy bars as a fundraiser. They paid $250 for the candy bars and will sell them for $2.00 each. The function that represents the relationship between the candy they sell, x, and the profit they make is represented by the function f(x) = 2x What is the dependent variable in the relationship? Profit made by the candy sales Selling price of the candy Number of people who bought candy Number of candy bars sold 32. The church preschool is selling candy bars as a fundraiser. They paid $250 for the candy bars and will sell them for $2.00 each. The function that represents the relationship between the candy they sell, x, and the profit they make is represented by the function f(x) = 2x What is the independent variable in the relationship? Profit made by the candy sales Selling price of the candy Number of people who bought candy Number of candy bars sold 33. You are shopping for a new pair of shoes. The total cost of the shoes is the price of the shoes (s) plus an 8% sales tax. If the total cost, c, is a function of s, the price of the shoes, which function models the situation? c = s c = 8s c = 1.08s c = s f(x) = x f(x) = 10x -550 f(x) = 10(x-550) f(x) = 10x +550 Page: 9

13 34. Gerry is shopping for a new suit. The total cost of the suit is the price of the suit (s) plus an 8.25% sales tax. There is also an alteration fee of $8.00. If c, the total cost, is a function of s, the price of the suit which function models the situation? c = s +8 c = ( s) +8 c = 8.25s +8 c = (s ) Chandra is working as a waitress. She earns $5.75 per hour plus tips. Last week Chandra worked 4 days for 7.25 hours each. Her tips totaled $ Find Chandra's total gross pay. $ $ $ $ Parker is working as a valet driver. If he works nights, he is paid $5.25 per hour plus tips. When Parker works the day shift, he receives $6.25 per hour plus tips. Last week Parker worked 3 night shifts of 4 hours each and 4 day shifts of 3 hours each. His tips totaled $156 for the nights and $82 for the days. Find Parker's gross salary for the week. $157 $219 $294 $ Angela works in a factory asssembling toys. She is paid $2.05 per toy assembled after the first 25. She also receives $4.25 per hour. Angie worked 40 hours this week and assembled 42 toys. Find Angie's gross pay for this week. $170 $ $ $ Mrs. Pearce conducted a survey in her class on the ages of famous people. The table below shows the results of her survey. Guess Actual Age Which equation could best represent the line-of-best-fit for the given data set? Page: 10

14 39. The table below shows Mary's salary each year from 1999 to Year Salary 1999 $30, $32, $34, $37, $40,000 If this trend continues, which is the best prediction of Mary's salary in 2006? $42,000 $44,000 $48,000 $60, A tanning club advertises a membership plan in which each member pays a flat fee of $30 to join and $7 per visit to use the spa. The scatter plot below shows the cost for a number of visits by a member. 41. Sean partially filled a container with water. The container was shaped like a box and had dimensions 9 inches long, 8 inches wide, and 10 inches high. If w represents the height of the water (in inches), and the volume V (in cubic inches) of the water is given by the formula V = 72w, which quantity is the independent variable? The height of the container The volume of the container The height of the water in the container The volume of the water in the container 42. Jared filled up his 20-gallon gas tank just before taking a 250-mile road trip. He did not stop for gas during his trip. The table below shows how much gas he had left in the tank after each 50 miles driven on his road trip. Miles driven Gallons of gas left Based on the data in the scatter plot, how much will a member pay on his or her 30th visit? $200 $210 $240 $275 Which is a possible formula for the number of gallons of gas, g, left in the tank after Jared had driven m miles on his road trip? Page: 11

15 43. Rachel bought a new refrigerator last year. The graph below represents the total cost Rachel will spend for electricity usage per year plus the original cost of the refrigerator. 44. Which of these graphs could generate this table of values? x y Which of these descriptions best describes the graph? Electricity to run the refrigerator costs $1,060 per year. The refrigerator originally costs $60 and $1,000 per year to run. The refrigerator originally costs $1,000 and $60 per year to run. The refrigerator originally costs $1,000 and $120 per year to run. Page: 12

16 45. Shirley rides her bike at an average speed of 12 miles per hour. The linear function represents the distance, d, in miles, that Shirley rides in a certain length of time, t, in hours. Which of the following best represents the graph of this function? 46. The city of Houston had a sales tax rate of. To calculate the cost, C, of buying a non-grocery item, Mr. Tran adds the price, p, of the item to the product of the sales tax rate and the price of the item. Which expression best represents this relationship? C = p C C = p p C = p C = p p 47. Al's Movies charges $7.00 for a membership and $1.00 per each movie rental. Beth's Videos has no membership fee and charges $2.75 per movie rental. The table below shows the movie charges for each store. Number of Movies Cost at Al's Movies Cost at Beth's Videos 0 $7.00 $ $8.00 $ $9.00 $ What is the number of videos a customer would need to rent from each store for the cost to be the same? Page: 13

17 48. The graph below represents the cost in dollars for printing T-shirts. 49. The graph below shows the test grading scale Mrs. Voyles used to determine the grades on a test she gave to her students last week. Which statement can be interpreted from analyzing the graph? T-shirt sales are up this year. The cost for printing T-shirts is increasing. The cost per T-shirt is $5, not including set-up fee. The cost per T-shirt is $10, not including set-up fee. What grade would a student make if six problems were answered incorrectly? The owner of a limousine service charges a flat fee of $75 dollars plus an additional charge of $20 per hour to rent a limousine. She uses the equation below to determine C, the total charge to rent a limousine for any number of full hours, h. C = h What is the greatest number of full hours that Kenneth can rent a limousine from this limousine service if he has $150 to spend? Page: 14

18 51. An electrician charges a fixed rate plus an hourly labor charge for a service call. The graph below shows the amount of money an electrician earns based on the number of hours spent on a job. 53. The graph shows the cost of buying snow cones as a function of the number of snow cones sold. What is the range of the function? Based on the graph, what is the amount of the fixed rate? $35 $40 $210 $ Master Plummer charges $30 per hour plus a service charge. If Carl paid $155 for a job and the plumber worked 4 hours, what was the service charge? $25.00 $35.00 $39.85 $ {0, 1, 2, 3, 4, 5, 6} {0, 0.75, 1.50, 2.25, 3.00, 3.75, 4.50} { } { } 54. Eric earns $7.50 per hour working at a grocery store. The total amount of money he earns on a given day is a function of how many hours he works that day. If he typically works between one and five hours each day, which is the reasonable range for this function? {$3.25, $10.75, $18.75, $25.75, $33.25} {$3.25, $10.75, $18.75, $25.75, $33.25, $40.75} {$7.50, $15.00, $22.50, $30,00, $37.50} {$7.50, $15.00, $22.50, $30.00, $37.50, $45.00} Page: 15

19 55. Carlene sells magazine subscriptions door-to-door. She receives $4 for each subscription sold. The greatest number of subscriptions that she has sold in one hour of working is five. Which of the following is a reasonable range of her hourly earnings? {$0, $1, $2, $3, $4} {$0, $1, $2, $3, $4, $5} {$0, $4, $8, $12, $16} {$0, $4, $8, $12, $16, $20} 56. Which table contains values for x and y that satisfy the equation? 57. The table below lists corresponding x and y values of a linear function. x y Which equation best represents this function? 58. Which equation best represents the graph below? Page: 16

20 59. The table below shows corresponding x and y values. x y Which equation best represents the relationship in this table? 60. Max earns $8 per hour working at his dad's automotive shop. He is saving his earnings to buy a car stereo system that costs $240. Which of these graphs best represents the number of hours Max needs to work in order to buy the car stereo system? 5x + 2x = 24 5x + 2y = 12 5x + 2y = 24 5y + 2x = 12 Page: 17

21 61. The graph of y = 2x 2 is shown below. Which of the following represents the graph of y = -2x 2? 62. What type of parent function is represented in the table of values shown below? x y Quadratic Linear Exponential Absolute Value 63. Which equation is the parent function of y = 3x + 5? y = x y = x² y = x 64. Which of the following situations is an example of a linear function? the area of a circle with respect to its radius the amount of money an hourly employee will make with respect to hours worked the amount of interest paid on a loan that is compounded monthly with respect to the number of months the volume of a cylindrical can for a given height with respect to its radius Page: 18

22 65. Which of the following represents a linear function? 68. What is the slope of the line on this graph? 66. Which set of ordered pairs satisfies the function? {(-1, -12), (0, -10), (1, -8), (2, -6)} {(-2, 6), (-1, 8), (0, 10), (1, 12)} {(-1, 12), (0, 10), (1, 8), (2, 6)} {(-2, -6), (-1, -8), (0, -10), (1, -12)} A positive number greater than 1 A positive number less than 1 A negative number greater than -1 A negative number less than What is the slope of the line that passes through the points M (-3, 5) and N (1, 8)? 67. Which of the following situations can be represented by a linear function? The volume of helium, h, in a balloon with diameter d The number of miles, m, a jogger can run at a constant rate for t minutes The heights, h, of n students in a physical education class The population, P, of bacteria in a culture dish for d days Page: 19

23 70. What is the slope of the line perpendicular to the line in the graph below? 71. What is the slope of the line defined by the equation? Alyssa's carpet cleaning service charges an initial fee of $45, plus $5 for every 100 square feet of carpet cleaned. Alyssa graphed y, the amount that her cleaning service charges, as a function of x, the number of square feet of carpet cleaned. What does the y-intercept of Alyssa's graph represent? The charge per square foot of carpet cleaned The number of square feet of carpet cleaned The total amount owed The initial fee Page: 20

24 73. The point-slope form of an equation of a line is represented by y - y 1 = m(x - x 1 ). Which of these could be used to determine the slope? 76. This is the graph of the equation y = x. Which of these graphs could represent the equation y = x - 3? 74. What is the effect of changing to? The x-intercept stays the same, while the y-intercept goes up 3. The y-intercept stays the same, and the x-intercept goes up 3. The x- and y-intercepts both increase. The x-intercept decreases, while the y-intercept increases. 75. Compare the graphs of these two equations: What translation would map the first equation onto the second equation? Shift 4 units up Shift 4 units down Shift 11 units up Shift 11 units down Page: 21

25 77. A linear function is graphed below. 78. The graph of the function shown below. is What is the equation of this line when it is translated 4 units down? What is the equation of a line perpendicular to? Page: 22

26 79. Look at the two equations written below. Which statement is true about the graphs of and? The graph of is parallel to. The graphs of and intersect at (0, 4). The graph of is perpendicular to. The graph of has a smaller slope than. 80. What is the equation of a line that has a slope of 2 and passes through point (-6, 3)? y = 2x + 15 y = 2x + 9 y = -3x + 9 y = -6x Given that a line has a y intercept of 3 and an x intercept of 4, write an equation for the line. y = 3x + 4 y = 4x John has $50 in his savings account. If he deposits $5 a week without making any withdrawals, he will have $100 in ten weeks. An equation for this situation would be $100 = $5(10) + $50, where the $5 represents the slope and the $50 represents the y-intercept. If John were to start his savings with $30 instead of $50 and the weekly deposits stay the same, what effect would it have on the length of time it would take to reach $100 in savings? It would take four fewer weeks to reach $100. It would take four more weeks to reach $100. It would take the same number of weeks to reach $100. It would take two more weeks to reach $ If a function is increasing at a rate of and the points (0,2) and (3,4) are both on the graph of f(x). what will be the y value when x is 3 if the rate is changed to and the point (0,2) remains on the new line. The y value will remain the same The y value will change to 7 The y value will change to 6 None of these Page: 23

27 84. A business is manufacturing computers at 2x a day. If the output increases to x per day, what will happen to the graph of the function? The slope becomes steeper The slope becomes less steep There will be no change 87. Which of the following sets of ordered pairs lie on a function that is a direct proportion (y is directly proportional to x)? (2,6) (4,8) (6,10) (8,12) (2,2) (4,2) (6,2) (8,2) (2,1) (4,3) (6,5) (8,7) (2,3) (4,6) (6,9) (8,12) The y intercept will move to 85. A linear function with a slope of represents the path taken by a hiker. The hiker starts on the path at coordinates (0,2). When he stops he finds that his horizontal change is 6. What must his vertical change be? An American paid 5 US dollars for 1½ units of a foreign currency. How many units of the foreign currency will she get for 1500 US dollars? Page: 24

28 88. Math Models Second Nine Weeks The graph below represents the parent function y = x The graph of the equation is shown below. Which graph best illustrates the graph of the equation? Changing this equation to result in a graph that is wider narrower shifted up shifted down will 90. The shape of the graph of the equation changes as the values of a changes. What is the general shape if a < 0? Opens upward Opens downward Opens to right Opens to left Page: 25

29 91. The table below represents the values of x and y for a function of the form y = ax 2. x -3-1 y Which of these represents the value of a for the function? 93. Which of the following describes the translation of the graph of the equation to the graph of the equation The graph is shifted 2 units to the right. The graph is shifted 2 units up. The graph is shifted 5 units down. The graph is shifted 1 unit to the left. 94. A ball is dropped from the top of a building that is 220 feet high. The function represents the distance, d, the ball is from the ground after t seconds. The graph of the function is shown below Which of the following equations represents the graph shifted down 5 units? Which of the following statements can be determined from the graph? It takes the ball about five seconds to reach the ground. After two seconds, the ball is halfway to the ground. After 2.5 seconds, the ball is 100 feet from the top of the building. After 2.5 seconds, the ball is 100 feet from the ground. Page: 26

30 95. Which of the following best describes the changes in the graph of equation is changed to? when the The graph is wider. The graph opens downward. The graph is narrower and opens downward. The graph is wider and opens downward. 96. The graph below shows the profit for Rick's Running Shoe Company. 97. Toni drew the graph of on a coordinate plane. She then translated the graph 5 units up. Which of these ordered pairs will Toni's second graph pass through? (2, 9) (3, 4) (3, 9) (8, 9) 98. For precisely which values of the constant c does the graph of contain two x-intercepts? 99. The graph below represents the function. How many shoes should Rick's Running Shoe Company produce in order to have a maximum profit? 5,000 15,000 25,000 30,000 If the function is transformed into the function, which translation would best describe the transformation of the graph? A shift to the left of 5 units A shift to the left of 2 units A shift down of 2 units A shift down of 5 units Page: 27

31 100. The graph below shows the height of a tennis ball from the time it is thrown straight up to the time it hits the ground. Math Models Second Nine Weeks How many seconds after the tennis ball is thrown straight up did it reach a height of 160 feet? 2 seconds 2.5 seconds 3 seconds 3.5 seconds Page: 28 STOP

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36 Catpin Bubble Test Generator Page 1 of 1 12/7/2009 Math Models Second Nine Weeks Name: Date: Teacher: Mrs. Carlile Room: