ACCELERATED ALGEBRA ONE SEMESTER ONE REVIEW NAME: The midterm assessment assesses the following topics. Solving Linear Systems Families of Statistics Equations Models and Matrices Functions 16% 24% 26% 12% 21% 1. Consider the equation 70 = x+y 3. Solve for y. 2 2. Circle the step in this solution where the student made a mistake in solving. Show how to correctly solve. 2 = 11w + 8 14w + +14w +14w 2 = 2w + 13 13 13 12 = 2w 2 2 12 2 = w Solve. 3x 3x 10 3. 18 = 3 4. 7 = 2. Which of the following are true about the square on the right? Circle ALL that apply. 6b a. Area = 36b 2 b. Perimeter = 12b 2 c. Perimeter = 24b d. Perimeter = 24b 4 6. The width of a rectangle is eight inches shorter than five times the length. a. Label the diagram to represent this figure. Let L = length. b. Write a variable expression for the perimeter.
Solve. 7. 2x + 4 = 3x + 16. 8. 2 = 3 + 2(p 4) Solve. 9. 2 = x + 3 + 3 10. 12 x 1 2 = 3 11. Describe the solutions to x = 1. 12. Solve. 2 < x+3 3 13. Describe the locations of the solutions to x < 0 on the number line. 14. Eight ounces of a hot beverage are poured into a ceramic mug. Every minute, the temperature of the liquid is measured. The experiment is repeated with five different beverages (coffee, tea, plain water, hot chocolate, hot cider). The results show a scatterplot whose line of best fit has a correlation coefficient of 0.7. What does this mean? Draw a scatterplot that could model the scenario and circle all correct descriptions from the list below. a. There is a not a relationship between time and temperature. b. As the number of minutes increases, the temperature decreases. c. As the number of minutes increases, the temperature increases d. The line of best fit is a decreasing line. e. The line of best fit is an increasing line.
1. Pete s Plumbing charges $48 to come to your house and diagnose the problem, and eighty dollars per hour to do the repair. Christina recently hired Pete s Plumbing to do some work on her sink. Her bill was $408. a. Write an equation to model this scenario. Let H = the number of hours worked. b. What is the rate of change for this scenario including units? c. How many hours did the plumber work? d. If this relationship were graphed, what would be the y intercept? What does the y intercept mean in the context of this scenario? 16. A hot air balloon takes off at 9:00 am. It rises according to the values shown in the table. a. Write a function to model the relationship between the minutes since take off and the height above the ground. Let y = height above the ground and let x = number of minutes. time (mins) height (ft) 30 10 60 20 120 b. At what time will the balloon be 72 feet above the ground? 17. The table shows the relationship between time after take off and altitude above the runway for a plane. A second plane rises according to the equation A = 64t. Is the second plane rising more slowly seconds 30 60 90 120 10 or more quickly than the first plane in part A? after take-off How do you know? feet above 1680 3360 040 6720 8400 runway
temperature 18. The scatter plot at the right shows the temperature in an oven over time as it preheats. The oven will stop heating when it reaches 30. Let m = minutes Let T = temperature a. Write the equation for the line of fit for the increasing portion of the graph. (10 min, 30 ) (2 min, 126 ) b. Identify the range for the increasing portion of the graph 70 minutes c. Write an equation for an oven whose temperature increases more slowly while preheating. 19. A certain SUV holds 20 gallons of gas when the gas tank is full. The equation that models the relationship between number of gallons of gas in the tank and number of miles that can be driven is G = 1 m + 20. Let m = number of miles driven. Let G = number of gallons 22 in the tank. a. What is the domain of this scenario? (0, 20) b. What is the range of this scenario? c. What does the coefficient 1 mean in the 22 context of the scenario/ (440, 0) d. How many miles can be driven when there is one quarter tank of gas left in the car?
20. Your neighborhood has just been dumped on with snow! You decide to help out your closest 12 neighbors and shovel their driveways. You know that you can shovel 3 driveways every two hours. a. Write an equation to represent the relationship between number of driveways still to be shoveled and time. Let x = hours and y = # of driveways left to shovel. b. What is the domain of this scenario? c. What is the range of this scenario? d. If you start shoveling driveways at 10 am, at what time will you have all the driveways shoveled? 21. a. Write the equation of the line that passes through the points (7, 4) and (7, 1) and identify its slope. b. Write the equation of a line parallel to the equation in part a. c. Write the equation of a line perpendicular to the equation in part b. 22. Write the equation of a line through (2, ) perpendicular to y = 1 x 4. 3 23. Write the equation of a line through (6, ) parallel to y = 1 x 4. 3 24. Are the equations 2y 4x = 3 and y = 2x parallel, perpendicular or neither? Explain your reasoning.
2. Explain and demonstrate how to graph 4y + 3x = 24 y x intercept: y intercept: x 26. The equation 2x + 0y < 200 represents a budget for back to school clothes shopping. Let x = # of shirts purchased and y = # of pairs of jeans purchased. a. How much money do you have to spend? How much do shirts cost? How much do jeans cost? b. If this scenario were graphed, what is the x intercept? What does this mean in terms of the scenario? c. How many shirts could you purchase if you buy 3 pairs of jeans? d. Identify the domain of this scenario. e. Sketch a graph of this scenario. Label the axes. 27. Solve the following system by elimination. 2m + n = 1, 3m + 3n = 1 28. Solve the following system of equations by graphing. x + y = 3, y = 2x + 6 y x
29. Solve the following system of equations by substitution. y = x + 4, 4x 3y = 10 30. Solve the following system of equations using the method of your choice. 4x + 2y = 8, y = 2x + 4 31. Find the value of y for which the two functions will be equivalent. f(x) = 2x + 6, g(x) = 4x 12 32. Given the following system of equations, circle ALL answers that apply. y = x 2 and 2y 6 = 2x a. parallel lines b. lines intersect once c. lines never intersect d. same line e. lines intersect more than once f. lines have the same slope
For the next seven questions, use the matrices below. P = [ 0 14 2 21 ] Q = [1 2 0 4 ] R = [ 1 1 2 0 1] S = [ 3 4 1 4 14 1 2 0 ] T = [ 11 7 0 2 ] U= [3 6 3 8 4 9 ] 2 4 V = [ 1 0 ] 3 1 33. What is the first row of T V? a. [ 9 6 8] b. [ 7 7 4] c. [ 9 2] d. not possible 34. What is the first row of 4Q P? a. [4 2] b. [4 22] c. [4 6] not possible 3. What is the first row of UV? a. [2 21] b. [0 14] c. [22 36 24] d. not possible 36. What is the inverse of matrix R? a. [P] b. [S] c. [Q] d. not possible 37. What are the dimensions of VT? a. 2 3 b. 3 3 c. 3 2 d. 2 2 38. Explain why the product [T][P] is impossible. 39. What is the product of [P] [P] 1? 40. Write a matrix equation for the given systems of equations. 3x 2y 4z = 2 3y 4z = -2 2y + 6z = -1
41. Model the scenario Water must be at least 212 F to be a vapor as an inequality and a graph. Let t = temperature of the water. 42. Write a scenario that could be modeled with the graph shown at right. 70 43. Kevin is buying new clothes. The inequality 7x + 3y 300 models his shopping budget, where x = # of pairs of pants and y = # of shirts. Which of the following are true? Circle all correct choices. A. Kevin buys 110 items. B. Kevin can purchase 1 t shirts. C. Kevin will spend at least $300. D. Kevin will spend no more than $300. E. Kevin could buy two pairs of pants and three t shirts. 44. Tricia is hiring a landscaping contractor to install flower beds at her home. The company charges $00 to build the flower beds and $ per plant for installation. Tricia will spend no more than $800 on her landscaping. Write an inequality to represent how much Tricia can spend on her landscaping. Let p = # of plants. Solve and graph the solution on a number line. Show your work. 4. 28n + 6 12n + 10 Graph each inequality or system of inequalities for the next three questions. Tell whether the point (0, 0) is part of the solution region and EXPLAIN how you know. 46. 2y + 4x 8 47. y > 2 48. y > 1 3 x + 2 y y < x < 3 y x x x - - - - - -
cups of lemonade 49. Mrs. Warfield s children plan on selling lemonade and brownies at their garage sale this summer. They will sell lemonade for $1 per cup and brownies for $2 each. a. Based on the graph, how much do the children want to earn? b. In previous years they have never sold more than 7 brownies. If this is true again, how many cups of lemonade do they need to sell to meet or exceed their goal? # of brownies Let g(x) = x 2 x + 2. Find the following. 0. g( 3) 1. g(a) Find f(a + 4) for the following functions. 2. f(x) = 3a 3 3. f(x) = 10 a 4. Consider two functions: f(x) = x + 7 and g(x) = 1 2 x + 4. Find the point where f(x) and g(x) are equal.. If h(x) = 3x, find x if h(x) = 27. 6. If p(t) = 4t, find t if p(t) = 27. 3x -27
7. What is the family name for diagram D? A. B. 8. What is the shape name for diagram G? 9. Which diagram shows an exponential function? C. D. 60. Which diagrams shows an absolute value function? 61. Which diagram has the parent function f(x) = x 2? 62. Which diagram has the parent function f(x) = x? E. F. 63. Which diagram shows a constant function? G. H. The function H(t) = -x 2 + 4x + models the height of an object after it is tossed up from a platform until it lands on the ground. 64. If H(0) is the expression that tells you the height of the object before it has been thrown, how high is the platform? 6. What does H(2) mean in the context of the scenario? 66. Make a table of values for this function. When H(t) = 0 the object will be on the ground. How long will the object be in the air? t (seconds) H(t) (feet) 0 1 2
For questions 67 and 68 decide if the situation would produce a random sample? 67. Surveying people at a Thai restaurant to find their favorite food. a. No, the people surveyed would be probably more likely than others to prefer Thai food. b. No, the people surveyed would be probably more likely than others to prefer Chinese food. c. Yes, the people surveyed would be probably more likely than other to prefer Thai food. d. Yes, the general preference of the people going to a Thai restaurant can be used to produce a random sample. 68. Having a list of information on newborn babies in a hospital, selecting every 4th baby to find the average weight of the newborn babies in this hospital. a. Yes, the weights of the babies were randomly selected and represent the population of babies at this hospital b. No, the weights of all the newborn babies are not required. c. Yes, the weight of each newborn baby is either less or more than the average weight. d. No, the weight of any newborn baby is the average weight of a newborn baby. The weights of grapefruits of a certain variety are approximately normally distributed with a mean of 1 pound and a standard deviation of 0.12 pounds. 69. Sketch the normal curve for this scenario and label the mean and at least two standard deviations above and below the mean. 70. What is the probability that a randomly-selected grapefruit weighs more than 1.12 pounds? 71. In a shipment of 100 grapefruits, how many will weigh between 0.76 and 1 pound? The weights of the male and female students in a class are summarized in the following boxplots: 72. Which of the following is NOT correct? a. About 0% of the male students have weights between 10 and 18 pounds. b. About 2% of female students have weights above 128 pounds. c. The median weight of male students is about 162 pounds. d. The male students have less variability than the female students.
73. In a survey, 32% of students spent at least 1 hour per night on homework with a margin of error ± 2%. What is the range of students that spent at least 1 hour per night on homework out of 320 students? a. 96 109 students b. 102 109 students c. 96 104 students d. 99 102 students A student studying the sleeping habits of seniors at his school asked 34 randomly-selected seniors how many hours of sleep they got the previous night. The data, rounded to the nearest half-hour, is given in the table below. 8 7. 9 7. 9 6 9 7. 7 8 6. 8. 8 6. 8. 6 7 7. 7 6 8. 7 8 7 7. 7 6 7 8 7. 6 7 74. Use your calculator to find the mean and standard deviation of this data set. 7. Find the five number summary for this data set. 76. If two students who received 12 hours of sleep the previous night were added to the data set, which measure of center would be changed the most: mean or median? Why? 77. If two students who received 12 hours of sleep the previous night were added to the data set, how would the standard deviation change? Why?