1. (1.1) Examine the dotplots below from three sets of data. 0 2 4 6 8 10 Set A 0 2 4 6 8 10 Set 0 2 4 6 8 10 Set C The mean of each set is 5. The standard deviations of the sets are 1.3, 2.0, and 2.9. Match each data set with its standard deviation. Set A: 1.3 Set B: 2.0 Set C: 2.9 Set A: 2.0 Set B: 1.3 Set C: 2.9 Set A: 2.0 Set B: 2.9 Set C: 1.3 Set A: 2.9 Set B: 1.3 Set C: 2.0 2015 2016 Page 1 of 38 Revised September 2015
Frequency of Test Scores ALGEBRA I 2. (1.2) Mrs. Johnson created this histogram of her 3 rd period students test scores. 8 6 4 2 50 60 70 80 90 100 Test Scores Which boxplot represents the same information as the histogram? 50 60 70 80 90 100 Test Scores 50 60 70 80 90 100 Test Scores 50 60 70 80 90 100 Test Scores 50 60 70 80 90 100 Test Scores 2015 2016 Page 2 of 38 Revised September 2015
Frequency ALGEBRA I 3. (1.2) This graph shows annual salaries (in thousands of dollars) for all workers in a certain city. 35 30 25 20 15 10 5 0 50 100 150 200 250 300 350 Salary The median salary is $80,500. Which value is the best approximation for the mean? $66,500 $80,500 $94,500 For questions 4 and 5, use the following scenario. A survey was made of high-school-aged students owning cell phones with text messaging. The survey asked how many text messages each student sends and receives per day. Some results are shown in the table below. Number of text messages sent/received per day among teens who text Group Number Surveyed Mean Median Girls, 14 17 years old 270 187 100 Boys, 14 17 years old 282 176 50 Total 552 4. (1.2) A histogram of the girls responses (not shown) has a strong right skew. Which statement would support that observation? The number of girls surveyed is greater than the mean number of texts sent by girls. The mean number of texts sent by girls is greater than the median number of texts sent by girls. The mean number of texts sent by girls is greater than the mean number of texts sent by boys. The median number of texts sent by girls is greater than the median number of texts sent by boys. 2015 2016 Page 3 of 38 Revised September 2015
5. (1.2) Which expression shows the mean number of text messages for all girls and boys, 14 17 years old? 187 176 2 187 176 552 270187 282176 552 It cannot be computed from the information given. 6. (1.2) Which group s data has the larger interquartile range? Boys Girls Neither, they are equal. It cannot be computed from the information given. 7. (1.2) A data set has 4 values: {1, 5, 6, 8}. The mean of the data set is 5. Which expression shows the computation of the standard deviation? 1 5 6 8 3 1 25 36 64 3 4 0 1 3 3 16 0 1 9 3 2015 2016 Page 4 of 38 Revised September 2015
8. (1.2) Use the scatterplot below. 30 y 25 20 15 10 5 10 12 14 16 18 20 x A linear model is fit to the data. What is the approximate value of its correlation coefficient? r = 0.8 r = 1.0 r = 0.8 r = 1.0 For questions 9-12, use the boxplots of two data sets, P and Q, below. Set P Set Q 0 20 40 60 80 100 120 140 9. (1.3) Which data set has the larger median? Set P Set Q Neither, the medians are the same. 2015 2016 Page 5 of 38 Revised September 2015
10. (1.3) Which data set has the larger interquartile range? Set P Set Q Neither, the interquartile ranges are the same. 11. (1.3) Which data set could be described as skewed left? Set P only Set Q only Both sets Neither set 12. (1.3) Which data set has values that are considered outliers? Set P only Set Q only Both sets Neither set 13. (1.3) The distributions of two classes final exam scores are shown below. Mr. Smith Mrs. Jones Final Exam Scores Which statement about the box-and-whisker plots is true? 50% of the scores for Mr. Smith s class are between 65 and 80. 50% of the scores for Mrs. Jones class are between 80 and 100. The median scores for the two classes are the same. The interquartile range of scores for Mr. Smith s class is greater than the interquartile range of the scores for Mrs. Jones class. 2015 2016 Page 6 of 38 Revised September 2015
For questions 14-16, use the following scenario. A survey asked 100 students whether or not they like two sports: soccer and tennis. The results of the survey are shown in the table. Likes Tennis Likes Soccer Yes No Yes 12 18 No 48 22 14. (1.4) What is the relative frequency of students who like tennis, soccer, or both? 0.12 0.66 0.78 0.90 15. (1.4) What is the relative frequency of students who like tennis? 0.12 0.18 0.25 0.30 16. (1.4) What is the relative frequency of students who like both tennis and soccer? 0.12 0.30 0.60 0.78 2015 2016 Page 7 of 38 Revised September 2015
17. (1.4) A high school principal randomly surveyed students about a change in the dress code. The results are shown in the table. Favors the change Class Freshmen Sophomores Juniors Yes 56 38 32 No 24 37 58 a) What percentage of all respondents favors the policy change? b) Which class has the highest favorable percentage? Which class has the lowest favorable percentage? c) Is there a relationship between class and favoring the dress code change? Explain. 18. (2.2) Use the diagram below. 9.3 cm 6.2 cm A rectangle s sides are measured to be 6.2 cm and 9.3 cm. What is the rectangle s area rounded to the correct number of significant digits? 57.66 cm 2 57.7 cm 2 58 cm 2 60 cm 2 19. (2.3) In the formula F I at, F and I are measured in meters per second and t is measured in seconds. In what units is a measured? meters seconds meters per second meters per second squared 2015 2016 Page 8 of 38 Revised September 2015
20. (2.5) What are the coefficients in the expression 3x 4y +2? 3x, 4y, and 2 3 and 4 2 x and y 21. (2.6) An athlete works out each day for 60 minutes, of which t minutes is spent running at 0.20 mi mi, and the rest of the time is spent walking at 0.05. Which expression represents the total min min distance the athlete travels in miles while working out each day? 0.25 60 For questions 22 and 23, use the solution to the equation 2x 3 = 11 below. Start: 2x 3 = 11 Step 1: 2x 3 + 3 = 11 + 3 Step 2: 2x = 14 1 1 2 2 Step 3: 2x 14 0.25t 60 t 0.20t0.05 60 t 0.200.05 t60 t Step 4: x = 7 22. (2.7) In Step 1, the addition property of equality was applied. True False 23. (2.7) In Step 3, the symmetric property of equality was applied. True False 2015 2016 Page 9 of 38 Revised September 2015
24. (2.8) Let the price of a meal at a restaurant be p. The tax and tip on the meal are generally a percentage of the meal s price. The total cost of the meal is its price plus tax plus tip. (a) Write an expression for the total cost of a meal where the tax is 8% and the tip is 15%. (b) Write an expression for the total cost of a meal where the tax is x% and the tip is g%. (c) David calculates a 15% tip by dividing the meal price by 10, dividing that number by 2, p 10 and then adding the two numbers, i.e. tip p. Explain whether or not this 10 2 method is correct. 25. (2.9) Tim was asked to solve the equation kx my mx for x. His solution is shown below. Start: Step 1: Step 2: Step 3: kx my mx kx mx my x k m my my x k m In which step did Tim make his first mistake when solving the equation? Step 1 Step 2 Step 3 Tim did not make a mistake. 2015 2016 Page 10 of 38 Revised September 2015
26. (2.9) The potential energy P of an object relative to the ground is equal to the product of its mass m, the acceleration due to gravity g, and its height above the ground h is represented in the equation P = mgh. Solve the formula for height h. P h mg mg h P h = Pmg h = P mg xf x0 27. (2.9) In the formula v, x f and x 0 are both measured in feet and t is measured in seconds. t (a) (b) In what units is v measured? Let x 0 = 3,300 ft. Convert x 0 to miles. (1 mile = 5280 feet) (c) Solve the formula for x f. 28. (3.4) An internet business sells U.S. flags for $16.95 each, plus $2.50 shipping per flag. Shipping is free, however, on orders where more than $100.00 of flags are purchased. Which correctly shows the number of flags f that must be purchased to get free shipping? 16.95 f 100 16.95 f 100 19.45 f 100 16.95 f 2.50 100 29. (3.5) Solve each absolute value equation. 87. Solve each absolute value equation. (a) x + 6 = 21 (b) 18 = 3 x - 1 (c) 3 y + 4= 31 (d) x - 3 + 14 = 5 2015 2016 Page 11 of 38 Revised September 2015
30. (3.7) Some fire extinguishers contain pressurized water. The water pressure should be 162.5 psi (pounds per square inch), but it is acceptable for the pressure to differ from this value by at most 12.5 psi. Write and solve an absolute-value inequality to find the range of acceptable pressures. p - 12.5 162.5 31. (4.2) Given f x x. What is f 4? 18 54-150.0 p 175.0 p - 12.5 162.5 20x 2 20x 8 32. (4.2) Kathy has two sets of numbers, A and B. The sets are defined as follows: A = {1, 2, 3} p - 150.0 or p ³ 175.0 p - 162.5 12.5 p 150.0 or p ³ 175.0 p - 162.5 12.5 150.0 p 175.0 5 2 B = {10, 20, 30} Kathy created four relations using elements from Set A for the domains and elements from Set B for the ranges. Which of Kathy s relations is NOT a function? {(1, 10), (1, 20), (1, 30)} {(1, 10), (2, 10), (3, 10)} {(1, 10), (2, 20), (3, 30)} {(1, 10), (2, 30), (3, 20)} 2015 2016 Page 12 of 38 Revised September 2015
33. (4.3) Justin plans to spend $20 on sports cards. Regular cards cost $3.50 per pack and foil cards cost $4.50 per pack. Which inequality shows the relationship between the number of packs of regular cards (r) and the number of packs of foil cards (f) Justin can afford to buy? 3.5 f 4.5r20 3.5r4.5 f 20 3.5 f 4.5r20 3.5r4.5 f 20 34. (4.3) The exchange rate for U.S. Dollars to Euros is $1.50 = 1 Euro. At a bank, there is a flat $20.00 service fee to exchange dollars for Euros. Which graph shows how many Euros E would be received if an amount D in U.S. Dollars were exchanged at the bank? 2015 2016 Page 13 of 38 Revised September 2015
35. (4.3) Lana is buying balloons for a party. Small balloons cost 30 cents each; large balloons cost 80 cents each. Lana has $3.00 to spend on balloons. The number of large balloons L she can buy as a function of the number of small balloons S bought 300 30S is given by LS. What are the domain and range of this function? 80 domain: all real numbers range: all real numbers domain: all real numbers, where 0 S 10 range: all real numbers, where 0 L 3.75 domain: all positive integers range: all positive integers domain: all integers, where 0 S 10 range: all integers, where 0 L 3 36. (4.3) To fix a clogged pipe, Dripmaster Plumbing charges $75 plus $40 per hour. NoClog Plumbers charges $50 plus $70 per hour for the same service. Which function shows the difference in charges between the two companies for a repair taking h hours? Difference = $20 $35h Difference = $25 $30h Difference = $25 $110h 37. (4.3) Steve borrows $4,800 from his parents to purchase a used car. No interest is charged on the loan and Steve will pay his parents $150 per month until the loan is paid off. (a) Write a function that describes the relationship between the amount Steve owes his parents and the number of months since the loan was made. (b) What are the domain and range of the function in part (a)? What do these represent in context of the situation? (c) Graph the function in part (a), identify important points, and explain why they are important. 2015 2016 Page 14 of 38 Revised September 2015
38. (4.3) Explain why the relation y = x 2 is a function even though x = 2 and x = 2 both produce y = 4. 39. (4.6) The first five terms of a sequence are given. 14 17 20 23 26 Which equation describes the n th term of the sequence? f ( n) 311n f ( n) 113n f ( n) 14 17n f ( n) 17 3n 40. (4.6) What are the first five terms of the sequence defined as a(1) = 3 a(n + 1) = a(n) 4, for n 1? 3, 2, 1, 0, 1 1, 5, 9, 13, 17 3, 1, 5, 9, 13 3, 1, 0, 1, 2 41. (4.6) Let g(x) = 2x 6. Which expression represents g(2x)? x 3 2x 12 4x 12 4x 6 2015 2016 Page 15 of 38 Revised September 2015
42. (4.6) A sequence t is defined as t n n, where n 1. Which is an equivalent recursive definition for sequence t? 0.57 0.06 t 1 0.57; t n 1 t n 0.06, for n 1 t 1 0.51; t n 1 t n 0.06, for n 1 t 1 0.57; t n 1 t n 0.51, for n 1 t 1 0.51; t n 1 t n 0.51, for n 1 43. (4.6) The graph shows the first five terms of an arithmetic sequence whose domain is the positive integers. Which is a definition of the sequence? 8 t n n 82 t n 10 t n n n 10 2 t n n 2015 2016 Page 16 of 38 Revised September 2015
44. (4.6) A sequence t is defined where the first term is 4. Each successive term is 3 more than the term before it. (a) Write an explicit formula for the sequence t. (b) A second function is defined as s(n) = 2 + 2n. Compare the rates of change of t(n) and s(n). (c) For what value(s) of n does t(n) = s(n)? Show your work. 45. (4.7) Sam is beginning an exercise program that begins the first week with 30 minutes of daily exercise. Each week, daily exercise is increased by 5 minutes. Which function represents the number of minutes of daily exercise in week n? f (1) 30; f ( n) 30n, for n 2 f (1) 30; f ( n) 5n 30, for n 2 f (1) 30; f ( n) f ( n 1) 5, for n 2 f (1) 30; f ( n) 5 f ( n 1), for n 2 For questions 46 and 47, use the table. x 3 5 8 12 17 y 12 16 22 30 40 46. (5.1) The ordered pairs (x, y) form a linear function. True False 47. (5.1) The value of y changes by increasingly larger amounts for each change of 1 in x. True False 2015 2016 Page 17 of 38 Revised September 2015
48. (5.2) What are the intercepts of the line with equation 2x 3y = 30? ( 10, 0) and (0, 15) (6, 0) and (0, 6) (15, 0) and (0, 10) (30, 0) and (0, 30) 49. (5.3) Use the table below. x f(x) 3 10 6 14 9 18 12 22 What is the slope of y = f(x)? 4 4 3 10 3 22 12 2015 2016 Page 18 of 38 Revised September 2015
50. (5.3) Which is the graph of y = 2x + 1? 2015 2016 Page 19 of 38 Revised September 2015
51. (5.3) This graph shows three lines named a, b, and c. a b c 1 Which ratio of the lines slopes equals? 2 slope of line a slope of line b slope of line a slope of line c slope of line b slope of line a slope of line c slope of line b 2015 2016 Page 20 of 38 Revised September 2015
52. (5.3) Use the graph. What is the slope of the line? 3 5 5 3 3 5 5 3 2015 2016 Page 21 of 38 Revised September 2015
For questions 53 and 54, use this graph that helps convert temperatures from degrees Fahrenheit to degrees Celsius. C Three important temperatures are shown on the graph: 40 F = 40 C, 32 F = 0 C, and 212 F = 100 C. 53. (5.3) A temperature increase of 9 F corresponds to an increase of 5 C. F True False 54. (5.3) The slope of the line is 1.8 F. C True False 55. (5.4) When the function f = k + ac is graphed on the axes shown, what quantity corresponds to the intercept on the vertical axis? f f k f k f k a c 2015 2016 Page 22 of 38 Revised September 2015
2 56. (5.4) A line is defined by the equation y x3. Which ordered pair does NOT represent a point 5 on the line? ( 5, 0) (0, 3) 17 (1, ) 5 (5, 5) 57. (5.4) A certain child s weight was measured at 16.6 pounds. The child then gained weight at a rate pounds of 0.65 pounds per month. On a graph of weight versus time, what would 0.65 represent? month The y-intercept of the graph The x-intercept of the graph The slope of the graph 58. (5.5) Which is the graph of 2x 3y < 12? 2015 2016 Page 23 of 38 Revised September 2015
59. (5.5) Use the graph. Which inequality is represented in the graph? x 1 x 1 y 1 y 1 x For questions 60-62, use the inequality y 1. 2 60. (5.5) (0, 1) is a solution of the inequality. True False 61. (5.5) (1, 2) is a solution of the inequality. True False 62. (5.5) (2, 0) is a solution of the inequality. True False 2015 2016 Page 24 of 38 Revised September 2015
63. (5.5) What is the equation of the horizontal line through the point (4, 7)? x = 4 x = 7 y = 4 y = 7 64. (5.6) Use the graph. y y = f(x) y = h(x) y = g(x) x If f x g x and g x h x, what is f x g x? 1 1 3 0 3 4 2 2 1 2 2015 2016 Page 25 of 38 Revised September 2015
65. (5.6) The graph shows a line segment. P(k) (28, 30) (12, 18) Which equation best describes the line segment? k P k P k P k P k 3 k 9 4 3 k 18 4 4 k 2 3 4 k 12 3 66. (5.7) What is the equation of the line that passes through the points (5, 1) and (4, 5)? y5 4 x 4 y 5 4 x 4 1 y5 x 4 4 1 y 5 x 4 4 2015 2016 Page 26 of 38 Revised September 2015
total cost ($) ALGEBRA I For questions 67-69, use the scenario below. A phone call using a prepaid card consists of a fixed fee to place the call plus an additional fee for each minute of the call. The cost of an n-minute phone call with a card from Company A is A(n) = $0.99 + $0.25n, where n is a positive integer. The cost of an n-minute phone call with a card from Company B is shown in the graph below. B(n) minutes used n 67. (6.1) The per minute fee for Company B is greater than Company A. True False 68. (6.1) The fixed fee for Company B is greater than Company A. True False 69. (6.1) A call using Company B will always cost more than the same length call using Company A. True False 2015 2016 Page 27 of 38 Revised September 2015
Total cost ($) ALGEBRA I 70. (6.2) An online music service charges a $25 start-up fee plus $8 per month for unlimited downloads. The graph illustrates the total cost of a membership for a given number of months. y Number of months x What would happen to the graph if the start-up fee changed from $25 to $32? The slope would increase by $7/month. The slope would decrease by $7/month. The graph would translate up $7. The graph would translate down $7. 2015 2016 Page 28 of 38 Revised September 2015
71. (6.2) The graph shows the linear function y f x. 4 y -4 4 x -4 Which graph shows y = f ( x) + 1? 4 y 4 y -4 4 x -4 4 x -4-4 4 y -4 4 x -4 2015 2016 Page 29 of 38 Revised September 2015
Foot length (cm) ALGEBRA I 72. (6.3) The scatterplot below represents the forearm lengths and foot lengths of 10 people. Forearm length (cm) Based on a linear model of the data, which is the best prediction for the length of a person s foot if his/her forearm length is 21 centimeters? 19 cm 20 cm 22 cm 24 cm 2015 2016 Page 30 of 38 Revised September 2015
73. (6.3) The line of best fit for the scatterplot below is yˆ 1.4x2.9 20 y 16 12 8 4 0 0 2 4 6 8 10 x Predict y when x = 6. 2.2 10.5 11.3 18.8 2015 2016 Page 31 of 38 Revised September 2015
74. (6.3) Which equation best describes fits the data shown in the scatterplot? y 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 x 3 y x 7 5 1 y x 8 3 yx8 y 4 2015 2016 Page 32 of 38 Revised September 2015
75. (6.3) The line of best fit for the scatterplot below is yˆ 1.4x2.9 20 y 16 12 8 4 0 0 2 4 6 8 10 x What is the residual for the point (4, 10)? 1.5 1.5 8.5 10 76. (6.3) A scatterplot is made of a city s population over time. The equation of the line of best fit is pˆ 629t150,000 where ˆp is the city s predicted population size and t is the number of years since 2000. What is the meaning of the slope of this line? In 2000, the city s population was about 629 people. In 2000, the city s population was about 150,000 people. The city s population increases by about 629 people each year. The city s population increases by about 150,000 people each year. 77. (6.3) The equation yˆ 31.4 0.12x, gives the predicted population ŷ of a city (in thousands) x years after 1975. What is meaning of the y-intercept? In 1975, the city s population was about 120 people. In 1975, the city s population was about 31,400 people. The city s population decreases by about 120 people each year. The city s population decreases by about 31,400 people each year. 2015 2016 Page 33 of 38 Revised September 2015
78. (6.3) The equation Pˆ 9.50m 509 gives the predicted price ˆP of a particular style of television m months after the style first became available. What is the meaning of the P-intercept? The original price of the television was about $9.50. The original price of the television was about $509.00. The price of the television decreases by about $9.50 each month. The price of the television increases by about $509.00 each month. 79. (6.3) The data below comes from a scatterplot. x 2 3 4 5 6 7 8 8 8 9 10 10 y 2 8 4 1 10 4 6 10 2 7 3 9 Which best describes the linear relationship between x and y? Weak or no correlation Strong positive correlation Strong negative correlation For questions 80-82, evaluate the truth of each statement about the correlation coefficient r. 80. (6.3) A value of r near zero indicates there is a weak linear relationship between x and y. True False 81. (6.3) A value of r = 0.5 indicates a weaker linear relationship between x and y than a value of r = 0.5. True False 82. (6.3) A value of r = 1 indicates that there is a cause-and-effect relationship between x and y. True False 2015 2016 Page 34 of 38 Revised September 2015
For questions 83 and 84, use the following scenario. A linear model describes the relationship between two variables, x and y. The correlation coefficient of the linear fit is r = 0.9. 83. (6.3) The slope of the line of best fit is negative. True False 84. (6.3) The linear relationship between x and y is weak. True False 2015 2016 Page 35 of 38 Revised September 2015
Frequenc y Frequency ALGEBRA I 85. (6.3) The table shows the amount of rainfall in Seattle during the month of December in the years 1980 1999. The histogram shows the distribution of rainfall in Seattle during the month of July in the same years, using intervals of 0.5 inches. July December Rainfall (inches) a) Create a histogram on the grid above that shows the distribution of rainfall in December using intervals of 1.0 inch. b) Describe the shapes of the distributions for July and December. Monthly Rainfall (inches) Year December 1980 7.4 1981 5.6 1982 6.2 1983 5.0 1984 5.0 1985 1.5 1986 6.8 1987 6.1 1988 7.5 1989 4.8 1990 3.1 1991 3.3 1992 4.1 1993 4.5 1994 8.2 1995 6.4 1996 5.2 1997 2.2 1998 9.0 1999 5.1 c) How does the mean rainfall for July compare to the median rainfall? Explain. d) Compare the median rainfalls for July and December over the period 1980 1999. e) Describe how to compute the standard deviation of the December rainfalls. (You do not have to actually compute it.) f) Which month s rainfall, July or December, has the greater standard deviation? Explain. 2015 2016 Page 36 of 38 Revised September 2015
Rainfall (inches) ALGEBRA I g) One of the rainfall amounts for July was recorded at 2.4 inches. In actuality, it was only 1.4 inches. Explain how this would affect the mean and median of July rainfall. h) On the grid below, create a scatterplot showing December monthly rainfall over the period from 1980 1999. December Year i) Describe the relationship between December rainfall and year. 2015 2016 Page 37 of 38 Revised September 2015
residuals residuals ALGEBRA I 86. (6.5) Two residual plots are shown below. Plot I x Plot II x Which residual plot(s) would indicate a linear model is appropriate? Plot I only Plot II only Both Plot I and Plot II Neither Plot I nor Plot II 2015 2016 Page 38 of 38 Revised September 2015