Algebra I EOC Review (Part 2) NO CALCULATORS

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1 1. A Nissan 370Z holds up to 18 gallons of gasoline. If it can travel on 22 miles per gallon in the city, write an equation to model this. 2. Carol wants to make a sculpture using brass and aluminum, with the dimensions show below. The area of the aluminum section can be found using the equation A = 1 ah 1 bh. Which of the following shows 2 2 the aluminum section s area formula solved for h? A) h = 2A(a b) B) h = 2A a b C) h = A 2(a b) D) h = A(a b) 2 3. Troy s car can go 24 miles on one gallon of gasoline. However, his gas mileage can vary from this value by 2 miles per gallon depending on where he drives. Write an absolute-value equation to find the minimum and maximum gas mileage, and then solve. 4. Which of the values could be a solution that satisfies y + 2 > 5? [ ] 6 [ ] 7 [ ] 8 [ ] 0 5. Jasmine and her sister are saving to buy a laptop. Jasmine has $50 and plans to save $10 per week. Her sister has $80 and plans to save $7 per week. In how many weeks will Jasmine have more money saved than her sister? A) 2 weeks B) 4 weeks C) 10 weeks D) 11 weeks 6. David is training for a marathon. He writes down the time and distance for each training run and then records the data on a scatter plot. He has drawn a line of best fit on the scatter plot, as shown below. Which statement best expresses the meaning of the slope as a rate of change for this line of best fit? A) It represents the number of miles he will have to run to finish the marathon. B) It represents the average speed, in miles per hours, of his training runs. C) It represents the number of hours he will need to finish the marathon. D) It represents the distances, in miles, that he ran while he was training.

2 7. Given y = 1 x + 5, what does the 5 represent? 2 8. Which function models the relationship between x and f(x) shown in the table? x f(x) A) f(x) = 1 2 x B) f(x) = x 1 C) f(x) = 2x 3 D) f(x) = 4x 7 9. Joel graphed the line shown on the coordinate plane below. What is the x-coordinate of the point at which this line intersects the x-axis? 10. What is the x-intercept of the line parallel to 2x 6y = 15 and passing through (8,1)? 11. On the coordinate grid below, line l is perpendicular to AB. What is slope of line l? 12. The annual average temperature of a location depends in part on its distance from the equator. The latitude at the equator is 0. Scientists collected data from a number of location. The line of best fit for the data is y = 90 x, where x is measured in degrees latitude and y is measured in degrees Fahrenheit. What is the meaning of the constant term in this equation? A) It is the average temperature at the equator. B) It is the rate of change in temperature at the equator. C) It is the number of different locations where data were collected. D) It is the rate of decrease of 1 degree in temperature for each degree in distance from the equator.

3 13. Kristen can spend up to $50 on rock to landscape her yard. She decides to use both pebble rock and river rock. Pebble rock costs $2 per pound, and river rock costs $5 per pound. The inequality 5x + 2y 50 models the possible number of pounds of pebble rock and river rock that Kristen can purchase. Which graph represents the inequality? A) C) B) D) 14. What is the vertex of f(x)? Is it a maximum or a minimum? A) (0, 2); minimum B) (3, 5); minimum C) ( 2,0); minimum D) (8,0); maximum 15. What are the x- and y-intercept(s) of f(x)? A) x-intercept: 1 B) y-intercept: 1 C) x-intercept: 5; y-intercept: 1 D) x-inercept: 5, 1; y-intercept: 1

4 16. The manager of a coffee shop suspects that as the outside temperature decreases in the evening, the number of hot beverages she sells will increase. The manager creates a model to see whether this is true. What are the most appropriate variables for this model? A) Independent variable: number of hot beverages sold; Dependent variable: hourly outside temperature B) Independent variable: hourly outside temperature; Dependent variable: number of hot beverages sold C) Independent variable: average evening outside temperature; Dependent variable: number of hot beverages sold D) Independent variable: number of hot beverages sold; Dependent variable: average evening outside temperature 17. Determine which relation is a function. A) {(2,2), (2,3), (2,4)} B) {(5,2), ( 2,1), ( 2,0)} C) {(4,4), (1,3), (4,2)} D) {( 1,3), (2,3), (5,5)} 18. Jerome is constructing a table of values that satisfies the definition of a function. Input Output What number(s) can be placed in the empty cell so that the table of values satisfies the definition of a function? [ ] 5 [ ] 1 [ ] 0 [ ] 2 [ ] 11 [ ] What are the domain and range of the function y = f(x) as shown on the graph? A) The domain is {0.25, 0.5, 1, 2, 4, 8}, and the range is { 3, 2, 1, 0, 1, 2}. B) The domain is { 3, 2, 1, 0, 1, 2}, and the range is {0.25, 0.5, 1, 2, 4, 8}. C) The domain is all real numbers between 3 and 2, and the range is all real numbers between 0.25 and 8. D) The domain is all real numbers between 0.25 and 8, and the range is all real numbers between 3 and What are the domain and range of the function as shown on the graph?

5 21. What are the domain and range of this function as shown in the graph? 22. The linear function f(x) has the domain x 6. Which of the following does not represent an element of the range? [ ] f (2 1 2 ) [ ] f(6) [ ] f( ) [ ] f(100,000) 23. The domain of the function f(x) is the set of integers greater than 5. Which of the following values represent elements of the range of f? [ ] f(4.8) [ ] f( 2) [ ] f( 5) [ ] f(8) [ ] f ( 1 2 ) [ ] f(0) [ ] f(14) [ ] f( 18) 24. Which of the values are in the domain of the function f(x) = 6x + 11 with a range { 37, 25, 13, 1}? [ ] 1 [ ] 2 [ ] 3 [ ] 4 [ ] 5 [ ] 6 [ ] 7 [ ] A student creates a function to represent the cost of pencils available for purchase at the school store. The school charges 5 cents per pencil for up to 20 pencils. What is the domain of the function? A) All integers from 0 to 20 B) All real numbers from 0 to 20 C) All integer multiples of 5 from 5 to 100 D) All real number multiplies of 5 from 5 to The cost to manufacture x pairs of sunglasses can be represented by a function C(x). If it costs $398 to manufacture 4 pairs of sunglasses, which of the following are true? A) C(4) = B) C(398) = 4 C) C(4) = 398 D) C(99.50) = A local theater sells admission tickets for $9.00 on Thursday nights. At capacity, the theater holds 100 customers. The function M(n) = 9n represents the amount of money the theater takes in on Thursday nights, where n is the number of customers. What is the domain M(n) in this context? A) All whole numbers B) All non-negative rational numbers C) All non-negative integers that are multiples of 9 D) All non-negative integers less than or equal to 100

6 28. The growth of a population of bacteria can be modeled by an exponential function. The graph models the population of the bacteria colony P(t) as a function of the time t, in weeks, that has passed. The initial population of the bacteria colony was 500. What is the domain of the function? What does the domain represent in this context? A) The domain is the real numbers greater than 500. The domain represents the time, in weeks, that has passed. B) The domain is the real numbers greater than 500. The domain represents the population of the colony after a given number of weeks. C) The domain is the nonnegative real numbers. The domain represents the time, in weeks, that has passed. D) The domain is the nonnegative real numbers. The domain represents the population of the colony after a given number of weeks. 29. The function h(n) describes the total amount of money a movie theater receives for n tickets sold. Which domain is appropriate for the function? A) All integers B) All real numbers C) All positive integers and zero D) All positive real numbers and zero 30. The population on the graph show the population data, in millions, of the state of Florida for each decade from 1900 to The data are modeled by the function P(x) = (1.43) x, shown on the graph. What is the domain of the graph of P(x) that is shown? A) x 0 B) 1900 x 2000 C) All whole numbers D) 0 x A quadratic function is shown below. Which function has the same domain? A) f(x) = x 2 B) g(x) = x 2 C) h(x) = x 2 D) k(x) = 3 x, x 2

7 32. Kim is driving from Miami to Key West. The graph shows her distance from Key West. During what interval is Kim driving the fastest? [ ] x [ ] 33. A linear function is represented in the table shown. x y Graph a linear function that has a greater y-intercept than the function represented by the table and is perpendicular to the function y + 1 x = The table shows the height of a sassafras tree at each of two ages. What was the tree s average rate of growth during this time period? Age (years) Height (meters) A) 0.4 meters per year B) 0.5 meters per year C) 2 meters per year D) 2.5 meters per year 35. Find the average rate of change of the function f(x) = 2 x from x = 9 to x = 21. A) 3 B) C) 3 D) Given that a circle has a radius of 4 inches and then a radius of 12 inches after it has expanded. Given that the formula for a circle is A(r) = πr 2, what is the rate of change? 37. The graph shows the height h, in feet, of a football at time t, in seconds, from the moment it was kicked at ground level. Estimate the average rate of change in height from t = 1.5 seconds to t = 1.75 seconds. A) 20 feet per second B) 12 feet per second C) 12 feet per second D) 20 feet per second

8 38. Let u = x Which equation is equivalent to (x 2 + 3) = 10x in terms of u? A) u u + 51 = 0 B) u 2 10u + 51 = 0 C) u u + 21 = 0 D) u 2 10u + 21 = Monika is running around a park on a trail that is 7 miles long. The number of miles Monika has run, d, after t minutes is modeled by the equation shown. d = 1 15 t + 1 Mark is running around the same trail and starts at the same time as Monika. His speed is 3 as fast as Monika s speed, 4 and he starts a mile behind her. a. Write the equation that models Mark s run at this speed if he runs one time around the park. b. Graph the equation that models Mark s run at this speed if he runs one time around the park. c. What is the domain for Mark s equation. 40. The function f(x) is defined for only the values given in the table. Which function has the same x-intercepts as f(x)? x y A) g(x) = 2x + 2 B) h(x) = 1 x C) j(x) = x 2 + 2x 3 D) k(x) = x The graph of g(x) is shown below. The graph of g(x) can be obtained by applying horizontal and vertical shifts to the 3 parent function f(x) = x. What is g(x)? 3 A) g(x) = x B) g(x) = x C) g(x) = x D) g(x) = x 4 + 2

9 42. What must be done to the graph of f(x) = x to obtain the graph of the function g(x) = 0.5 x ? A) The graph of f(x) is shifted left 4 units, horizontally shrunk by a factor of 0.5, and shifted down 10 units. B) The graph of f(x) is shifted right 4 units, vertically shrunk by a factor of 0.5, and shifted down 10 units. C) The graph of f(x) is shifted left 4 units, vertically shrunk by a factor of 0.5, and shifted down 10 units. D) The graph of f(x) is shifted left 4 units, vertically shrunk by a factor of 0.5, and shifted up 10 units. 43. If f(x) = 5x + 2, write the new equation as y = f(x) Given f(x) = 1 x 3, write an equation that translates the function 8 units to the right Given f(x) = x 2 4x, write an equation that translates the function 2 units to the left. 46. A rectangle has side lengths (x + 4) feet and (2x + 1) feet for x > 0. Write a function that describes the area A, in square feet, in terms of x. A) A(x) = 3x + 5 B) A(x) = 6x + 10 C) A(x) = 2x 2 + 9x + 4 D) A(x) = 2x 2 + 7x The volume of a rectangular pyramid is 1 (x + 1)(x 3)(x + 8) cubic centimeters, where x + 8 is the height. If the 3 height is 20 centimeters. a. Find the dimensions of the other lengths. b. Find the volume. 48. Let f(x) = x 2 x 2 and g(x) = x 2 + x 6. Classify each function below has linear, quadratic, or neither a. f(x) + g(x) [ ] Linear [ ] Quadratic [ ] Neither b. f(x) g(x) [ ] Linear [ ] Quadratic [ ] Neither c. f(x) g(x) [ ] Linear [ ] Quadratic [ ] Neither d. f(x) g(x) [ ] Linear [ ] Quadratic [ ] Neither 49. Use the labeled dimensions of the rectangle, as shown below. a. Find the perimeter of the shaded portion. b. Find the area of the shaded portion. 50. The city of Plantation plans to build a new community park with a public swimming pool. The diagram below shows the area of the proposed swimming pool and the stone deck that will surround it. If the area of the deck region is 24 square units, find the value for x. A) x = 2 units B) x = 3 units C) x = 4 units D) x = 5 units

10 51. Charlie needs to simplify the expression below before he substitutes values for x and y. x 18 y 12 +x 9 y 8 x 3 y 4 If x 0 and y 0, which of the following is a simplified version of the expression above? A) x 9 y 5 B) x 24 y 16 C) x 6 y 3 + x 3 y 2 D) x 15 y 8 + x 6 y If x 3, which of the following shows the expression below in simplest form? 3x 2 27 x 3 A) 3(x + 3) B) 3(x 3) C) 3(x + 9) D) 3(x 9) 53. A figure shows a graph of the function f(x) in the xy-coordinate plane, with the vertex at (1,9) and the zeros at 2 and 4. The function g is defined by g(x) = 3x + 2. Which statements are true? [ ] f( 2) is greater than g( 2) [ ] f( 1) is greater than g(0) [ ] f(0) is greater than g(0) [ ] f(1) is less than g(1) [ ] f(2) is greater than g(2) 54. A manufacturer compares its income, f(x), to its expenses, g(x), for x number of units sold. What does the solution to f(x) = g(x) represent for the manufacturer? A) The number of units sold when the manufacturer had an overall loss for the year B) The number of units sold when the manufacturer had an overall profit for the year C) The number of units sold when the manufacturer s income equaled the manufacturer s expenses D) The number of units sold when the manufacturer s income and expenses were both positive values 55. The figure shows the graphs of the functions y = f(x) and y = g(x). The four indicated points all have integer coordinates. If g(x) = k f(x), what is the value of k? 56. A ball was thrown upward into the air. The height, in feet, of the ball above the ground t seconds after being thrown can be determined by the expression 16t t + 3. What is the meaning of the 3 in the expression? A) The ball takes 3 seconds to reach its maximum height. B) The ball takes 3 seconds to reach the ground. C) The ball was thrown from a height of 3 feet. D) The ball reaches a maximum height of 3 feet.

11 57. The graph below shows the height h(t) of a model rocket t seconds after it is launched from the ground at 48 feet per second. Where is the height of the rocket increasing? Where is it decreasing? A) The height of the rocket is always increasing. B) The height of the rocket is always decreasing. C) The height of the rocket is increasing when 0 < t < 3 and decreasing when 3 < t < 6. D) The height of the rocket is increasing when 3 < t < 6 and decreasing when 0 < t < Timmy and Kelli had a water balloon launcher. When launched, the water balloon s height could be modeled by the quadratic equation y = 4.9x x The graph shown below represents the water balloon s height. Which of the following is true about the water balloon? A) The water balloon reaches a height of 16 meters. B) The water balloon reaches the height of 7.85 meters twice. C) The water balloon has a maximum height of meters. D) The water balloon travels for 4.9 seconds before it hits the ground. 59. Matthew solved the quadratic equation shown. 4x 2 24x + 7 = 3 One of the steps that Matthew used to solve the equation is shown. Fill in values to complete the step and the solution. Step: 4(x [ ]) 2 = [ ] Solution: x = [ ] ± [ ]

12 60. Martha solved the quadratic equation shown. 3x 2 12x + 7 = 4 One of the steps that Martha used to solve the equation is shown. Fill in values to complete the step and the solution. Step: 3(x [ ]) 2 = [ ] Solution: x = [ ] ± [ ] 61. The production cost, C, in thousands of dollars, for a toy company to manufacture a ball is given by the model C(x) = x 0.68x 2, where x is the number of balls produced in one day, in thousands. The company wants to keep its production cost at or below $115,000. The graph shown models the situation. What is a reasonable constraint for the model. A) 2.16 x B) 2.71 x C) 2.16 x 2.71 and x D) 0 x 2.71 and x Several points are plotted on the graph. Which of the plotted points on the graph represent the zeros of the function f(x) = (x 2 + 2x 8)(x 6)? [ ] (2,0) [ ] (6,0) [ ] (0, 8) [ ] ( 4,0) [ ] ( 6,0) [ ] (0,2) [ ] (0,8)

13 63. What is the axis of symmetry of the graph of f(x) = 3x 2 6x + 6? A) x = 1 B) x = 1 C) y = 1 D) y = Sue removes the plug from a trough to drain the water inside. The volume, in gallons, in the trough after it has been unplugged can be modeled by 4t 2 32t + 63, where t is time, in minutes. Select the correct property that will give Sue the amount of time it takes the trough to drain. A) Minimum B) Maximum C) y-intercept D) Zero Select the expression(s) that will reveal the property. A) 4(0) 2 32(0) + 63 B) (2t 7)(2t 9) C) 4(t 4) 2 1 D) 4(t 8) Which of these functions describe exponential growth? [ ] f(t) = 1.25 t [ ] f(t) = 2(0.93) 0.5t [ ] f(t) = 3(1.07) 3t [ ] f(t) = 18(0.85) t [ ] f(t) = 0.5(1.05) t [ ] f(t) = 3(1.71) 5t [ ] f(t) = t [ ] f(t) = 8(1.56) 1.4t 66. Each bacterium in a petri dish splits into 2 bacteria after one day. The function b(d) = d models the number of bacteria b in the petri dish after d days. What is the initial number of bacteria in the petri dish? A) 2 B) 300 C) 600 D) The table below shows the combined estimates for Etosha National Park and the Northwestern population of elephants. Year Base Year Estimated Number of Elephants , , , ,571 The elephant population in Northwest Namibia and Etosha National Park can be predicted by the expression 2,649(1.045) t, where t is the number of years since What does the value 2,649 represent? A) The predicted increase in the number of elephants in the region each year. B) The predicted number of elephants in the region in C) The year when the elephant population is predicted to stop increasing. D) The percentage the elephant population is predicted to increase each year. 68. The function a(t) = 44,000(1.045) t models Johanna s annual earnings, a, in dollars, t years after she starts her job. Which of the following statements are true about Johanna s salary? [ ] Johanna initially earns $44,000 per year. [ ] Johanna initially earns $45,980 per year. [ ] Johanna s salary increases by 1.045% per year. [ ] Johanna s salary increases by 4.5% per year. [ ] Johanna s salary increases by 104.5% per year. 69. Mark deposits $2,400 into a bank, which is represented by the exponential function f(x) = 2,400( ) x. a. What interest rate is the bank offering? b. What would the function be if the bank increased the interest rate by 0.4%?

14 70. Sasha invests $1000 that earns 8% interest compounded annually. Which function describes the value V of the investment after t years? A) V(t) = t B) V(t) = 1000(0.08) t C) V(t) = 1000(0.92) t D) V(t) = 1000(1.08) t 71. If a brand new car is purchased for $60,000, the value of the car depreciates by 15% every year. Which function models this situation? A) f(x) = 60, x B) f(x) = 60, x C) f(x) = 60,000(0.15) x D) f(x) = 60,000(0.85) x 72. During the summer, Bill charges $1.25 to mow the lawn for the first week and plans to charge double the amount every week. Which function to models this situation? A) f(x) = 1.25(2x) B) f(x) = 1.25(2) x C) f(x) = 1.25(2) x 1 D) f(x) = x 73. A salesperson earns a monthly salary of $500 a month plus a percentage of the proceeds from the number of items he sells. Which graph could be a model of this situation? A) C) B) D) 74. The graph shows T, the temperature of water, in degrees Celsius, in a test tube after m minutes of an experiment. Match the correct terms to each box to correctly identify the type of rate of change between temperature and time on each part of the graph. zero constant quadratic exponential

15 75. If f(x) = 2 x and g(x) is a linear function, such that x = 1 and x = 3 when f(x) = g(x). Write a possible function for g(x). 76. If f(x) = 3 x + 4 and g(x) is an exponential function, such that x = 0 and x = 2 when f(x) = g(x). Write a 2 possible function for g(x). 77. Max collected data on the height of each of his 20 classmates. The box plot shown represents his data. Make a dot plot that could also represent these data. 78. Which quantities are most likely to have a cause-and-effect relationship? A) The average number of televisions per household in a country and the country s average life expectancy B) A student s grade in history class and the student s grade in math class C) The level of nutrients in soil and the rate of plant growth D) The amount of ice cream and the number of people wearing sunglasses 79. Kacey found a line of fit for a set of data and calculated that the correlation coefficient for the model is Which statement best describes the fit of the model to the data? A) The correlation coefficient suggests a strong positive correlation, so this model is a good fit for the data. B) The correlation coefficient suggests a weak positive correlation, so this model is not a good fit for the data. C) The correlation coefficient suggests a weak negative correlation, so this model is not a good fit for the data. D) The correlation coefficient suggest a strong negative correlation, so this model is a good fit for the data. 80. A company creates the equation y = 11.26x 76.1 to model the relationship between the number of pages in its catalog and the number of orders, in thousands, that were received. To determine how well the equation models the relationship, the company plots the residuals as shown. Select all possible reasons for why the equation would or would not be a good model for the relationship. [ ] It would be a good model because residual plot indicates a strong linear trend. [ ] It would be a good model because the residual values are allowed to form a linear pattern. [ ] It would be a good model because there seems to be an equal number of points above and below the x-axis. [ ] It would not be a good model because the points on the residual plot have a linear pattern. [ ] It would not be a good model because the points on the residual plot are not randomly distributed. [ ] It would not be a good model because the points are too far from 0. [ ] It would not be a good model because the residual values should be randomly distributed and have values close to 0.

16 Px + Qy = R 81. The system { has the solution (3, 1), where F, G, H, P, Q, and R are nonzero real numbers. Select all Fx + Gy = H the systems that are also guaranteed to have the solution (3, 1). (P + F)x + (Q + G)y = R + H Fx + Gy = H (P + F)x + Qy = R + H Fx + (G + Q)y = H Px + Qy = R (3P + F)x + (3Q + G)y = 3H + R Px + Qy = R (F 2P)x + (G 2Q)y = H 2R Px + Qy = R 5Fx + 5Gy = 5H 82. The system below has the solution ( 10,3), where a, b, c, f, g, and h are non-zero numbers. ax + by = c { fx + gy = h Select all the systems that also have ( 10,3) as a solution. (a + f)x + (b + g)y = c + h fx + gy = h (a + f)x + (b + g)y = c + h (b + f)x + (a + g)y = c + h ax + by = c (a + f)x + (b + g)y = c + h fx + gy = h (f a)x + (g b)y = h c (3a f)x + (3b g)y = 3c h ax + by = c ax2 + bxy = xc 5fx 5gy = 5h (5a 3f)x + (3b 5g)y = 3c 5h 2fx + 2gy = 2h ax + by = c 3ax + 3by = 3c