Page 1 ALGEBRA I END-OF-COURSE EXAM: PRACTICE TEST 1. Order the following numbers from least to greatest:, 6, 8.7 10 0, 19 b. 19,, 8.7 100, 6 6, 8.7 10 0,, 19 c. d. 8.7 10 0,, 19, 6, 6, 19, 8.7 100. If y, then when is y a positive number? Always b. when > - c. when > d. never. Simplify 0 10 b. 4 5 c. 5 d. 5 4. Solve the equation for d vt 1 at a d vt b. a d vt t c. a d vt d. t a d vt t y 10 5. Simplify the epression: 5 y y 17 6. Determine what values of the epression Epress your answer with an inequality. b. Write your answer on the line. y 15 5 c. y 9 d. 5 is defined for. y 6 7 What are the defined values of?
Page 1 7. Solve: 8 5 41 5 b. 41 5 8. Which equation is y 1 5 in standard form? 1 1 y 5 b. y 5 c. c. 1 d. 1 9. Which of these is the equation of a line with y-intercept (0, ) and slope? y 1 b. y 1 c. 1 y 15 d. 1 y d. y 15 y 1 10. Fred, Thomas, and Zachary worked at the ice cream store in the mall. Last week, Fred earned more money than Thomas, but less than Zachary. The graph shows the money earned by Zachary and Thomas. Which area of the graph represents Fred s possible weekly pay? P b. R c. S d. T
Page 11. Tara s cell phone plan costs $9.00 a month, which includes 100 tet messages. After she uses all of her tet messages, it will cost her $.15 per tet message. Write an equation or inequality that could be used to determine the total cost of her cell phone bill after her first 100 tet messages. If Tara only wants to spend $4 on her cell phone bill, how many tet messages can she send? 1. The equation 1 5 has two real solutions. Determine the negative solution of the equation. Write your answer on the line. What is the negative solution of the equation? 1. Write an equation of the line that passes through the pair of points. (-5, -), (, -1) y 1 8 11 8 b. y 1 8 11 8 c. y 1 8 11 8 d. y 1 8 8 11
Page 4 14. A 1,500-gallon tank contains 00 gallons of water. Water begins to run into the tank at the rate of 75 gallons per hour. When will the tank be full but not overflowing? 7 hours, 8 min b. 17 hours, 0 min c. 0 hours d. hours, 40 min 15. According to the graph, which statement best describes the slope? As the distance traveled increases by 0, the amount of gas in the tank decreases by. b. As the distance traveled decreases by, the amount of gas in the tank increases by 0. c. As the distance traveled increases by 0, the amount of gas in the tank increases by. d. As the distance traveled decreases by 0, the amount of gas in the tank decreases by. 16. Solve for in 4 14. Display the set of solutions that makes the compound inequality true by graphing them on the number line below.
Page 5 17. Which is the graph of the solution set of the system of inequalities? y 10 y 0 18. Write an equation of the line that is perpendicular to y 1 8 and goes through (-4, 5). y 1 b. y 1 7 c. y 8 d. y 0. In 000, 5500 people attended the State B basketball tournament. The enrollment has been increasing % annually. Select the equation that would determine the total number of people who attend t years after 000. y 5500(.0) b. y 5500(0.) c. y 5500(1.0) d. y 5500(1.) 1. You are a full time employee at a marketing firm. In order to maintain fulltime status you must work a minimum of 5 hours a week, and you cannot work more than 45 hours in a week. You make $0 per hour. Define the domain and range in the contet of the problem. Write your answer on the line. Domain: Range:
Page 6. Only chocolate and vanilla ice cream cones are sold at an ice cream store. In one day, the number of chocolate cones sold was 1 more than 4 times the number of vanilla cones sold. A total of 11 cones were sold that day. Let c = the number of chocolate cones sold. Let v = the number of vanilla cones sold. Write equations to determine the number of chocolate cones sold that day. Use the equations to determine the number of chocolate cones sold that day. Show your work using words, numbers, and/or diagrams.. The chart shows the amount of total salary (commission plus base salary) paid to employees of a store that specializes in big screen televisions. Which equation best represents the total salary (T) that an employee makes for selling any number of television sets (n)? T = 50n + 100 b. b. T = 100(n + 50) c. c. T = 100n + 50 d. d. T = 50(n + 100)
Page 7 4. Mr. Shindler begins traveling east on Interstate 90 from Spokane with a full tank of gasoline. His car has a 15-gallon gas tank and gets 0 miles per gallon during highway travel. Let m = the number of miles Mr. Shindler has driven Let g = the number of gallons of gas remaining in his tank Select and justify in the answer bo which equation describes the relationship between the number of miles Mr. Shindler has traveled and the number of gallons remaining in his gas tank. g 15 0m b. m 0g 15 c. g 15 m d. d. m 0 0 g 15 Show your work using words, numbers, and/or diagrams. 5. Which function best represents the values in the table below? f() - -7-1 -1 0 0 8 5 15 f () b. f () c. f () 1 d. f ()
Page 8 6. Look at the function: f () 4 5 Evaluate f () at f (). Write your answer on the line. What is f () = 7. Which best describes the difference(s) between the graphs of f () 5 4 and g() 10 4? The graph of f() is twice as steep as the graph of g(). b. The graph of f() is half as steep as the graph of g(). c. The graph of f() has a y-intercept of 5 while g() has a y-intercept of 10. d. Both A and C are true. 8. Graph A is the graph of y () and graph B is the graph of y (). Which statement about the two graphs is true? Both graphs A and B rise at the same rate. b. Graph B rises at a faster rate than graph A. c. Graph A rises at a faster rate than graph B. d. The y-intercept of graph A is above the y-intercept of graph B. 9. Solve the equation 79. = 5 b. = 6 c. = 4 d. = 76 0. Brad and Tom are comparing their classes' scores on a math test. Both of their classes had mean scores of 80 on the test, but Brad's class had a range of 6 while Tom's class had a range of 0. If the highest possible score was 100, which class had the LOWEST score in it? Brad's class had the lowest score in it. b. Tom's class had the lowest score in it. c. The lowest score occurred in both classes. d. It cannot be determined from the information.
Page 9 1. Which table represents the recursive formula: an = an-1-6. Marcy recorded and graphed the daily height of a growing plant. Marcy's graph was linear. Which table could be Marcy's data?
Page 10. This graph shows the relationship between the age of a planet in millions of years and the number of moons the planet has. Which of these statements is true about the graph? The dependent variable is the number of moons. b. The independent variable is the number of moons. c. Since the number of moons is staying the same, there is no dependent variable. d. Since the number of moons is staying the same, there is no independent variable. 4. A college professor at the University of Washington surveyed 150 students at the university. The students were asked if they prefer in class or take home tests. The professor drew the conclusion: One out of four college students prefer take home tests. Eplain why this conclusion is misleading. The professor surveyed a small sample of the population at one university but made the conclusion about the entire population of college students. b. The survey question was biased toward in class tests. c. The students were not selected randomly. d. The sample size was too small. 5. At a particular company, every employee receives a 4% cost-of-living increase to their salary. What impact does this cost-of-living increase have on the mean and on the range of employee salaries at the company? The mean increases but the range does not change. b. The mean does not change but the range increases. c. The mean and range both increase. d. The mean and range do not change.
Page 11 6. The graph shows the stock value for a technology company from 00 to 005. From this graph, draw a line that fits the data and determine what is the most likely value of the stock for the year 000? $0 b. $10 c. $0 d. $0 7. Vance graphed the relation between fund-raising profits for the chess club and the number of members. Which equation represents a line that fits the 1 data? y 9n 180 b. y 60n 180 c. d. y n 180 y 00 n 180
Page 1 8. Which term best describes the scatterplot? Positive correlation b. Negative correlative c. Zero correlation d. Perfect correlation English Sentences and Mathematical Sentences 9. Match each mathematical sentence on the left with its translation on the right. Then, for each mathematical sentence, declare what the variable represents. 8 means b. ( ) ( ) 1. Rob s number is equal to twice Bob s number. Cob s number is eight times larger than two less than Bob s number. The sum of Rob s number and Cob s number is.. Jenna earned $ by working hours and receiving an $8 bonus. means c. 8( ) means d. 8 means. Toby s cup can hold 8 times as many ounces of water as Terry s. Together, the cups hold ounces of water. 4. A -ounce metal bracelet is created by miing gold, silver, and zinc. There are two ounces less zinc than gold, and there is twice as much silver as zinc.
Page 1 40. Pearl s work for solving this system of equations is shown here. All her work is correct. Which method is she using? System: y = 5 Pearl s Solution: + y = 0 A. Equal Values method B. Substitution C. Elimination D. Multiplication and then Elimination + ( 5 ) = 0 5 = 0 +5 +5 = 5 y = -5 (5) y = -0 41. Edith is using substitution to solve the system of equations below. What should the first step be? y 8y A. 8() B. ( 8y) C. () 8y D. ( 8) 4. Mrs. Goolsby wants to use Elimination to solve the system of equations below. Choose the best first step. A. Multiply the first equation by. B. Multiply the second equation by. C. Multiply the first equation by. D. Multiply the second equation by. y 5 y 10 4. Mr. Glass solved a system of equations using substitution and got the following result: 1 = -4 What should he write as his final answer? b. What does this tell you about the graph of the sytem?
Page 14 Decide whether the relation defines a function. 44. ( 6,7),( 6,9),(1, 4), (4,4), (8, 1) A) Not a function B) Function Find the domain and range. 45. ( 4,4), ( 1,1), (,8), (,)} domain = {-4,8,1,}; range = {-4,-,-1} B) domain = {-4,-,-1,}; range = {-4,8,1,} C) domain = {-4,-,-1}; range = {4,8,1,} D) domain = {-4,-,-1,-1}; range = {-4,8,1,} Given the function, find the indicated value. 46. Find f(-) when f() = +4+4. 0 B) 0 C) -4 D) 4 Solve the system by graphing. 47. y 4 = 5y = 0 + 10 y 6 4-6 -4-4 6 - -4-6 The -value of the solution is: A) -1.5 B) 1 C) Infinite # of solutions D) No solution Solve the system. 48. + y = -5 5y = 1 The y-value of the solution is: A) B) 7 C) - D) No solution Simplify the epression. 4 49. 4 p 4p p 7 16 B) 16p 1 C) 16p 1 D) 16p 7
Page 15 Simplify the epression. Write the answer with positive eponents. 50. 4 y z 9 10 y z 11 1 7 y z 8 B) 8 y 8 C) y z D) 8 y z Simplify. Use positive eponents to write the answer. 7 5 51. 8 4 4 B) 1 11 C) 1 4 D) 4 Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. 5. 10 4 w 7w 5y 5 4 degree 5; trinomial B) degree 5; none C) degree 1; trinomial D) degree 14; binomial Perform the indicated operations. 4 4 5. 9 9 4 6 5 5 4 4 8 1 9 B) 14 4 8 1 9 4 C) 4 4 6 1 D) 14 4 8 1 1 Multiply. 54. (-5 + y) ( 1y + 1) 10 60y 5 6y B) 10 66y 66y C) 10 66y 5 6y y D) 10 6y 5 6y y 55. (-6 + ) (4 8) B) 4 48 C) 4 48 D) 4 48 56. ( 4 y) 16 9y B) 4 4y 9y C) 16 4y 9y D) 4 9y 4 4 57. 6 6 4 4 9 B) 4 4 C) 9 4 9 D) 4 9
Page 16 Factor the trinomial. 58. 1 y 11y 15y 5y4 y B) y 51 C) 4 5y y D) y 54 Factor the polynomial. 59. y 81y 6 4 4 y 9 B) y 9 4 C) prime polynomial D) y 9 60. 49 16 7 4 B) 7 47 4 C) prime polynomial D) 7 4 61. 4 y 10 5y y 5 B) y 5 C) 5y 1 D) prime polynomial Solve the equation by factoring. 6. 9b 1b 1 9 5, B), 5 C), 5 D) 5, Find the cube root. Round to the nearest thousandth, if necessary. 6. 1 64 y 6 4y 4 B) 4 4y C) 4y D) 4 16y Use radical notation to write the epression. Simplify if possible. 64. 7 5 7 5 B) 5 49 C) 7 5 D) 5 7 Write with positive eponents. Simplify if possible. 65. 5-15 B) 15 C) 1 15 D) 1 15
Page 17 66. 4 5 1 16 B) 16 C) 1 16 D) not a real number Use the properties of eponents to simplify the epression. Write with positive eponents. 4 5 5 67. 6 7 1 B) 1 1 105 105 C) 1 D) 181 181 105 105 Use the product rule to multiply. Assume all variables represent positive real numbers. 5 68. 1 1 169 8 B) 1 4 C) 4 6 D) 1 Simplify the epression. Assume all variables represent positive real numbers. 69. 54 7 B) C) D) Add or subtract. Assume all variables represent positive real numbers. 4 70. 7 7 7 1 B) 1 C) 1 D) 1 Multiply, and then simplify if possible. Assume all variables represent positive real numbers. 71. 4 5 7 5 5 4 8 0 5 16 5 B) 48 5 16 C) 65 5 D) 18 51 5 Rationalize the denominator. Assume all variables represent positive real numbers. 7. 4 a 4 a a B) 4 a a C) 4 a a D) 4 a
Page 18 Use the square root property to solve the equation. Round to the nearest tenth, if necessary. 7. p 6 6 b. ± 6 c. + 6 d. ± 6 75. What is a quadratic equation? An equation that has two terms b. An equation that has four terms c. An equation that has degree 4 d. An equation that has degree 76. Use the discriminant to determine how many real solutions eist for the quadratic equation + 4 + = 0. 0 solutions 1 solution solutions solutions 77. Solve + 4 = 0. {-8, -4} b. {8, 4} c. {-8, 4} d. {8, -4}
Page 19 78. Which is a graph of a quadratic equation? (a) (b) (c) (d) 79. Which is one of the solutions to the equation 4 = 0? A 1 4 B 1 4 C 1 4 D 1 4 80. Toni is solving this equation by completing the square. a + b + c = 0 (where a > 0) Step 1: a + b = -c Step : b a c a Step :? Which should be Step in the solution? A c b b a B b a c a C b a b a c a b a D b a b c a a b a
Page 0 81. Four steps to derive the quadratic formula are shown below. I II III IV b a c a b b 4ac a 4a b 4ac b 4a a b a b c a a b a What is the correct order for these steps? A I, IV, II, III B I, III, IV, II C II, IV,I, III D II, III, I, IV 8. Which statement best eplains why there is no real solution to the quadratic equation + + 7 = 0? A The value of 1 4 7 is positive. B The value of 1 4 7 is equal to 0. C D The value of 1 4 7 is negative. The value of 1 4 7 is not a perfect square. 8. What is the solution set of the quadratic equation 8 + + 1 = 0? A 1, 1 4 B 1,1 C 1 7 8, 1 7 8 D no real solution
Page 1 84. The graph of the equation y = 4 is shown below. f = --4 10 8 6 4-15 -10-5 5 10 15 - -4-6 -8-10 -1 For what value or values of is y = 0? A = -1 only B = -4 only C = -1 and = 4 D = 1 and = -4 85. How many times does the graph of y = + intersect the -ais? A none B one C two D three 86. An object that is projected straight downward with an initial velocity, v, feet per second travels a distance s = vt + 16t, where t = time in seconds. If Ramon is standing on a balcony 84 feet above the ground and throws a penny straight down with an initial velocity of 10 feet per second, in approimately how many seconds will it reach the ground? A seconds B seconds C 6 seconds D 8 seconds 87. The height of a triangle is 4 times greater than twice its base. The area of the triangle is 168 square inches. Which number is closest to the base length? A 7 in. B 8 in. C 9 in. D 10 in. 88. What are the solutions to the equation + 4 = 7? A 4 B 4 6 C 6 D
Page 89. The graph of a parabolic curve is shown below. Which of the following equations is represented by the graph? 10 8 6 4-10 -5 5 10 - -4-6 -8-10 A B C D 90. A construction worker drops a tool from the top of a building that is 00 ft high. The height of the tool above ground can be modeled by h = -16t + 00, where h is the height in feet and t is the time in seconds. How long will it take for the tool to hit the ground? A 5.6 s B.5 s C 4. s D 0.1 s 91. What are the real roots of the quadratic function in the graph below? 6 4 A - and 0 B 4.5 and 0-5 5 10 C No real roots - D -1.5-4 -6-8 9. The graph of the equation y = + + intersects the -ais at how many points? A 0 B 1 C D