ALGEBRA 1 FINAL EXAM TOPICS

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1 ALGEBRA 1 FINAL EXAM TOPICS Chapter Writing Equations 2-2 Solving One Step Equations 2-3 Solving Multi-Step Equations 2-4 Solving Equations with the Variable on Each Side 2-5 Solving Equations Involving Absolute Value 2-6 Rations and Proportions 2-8 Literal Equations Chapter Graphing Linear Equations 3-2 Solving Linear Equations by Graphing 3-3 Rate of Change and Slope 3-4 Direct Variation Chapter Graphing Equations in Slope-Intercept Form 4-2 Writing Equations in Slope-Intercept Form 4-3 Standard Form 4-4 Parallel and Perpendicular Lines Chapter Solving Inequalities by Addition and Subtraction 5-2 Solving Inequalities by Multiplication and Division 5-3 Solving Multi-Step Inequalities 5-4 Solving Compound Inequalities 5-5 Inequalities Involving Absolute Value 5-6 Graphing Inequalities in Two Variables Chapter Graphing Systems of Equations 6-2 Substitution 6-3 Elimination Using Addition and Subtraction 6-4 Elimination Using Multiplication 6-5 Applying Systems of Linear Equations 6-6 Systems of Inequalities Chapter Exponential Functions 7-6 Growth and Decay Chapter Solving x 2 + bx + c = Solving ax 2 + bx + c = 0 Chapter Graphing Quadratic Functions, including vertex form, standard form, domain, range, and word problems 9-2 Solving Quadratic Equations by Graphing 9-5 Solving Quadratic Equations by Using the Quadratic Formula

2 ***To study for this exam you should complete the review packet, review your notes, and look at old tests and quizzes. Indicate the answer choice that best completes the statement or answers the question. You must show all of your work on separate paper. 1. Identify the vertex, axis of symmetry, domain and range of: y = 2(x 1) What transformations can be done to f(x) = x 2 to get f(x) = (x 3) 2 1? 3. Write the equation in standard form: y = 2(x 1) Write the equation in vertex form: f(x) = 2x 2 + 8x 5 5. The height, in feet of an object above the ground is given by h(t) = 16t t + 190, t 0 where t is the time in seconds. Find the time it takes the object to strike the ground and find the maximum height of the object. 6. Julie jumped off of a cliff into the ocean while vacationing with some friends. Her height as a function of time could be modeled by the function h(t) = 16t t where t is the time in seconds and h is the height in feet. a. How long did it take for Julie to reach her maximum height? b. What was the highest point that Julie reached? c. How long did it take Julie to hit the ocean? 7. The product of two consecutive negative integers is What are the possible numbers? 8. The length of a rectangle is 4 less than twice the width. The area of the rectangle is 70. Find the dimensions of the rectangle. Graph the function. 9. a. b. c. d.

3 10. a. b. c. y-intercept = 1 domain: all real numbers range: y > 0 d. y-intercept = 1 domain: all real numbers range: y > 2 y-intercept = 3 domain: all real numbers range: y > 2 y-intercept = 1 domain: all real numbers range: y > Given y = 2( 2 3 )x 1 a. Does this model growth or decay? b. What is the equation of the asymptote? Solve the problem of exponential growth. 12. A company's value increased by 5.75% from 2010 to Assume this continues. If the company had a value of $11,140,000 in 2010, write an equation for the value of the company for t years after a. b. c. d.

4 Solve the equation of exponential decay. 13. A car sells for $25,000. If the rate of depreciation is 15%, what is the value of the car after 7 years? Round to the nearest hundred. a. $8000 b. $9400 c. $7400 d. $ In the exponential equation y = 25(1.04) t, what is a. the rate of growth per year b. the initial amount 15. Translate the following sentence into an equation. The product of five and a number y is two less than the quotient of four and y. a. b. c. d. 16. A number is divided by four. The result is added to five. This result is multiplied by three to give 27. What is the number? a. 16 b. 1 c. d. 17. Solve 9a + 28 = 4a + 3. a. 30 b. 20 c. d Solve: 2x 3 4 = 1 2 x Solve. a. 0 b. all numbers c. no solution d Solve 4(3r 2) = 3(r + 7). a. b. c. d Solve ab + c = d for b 22. The length of a rectangle is two less than the width. If the perimeter is 20 cm, find the dimensions. 23. Susan s grades on her tests are 87, 85, and 78. What grade does she need on her fourth test to have an average of 85? 24. If (a, 7) is a solution to the equation 8a = 3b 5, what is a? a. 17 b. 2 c. 8 d What is the slope of the line through (2, 8) and (4, 1)? a. b. c. d.

5 26. Which equation is not a linear equation? a. 2x + 5y = 3 b. y = 10 c. 5 = 3xy d. y = What is the slope of the line through ( 4, 6) and (9, 6)? a. b. c. 0 d. undefined 28. In 2005, MusicMart sold 12,000 CDs. In 2010, they sold 14,550 CDs. What is the rate of change in the number of CDs sold? a per yr b. 510 per yr c. 510 per yr d per yr 29. Find the value of r if the slope of the line through (2,6) and (r,12) is Which is the graph of? a. b. c. d. 31. If y varies directly as x and y = 5 when x = 8, find y when x = 9. a. b. c. d SPRINGS The amount a spring stretches varies directly as the weight of the object attached to it. If an 8-ounce weight stretches a spring 10 centimeters, how much weight will stretch it 15 centimeters? a. 16 oz b. 6 oz c. 10 oz d. 12 oz 33. Which line shown below is the graph of x + 2y = 6? a. r b. n c. t d. v 34. Which equation has a graph that is a horizontal line? a. x 7 = 0 b. 2y + 3 = 4 c. x = y d. x + y = What is the standard form of? a. x + 2y = 0 b. x 2y = 8 c. 2x y = 10 d. 4x 2y = 0

6 36. Write an equation in function notation for the relation. a. f (x) = 2x b. f (x) = x 2 c. f (x) = x + 2 d. f (x) = 2x What is the slope-intercept form of the equation of the line with a slope of and y-intercept at the origin? a. y = 4x b. y = x c. y = x + d. y + = x 38. Which equation is graphed below? a. y 2x = 4 b. 2x + y = 4 c. 2x + y = 4 d. y 4 = 2x 39. Which is an equation of the line that passes through (4, 5) and (6, 9)? a. y = x 3 b. y = x + 3 c. y = 2x + 3 d. y = 2x What is the standard form of the equation of the line through (6, 3) with a slope of? a. 2x + 3y = 24 b. 2x 3y = 21 c. 3x 2y = 24 d. 3x 2y = What is the equation of the line through ( 2, 3) with an undefined slope? a. x = 2 b. y = 3 c. 2x 3y = 0 d. 3x + 2y = Find the slope-intercept form of the equation of the line that passes through ( 1, 5) and is parallel to 4x + 2y = 8. a. y = 2x + 9 b. y = 2x 9 c. y = 4x 9 d. y = 2x If line q has a slope of 2, what is the slope of any line perpendicular to q? a. 2 b. 2 c. d. 44. Are the lines parallel, perpendicular or neither? y = 2x 7 and 4x + 2y = A baby blue whale weighed 3 tons at birth. Ten days later, it weighed 4 tons. Assuming the same rate of growth, which equation shows the weight w when the whale is d days old? a. w = 10d + 3 b. w = 10d + 4 c. w = 0.1d + 3 d. w = d + 10

7 46. Find the x- and y- intercepts of 8x 2y = 16 Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. 47. a. infinitely many b. no solution c. one solution; (0, 1) d. one solution; (1, 0) 48.

8 a. one solution; (2, 1) b. infinitely many c. no solution d. one solution; (1, 2) Use substitution to solve the system of equations. 49. y = 5x x 5y = 1 a. ( 8, 3) b. ( 2, 12) c. ( 3, 8) d. (3, 2) Use substitution to solve the system of equations = x 4y 4x 48 = 3y a. ( 6, 8) b. (2, 10) c. (5, 10) d. infinitely many solutions 51. The length of a rectangular poster is 10 inches longer than the width. If the perimeter of the poster is 124 inches, what is the width? Write and solve a system of equations. a. 16 inches b. 26 inches c inches d. 36 inches

9 52. The sum of two numbers is 90. Their difference is 12. What are the numbers? Write and solve a system of equations. a. no solution b. 31 and 59 c. 35 and 47 d. 39 and At a local electronics store, CDs were on sale. Some were priced at $14.00 and some at $ Sabrina bought 9 CDs and spent a total of $ How many $12.00 CDs did she purchase? a. 9 b. 6 c. 5 d Jordan is 3 years less than twice the age of his cousin. If their ages total 48, how old is Jordan? a. 15 b. 12 c. 31 d At a show, adult tickets are $8 and child tickets are $5. If Jane purchased 20 tickets and the total was $139, how many of each did she purchase? Use elimination to solve the system of equations x + 10y = 101 7x + 5y = 61 a. ( 3, 8) b. (3, 8) c. ( 12, 7) d. (12, 7) x 4y = 122 3x + 6y = 75 a. (3, 3) b. (8, 9) c. ( 3, 3) d. ( 9, 8) 58. The cost of 3 large candles and 5 small candles is $6.40. The cost of 4 large candles and 6 small candles is $7.50. Which pair of equations can be used to determine, t, the cost of a large candle, and s, the cost of a small candle? a. b. c. d. 59. Joe had $3.90 in quarters and nickels. He had a total of 30 coins. Write a system of equations and determine how many quarters he had.

10 Determine the best method to solve the system of equations. Then solve the system. 60. a. elimination using subtraction; b. elimination using addition; c. elimination using subtraction; d. elimination using addition; Solve the system of inequalities by graphing. 61. a. b. c. d. 62. Using question 59, determine if (3,4) is a solution.

11 63. a. b. c. d. 64. Which ordered pair is part of the solution set of the inequality 5 y 3x? a. (2, 1) b. ( 2, 1) c. ( 3, 5) d. (3, 5) 65. Alicia has at most $196 to buy a new baseball glove and a new baseball bat. Which inequality represents this situation? a. y 196 x b. y x c. 196 y + x d. y x Determine which of the ordered pairs are a part of the solution set of y + 3 < 2x 1. a. (0, 0) b. (2, 0) c. (0, 4) d. (2, 2) 67.You can work a total of no more than 10 hours each week at your two jobs. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at least $56 each week to pay your bills. Write a system of inequalities that shows the various numbers of hours you can work at each job. Solve each inequality > w + 12 a. {w w < 25} b. {w w > 25} c. {w w > 1} d. {w w < 1}

12 69. x a. b. c. d. 70. < 3 a. {m m > 15} b. {m m < 15} c. {m m < 15} d. {m m > 15} t 4.62 a. {t t 5.72} b. {t t 5.72} c. {t t 4.2} d. {t t 4.2} 72. 5z 4 > 2z + 8 a. {z z > 4} b. {z z < 1} c. {z z < 4} d. {z z > 1} r (r + 12) 25 a. {r r 3} b. {r r 0.6} c. {r r 3} d. {r r 0.6} 74. The sum of two consecutive integers is at most 7. What is the largest possible value for the lesser integer? a. 1 b. 3 c. 2 d Jane wants to buy two necklaces for $12 each, a bracelet for $8 and some earrings for $10 each. How many pairs of earrings can she buy if she wants to spend at most $60 total? 76. Which of the following is the graph of the solution set of x > 0 or x < 4? a. b. c. d. 77. Which compound inequality has the solution set shown in the graph? a. 2 < y < 3 b. 2 < y 3 c. y 2 or y < 3 d. 2 y < Which of the following is the solution set of 3 < 2x ? a. {x 5 < x 3} b. {x x < 3 or x > 5} c. {x x < 5} d. {x 5 x < 3} 79. Which of the following is the graph of the solution set of 7a + 3 a 15 or 5a 3 < 8a? a. b. c. d.

13 80. Which inequality corresponds to the graph shown? a. x 3 > 1 b. x 3 < 1 c. x 1 > 3 d. x 1 < Which of the following is the solution set of? a. b. {x x is a real number.} c. d. {x 1 x 7} 82. Katrina s weight is within 8 pounds of her ideal weight of 120 pounds. What is her range of weight? a. x 112 or x 128 b. x 112 or x 128 c. 112 x 128 d. 112 x Solve 2n + 5 = 11. a. {3, 3} b. {3, 8} c. {8, 8} d. no solution 84. Which inequality has a solution set of {x x > 4 and x < 8}? a. b. c. d. < 1 > 1 < 3 > Solve 2 2x 6 4 > Match each equation to the type of function: a. Linear I. y = 2(.86) x b. Quadratic II. y = 2x 6 c. Exponential III. y = 2x 2 3x + 7

14 Answer Key: 1. (1,3); x=1; domain: all real numbers; range: y 3 2. right 3, down 1 3. y = 2x 2 + 4x f(x) = 2(x + 2) seconds; 254 ft 6. a. ½ second b. 484 feet c. 6 second and w = 7 and l = b 10. b 11. a. decay b. y= c 13. a 14. a. 4% b b 16. a 17. d /2 19. c 20. a 21. d c a 22. length = 4 cm; width = 6 cm b 25. 9/2

15 26. c 27. c 28. b b 31. b 32. d 33. a 34. b 35. b 36. c 37. b 38. a 39. c 40. b 41. a 42. d 43. c 44. neither 45. c 46. x-int: (2,0); y-int: (0,-8) 47. b 48. d 49. d

16 50. a 51. L = 10 + W 2L + 2W = 124 b 52. X + Y = 90 X Y = 12 d 53. d 54. c adult and 7 child 56. a 57. d 58. a 59. Q + D = 30.25Q +.10D = quarters 60. d 61. d 62. no 63. c 64. b 65. a 66. d d

17 69. a 70. d 71. d 72. a 73. c 74. c 75. No more than 2 pairs 76. c 77. d 78. a 79. c 80. c 81. c 82. d 83. b 84. a 85. x > 8 or x < a. II b. III c. I