Algebra 1 Midterm Review Packet Name ____________________ Date______________________ CHAPTER 1 Match the following with the appropriate property. 1. x y y x A. Distributive Property 2. 6u 2v 6u 12v B. Commutative Property of Multiplication 3. 5m n 5 m n C. Associative Property of Addition 4. gx xg D. Commutative Property of Addition 5. 2a 3b 4c 2a 3b 4c E. Associative Property of Multiplication Simplify 6. 47+ 28 7. 27.9 36 6.__________________ 7.__________________ 8. 14 8 9. -15 + 6 8.__________________ 9.__________________ 10. 5(-3) + 4(6) 11. 12 3 2 9 10._________________ 11._________________ 12. 6 8 22 1 13. (6 2) (3 1) 12._________________ 13._________________ 14. 10 5 3 42 15. 12 3 4 1 14._________________ 15._________________ 16. 2 1 2 3 17. 1 (19 + 11 - 3) 2 16._________________ 17._________________ 18. 5 3 2 2 19. 17 28 2 4 18._________________ 19._________________ 20. 3 6 9 3 6 21. 6 8 8 3 9 3 2 20._________________ 21._________________ 22. 81 27 23. 1 3 2 2 22._________________ 23._________________ 24. 2 1 3 6 25. 3 5 4 4 24._________________ 25._________________ 26. 1 3 4 2 27. 1 2 3 5 26._________________ 27._________________ 28. 5 6 4 2 29. 4 3 3 28._________________ 29._________________ 30. 2 1 5 6 31. 2 6 3 30._________________ 31._________________ 9 32. 8 14 33. 40 8 32._________________ 33._________________ Rewrite the following using exponents. 34. 2 2 a a b 35. 37 x x x z z z z 34._________________ 35._________________ Rewrite the following without using exponents. 3 36. a 2 b 3 37. 4 y 36._________________ 37._________________ Evaluate the following expressions when x = 3 and y = 5. 38. ( y x) 3 39. 2x 2 y 38._________________ 39._________________ 40. 7 y 25 x 41. 2 y 2 3x y 2 40._________________ 41._________________ Check whether the given number is a solution of the equation or inequality. Write “Yes” or “No” 42. 2x 3 17 ; 7 43. x 5 7 ; 12 42._________________ 43._________________ 44. x 2 7 10; 45. 6x 1 8x 7 ; 2 2 44._________________ 45._________________ Match the following phrases with their algebraic expression. 46. Six times a given number 47. Six less a number 48. Six less than a number 49. Fourteen is less than seven times a given number 50. Fourteen less than a given number is seven 51. 14 less the product of a given number and seven 52. Six less a number z is less than 21 53. Six less than a number z is less than 21 54. The product of six and a number z is less than 21 A. 6–x B. x–6 C. 6x D. 14 < 7x E. 14 – 7x F. x – 14 = 7 G. 6 - z < 21 H. z – 6 < 21 I. 6z < 21 Write an equation that correctly models the situation. Then solve. 55. You are 72 inches tall. You are 15 inches taller than your younger sister. How tall is your sister? 55._____________________ 55._____________________ 56. Your teacher gave you 10 days to read a 290-page book. How many pages a night will you have to read? Let p be the number of pages read. 56._____________________ 56._____________________ 57. A movie theater charges $8 admission. The total sales on a given day were $560. How many admission tickets were sold that day? 57._____________________ 57._____________________ Use the Chapter 1 Formulas to help solve the following application problems. 58. An airplane travels at a rate of 500 59. A car travels at 120 kilometers miles per minute for 13 minutes. per hour for 4 hours. How far How far does the plane travel? does the car travel? 58._________ 59._________ 60. Find the perimeter of the triangle below if x = 6. 2x 61. Find the area of a triangle with a height of 7 inches and a base of 12 inches. 60._________ x 3x 62. Find the volume of a cubic package with a base of 3 feet. 61._________ 63. Find the area of a rectangular pig pen with a length of 17 feet and a width of 11 feet. 62._________ 63._________ Algebra 1 Midterm Review Packet CHAPTER 2 In 1-4, replace the ? 7 1. ? -7 3 with >, < or = to make each sentence true. 4 5 2. ? 5 9 Name ____________________ Date______________________ 1.__________________ 2.__________________ 3. 11 5 ? 17 8 4. 2 3 ? 3 7 3.__________________ 4.__________________ 5. Write 6 9 7 , , in order from least to greatest: 11 14 13 5.__________________ 6. 5 4 Write 4, , , 1.5 in order from greatest to least: 4 5 6.__________________ Evaluate the following expressions. 7. 18 8. 18 9. 18 Evaluate the following when a = -13 and b = 7 11. a b 12. b 42 a 10. 18 11._________________ 12._________________ Use the Distributive Property to help simplify the following. 4 13. 2 x 10 14. 5r 2 7 r 5 13._________________ 14._________________ 15. 2x 8x 16. 12 2x 5 10 15._________________ 16._________________ 17. 64a 3b 18. 36a 9b 17._________________ 18._________________ 19. 3 x 4 2 x 5 20. 4 x 2 x 5 19._________________ 20._________________ 21. 3 p 6 p 2 p 22. 3 2x 3x 4 x 7 7 21._________________ 22._________________ 23. 32 y 4 5 y 3 24. 15a 20b 5 23._________________ 24._________________ 25. 2x 8 4 26. 3ab 2a 7b 6ab 25. _________________ 26._________________ 2t 2 3n 27. 4 2t 28. (5xy - x - 7) + (2xy + 3x + 4) 27. _________________ 28._________________ 29. b 9 2 b 30. 11m 7n 2m 6n 29._________________ 30._________________ 31. On February 13th you deposit $150 into your bank account. On April 12th you withdraw $125 and on May 6th you deposit $25. How much money do you have in your bank account? 31._________________ 32. One quarter will give 40 minutes at a parking meter. If you will be gone 2 hours (120 minutes), how many quarters do you need to deposit? 32._________________ Algebra 1 Midterm Review Packet CHAPTER 3 Solve the following equations. 1. x 4 12 2. x 13 5 Name ____________________ Date______________________ 1.__________________ 2.__________________ 3. 2 3 x 7 4 4. 288 16u 3.__________________ 4._________________ 5. x 7 2 6. 4 8 y 5.__________________ 6.__________________ 7. x3 7 5 8. 7 14 x 2 7.__________________ 8.__________________ 9. 8 x 4 3 10. 2a 4 5 6 9.__________________ 10._________________ 11. 2 x 5 14 3 12. 2 x 12 20 11._________________ 12._________________ 13. 2(a + 3) = 16 14. 3b 8 5 9b 2 1 13._________________ 14._________________ 16. 3 y 1 3 y 3 15. 2 x 3 4 x 5 15._________________ 16._________________ 17. 3d 4 4d 10 18. 1 2 x 7 x 3 3 17._________________ 18._________________ 20. 3 4 x 4 x 5 19. 8a 9 8a 19._________________ 20._________________ 21. 10 y 3 y 12 22. 22x 3 4x 6 21._________________ 22._________________ Solve the following formulas for the indicated value. 23. y mx b ; x 24. A bh ; h 23._________________ 24._________________ 25. P 2 L 2W ; L 1 26. V Bh ; 3 h 25._________________ 26._________________ Solve the following proportions. x 4 27. 18 3 28. 9 3 2 y 27._________________ 28._________________ 29. 2x 4 3 5 30. 3 5 5 x2 29._________________ 30._________________ Convert each of the following units. 31. 4 years to months 32. 156 inches to feet 31._________________ 32._________________ Solve each of the following percentage questions. 33. What percent of 80 is 72? 34. What is 35% of 80? 33._________________ 34._________________ 35. 45% of what is 9? 36. What is 100% of 232? 35._________________ 36._________________ 37. 20% of what is 15? 38. What percent of 20 is 30? 37._________________ 38._________________ 39. What is 200% of 54? 40. 45% of what is 10? 39._________________ 40._________________ Algebra 1 Midterm Review Packet CHAPTER 4 Write the ordered pairs that correspond to points A, B, C, and D 1. 2. A A B B C C D D 3. Label the quadrants, axes, and the origin on the coordinate plane to the right. 4. List the quadrant that each of the points is in DO NOT PLOT THE POINTS A. (-5, 22) B. (0, -7) C. (2, 16) D. (12, -80) E. (10, 0) F. (-30, -60) Identify the Ordered Pair that IS a solution to the equation 5. 3x y 18 6. y 18 A. (-1, 21) C. (3, -9) A. (0, -18) B. (1, -21) D. (9, 3) B. (18, 0) 7. x 8 A. (-8, 1) B. (1, -8) 9. 8. C. (8, -1) D. (-1, 8) Find the range of y Name ____________________ Date______________________ y 4 x 23 A. (3, 5) B. (5, 3) 2x 1 if the domain is {0, 1, 2, 3} 3 5.__________________ C. (0, 18) D. (-18, 0) 6.__________________ 7.__________________ C. (3, -5) D. (5, -3) 8.__________________ 9.__________________ 10. Find the range for y = 2x – 1 if the domain is {-1, 0, 1} 10._________________ 11. Find the output values for y = 7 – 3x if the input values are {-2, -1, 0, 1, 2} 11._________________ Use the following tables to a) List the Domain; b) List the Range; c) Does it represent a function? 12. 13. 14. x y x y x y 0 1 2 3 2 4 6 8 7 9 10 10 7 9 8 10 1 3 5 7 1 2 3 1 Domain:_________________ Domain:_________________ Domain:_________________ Range:__________________ Range:__________________ Range:__________________ Function?________________ Function?________________ Function?________________ Determine whether each of the relations below is a function. 15. {(2, -6), (3, 4), (-2, -6), (5, 0)} 16. {(1, 2), (3, 6), (1, -4), (5, 0), (8, -3)} 15._________________ 16._________________ 17. 18. 17._________________ 18._________________ Write an equation for the graphs shown below. 19. 20. 21. 22. 23. Which of the following equations has a graph that is vertical? A. y = 2x + 3 B. y=3 C. x=4 D. y = x 24. Which of the following equations has a graph that is horizontal? A. y = 2x + 3 B. y=3 C. x=4 D. y = x Use the graph below to find the x-intercept and the y-intercept. 25. 26. 27. x-int_______ x-int_______ y-int_______ x-int_______ y-int_______ y-int_______ Find the x-intercept and the y-intercept of the following equations. Use the intercepts to graph the equation. 28. 3x + 2y = 6 29. 4x – 2y = 10 28. x:_______________ y:_______________ 29. x:_______________ y:_______________ 30. y 3 x 3 5 31. 3 y 5 x 9 30. x:_______________ y:_______________ 31. x:_______________ y:_______________ Rewrite the equation in Slope-Intercept Form:_____________________ 32. 6 x y 18 33. 3x y 14 32._________________ 33._________________ 34. 3x 6 y 24 35. 4 y 6x 12 34._________________ 35._________________ 36. Find the slope of the line passing through the points (2, -1) and (3, 4) 37. Find the slope of the line passing through the points (0, 8) and (-1, 8) 36._________________ 38. Find the slope of the line passing through the points (2, 4) and (5, 0) 39. Find the slope of the line passing through the points (3, 4) and (3, -2) 38._________________ 40. Sketch the graph of a line with: A. a positive slope B. a negative slope C. no-slope (undefined ) Identify the slope and y-intercepts, then graph the line. 41. y 3x 2 2 42. y x 4 3 slope: slope: y-int: y-int: 37._________________ 39._________________ D. zero-slope 43. Write the equation of a line 44. Write the equation of a line 3 with a slope of and a 5 y-intercept of -4. Then graph. with a slope of -2 and a y-intercept of 6. Then graph. Match the following picture with the correct equation. 45. 43._________________ 44._________________ 46. A. y 2x 1 A. B. y x2 B. C. y x 2 C. D. y 2x 2 D. y 2 x 1 2 1 y x2 2 1 y x2 2 y 2x 2 Evaluate. 47. g x 8x 2 when x 2 48. hx 3 x6 4 when x8 47._________________ 48._________________ 49. Given f(x) = 2x – 8, find f(3) 50. Given f(x) = 17 – 3x + 9, find f(-1) 49._________________ 50._________________ 51. The cost of a one day car rental from City Wide Rentals is given by the function Cx 0.18x 35 where x is the number of miles driven. What is the cost of the car rental if 587 miles are driven in one day? 51._________________ Algebra 1 Midterm Review Packet Name ____________________ Date______________________ CHAPTER 5 1. Write the equation of the line in slope-intercept form given the following graph. 2. 1.__________________ Which of the following lines is the graph of 4x + 2y = 8 A. B. C. 2 x 5 y 10 3. Rewrite in slope-intercept form: 3.__________________ 4. Write the equation of the line through (10, 8) with slope 1 in point-slope form. 2 4.__________________ 5. Write the equation of the line through (1, -3) with slope -2 in point-slope form. 4.__________________ 6. Write the equation of the line through (7, 6) with slope 3 in point-slope form. 5 6.__________________ 7. Write the equation of the line through (2, 5) with slope 6 in slope-intercept form. 8. Write the equation of the line through (4, 5) with slope 7.__________________ 1 in slope-intercept form. 7.__________________ 2 9. Determine the slope of the line passing through (-4, 5) and (3, -2). 9.__________________ 10. Write the equation of the line that passes through the points (-4, 5) and (3, -2). 10._________________ 11. Write the equation of the line that passes through the points (-8, -4) and (6, 3) 11._________________ 12. Write the equation of the line that passes through the points (-3, 5) and (1, 5) 12._________________ 13. Write the equation of the line that passes through the points (2, -1) and (4, 5) 13._________________ Rewrite the following equations in Standard Form. 14. 3x 2 y 7 15. 2 y 4 x 6 14._________________ 15._________________ 1 16. y x 3 2 17. 3 y 2 x4 5 16._________________ 17._________________ 18. What is the slope of a line parallel to the line with the equation y 2 x 7 19. What is the slope of a line parallel to the line with the 3 equation y x 2 18._________________ 19._________________ 20. What is the slope of a line perpendicular to the line with the equation y 2 x 7 21. What is the slope of a line perpendicular to the line with the 3 equation y x 2 20._________________ 21._________________ Determine whether the following sets of lines are Parallel, Perpendicular, or Neither. 22. 2y = -6x 23. y = 3x + 1 22._________________ -12y = -4x 4y = 3x + 1 23._________________ 24. y = 3x + 6 -2y = 6x – 4 25. y = -½ x + 3 2y = -x + 4 24._________________ 25._________________ 26. Write an equation of a line that passes through the point (4, -1) 1 and is parallel to the line y x 1 2 26._________________ 27. Write an equation of a line that passes through the point (2, -3) and is parallel to the line y 3x 6 27._________________ 28. Write an equation of a line that passes through the point (-4, 6) and is perpendicular to the line y 2x 3 28._________________ 29. Write an equation of a line that passes through the point (0, 11) and is perpendicular to the line y x 6 29._________________ Algebra 1 Midterm Review Packet CHAPTER 6 Solve the following inequalities and graph their solutions. 1. 12 + x < 18 2. -3a > 18 Name ____________________ Date______________________ 1.__________________ 2.__________________ 3. 15 x 4 4. y 7 5 3 3.__________________ 4.__________________ 5. 15 c 4 6. 4n 6 6n 20 5.__________________ 6.__________________ 7. 3 2 y 15 8. 52 3x 46 7.__________________ 8.__________________ 9. 7x 2 3x 2 10. 3 y 2 2 y 51 9.__________________ 10._________________ Write the inequality for each graph shown below. 11. 12. -5 -4 -3 -2 -1 0 1 2 3 4 -5 5 13. 11._________________ -4 -3 -2 -1 0 1 2 3 4 5 14. -5 -4 -3 -2 -1 0 1 2 3 4 5 15. 13._________________ -5 -4 -3 -2 -1 0 1 2 3 4 5 16. -5 -4 -3 -2 -1 0 1 2 3 4 5 12._________________ 14._________________ 15._________________ -5 -4 -3 -2 -1 0 1 2 3 4 Solve the following compound inequalities and graph the solution. 17. -14 < 7x < 21 18. 3 < x – 3 ≤ 5 5 16._________________ 17._________________ 18._________________ 19. -3 ≤ 2x + 1 < 9 20. 6 + 2x > 20 or 8 + x ≤ 0 19._________________ 20._________________ 21. x 3 or 5 6 x 3 22. 2x + 1 > 13 or -18 > 7x + 3 21._________________ 22._________________ 23. You earn $8.75 per hour at your math tutoring job. Write and solve an inequality to show how many full hours h you need to work to save at least $650 so that you can buy Ms. Kurtz something awesome! Inequality:_______________________ Solution:________________________ 24. A membership to the “Math Is Cool Club” has an initiation fee of $90. Each month you are billed an additional $30. Write and solve an inequality to find the maximum amount of time you can be a member for $600. Inequality:_______________________ Solution:________________________ Algebra 1 Midterm Review Packet Name ____________________ Date______________________ PRACTICE STORY PROBLEMS Define your variable(s), write an equation, and solve. Be sure to include units!! 1. The sum of two numbers is 18. The less of the two is 6, what is the greater number? 2. 1.__________________ The difference of two numbers is 8. The greater number is 2, what is the lesser number? 2.__________________ For $1.89, you can buy 75 square feet of plastic wrap. At this rate, how much does 125 square feet of plastic wrap cost? 3.__________________ Lisa is 7 years older than Claire. The sum of their ages is 51. What is Claire’s age? 4.__________________ 5. Jack drove 260 miles in 4 hours. How fast was he driving? 5.__________________ 6. Manny can average 16 mi/hr on his bicycle in a race. How long will a 44 mile race take? 6.__________________ 3. 4. Midterm Review Chapter 1 Answers Algebra 1 1. D 2. A 3. E 9. -9 17. 4. B 10. 9 27 25. − 11. 9 18. 6 2 1 26. − 2 7 27. 4 34. 22 𝑎2 𝑏 41. 46 42. Yes 52. G 20. 15 2 28. − 15 35. 31 71 𝑥 3 𝑧 4 5 59. 480 30. − 9 23. 2 12 44. No 45. Yes 62. 27 46. C 1 5 6 32. 9 39. 13 8. 22 15. 17 24. 31. − 5 36. 𝑎 ∙ 𝑎 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 37. 4𝑦 ∙ 4𝑦 ∙ 4𝑦 38. 8 43. Yes 60. 36 61. 42 14. 3 22. 3 4 29. 3 7. 8.1 13. 1 21. 7 53. H 54. I 55. a) x + 15 = 72 b) 57 inches 58. 6500 6. 19 12. 5 19. 25 33. -5 5. C 112 9 40. 103 47. A 48. B 49. D 50. F 51. E 56. a) 10p = 290 b) 29 57. a) 8x = 560 b. 70 63. 187 Midterm Review Chapter 2 Answers Algebra 1 1. > 2. > 3. < 4. > 5. 7 8 13. 𝑥 − 8 12. -48 20. 2x – 10 3𝑡𝑛 28. 7xy + 2x – 3 4 6 , 9 4 5 5 4 6. − , − , −1.5, −4 14. 12r + 10 5 19. 5x – 9 27. , 13 11 14 22. − 21. 11p 15. 10x 11 7 𝑥 8. -18 16. -2x + 32 23. 11y + 3 30. 9m – 13n 29. -11 7. 18 10. -18 11. 20 18. -18a – 27b 17. 24a + 18b 1 24. 3a – 4b 31. $50 9. 18 26. 9ab – 2a + 7b 25. 𝑥 − 2 2 32. 3 quarters Midterm Review Chapter 3 Answers Algebra 1 1. 8 2. 8 14. 0 15. -1 23. 𝑥 = 𝑦−𝑏 𝑚 33. 90% 3. 29 4. -18 5. -14 6. 2 7. -32 16. All real #’s 17. -2 18. 7 19. No sol. 28 24. ℎ = 34. 28 𝐴 𝑏 35. 20 25. 𝐿 = 𝑃−2𝑊 36. 232 2 26. ℎ = 37. 75 3𝑉 𝐵 38. 150 8. -4 9. 20 20. 1 10. 13 11. -13.5 28. 39. 108 40. 2 29. 3 13. 5 31. 48 32. 13 22. All real #’ 21. -11 27. 24 12. 4 6 5 30. 31 3 200 9 Midterm Review Chapter 4 Answers Algebra 1 1. A(5, 1) B(0, 4) C(-3, -1) D(0, 0) 2. A(-4, 0) B(2, 3) C(1, -1) D(-3, -5) 3. On graph 4. A. Quad 1, B. y-axis, C. Quad 1, D. Quad 4, E. x – axis, F. Quad 3 5. A 1 5 7 3 3 3 9. , 3, , 6. C 7. A 8. D 10. -3, -1, 1 11. 13, 10, 7, 4, 1 12. D: 0, 1, 2, 3 R: 2, 4, 6, 8 yes 13. D: 7, 9, 10 R: 7, 9, 8, 10, no 16. 2 9 14. D: 1, 3, 5, 7 R: 1, 2, yes 22. y = -3.5 23. C 24. B 15. Yes 16. No 17. Yes 18. No 19. x = 2 25. x: (3, 0) y: (0, 3) 26. x: (-1, 0) y: (0, 3) 20. y = 4 21. x = -3.5 27. x: (2, 0) y: (0, -2) 5 9 2 5 28. x: (2, 0) y: (0,3) 29. x: ( , 0) y: (0, -5) 30. x: (5, 0) y: (0, -3) 31. x: (− , 0) y: (0, -3) 1 33. 𝑦 = 3𝑥 − 14 40. positive 3 34. 𝑦 = 𝑥 + 4 35. 𝑦 = 𝑥 + 3 negative undefined zero 2 44. 2 45. B 36. 5 38. − 37. 0 41. 46. B 4 32. 𝑦 = 6𝑥 + 18 39. Undefined 3 42. 43. 47. 14 48. 0 49. -2 y = -2x +6 50. 29 3 y= x-4 5 51. $140.66 Midterm Review Chapter 5 Answers Algebra 1 3 1. 𝑦 = 𝑥 + 1 2 1 8. 𝑦 = 𝑥 + 3 2 2 1 2. A 3. 𝑦 = − 𝑥 − 2 4. 𝑦 = 𝑥 + 3 9. -1 10. 𝑦 = −𝑥 + 1 11. 𝑦 = 𝑥 − 6 15. 4𝑥 + 2𝑦 = 6 5 16. 𝑥 + 2𝑦 = −6 22. perpendicular 23. Neither 1 28. 𝑦 = − 𝑥 + 4 5. 𝑦 = −2𝑥 − 1 2 1 12. 𝑦 = 5 2 17. 2𝑥 − 15𝑦 = −20 24. neither 25. Parallel 18. -2 1 9 5 5 13. 𝑦 = 3𝑥 − 7 19. 26. 𝑦 = 𝑥 − 3 2 3 6. 𝑦 = 𝑥 + 3 2 20. 1 7. 𝑦 = 6𝑥 − 7 14. 3𝑥 + 2𝑦 = 7 21. − 2 2 3 27. 𝑦 = 3𝑥 − 9 29. 𝑦 = 𝑥 + 11 2 Midterm Review Chapter 6 Answers Algebra 1 1. x < 6 2. a < -6 3. x ≤ 60 10. y ≤ -9 17. -2 < x < 3 11. x ≥ -2 4. y ≤ 6 12. x > 2 18. 6 < x ≤ 8 22. x > 6 OR x < -3 5. c > 60 13. x ≤ -3 19. -2 ≤ x < 4 23. 8.75x ≥ 650, x ≥ 75 6. n < 7 7. y ≥ -6 14. 0 < x ≤ 3 8. x ≥ -2.4 9. x ≤ 2 15. x ≤ -2 OR x ≥ 4 16. -3 < x < 1 20. x > 7 OR x ≤ -8 21. x < -9 OR x > -1 24. 90 + 30x ≤ 600, x ≤ 17 Midterm Review Story Problems Answers Algebra 1 1. 12 2. -6 3. $3.15 4. 22 5. 65 mph 6. 2.75 hours