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Algebra ii study guide

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1) The document is an algebra II study guide containing 50 problems covering various algebra topics including properties, evaluating expressions, solving equations and inequalities, graphing lines and parabolas, working with complex numbers, and other concepts. 2) Many of the problems ask students to reference the specific section of their textbook that covers the relevant concept. The responses provide the answer and cite the textbook reference. 3) The study guide is designed to help students review major algebra II concepts in preparation for a test or exam through practicing worked examples. The answers allow students to check their work and understanding of these essential skills.

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Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 1. State the property that is illustrated. 3 ⋅ (5 ⋅ 7) = (3 ⋅ 5) ⋅ 7 2. Evaluate –3y + x + 30 when x = –3 and y = 9. 3. Evaluate the expression. 60 – (15)(2) ÷ 3 4. Evaluate (7 + 5y) ÷ 3x when x= 1 6 and y = 3. 5. Solve the equation. − 3x + 5 = −7 x − 4 6. Solve the equation. − x + 3 = 7 x + 8 7. For 1980 through 1990, the population, P, (in thousands), of Hawaii can be modeled by P = 17(t + 56.6) where t = 0 represents 1980. What was the population in 1987? 5 ( F − 32) 8. Solve for F: C = 9 9. Solve for P: A = P + Prt 10. A rectangle is 5 feet longer than it is wide. The perimeter of the rectangle is 34 feet. What is the length of the rectangle? 11. Solve the inequality. Then graph your solution. 2 x + 5 ≥ 2 − ( x − 9)
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 12. Is x = –7 a solution of the inequality 5x − 7 ≤ 3( x − 7) ? Solve: 13. x − 4 ≥ 3 14. x + 7 ≥ 9 15. Is the relation 4 – – la, – 2f, a5, – 2f, a6, – 2fqa function? 16. Find the range of the relation {(4, – 3), (– 5, 1), (– 1, 2)}. 17. Find F1I. f ( x) = 18x H3K f − 2 − 12 x − 3 18. Find the slope of the line passing through the points (–3, 3) and (6, 2). 5 [A] 3 [B] 1 [C] −9
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 1 − [D] 9 19. Find the slope and y-intercepts of the line. 5x − 4 y = 20 2 y = − x−2 3 20. Graph the line. 21. Find the slope and y-intercepts of the line. 4 x − 3y = 36 22. Write the equation of the line, in slope-intercept form, that passes through the point (− 2, − 2) and has slope − 3 . 23. Write the equation in slope-intercept form. Then identify the slope and y-intercept. 18x − 42 y = 24 24. The variables x and y vary directly and y = –7 when x = 14. Write an equation that relates the variables. 25. For the following data:
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ A. Make a scatter plot of the data. B. Approximate the best fitting line for the data. C. Find an equation of your line of best fit. x 1 2 3 4 5 6 7 8 y 175 41 4.95 7 815 111 1195 14 . . . . . y x 2 4 y>− 3 26. Graph the inequality in a coordinate plane. 3 27. Is the ordered pair (–7, 2) a solution of the inequality 3x + 10 y ≥ −1 ? 28. Graph: − y ≤ 4 x − 7
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 29. Graph the equation. y = 2 x + 5 30. Find the solution to the system by graphing. x+ y = –7 2x − y = – 2 31. Is (5, –2) a solution of the system? 2x + 6y = –2 2x + y = 6 32. The drama club sold 1500 tickets for the end-of-year performance. Admission prices were $12 for adults and $6 for students. The total amount collected at the box office was $16,200. How many students attended the play? 4x − 4 y = 4 33. Solve the linear system: 3x + 4 y = – 25 34. Graph the system of linear inequalities: y ≥ x−3 3x + y ≥ – 1 35. Decide if the given ordered triple is a solution of the following system of equations: (1, –2, 4)
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 3x + 2 y + 3z = 11 2 x − 4 y + z = 14 x + y − 5z = – 21 36. Solve the system of equations: x + y + z = 5 − 2 x − y + z = – 15 x − 2y − z = 6 2 37. Does the parabola open up or down? y = 4 + 6x − 2 x 2 38. Sketch the graph of the equation. y = x − 2 x + 3 2 39. Write in standard form and graph: y = ( x − 1) + 2 40. Factor the expression: 8x 2 − 25 + 10x 41. The height of a triangle is three feet longer than the base. The area of the triangle is 44 square feet. Find the height and base of the triangle.
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 42. Find the zeros of the equation. x 2 + 2 x − 15 = y 43. Simplify the expression: 175 44. Solve for x: 5 x 2 = 405 45. Solve the equation. Round the solutions to two decimal places. 7 x 2 − 2 = 23 46. Solve: x 2 + 2 x + 5 = 0 Write the expression as a complex number in standard form. 2 3 − 2i 47. a f 48. − i + (7 − 5i) − 3(2 − 3i) 49. Solve the equation by completing the square. x 2 + 2 x − 35 = 0 2 50. Sketch the graph of the inequality. y ≥ 2 x + 4 x − 1
Algebra II Regular Study Guide Name________________________________ Date_______ Period____
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ Reference: [1.1.2.13] [1] Associative property for multiplication Reference: [1.2.1.21] [2] 0 Reference: [1.2.1.25] [3] 50 Reference: [1.2.1.27] [4] 44 Reference: [1.3.1.46] 9 x=− 4 [5] Reference: [1.3.1.42]
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 5 x=− 8 [6] Reference: [1.3.2.52] [7] 1,081,200 Reference: [1.4.2.62] 9 C + 32 [8] F = 5 Reference: [1.4.2.64] A P= 1 + rt [9] Reference: [1.5.2.75] [10] 11 feet Reference: [1.6.1.81]
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ [11] x ≥ 2 – 0 1 2 3 4 5 1 x Reference: [1.6.1.85] [12] Yes Reference: [1.7.1.92] [13] x ≤ 1 or x ≥ 7 Reference: [1.7.1.90] [14] x ≤ – 16 or x ≥ 2 Reference: [2.1.1.3] [15] Yes Reference: [2.1.1.1]
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ [16] {–3, 1, 2} Reference: [2.1.2.10] [17] 3 Reference: [2.2.1.15] [18] [D] Reference: [2.3.1.32] 5 slope = 4 ; y-intercept = (0, -5) [19] Reference: [2.3.1.40] 1 1 x –5 –4 –3 –3 –4 –5 [20] y
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ Reference: [2.3.1.34] 4 slope = 3 ; y-intercept = (0, –12) [21] Reference: [2.4.1.46] [22] y = − 3x − 8 Reference: [2.4.1.50] 3 4 3 4 y= x− − 7 7 ; Slope: 7 ; y-intercept: (0, 7 ) [23] Reference: [2.4.2.63] 1 y=− x 2 [24] Reference: [2.5.2.72]
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ y x [25] . y = 175x Reference: [2.6.1.85] y 3 2 1 –3 –2 –1 [26] 1 2 3 x –3 Reference: [2.6.1.80] [27] Yes Reference: [2.6.1.74]
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ y 10 10 x 10 –10 x –10 [28] Reference: [2.8.1.114] y 10 –10 [29] –10 Reference: [3.1.1.3]
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ y 10 –10 [30] (–3, –4) 10 –10 Reference: [3.1.1.11] [31] No Reference: [3.1.2.18] [32] 300 Reference: [3.2.1.23] [33] (–3, –4) Reference: [3.3.1.45] x
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 10 y −10 [34] 10 −10 Reference: [3.6.1.74] [35] yes Reference: [3.6.1.77] [36] (6, 1, –2) Reference: [5.1.1.5] [37] Down Reference: [5.1.1.11] x
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ y 3 2 (1, 2) 1 –2 1 2 3 4 x [38] Reference: [5.1.1.15] 2 [39] y = x – 2 x + 3 y 5 −5 5 x −5 Reference: [5.2.1.27] [40] (2 x + 5)(4 x − 5) Reference: [5.2.1.36]
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ [41] Base: 8 ft; Height: 11 ft Reference: [5.2.2.39] [42] –5, 3 Reference: [5.3.1.41] [43] 5 7 Reference: [5.3.1.44] [44] 9 Reference: [5.3.1.52] . [45] ± 189 Reference: [5.4.1.58] [46] – 1 + 2i, – 1 – 2i
Algebra II Regular Study Guide Name________________________________ Date_______ Period____ Reference: [5.4.1.81] [47] 5 − 12i Reference: [5.4.1.77] [48] 1 + 3i Reference: [5.5.1.101] [49] 5, –7 Reference: [5.7.1.140] y 2 1 –4 –3 1 –1 (–1, –3) [50] –4 2 x

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Algebra ii study guide

  • 1. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 1. State the property that is illustrated. 3 ⋅ (5 ⋅ 7) = (3 ⋅ 5) ⋅ 7 2. Evaluate –3y + x + 30 when x = –3 and y = 9. 3. Evaluate the expression. 60 – (15)(2) ÷ 3 4. Evaluate (7 + 5y) ÷ 3x when x= 1 6 and y = 3. 5. Solve the equation. − 3x + 5 = −7 x − 4 6. Solve the equation. − x + 3 = 7 x + 8 7. For 1980 through 1990, the population, P, (in thousands), of Hawaii can be modeled by P = 17(t + 56.6) where t = 0 represents 1980. What was the population in 1987? 5 ( F − 32) 8. Solve for F: C = 9 9. Solve for P: A = P + Prt 10. A rectangle is 5 feet longer than it is wide. The perimeter of the rectangle is 34 feet. What is the length of the rectangle? 11. Solve the inequality. Then graph your solution. 2 x + 5 ≥ 2 − ( x − 9)
  • 2. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 12. Is x = –7 a solution of the inequality 5x − 7 ≤ 3( x − 7) ? Solve: 13. x − 4 ≥ 3 14. x + 7 ≥ 9 15. Is the relation 4 – – la, – 2f, a5, – 2f, a6, – 2fqa function? 16. Find the range of the relation {(4, – 3), (– 5, 1), (– 1, 2)}. 17. Find F1I. f ( x) = 18x H3K f − 2 − 12 x − 3 18. Find the slope of the line passing through the points (–3, 3) and (6, 2). 5 [A] 3 [B] 1 [C] −9
  • 3. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 1 − [D] 9 19. Find the slope and y-intercepts of the line. 5x − 4 y = 20 2 y = − x−2 3 20. Graph the line. 21. Find the slope and y-intercepts of the line. 4 x − 3y = 36 22. Write the equation of the line, in slope-intercept form, that passes through the point (− 2, − 2) and has slope − 3 . 23. Write the equation in slope-intercept form. Then identify the slope and y-intercept. 18x − 42 y = 24 24. The variables x and y vary directly and y = –7 when x = 14. Write an equation that relates the variables. 25. For the following data:
  • 4. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ A. Make a scatter plot of the data. B. Approximate the best fitting line for the data. C. Find an equation of your line of best fit. x 1 2 3 4 5 6 7 8 y 175 41 4.95 7 815 111 1195 14 . . . . . y x 2 4 y>− 3 26. Graph the inequality in a coordinate plane. 3 27. Is the ordered pair (–7, 2) a solution of the inequality 3x + 10 y ≥ −1 ? 28. Graph: − y ≤ 4 x − 7
  • 5. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 29. Graph the equation. y = 2 x + 5 30. Find the solution to the system by graphing. x+ y = –7 2x − y = – 2 31. Is (5, –2) a solution of the system? 2x + 6y = –2 2x + y = 6 32. The drama club sold 1500 tickets for the end-of-year performance. Admission prices were $12 for adults and $6 for students. The total amount collected at the box office was $16,200. How many students attended the play? 4x − 4 y = 4 33. Solve the linear system: 3x + 4 y = – 25 34. Graph the system of linear inequalities: y ≥ x−3 3x + y ≥ – 1 35. Decide if the given ordered triple is a solution of the following system of equations: (1, –2, 4)
  • 6. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 3x + 2 y + 3z = 11 2 x − 4 y + z = 14 x + y − 5z = – 21 36. Solve the system of equations: x + y + z = 5 − 2 x − y + z = – 15 x − 2y − z = 6 2 37. Does the parabola open up or down? y = 4 + 6x − 2 x 2 38. Sketch the graph of the equation. y = x − 2 x + 3 2 39. Write in standard form and graph: y = ( x − 1) + 2 40. Factor the expression: 8x 2 − 25 + 10x 41. The height of a triangle is three feet longer than the base. The area of the triangle is 44 square feet. Find the height and base of the triangle.
  • 7. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 42. Find the zeros of the equation. x 2 + 2 x − 15 = y 43. Simplify the expression: 175 44. Solve for x: 5 x 2 = 405 45. Solve the equation. Round the solutions to two decimal places. 7 x 2 − 2 = 23 46. Solve: x 2 + 2 x + 5 = 0 Write the expression as a complex number in standard form. 2 3 − 2i 47. a f 48. − i + (7 − 5i) − 3(2 − 3i) 49. Solve the equation by completing the square. x 2 + 2 x − 35 = 0 2 50. Sketch the graph of the inequality. y ≥ 2 x + 4 x − 1
  • 8. Algebra II Regular Study Guide Name________________________________ Date_______ Period____
  • 9. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ Reference: [1.1.2.13] [1] Associative property for multiplication Reference: [1.2.1.21] [2] 0 Reference: [1.2.1.25] [3] 50 Reference: [1.2.1.27] [4] 44 Reference: [1.3.1.46] 9 x=− 4 [5] Reference: [1.3.1.42]
  • 10. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 5 x=− 8 [6] Reference: [1.3.2.52] [7] 1,081,200 Reference: [1.4.2.62] 9 C + 32 [8] F = 5 Reference: [1.4.2.64] A P= 1 + rt [9] Reference: [1.5.2.75] [10] 11 feet Reference: [1.6.1.81]
  • 11. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ [11] x ≥ 2 – 0 1 2 3 4 5 1 x Reference: [1.6.1.85] [12] Yes Reference: [1.7.1.92] [13] x ≤ 1 or x ≥ 7 Reference: [1.7.1.90] [14] x ≤ – 16 or x ≥ 2 Reference: [2.1.1.3] [15] Yes Reference: [2.1.1.1]
  • 12. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ [16] {–3, 1, 2} Reference: [2.1.2.10] [17] 3 Reference: [2.2.1.15] [18] [D] Reference: [2.3.1.32] 5 slope = 4 ; y-intercept = (0, -5) [19] Reference: [2.3.1.40] 1 1 x –5 –4 –3 –3 –4 –5 [20] y
  • 13. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ Reference: [2.3.1.34] 4 slope = 3 ; y-intercept = (0, –12) [21] Reference: [2.4.1.46] [22] y = − 3x − 8 Reference: [2.4.1.50] 3 4 3 4 y= x− − 7 7 ; Slope: 7 ; y-intercept: (0, 7 ) [23] Reference: [2.4.2.63] 1 y=− x 2 [24] Reference: [2.5.2.72]
  • 14. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ y x [25] . y = 175x Reference: [2.6.1.85] y 3 2 1 –3 –2 –1 [26] 1 2 3 x –3 Reference: [2.6.1.80] [27] Yes Reference: [2.6.1.74]
  • 15. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ y 10 10 x 10 –10 x –10 [28] Reference: [2.8.1.114] y 10 –10 [29] –10 Reference: [3.1.1.3]
  • 16. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ y 10 –10 [30] (–3, –4) 10 –10 Reference: [3.1.1.11] [31] No Reference: [3.1.2.18] [32] 300 Reference: [3.2.1.23] [33] (–3, –4) Reference: [3.3.1.45] x
  • 17. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ 10 y −10 [34] 10 −10 Reference: [3.6.1.74] [35] yes Reference: [3.6.1.77] [36] (6, 1, –2) Reference: [5.1.1.5] [37] Down Reference: [5.1.1.11] x
  • 18. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ y 3 2 (1, 2) 1 –2 1 2 3 4 x [38] Reference: [5.1.1.15] 2 [39] y = x – 2 x + 3 y 5 −5 5 x −5 Reference: [5.2.1.27] [40] (2 x + 5)(4 x − 5) Reference: [5.2.1.36]
  • 19. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ [41] Base: 8 ft; Height: 11 ft Reference: [5.2.2.39] [42] –5, 3 Reference: [5.3.1.41] [43] 5 7 Reference: [5.3.1.44] [44] 9 Reference: [5.3.1.52] . [45] ± 189 Reference: [5.4.1.58] [46] – 1 + 2i, – 1 – 2i
  • 20. Algebra II Regular Study Guide Name________________________________ Date_______ Period____ Reference: [5.4.1.81] [47] 5 − 12i Reference: [5.4.1.77] [48] 1 + 3i Reference: [5.5.1.101] [49] 5, –7 Reference: [5.7.1.140] y 2 1 –4 –3 1 –1 (–1, –3) [50] –4 2 x