Algebra II First Semester Exam

Class: Date: Algebra II First Semester Exam 2013-14 1. Which number line shows the graphs of 10 and 7 3? b. c. d. 2. A string is 0.5 meters long. What is its length in centimeters? 0.5 centimeters b. 0.05 centimeters c. 500 centimeters d. 50 centimeters 3. 3x = 42 16 b. 17 c. 15 d. 14 Determine which value is a solution of the equation. 4. 10x + 7 = 57 64 b. 50 c. 2 d. 5 5. 10 5w = 25 20 c. 3 b. 7 d. 15 1

6. The literature club is printing a storybook to raise money. The print shop charges $3 for each book, and $45 to create the film. How many books can the club print if their budget is $525? 165 b. 170 c. 175 d. 160 7. Use an equation to model the sentence. How many raisins are left in a jar of 49 raisins after you have eaten some? R = 49 N b. R = 49 N c. R = N 49 d. R = 49 + N 8. Solve for A : B = 5 (A 11) 7 7B + 55 5 b. 7B + 50 7 c. 7B + 77 5 d. 7B + 72 7 9. An oil tank contains 208.3 gallons of oil. Whenever the amount of oil drops below 50 gallons, an alarm sounds. If 182.5 gallons are pumped into a delivery truck, how many gallons must be pumped back into the tank in order to shut off the alarm? at least 25.4 gallons b. at least 24.2 gallons c. at least 134.1 gallons d. at least 25.8 gallons 10. On a road in the city of Hinkley, the maximum speed is 50 miles per hour and the minimum speed is 20 miles per hour. If x represents speed, which sentence best expresses this condition? 50 x 20 b. 50 x 20 c. 50 x 20 d. x 20 < 50 Ï 11. Find the range of the relation ÔÊ Ë 4,5 Ê Ë Á 3, 2 ˆ, Ê Ì Ë Á 1, 1ˆ Ô ÓÔ Ô { 5, 2, 1} c. { 4, 3,1} b. { 4,3, 1} d. { 5,2,1} 2

12. Graph f (x) = 1 4 x +6. c. b. d. 13. Find the slope of the line passing through the points Ê Ë Á 5,7 ˆ and Ê Ë Á 4,2 ˆ. 9 1 c. 5 9 5 b. 9 d. 9 3

Graph the equation. 14. 4x + 8y = 32 c. b. d. 15. Write the equation of the line, in slope-intercept form, that passes through the point Ê Ë Á 2,3ˆ and has slope 3. y = 3x + 9 c. y = 3x 9 b. y = 3x 9 d. y = 3x + 9 16. Which equation represents a line that passes through the point ( 5, 5) and has slope 3? y = 3x 10 c. y = 3x 10 b. y = 3x + 10 d. y = 3x + 10 17. Write an equation to model the following situation. An amusement park charges $10.00 admission and $2.00 per ride. y = 2x + 10 c. y = 10x + 2 b. y = 10x 2 d. y = 2x + 10 4

18. In 1979 the Wincom river was 27 feet below the bridge. Because of silt build-up in the river bottom the river was only 18 feet below the bridge by 1989. Which of the following gives the correct equation for d, the distance of the river from the bridge, where t = 0 represents 1979? If the silt build-up continues at the same rate, what year will the river reach the bridge? d = 10 9 t 27; 2011 c. d = 27 9 t; 2009 10 b. d = 27 + 10 9 t; 2011 d. d = 27 + 9 t; 2009 10 19. Write the standard form of the equation of the line that passes through the point Ê Ë Á4,1ˆ and is parallel to the line 3x + 2y = 5. 3x 2y = 5 c. 4x + y = 5 b. 3x + 2y = 11 d. 3x + 2y = 14 20. Which equation represents the scatter plot? y = 2 3x c. y = 3 3x b. y = 3x + 2 d. y = 3x 2 21. The number of in-line skates sold between 1982 and 1991 can be modeled by the equation I = 7735 + 1 9 9 x. The number of roller skates sold during the same period can be modeled by S = 6305 1 x, where x is the 4 4 year. Use a graph to determine what year sales of in-line skates will exceed sales of roller skates. 1985 b. 1984 c. 1986 d. 1983 Solve the linear system. 22. 4x 3y = 27 4x + 4y = 8 ( 5, 5) c. (3, 5) b. ( 1, 5) d. no solution 5

23. Which ordered triple is a solution of the system of equations? 16x 8y + 4z = 2 8x 4y 8z = 8 12x 4y 16z = 7 ( 3 2, 3 4, 1 2 ) c. ( 3 4, 3 2, 1 2 ) b. ( 3 4, 3 2, 1 2 ) d. (1, 3 2, 1 4 ) Solve the system of equations. 24. x + y + z = 13 2x y + z = 4 x 2y z = 18 (7, 5, 7) c. ( 7, 5, 7) b. ( 1, 7, 5) d. (1, 7, 5) 25. If A = 3 8, find 2A. b. 7 4 6 16 7 4 5 10 9 2 c. d. 6 8 14 4 6 16 14 8 6

26. Student Government and the cheerleaders at a local school are ordering supplies. The supplies they need are listed below. If a bottle of paint costs $5, a roll of paper costs $12, and a roll of tape costs $2, which of the following shows the use of matrices to find the total cost of supplies for each group? 5 12 15 5 12 = [ 482] 10 14 7 2 12 15 5 b. 5 12 2 = [ 482] 10 14 7 5 12 15 5 c. 12 = 250 10 14 7 2 232 12 15 5 d. 5 12 2 = 250 10 14 7 232 7

27. A real estate agent is writing a listing for a triangular piece of land. She has to include the number of square feet for the property and has to calculate it from a plot that shows the following information: one corner of the plot is 140 feet south and 148 feet east from the upper vertex of the plot, the other corner is 20 feet south and 252 feet east from the upper vertex of the plot. Which of the following shows the use of matrices to find the area of the piece of land? 0 0 1 Area = ± 1 148 140 1 2, Area = 16,160 square feet 252 20 1 1 1 1 b. Area = ± 1 148 140 1 2, Area = 16,160 square feet 252 20 1 1 1 1 c. Area = ± 1 148 140 1 2, Area = 32,320 square feet 252 20 1 0 0 1 d. Area = ± 1 148 140 1 2, Area = 32,320 square feet 252 20 1 Find the inverse of the matrix. 1 0 1 28. 1 1 9 0 1 9 0 1 1 È 0 1 1 9 9 8 c. 9 9 9 1 1 1 0 1 1 È 1 1 1 0 1 1 b. 9 9 10 d. 9 9 10 1 1 1 1 1 1 8

29. Use an inverse matrix to solve the linear system. 16x + 5y = 211 16x + y = 183 Which of the following shows the correct solution? 1È 16 16 211 = 11 c. 5 16 183 7 1È 16 5 211 b. = 11 d. 16 1 183 7 1È 16 5 211 = 15 16 1 183 4 1È 16 16 211 = 15 5 16 183 4 The inverse of the coefficient matrix is given. Use the inverse to solve the linear system. 30. 3x + y + 4z = 34 2x 3z = 23 4x + y + 6z = 48 È 3 2 3 A 1 = 0 2 1 2 1 2 x = 4, y = 2, z = 5 c. x = 4, y = 2, z = 5 b. x = 5, y = 5, z = 5 d. x = 5, y = 5, z = 5 31. Graph y = 1 4 x 2. c. b. d. 9

Graph. 32. y = x 2 3 c. b. d. 33. y = 3x 2 + x + 1 c. b. d. 10

34. Graph the function. Label the vertex, axis of symmetry, and x-intercepts. y = 2( x + 2) ( x + 4) c. b. vertex: ( 3, 2) axis of symm: x = 3 x-intercepts: 4, 2 d. vertex: (3, 2) axis of symm: x = 3 x-intercepts: 2, 4 vertex: ( 3, 2) axis of symm: x = 3 x-intercepts: 4, 2 vertex: (3, 2) axis of symm: x = 3 x-intercepts: 2, 4 11

Write in standard form and graph. 35. y = 3( x 5) ( x 6) y = 3x 2 11x + 30 c. y = 3x 2 33x + 90 b. y = 3x 2 11x + 30 d. y = 3x 2 33x + 90 12

36. y = ( x 1) 2 + 2 y = x 2 2x+ 1 c. y = x 2 + 2x+ 3 b. y = x 2 2x+ 3 d. y = x 2 + 2x+ 1 Factor the expression. 37. x 2 + 7x+ 12 ( x+ 4) ( x+ 3) c. ( x 4) ( x 3) b. ( x 6) ( x 2) d. ( x+ 6) ( x+ 2) 38. Write as the product of two factors: x 2 + 3x 40 ( x 5) ( x + 8) c. ( x + 5) ( x 8) b. ( x 5) ( x 8) d. ( x + 5) ( x + 8) 13

39. Find the x-intercepts of the graph of y = x 2 11x + 18. 2, 9 c. -3, -5 b. 3, 5 d. -2, -9 Factor the expression. 40. 64y 2 49 (64y + 1)(y 49) c. (8y 7)(8y 7) b. (8y + 7)(8y 7) d. (8y + 7)(8y + 7) Find the zeros of the function if y is a function of x. 41. 4x 2 5x = 21 + y x = 7 and x = 3 4 c. x = 7 and x = 3 4 b. x = 3 and x = 7 4 d. x = 3 and x = 7 4 Solve. 42. 3( x 8) 2 29 = 37 8 ± 22 c. 8 ± 22 b. 66 ± 3 d. 66 ± 3 14

Solve. 43. x 2 10x + 29 = 0 5 + 4i, 5 4i c. 5 + 4i, 5 4i b. 5 + 2i, 5 2i d. 5 + 2i, 5 2i 44. Solve by completing the square: x 2 2x 24 = 0-4, 6 c. -4, -6 b. 4, 6 d. 4, -6 Solve by completing the square. 45. 36x = 4x 2 50 b. 9 31 4 9 31 2 and 9 + 31 4 and 9 + 31 2 c. d. 9 31 4 9 31 2 and 9 + 31 4 and 9 + 31 2 Find the maximum value of the quadratic equation. 46. y = 8x 2 + 96x 182 max = 94 c. max = 106 b. max = 182 d. max = 6 47. y = 6x 2 + 36x + 18 max = 72 c. max = 3 b. max = 48 d. max = 18 Solve. 48. 3x 2 + x = 9 b. 1 + i 109 6 1 + i 107 6, 1 i 109 6, 1 i 107 6 c. d. 1 + i 107 6 1 + i 109 6,, 1 i 107 6 1 i 109 6 49. A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given by d = 16t 2 2t + 733. How long after the rock is thrown is it 400 feet from the ground? 37 8 sec b. 45 8 sec c. 11 2 sec d. 9 2 sec 50. Write the equation y = x 2 + 8x + 7 in the form y = a( x h) 2 + k. y = ( x + 4) 2 9 c. y = ( x + 4) 9 b. y = ( x 9) 2 4 d. y = ( x 4) 2 9 15

Algebra II First Semester Exam 2013-14 Answer Section 1. ANS: D PTS: 1 DIF: Level A REF: MAL20070 NAT: NCTM 9-12.NOP.1.b TOP: Lesson 1.1 Apply Properties of Real Numbers KEY: square root graph number line BLM: Comprehension 2. ANS: D PTS: 1 DIF: Level B REF: MAL20091 TOP: Lesson 1.1 Apply Properties of Real Numbers KEY: word convert metric measure BLM: Application 3. ANS: D PTS: 1 DIF: Level A REF: MAL20118 TOP: Lesson 1.3 Solve Linear Equations KEY: solve equation division variable divide multiply multiplication one-step BLM: Comprehension 4. ANS: D PTS: 1 DIF: Level A REF: MAL20115 TOP: Lesson 1.3 Solve Linear Equations KEY: linear whole solve equation two-step BLM: Comprehension 5. ANS: C PTS: 1 DIF: Level B REF: MAL20120 TOP: Lesson 1.3 Solve Linear Equations KEY: solve integer equation two-step linear BLM: Comprehension 6. ANS: D PTS: 1 DIF: Level B REF: MAL20126 TOP: Lesson 1.3 Solve Linear Equations KEY: solve word linear step(2) BLM: Application 7. ANS: A PTS: 1 DIF: Level B REF: MAL20127 TOP: Lesson 1.3 Solve Linear Equations KEY: sentence equation model BLM: Application 8. ANS: A PTS: 1 DIF: Level B REF: MAL20146 NAT: NCTM 9-12.ALG.1.b TOP: Lesson 1.4 Rewrite Formulas and Equations KEY: solve equation variable BLM: Comprehension 9. ANS: B PTS: 1 DIF: Level B REF: MAL20168 TOP: Lesson 1.6 Solve Linear Inequalities KEY: inequality solve word BLM: Application 10. ANS: C PTS: 1 DIF: Level B REF: MAL20176 TOP: Lesson 1.6 Solve Linear Inequalities KEY: English units inequality word metric condition BLM: Application 11. ANS: A PTS: 1 DIF: Level A REF: MAL20194 TOP: Lesson 2.1 Represent Relations and Functions KEY: function domain range relation BLM: Knowledge 12. ANS: C PTS: 1 DIF: Level B REF: MAL20202 NAT: NCTM 9-12.ALG.1.c TOP: Lesson 2.1 Represent Relations and Functions KEY: linear equation slope-intercept graph BLM: Comprehension 13. ANS: D PTS: 1 DIF: Level A REF: MAL20211 STA: MI.MIGLC.MTH.06.9-12.A1.2.9 TOP: Lesson 2.2 Find Slope and Rate of Change KEY: slope BLM: Knowledge 1

14. ANS: D PTS: 1 DIF: Level B REF: MAL20240 TOP: Lesson 2.3 Graph Equations of Lines KEY: graph linear equation BLM: Knowledge 15. ANS: D PTS: 1 DIF: Level B REF: MAL20251 TOP: Lesson 2.4 Write Equations of Lines KEY: slope-intercept line point BLM: Knowledge 16. ANS: C PTS: 1 DIF: Level B REF: MAL20252 TOP: Lesson 2.4 Write Equations of Lines KEY: linear point equation slope slope-intercept BLM: Knowledge 17. ANS: A PTS: 1 DIF: Level B REF: MAL20261 TOP: Lesson 2.4 Write Equations of Lines KEY: equation word model linear BLM: Application 18. ANS: C PTS: 1 DIF: Level B REF: MAL20264 STA: MI.MIGLC.MTH.06.9-12.A3.1.1 MI.MIGLC.MTH.06.9-12.A3.1.2 TOP: Lesson 2.4 Write Equations of Lines KEY: word linear equation BLM: Application 19. ANS: D PTS: 1 DIF: Level B REF: MAL20271 TOP: Lesson 2.4 Write Equations of Lines KEY: parallel line general equation BLM: Comprehension 20. ANS: B PTS: 1 DIF: Level B REF: MAL20291 NAT: NCTM 9-12.DAP.2.b NCTM 9-12.DAP 2.e NCTM 9-12.DAP.1.d TOP: Lesson 2.6 Draw Scatter Plots and Best-Fitting Lines KEY: scatter plot BLM: Knowledge 21. ANS: A PTS: 1 DIF: Level C REF: MAL20352 NAT: NCTM 9-12.ALG.2.b TOP: Lesson 3.1 Solve Linear Systems by Graphing KEY: word linear system graph BLM: Application 22. ANS: C PTS: 1 DIF: Level A REF: MAL20356 NAT: NCTM 9-12.ALG.2.b TOP: Lesson 3.2 Solve Linear Systems Algebraically KEY: linear solve system substitution two variables BLM: Comprehension 23. ANS: B PTS: 1 DIF: Level B REF: MAL20400 TOP: Lesson 3.4 Solve Systems of Linear Equations in Three Variables KEY: substitute equation identify system ordered triple BLM: Comprehension 24. ANS: D PTS: 1 DIF: Level B REF: MAL20405 TOP: Lesson 3.4 Solve Systems of Linear Equations in Three Variables KEY: solve system linear three three equations three-variable BLM: Comprehension 25. ANS: D PTS: 1 DIF: Level A REF: MAL20429 NAT: NCTM 9-12.NOP.3.a NCTM 9-12.NOP.2.b TOP: Lesson 3.5 Perform Basic Matrix Operations KEY: multiply matrix constant BLM: Knowledge 26. ANS: C PTS: 1 DIF: Level C REF: MAL20464 NAT: NCTM 9-12.NOP.2.b NCTM 9-12.NOP.3.a TOP: Lesson 3.6 Multiply Matrices KEY: word matrix multiply BLM: Application 2

27. ANS: A PTS: 1 DIF: Level B REF: MAL20478 TOP: Lesson 3.7 Evaluate Determinants and Apply Cramer's Rule KEY: word matrix determinant area BLM: Application 28. ANS: A PTS: 1 DIF: Level B REF: MAL20502 TOP: Lesson 3.8 Use Inverse Matrices to Solve Linear Systems KEY: inverse matrix BLM: Knowledge 29. ANS: B PTS: 1 DIF: Level B REF: MAL20504 TOP: Lesson 3.8 Use Inverse Matrices to Solve Linear Systems KEY: equation matrix inverse matrix BLM: Comprehension 30. ANS: A PTS: 1 DIF: Level B REF: MAL20507 NAT: NCTM 9-12.NOP.1.c NCTM 9-12.NOP.2.b TOP: Lesson 3.8 Use Inverse Matrices to Solve Linear Systems KEY: system matrix inverse matrix solve BLM: Comprehension 31. ANS: C PTS: 1 DIF: Level A REF: MAL20514 TOP: Lesson 4.1 Graph Quadratic Functions in Standard Form KEY: graph quadratic function BLM: Knowledge 32. ANS: B PTS: 1 DIF: Level B REF: MAL20517 TOP: Lesson 4.1 Graph Quadratic Functions in Standard Form KEY: graph parabola standard form quadratic function BLM: Knowledge 33. ANS: C PTS: 1 DIF: Level B REF: MAL20522 TOP: Lesson 4.1 Graph Quadratic Functions in Standard Form KEY: quadratic graph BLM: Knowledge 34. ANS: A PTS: 1 DIF: Level B REF: MAL20545 TOP: Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form KEY: parabola quadratic function intercept BLM: Knowledge 35. ANS: C PTS: 1 DIF: Level B REF: MAL20549 TOP: Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form KEY: graph factored form quadratic function BLM: Knowledge 36. ANS: B PTS: 1 DIF: Level B REF: MAL20553 TOP: Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form KEY: graph parabola quadratic BLM: Knowledge 37. ANS: A PTS: 1 DIF: Level B REF: MAL20566 TOP: Lesson 4.3 Solve x2 + bx + c = 0 by Factoring KEY: factor quadratic trinomial BLM: Knowledge 38. ANS: A PTS: 1 DIF: Level B REF: MAL20567 TOP: Lesson 4.3 Solve x2 + bx + c = 0 by Factoring KEY: factor quadratic trinomial BLM: Knowledge 39. ANS: A PTS: 1 DIF: Level B REF: MAL20550 TOP: Lesson 4.3 Solve x2 + bx + c = 0 by Factoring KEY: quadratic x-intercepts factor BLM: Knowledge 40. ANS: B PTS: 1 DIF: Level B REF: MAL20585 TOP: Lesson 4.4 Solve ax2 + bx + c = 0 by Factoring KEY: factor difference of squares BLM: Knowledge 3

41. ANS: B PTS: 1 DIF: Level C REF: MAL20599 NAT: NCTM 9-12.ALG.1.c TOP: Lesson 4.4 Solve ax2 + bx + c = 0 by Factoring KEY: factor rational root quadratic BLM: Knowledge 42. ANS: C PTS: 1 DIF: Level B REF: MAL20616 STA: MI.MIGLC.MTH.06.9-12.A1.1.4 TOP: Lesson 4.5 Solve Quadratic Equations by Finding Square Roots KEY: solve quadratic BLM: Knowledge 43. ANS: D PTS: 1 DIF: Level B REF: MAL20661 STA: MI.MIGLC.MTH.06.9-12.A1.2.9 TOP: Lesson 4.7 Complete the Square KEY: solve equation complex quadratic BLM: Knowledge 44. ANS: A PTS: 1 DIF: Level B REF: MAL20663 TOP: Lesson 4.7 Complete the Square KEY: solve equation quadratic complete square BLM: Knowledge 45. ANS: D PTS: 1 DIF: Level B REF: MAL20672 TOP: Lesson 4.7 Complete the Square KEY: square solve equation quadratic complete BLM: Knowledge 46. ANS: C PTS: 1 DIF: Level B REF: MAL20679 NAT: NCTM 9-12.ALG.1.c TOP: Lesson 4.7 Complete the Square KEY: quadratic max parabola vertex BLM: Knowledge 47. ANS: A PTS: 1 DIF: Level B REF: MAL20680 NAT: NCTM 9-12.ALG.1.c TOP: Lesson 4.7 Complete the Square KEY: parabola vertex quadratic maximum BLM: Knowledge 48. ANS: C PTS: 1 DIF: Level B REF: MAL20690 NAT: NCTM 9-12.NOP.1.b TOP: Lesson 4.8 Use the Quadratic Formula and the Discriminant KEY: equation complex quadratic function imaginary root BLM: Knowledge 49. ANS: D PTS: 1 DIF: Level B REF: MAL20699 TOP: Lesson 4.8 Use the Quadratic Formula and the Discriminant KEY: solve equation word quadratic BLM: Application 50. ANS: A PTS: 1 DIF: Level B REF: MAL20716 TOP: Lesson 4.10 Write Quadratic Functions and Models KEY: equation quadratic parabola vertex BLM: Knowledge 4