Algebra 2 Honors Mid-Term Exam

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1 lass: ate: I: E lgebra 2 Honors Mid-Term Exam Multiple hoice Identify the choice that best completes the statement or answers the question. Write the following quadratic function in vertex form. Then, identify the axis of symmetry. 1. y = x x 3 a. The vertex form of the function is y = ( x + 5) The equation of the axis of symmetry is x = 28. b. The vertex form of the function is y = ( x + 5) The equation of the axis of symmetry is x = 28. c. The vertex form of the function is y = ( x + 5) The equation of the axis of symmetry is x = 5. d. The vertex form of the function is y = ( x 5) The equation of the axis of symmetry is x = 5. Efficient Homemakers Ltd. makes canvas wallets and leather wallets as part of a money-making project. For the canvas wallets, they need two yards of canvas and two yards of leather. For the leather wallets, they need four yards of leather and three yards of canvas. Their production unit has purchased 44 yards of leather and 40 yards of canvas. Let x be the number of leather wallets and y be the number of canvas wallets. 3. Write a system of inequalities to represent the number of the leather and canvas wallets that can be produced. a. 4x + 2y 44 and 3x + 2y 40 x 0 and y 0 b. 5x + 3y 40 and 4x + 6y 44 x 0 and y 0 c. 2x + 4y 44 and 2x + 3y 40 x 0 and y 0 d. 4x 2y 44 and 3x 2y 40 x 0 and y 0 4. If the profit on a canvas wallet is $25 and the profit on a leather wallet is $40, write a function for the total profit for both wallets. a. f(x, y) = x + 25y b. f(x, y) = 40x + y c. f(x, y) = 40x + 25y d. f(x, y) = 25x + 40y 5. raw the graph showing the feasible region to represent the number of the leather and canvas wallets that can be produced. a. 2. List the coordinates of the vertices of the feasible region to represent the number of the leather and canvas wallets that can be produced. a. (0, 0), (0, 20), (11, 0), (3, 19) b. (0, 0), (5, 0), (0, 11), (2, 8) c. (0, 0), (22, 0), (0, 11), (14, 4) d. (0, 0), (4, 14), (11, 0), (0, 20) 1

2 I: E b. 6. What is the maximum profit? a. $440 b. $510 c. $550 d. $250 c. d Find the product, if possible a. Not possible b. c. d. a. b. c d. Not possible 2

3 I: E 9. shley bought 7 boxes of erasers. Each bag contained the same number of erasers. ltogether the bags contained a total of 84 erasers. Using the equation 7b = 84, how many erasers are in each box? a. 7 b. 11 c. 10 d Marie changed the dimensions of a planter she was building. The sketch below shows the dimension of the original planter. The new planter is to have dimensions that are half as large. What is the difference in area between the two planters? a. 432 in 2 c. 576 in 2 b. 144 in 2 d. 100 in 2 3

4 I: E Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located x 2 x + 2 = 0 a. c. b. One solution is between 0 and 2, while the other solution is between 1 and 1. d. One solution is between 0 and 1, while the other solution is between 1 and 2. One solution is between 0 and 1, while the other solution is between 1 and 2. One solution is between 1 and 2, while the other solution is between 0 and 1. 4

5 I: E 12. On a sunny day, a 3-foot red kangaroo casts a shadow that is 5 feet long. The shadow of a nearby eucalyptus tree is 15 feet long. Find the height of the tree. a. 9 ft b. 75 ft c. 45 ft d. 25 ft 13. The Studio charges a $63 starting fee plus $12 per class. rt! charges no starting fee and $15 per class. For how many classes will the cost be the same at both places? a. 27 b. 5 c. 21 d Find the value of the determinant a. 17 b. 37 c. 19 d The range of a set of scores is 23, and the lowest score is 39. Write and solve an equation to find the highest score. (Hint: In a data set, the range is the difference between the highest and the lowest values.) a. h + 39 = 23 The highest score is 16. b. h 39 = 2 23 The highest score is 85. c. h 39 = 23 The highest score is 62. d. h + 23 = 39 The highest score is 16. Simplify. 16. ( 5)( 6i)(7i) a. 210 b. 210i c. 210i d ( 2 + 7i)(7 10i) a i b i 70i 2 c i d i Write an equation in slope-intercept form for the line that satisfies the following condition. passes through ( 1, 18), perpendicular to the graph of 2x + 17y = 10 a. y = 1x b. y = 1x + 17 c. y = 17 2 x d. y = 17 2 x Solve the given system of equations. 19. a = 36 2a + c = 0 7b + 7c = 21 a. a = 36, b = 72, c = 69 b. a = 36, b = 69, c = 72 c. a = 36, b = 69, c = 72 d. a = 72, b = 36, c = Solve V = IR for R. a. R = I V b. R = VI c. R = V + I d. R = V I 5

6 I: E Find the exact solution of the following quadratic equation by using the Quadratic Formula. 21. x 2 x = 30 Ï a. Ì Ô 10, 12 ÓÔ Ô Ô Ï b. Ì Ô 6, 5 ÓÔ Ô Ô Ï c. Ì Ô 5, 6 ÓÔ Ô Ô Ï d. Ì Ô 30, 31 ÓÔ Ô Ô 22. Write the equation 3y = 5 x 0.4 in standard 14 form. Identify,, and. a. 420x 5y = 56 where = 420, = 50, and = 56. b. 50x 420y = 56 where = 50, = 420, and = 56. c. 5x + 42y = 5.6 where = 5, = 42, and = 0.4. d. 420x + 50y = 56 where = 420, = 50, and = There are four fruit trees in the corners of a square backyard with 30-ft sides. What is the distance between the apple tree and the plum tree P to the nearest tenth? 24. The triangle has an area of 150 square centimeters. Use the formula = 1 bh to find 2 its height. a. 5 centimeters b. 20 centimeters c. 10 centimeters d. 75 centimeters Find the coordinates of the vertices of the figure formed by each system of inequalities. 25. y 6 2x + y 2 y 2x + 6 a. (4, 6), (6, 6), (1, 4) b. (4, 4), ( 1, 6), ( 6, 6) c. (4, 6), ( 6, 6), ( 1, 4) d. (4, 6), (6, 6), (0, 8) a ft b ft c ft d ft 6

7 I: E 26. The city of Plantation plans to build a new community park with a public swimming pool. The diagram below shows the area of the proposed swimming pool and the stone deck that will surround it. Write a polynomial to represent the area of the deck region. Then find the value for x, given that the area of the deck region is 24 square units. a. 3x 2 + 7x 6; x = 5 units c. 3x 2 + 7x 6; x = 2 units b. 3x 2 + x 6; x = 4 units d. 3x 2 + x 6; x = 3 units 27. Write an equation in slope-intercept form for the line that satisfies the following condition. 7 slope and passes through (6, 20) 12 a. y = 7 12 x 20 b. y = 7 12 x 23.5 c. y = 20x d. y = 6x The average of Paula s two test scores must be 80 or more for her to get at least a in the class. She got a 72 on her first test. What grades can she get on the second test to make at least a in the class? a. at least 92 b. at least 76 c. at least 84 d. at least 88 7

8 I: E 29. Latisha is on page 30 of her book and reads 3 pages every night. Sal is on page 40 of the same book and reads 2 pages every night. How long will it take Latisha to be further in the book than Sal? a. 3 nights b. 71 nights c. 11 nights d. 15 nights 30. Solve the given equation. x + 2y y = 16 x 3 a. The solution set is ( 10 3, 1 3 ). b. The solution set is ( 22 3, 13 3 ). c. The solution set is ( 13 3, 22 3 ). d. The solution set is (8, 8). 31. The size of a TV screen is given by the length of its diagonal. The screen aspect ratio is the ratio of its width to its height. The screen aspect ratio of a standard TV screen is 4:3. What are the width and height of a 27" TV screen? Write a quadratic equation with the given roots. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers and 4 a. x 2 13x 36 = 0 b. x 2 + 5x 36 = 0 c. x 2 5x 36 = 0 d. x x + 36 = Megaopy will charge $10 for a job plus $0.25 per page. nother company will charge $20 per job $0.05 per page for the same project. For how many pages will the costs be the same regardless of which company is used? a. 25 b. 200 c. 10 d The door on a spacecraft is formed with 6 straight panels that overlap to form a regular hexagon. What is the measure of YXZ? a. m YXZ = 120 o b. m YXZ = 60 o c. m YXZ = 720 o d. m YXZ = 45 o a. width: 16.2 in., height: 21.6 in. b. width: 5.4 in., height: 21.6 in. c. width: 21.6 in., height: 5.4 in. d. width: 21.6 in., height: 16.2 in. 8

9 I: E 35. Find the area of the parallelogram. a. 96 in 2 b. 72 in 2 c. 48 in 2 d. 120 in lex wrote the following equation: 9 7 = 63 Using the commutative propertiy which of the following is equivalent to lex s equation? a = 7 b. 7 9 = 63 c. 9 7 = 63 d = professional cyclist is training for the Tour de France. What was his average speed in kilometers per hour if he rode the 194 kilometers from Laval to lois in 4.5 hours? Use the formula d = rt, and round your answer to the nearest tenth. a kph b kph c kph d kph 9

10 I: E 38. rlene wants to install cable television in her new apartment. There are two cable companies in the area whose prices are listed below. Seven Star able iti able asic Service (30 channels) $10 asic Service (30 channels) $9 Standard Service (57 channels) $30 Standard Service (57 channels) $33 Premium hannels Premium hannels (In addition to the standard service) (In addition to the standard service) One Premium $8 One Premium $7 Two Premiums $13 Two Premiums $14 Three Premiums $20 Three Premiums $21 Write a matrix that represents this information. a. asic Standard One T wo T hree Premium Premium Premium Seven Star iti b. asic Standard Premium Seven Star iti c. asic Standard One T wo T hree Premium Premium Premium Seven Star iti d. asic Standard One T wo T hree Premium Premium Premium Seven Star iti

11 I: E 39. In the figure, Runway 3 crosses Runways 1 and 2 and acts as a transversal. Which pair of angles formed by the runways must be congruent? Write a verbal expression to represent the given equation. 41. w 2 = 32w a. The square of a number is equal to the product of 23 and that number. b. The square of a number is equal to the product of that number. c. The square of a number is equal to the product of 32 and that number. d. The square of a number is equal to 32. Solve the following system of equations by graphing. a. 2 and 4 b. 5 and 6 c. 2 and 8 d. 1 and 2 Find the inverse of the matrix, if it exists. 40. P = a. P 1 does not exist. b. c. d. 1 / 12 1 / 6 5 / 12 1 / 6 1 / 12 1 / 6 5 / 12 1 / 12 1 / 6 1 / 6 5 / 12 1 / y + 3x = 59 y 7x = 4 a. (25, 3) b. (2, 25) c. (5, 24) d. (3, 25) 43. Graph the given relation or equation and find the domain and range. Then determine whether the relation or equation is a function. (3.4, 5.4), ( 1.6, 5.4), ( 4.6, 3.4), ( 4.6, 2.6) a. omain: { 2.6, 3.4, 5.4} Range: { 4.6, 1.6, 3.4} The equation is a function. 11

12 I: E b. d. c. omain: { 4.6, 1.6, 3.4} Range: { 2.6, 3.4, 5.4} The equation is not a function. omain: { 4.6, 5.4, 3.4} Range: { 2.6, 3.4, 1.6} The equation is not a function. Solve the equation by completing the square. 44. x 2 x 6 = 0 Ï a. Ì Ô 3, 2 ÓÔ Ô Ô Ï b. Ì Ô 2, 3 ÓÔ Ô Ô Ï c. Ì Ô 4, 3 ÓÔ Ô Ô Ï d. Ì Ô 4, 6 ÓÔ Ô Ô omain: { 4.6, 1.6, 3.4} Range: { 2.6, 3.4, 5.4} The equation is a function. 12

13 I: E 45. The side of a wooden chest is a quadrilateral with Ä, and Ä. If m = 90, what is the most accurate description of? 46. Meteorologists are planning the location of a new weather station. To optimize radar coverage, the station must be equidistant from three cities located at ( 16, 1), (1, 6), and (1, 18). What are the coordinates where the station should be built? a. ( 4.3, 4.3) b. ( 4, 6) c. ( 7, 9.5) d. ( 7.5, 2.5) Solve each system of equations by using substitution. a. oth pairs of opposite sides are parallel so is a rhombus. Since one angle measures 90, it is a right angle and a rhombus with one right angle is a square. b. oth pairs of opposite sides are parallel so is a parallelogram. Since one angle measures 90, it is a right angle and a parallelogram with one right angle is a square. c. oth pairs of opposite sides are parallel so is a parallelogram. Since one angle measures 90, it is a right angle and a parallelogram with one right angle is a rectangle. d. oth pairs of opposite sides are parallel so is a parallelogram. One angle measuring 90 does not provide enough information to change its description r + 6s = 18 3r 3s = 18 a. (7.5, 4) b. (4, 0) c. (6, 0) d. (6, 0.5) 48. onsider the quadratic function f( x) = 2x 2 + 3x + 2. Find the y-intercept and the equation of the axis of symmetry. a. The y-intercept is 2. The equation of the axis of symmetry is x = 3 4. b. The y-intercept is 3 4. The equation of the axis of symmetry is x = 2. c. The y-intercept is + 2. The equation of the axis of symmetry is x = 3 4. d. The y-intercept is 3 4. The equation of the axis of symmetry is x = 2. 13

14 I: E 49. Graph the quadratic function f(x) = 2x 2 2x 2. a. c. b. d. 14

15 I: E 50. Students in grades 6, 7, and 8 sold a total of 320 concert tickets. Grade 7 students sold 107 tickets and Grade 8 students sold 98 tickets. Use the equation x = 320 to find how many tickets were sold by Grade 6. a. 305 tickets b. 115 tickets c. 9 tickets d. 525 tickets 51. Mrs. Nelson is buying folding chairs that are on sale for $10. If she has $50, which inequality can be solved to show the number of chairs c she can buy? a. 10c < 50 b. 10c 50 c. 10c 50 d. 10c > 50 b. c. 52. Graph the line that passes through (2, 5), perpendicular to a line whose slope is 1 9. a. d. 15

16 I: E 53. Nathan s computer needs repairs. The omputer Guys will charge $75 per hour plus $120 for a new hard drive. omputer Rx will charge $80 per hour plus $95 for a new hard drivet. How long will it take to complete the charge if the total estimates are the same? a. 17 hpurs b hours 56. wooden frame has screws at,,, and so that the sides of it can be pressed to change the angles occurring at each vertex. and Ä, even when the angles change. Why is the frame always a parallelogram? c. 5 hours d. 20 hours 54. Write an equation for the parabola whose vertex is at Ê Ë Á 3, 6 ˆ and which passes through Ê ËÁ 4, 1 ˆ. a. y = ( x + 3) 2 6 b. y = 5 ( x + 3) 2 6 c. y = 5 ( x 3) d. y = 5 ( x 3) Write an equation in slope-intercept form for the line that satisfies the following condition. passes through (4, 4), parallel to the graph of y = 2x + 6 a. y = 2x 12 b. y = 10x 12 c. y = 2x + 2 d. y = 20x + 2 a. One pair of opposite sides is congruent, so is a parallelogram. b. The angles always stay the same, so is a parallelogram. c. One pair of opposite sides is congruent and parallel, so is a parallelogram. d. ll sides are congruent, so is a parallelogram. 57. Jolene bought 3 plants at a greenhouse. Each plant cost $2.50. To calculate the total cost of the plants, Jolene added 3 2 and What property of multiplication did she use? a. ommutative Property b. istributive Property c. Identity Property d. ssociative Property 16

17 I: E 58. In kite PQRS, m QPO = 50 and m QRO = 70. Find m PSR. a. vertice a. m PSR = 120 b. m PSR = 90 c. m PSR = 60 d. m PSR = 100 etermine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value of the function. s: (5, 3), (5, 5), (1, 3) max: f(5, 5) = 10 min: f(1, 3) = 2 b. vertice 59. f(x) = x 2 + 8x + 2 a. The function has a maximum value. The maximum value of the function is 18. b. The function has a minimum value. The minimum value of the function is 46. c. The function has a maximum value. The maximum value of the function is 46. d. The function has a minimum value. The minimum value of the function is triangle has a perimeter of 60 cm. If the area of a triangle is doubled and its height remains constant, what happens to its base length? a. The base length is divided by 2. b. The base length is multiplied by 2. c. The base length is decreased by 2. d. The base length is increased by 2. s: (5, 3), (5, 5), (1, 3) max: f(5, 5) = 10 min: f(1, 3) = 2 Given below are some inequalities. Plot the feasible region graphically. 61. y 3 x 5 y 2x 5 fê ËÁ x,yˆ = x + y 17

18 I: E c. vertice 63. wooden gate has z-shaped boards for support, as shown. Which theorem allows you to conclude that 1 2? s: (5, 3) max: f(5, 3) = 2 min: f(5, 3) = 2 d. vertice a. onsecutive Interior ngles Theorem b. lternate Interior ngles Theorem c. lternate Exterior ngles Theorem d. Perpendicular Transversal Theorem Write an algebraic expression to represent the following verbal expression. 64. the cube of the difference of a number and 43 a. ( 43 x) b. ( x 43) c. ( x + 43) d. x Solve the system of inequalities by graphing. s: (5, 3), (5, 5), (1, 3) max: f(5, 5) = 10 min: f(1, 3) = x > 3 y > 8 a. Solve the equation by using the Square Root Property x x + 16 = 81 a. { 13 2, 5 2 } b. { 5 2, 13 2 } c. { 2, 9} d. { 2} 18

19 I: E b. 66. baker has 16 cups of chocolate chips. His recipe for chocolate chip cookies calls for cups of chocolate chips per batch. Which inequality shows the number of batches of chocolate chip cookies the baker can make? a c < 16 c. b. c. c c 16 < d c Find the area of the triangle with vertices ( 3, 2), (1, 2), and (1, 3). d. a. 12 units 2 b. 20 units 2 c. 8 units 2 d. 10 units 2 19

20 I: E Evaluate the determinant by using diagonals. c a. 20 b. 4 c. 12 d Graph the given inequality. 3x + 12y 1 a. d. b. 20

21 I: E Identify the type of function represented by the graph. 70. a. rational function c. quadratic function b. inverse variation function d. absolute value function Graph the quadratic inequality. b. 71. y < 2x 2 4x + 6 a. c. 21

22 I: E d. FILL-IN RESPONSES Use the spaces below to respond your answers. 72. Find the value of f( 8) and g(3) if f( x) = 1x + 6 and g ( x) = 10x + 29x f( 8) =. g(3) =. 22

23 I: E lgebra 2 Honors Mid-Term Exam nswer Section MULTIPLE HOIE 1. NS: The vertex form of a quadratic function is y = a(x h) 2 + k. The equation of the axis of symmetry of a parabola is x = h. id you use the correct equation of the axis of symmetry of a parabola? id you identify the coordinates of the vertex correctly? orrect! id you check the x-coordinate of the vertex? PTS: 1 IF: asic REF: Lesson 5-7 OJ: nalyze quadratic functions in the form y = a(x - h)^2 + k. ST: M TOP: nalyze quadratic functions in the form y = a(x - h)^2 + k. KEY: Quadratic Functions xis of Symmetry 2. NS: Write the system of inequalities and then graph them. Plot the feasible region to find the vertices. id you plot the inequalities correctly? id you check the intercept of the inequalities? id you check the values of the inequalities? orrect! PTS: 1 IF: verage REF: Lesson 3-4 OJ: Solve real-world problems using linear programming. ST: M M TOP: Solve real-world problems using linear programming. KEY: Linear Programming Real-World Problems 1

24 I: E 3. NS: Read the scenario carefully and frame the required system of inequalities. orrect! You have taken incorrect values for the units of canvas and leather purchased. The values in the first inequality are incorrect. id you check the sign used in the system of inequalities? PTS: 1 IF: asic REF: Lesson 3-4 OJ: Solve real-world problems using linear programming. ST: M M TOP: Solve real-world problems using linear programming. KEY: Linear Programming Real-World Problems 4. NS: Write a suitable function denoting the total profits for both wallets. id you consider the profit on the leather wallets? id you consider the profit on the canvas wallets? orrect! id you substitute the correct values? PTS: 1 IF: asic REF: Lesson 3-4 OJ: Solve real-world problems using linear programming. ST: M M TOP: Solve real-world problems using linear programming. KEY: Linear Programming Real-World Problems 5. NS: Graph the system of inequalities. orrect! id you check the intercept of the inequality? id you plot the inequalities correctly? id you check the values of the inequalities? PTS: 1 IF: verage REF: Lesson 3-4 OJ: Solve real-world problems using linear programming. ST: M M TOP: Solve real-world problems using linear programming. KEY: Linear Programming Real-World Problems 2

25 I: E 6. NS: Substitute the coordinates of the vertices of the feasible region into the appropriate function. id you check the values of inequalities? orrect! You have applied the incorrect intercept of the system of inequalities. id you calculate correctly? PTS: 1 IF: dvanced REF: Lesson 3-4 OJ: Solve real-world problems using linear programming. ST: M M TOP: Solve real-world problems using linear programming. KEY: Linear Programming Real-World Problems 7. NS: Multiplication of matrices is possible if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. The number of columns in the first matrix is equal to the number of rows in the second matrix. orrect! id you check the signs of the resulting matrix? The product of two matrices is obtained by multiplying the columns and rows. PTS: 1 IF: dvanced REF: Lesson 4-3 OJ: Multiply matrices. ST: M TOP: Multiply matrices. KEY: Matrices Multiply Matrices 8. NS: Multiplication of matrices is possible if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. The number of columns in the first matrix is not equal to the number of columns in the second matrix. id you check if the inner dimensions are equal? Is the number of columns in the first matrix equal to the number of rows in the second matrix? orrect! PTS: 1 IF: dvanced REF: Lesson 4-3 OJ: Multiply matrices. ST: M TOP: Multiply matrices. KEY: Matrices Multiply Matrices 9. NS: PTS: 1 ST: M NS: PTS: 1 ST: M.912.G.3.2 3

26 I: E 11. NS: When exact roots cannot be found by graphing, you can estimate solutions by stating the consecutive integers between which the roots are located. id you graph the function correctly? Is the coefficient of x 2 greater than 0? When the coefficient of x 2 is less than 0, the graph opens down. orrect! PTS: 1 IF: dvanced REF: Lesson 5-2 OJ: Estimate solutions of quadratic equations by graphing. ST: M M TOP: Estimate solutions of quadratic equations by graphing. KEY: Quadratic Equations Solve Quadratic Equations 12. NS: PTS: 1 ST: M.912.G NS: PTS: 1 ST: M M NS: The value of the second-order determinant is obtained by calculating the difference of the products of the two diagonals. First, find the products of the diagonals and then find their difference. orrect! id you use the definition of determinant correctly? The value of the second-order determinant is obtained by calculating the difference of the products of the two diagonals. PTS: 1 IF: asic REF: Lesson 4-5 OJ: Evaluate the determinant of a 2 x 2 matrix. ST: M TOP: Evaluate the determinant of a 2 x 2 matrix. KEY: Matrices eterminants 15. NS: highest score minus lowest score equals score range h l = 23 h l = 23 Write an equation to represent the relationship. h 39 = 23 Substitute 39 for l. h = 62 Solve the equation. PTS: 1 ST: M M

27 I: E 16. NS: Multiply the real numbers and imaginary numbers separately. orrect! heck your calculation. Multiply the imaginary numbers again. heck the sign. PTS: 1 IF: verage REF: Lesson 5-4 OJ: Perform operations with pure imaginary numbers. ST: M TOP: Perform operations with pure imaginary numbers. 17. NS: Use the FOIL method to multiply the complex numbers and use the formula i 2 = 1. ombine the real parts and then the imaginary parts of the two numbers. orrect! Use the value of i 2. id you use the FOIL method to find the product? id you combine the real parts? PTS: 1 IF: verage REF: Lesson 5-4 OJ: Perform multiplication operations with complex numbers. ST: M TOP: Perform multiplication operations with complex numbers. KEY: omplex Numbers Multiply omplex Numbers 18. NS: The point-slope form of the equation of a line is y y 1 = m Ê x x ˆ ËÁ 1, where Ê x,y ˆ ËÁ 1 1 are the coordinates of a point on the line and m is the slope of the line. The slopes of perpendicular lines are opposite reciprocals. You have to calculate the slope using slope formula. The slope value is incorrect. orrect! Substitute the value for the y-intercept. PTS: 1 IF: dvanced REF: Lesson 2-4 OJ: Write an equation of a line perpendicular to a given line. ST: M TOP: Write an equation of a line perpendicular to a given line. KEY: Perpendicular Lines Equations of Perpendicular Lines 5

28 I: E 19. NS: Solve three equations simultaneously. heck whether the values of the variables have been interchanged. Only two of the values are correct. orrect! The values of a, b, and c are interchanged. PTS: 1 IF: verage REF: Lesson 3-5 OJ: Solve systems of linear equations in three variables. ST: M M TOP: Solve systems of linear equations in three variables. KEY: System of Equations Three Variables 20. NS: PTS: 1 ST: M NS: The solution of a quadratic equation of the form ax 2 + bx + c = 0, where a 0, is obtained by using the formula x = b ± b 2 4ac 2a. id you substitute the values of a, b, and c correctly in the formula? id you check the signs of the solution? orrect! id you use the correct formula? PTS: 1 IF: verage REF: Lesson 5-6 OJ: Solve quadratic equations by using the Quadratic Formula. ST: M M M TOP: Solve quadratic equations by using the Quadratic Formula. KEY: Quadratic Equations Solve Quadratic Equations Quadratic Formula 22. NS: The standard form of the equation is x + y =, where 0 and and are non-zero numbers. What is the coefficient of y? orrect! Is the equation in standard form? What is the standard form of linear equations? PTS: 1 IF: asic REF: Lesson 2-2 OJ: Write linear equations in standard form. ST: M M TOP: Write linear equations in standard form. KEY: Linear Equations Standard Form 23. NS: PTS: 1 ST: M.912.G NS: PTS: 1 ST: M

29 I: E 25. NS: Solve the system of inequalities by graphing the inequalities on the same coordinate plane. The solution set is represented by the intersection of the graphs. id you check the sign of the coordinates? You have interchanged the coordinates. orrect! id you plot the inequalities correctly? PTS: 1 IF: dvanced REF: Lesson 3-3 OJ: etermine the coordinates of the vertices of a region formed by the graph of a system of inequalities. ST: M M TOP: etermine the coordinates of the vertices of a region formed by the graph of a system of inequalities. KEY: System of Inequalities Graphs 26. NS: PTS: 1 ST: M M NS: Substitute values of the x- and y-coordinates in the equation y y 1 = m Ê x x ˆ ËÁ 1. Manipulate the equation to get it in the slope-intercept form. id you calculate the value of y-intercept correctly? orrect! id you calculate the value of the slope correctly? You have to substitute the values of x- and y-coordinates to acquire the slope-intercept equation. PTS: 1 IF: dvanced REF: Lesson 2-4 OJ: Write an equation of a line given the slope and a point on the line. ST: M TOP: Write an equation of a line given the slope and a point on the line. KEY: Equations of Lines Slope Graphs 28. NS: PTS: 1 ST: M NS: PTS: 1 ST: M NS: Obtain two linear equations using the definition of equal matrices. id you obtain two linear equations using the definition of equal matrices? orrect! id you interchange the values of x and y? The values of x and y cannot be equal. PTS: 1 IF: verage REF: Lesson 4-1 OJ: Solve equations involving matrices. ST: L TOP: Solve equations involving matrices. KEY: Matrices Matrix Equations 31. NS: PTS: 1 ST: M.912.G.4.4 7

30 I: E 32. NS: quadratic equation with roots p and q can be written as (x p)(x q) = 0, which can be further simplified. id you check the signs of the coefficients? id you calculate the coefficients correctly? id you verify the answer by substituting the values? orrect! PTS: 1 IF: verage REF: Lesson 5-3 OJ: Write quadratic equations in intercept form. ST: M M TOP: Write quadratic equations in intercept form. KEY: Quadratic Equations Roots of Quadratic Equations 33. NS: PTS: 1 ST: M M NS: PTS: 1 ST: M.912.G NS: PTS: 1 ST: M.912.G NS: PTS: 1 ST: M M NS: PTS: 1 ST: M NS: Organize the prices of services and cable companies in labeled columns and rows, and then write the data in a matrix form. The costs of premium channels should be added to the standard service, not to the basic service. dd the cost of premium channels to the standard service, not the costs of all the premium channels. orrect! dd the costs of premium channels to the standard service. PTS: 1 IF: verage REF: Lesson 4-1 OJ: Organize data in matrices. ST: L TOP: Organize data in matrices. KEY: Matrices Organize ata 39. NS: PTS: 1 ST: M.912.G.1.3 8

31 I: E 40. NS: The inverse of a matrix does not exist. a c b is equal to d 1 ad bc d c b a. If the determinant equals zero, the inverse The determinant is not equal to zero. orrect! Two matrices n n are inverses of each other if their product is the identity matrix. id you calculate the inverse correctly? PTS: 1 IF: verage REF: Lesson 4-6 OJ: Find the inverse of a 2 x 2 matrix. TOP: Find the inverse of a 2 x 2 matrix. 41. NS: Read the algebraic expression and represent it verbally. ST: M KEY: Matrices Inverses of Matrices heck the values in the equation. You have missed one of the values in the equation. orrect! You have not written the entire expression. PTS: 1 IF: verage REF: Lesson 1-3 OJ: Translate algebraic equations into verbal expressions. ST: M TOP: Translate algebraic equations into verbal expressions. KEY: Translate Equations Verbal Expressions 42. NS: Graph the equations and find their point of intersection. id you plot the graphs correctly? What is the x-coordinate of the intersection? id you read the intersection of the graphs correctly? orrect! PTS: 1 IF: verage REF: Lesson 3-1 OJ: Solve systems of linear equations by graphing. TOP: Solve systems of linear equations by graphing. ST: M M KEY: System of Linear Equations Graphs 9

32 I: E 43. NS: relation is a set of ordered pairs. The domain of a relation is the set of all first coordinates from the ordered pairs, and the range is the set of all second coordinates from the ordered pairs. Each element of the domain is paired with exactly one element of the range. orrect! oes the relation pass the vertical line test? The domain is the set of all first coordinates and the range is the set of all second coordinates. PTS: 1 IF: verage REF: Lesson 2-1 OJ: nalyze and graph relations. ST: M TOP: nalyze and graph relations. KEY: Relations Graphs Graph Relations 44. NS: To complete the square for any quadratic expression of the form x 2 + bx, find half of b, and square the result. Then, add the result to x 2 + bx. id you check the signs of the roots? orrect! id you verify the answer by substituting the values? id you make the quadratic expression a perfect square? PTS: 1 IF: verage REF: Lesson 5-5 OJ: Solve quadratic equations by completing the square. ST: M M TOP: Solve quadratic equations by completing the square. KEY: Quadratic Equations Solve Quadratic Equations ompleting the Square 45. NS: PTS: 1 ST: M.912.G NS: PTS: 1 ST: M.912.G NS: y using the method of substitution, solve one equation for one variable in terms of the other variable. Then, substitute this expression for the variable in the other equation. id you calculate correctly? Recalculate the value of r. orrect! Recalculate the value of s. PTS: 1 IF: verage REF: Lesson 3-2 OJ: Solve systems of linear equations by using substitution. ST: M M TOP: Solve systems of linear equations by using substitution. KEY: System of Linear Equations Substitution 10

33 I: E 48. NS: For the quadratic equation ax 2 + bx + c, the y-intercept is c and the equation of axis of symmetry is x = b 2a. id you check the signs? id you interchange the y-intercept and the x-coordinate of the vertex? orrect! id you use the correct formulas for the y-intercept and the x-coordinate of the vertex? PTS: 1 IF: verage REF: Lesson 5-1 OJ: Graph quadratic functions. ST: M M M TOP: Graph quadratic functions. KEY: Quadratic Functions Graph Quadratic Functions 49. NS: First, choose integer values for x. Then evaluate the function for each x value. Graph the resulting coordinate pairs and connect the points with a smooth curve. orrect! When the coefficient of x 2 is less than 0, the graphs opens down. id you plot the graph correctly? Graph ordered pairs that satisfy the function. PTS: 1 IF: dvanced REF: Lesson 5-1 OJ: Graph quadratic functions. ST: M M M TOP: Graph quadratic functions. KEY: Quadratic Functions Graph Quadratic Functions 50. NS: PTS: 1 ST: M NS: PTS: 1 ST: M NS: Substitute the values of x 1 and y 1 in the equation y y 1 = m Ê x x ˆ ËÁ 1 to get the equation of the line passing through the point ( 3, 5). You performed addition instead of subtraction. orrect! What should be the slope of the line? You have not substituted the correct values for all the mathematical operations. PTS: 1 IF: verage REF: Lesson 2-3 OJ: Graph perpendicular lines. ST: M TOP: Graph perpendicular lines. KEY: Graphs Perpendicular Lines 53. NS: PTS: 1 ST: M

34 I: E 54. NS: If the vertex and another point on the graph of a parabola are known, the equation of the parabola can be written in vertex form. id you substitute correctly in the vertex form of the equation? id you check the signs of the coefficients? id you find the correct coefficient values? orrect! PTS: 1 IF: verage REF: Lesson 5-7 OJ: Write a quadratic function in the form y = a(x - h)^2 + k. ST: M TOP: Write a quadratic function in the form y = a(x h)^2 + k. KEY: Quadratic Functions 55. NS: The point-slope form of the equation of a line is y y 1 = m Ê x x ˆ ËÁ 1, where Ê x,y ˆ ËÁ 1 1 are the coordinates of a point on the line and m is the slope of the line. orrect! Substitute the values of x- and y-coordinates in slope formula to calculate the slope. You have calculated the value of y-intercept incorrectly. You have to calculate the ratio of change in x- and y-coordinates. PTS: 1 IF: dvanced REF: Lesson 2-4 OJ: Write an equation of a line parallel to a given line. ST: M TOP: Write an equation of a line parallel to a given line. KEY: Parallel Lines Equations of Parallel Lines 56. NS: PTS: 1 ST: M.912.G NS: PTS: 1 ST: M NS: PTS: 1 ST: M.912.G NS: The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the function. orrect! The coefficient of x 2 is less than zero. What is the value of the y-coordinate of the vertex? The graph of the function opens down. PTS: 1 IF: verage REF: Lesson 5-1 OJ: Find and interpret the maximum and minimum values of a quadratic function. ST: M M M TOP: Find and interpret the maximum and minimum values of a quadratic function. KEY: Maximum Values Minimum Values Quadratic Functions 12

35 I: E 60. NS: The area of a triangle is one half its base multiplied by its height. Since the height remains constant, if its area is doubled, the original base length is multiplied by 2. PTS: 1 ST: M.912.G NS: Plot all the four graphs and shade the feasible region. Then find the coordinates of the feasible region, maximum value, and minimum value. orrect! You have plotted the first equation incorrectly. You have not plotted all the inequalities. id you check the graph properly? PTS: 1 IF: verage REF: Lesson 3-4 OJ: Find the maximum and minimum values of a function over a region. ST: M M TOP: Find the maximum and minimum values of a function over a region. KEY: Maximum Values Minimum Values 62. NS: For any real number n, if x 2 = n, then x = ± n. id you factor the perfect square trinomial correctly? orrect! id you verify the answer by substituting the values? id you use the Square Root Property correctly? PTS: 1 IF: verage REF: Lesson 5-5 OJ: Solve quadratic equations by using the Square Root Property. ST: M M TOP: Solve quadratic equations by using the Square Root Property. KEY: Quadratic Equations Solve Quadratic Equations Square Root Property 63. NS: PTS: 1 ST: M.912.G

36 I: E 64. NS: Represent the expression by using appropriate numbers and variables. You have interchanged the number and the variable. orrect! Find the cube of the difference, not the sum. Find the cube of the difference of the number and 43, not the difference of the cubes of the number and 43. PTS: 1 IF: verage REF: Lesson 1-3 OJ: Translate verbal expressions into algebraic expressions. ST: M TOP: Translate verbal expressions into algebraic expressions. KEY: Translate Expressions Verbal Expressions lgebraic Expressions 65. NS: oth the inequalities should be plotted and the region common to both should be shaded. You have plotted the inequalities incorrectly. orrect! You have plotted the second inequality incorrectly. You have plotted the first inequality incorrectly. PTS: 1 IF: verage REF: Lesson 3-3 OJ: Solve systems of inequalities by graphing. ST: M M TOP: Solve systems of inequalities by graphing. KEY: System of Inequalities Graphs 66. NS: PTS: 1 ST: M NS: PTS: 1 ST: M.912.G NS: Rewrite the first two columns to the right of the determinant. Then, find the products of the elements of the diagonals. Finally, add the bottom products and subtract the top products. orrect! id you identify the elements of the diagonals correctly? id you evaluate the determinant correctly? id you add the bottom products and subtract the top products? PTS: 1 IF: verage REF: Lesson 4-5 OJ: Evaluate the determinant of a 3 x 3 matrix using diagonals. ST: M TOP: Evaluate the determinant of a 3 x 3 matrix using diagonals. KEY: Matrices eterminants iagonals 14

37 I: E 69. NS: Plotting the x-coordinates and the y-coordinates gives a graph of the inequality. alculate the x- and y-coordinates using correct mathematical operators. You have performed the division incorrectly. You have multiplied instead of divided. orrect! PTS: 1 IF: verage REF: Lesson 2-8 OJ: Graph linear inequalities. ST: M M TOP: Graph linear inequalities. KEY: Linear Inequalities Graphs Graph Inequalities 70. NS: Identify the general function represented by the graph. Is the equation of a rational function applicable to this graph? oes the equation of an inverse variation function apply to this graph? orrect! The graph of an absolute value function is in the shape of a V. PTS: 1 IF: asic REF: Lesson 2-7 OJ: Identify graphs as different types of functions. ST: M M M TOP: Identify graphs as different types of functions. KEY: Graphs Types of Functions Functions 71. NS: Graph the related quadratic equation. Since the inequality symbol is <, the parabola should be dashed. Test a point (x 1, y 1 ) inside the parabola. If (x 1, y 1 ) is the solution of the inequality, shade the region inside the parabola. If (x 1, y 1 ) is not a solution, shade the region outside the parabola. What is the inequality symbol used in the equation? id you shade correctly? orrect! id you test a point inside the parabola correctly? PTS: 1 IF: dvanced REF: Lesson 5-8 OJ: Graph quadratic inequalities in two variables. TOP: Graph quadratic inequalities in two variables. KEY: Quadratic Inequalities Graph Quadratic Inequalities ST: M M

38 I: E SHORT NSWER 72. NS: f( 8) = 14 g(3) = Substitute x = 8 in the equation f(x) and x = 3 in the equation g(x). PTS: 1 IF: verage REF: Lesson 2-1 OJ: Find functional values. ST: M TOP: Find functional values. KEY: Functional Values Functions 16

39 lgebra 2 Honors Mid-Term Exam [Version Map] E M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M E M M M M M M M M M M M M M M M M M M M M M M M S