Accelerated Geometry/Algebra 2 Final Exam Review 2015

Transcription

1 Name: lass: ate: I: ccelerated Geometry/lgebra 2 Final Exam Review 2015 Multiple hoice Identify the choice that best completes the statement or answers the question. Solve the following system of equations by graphing. 1. y = 11x 6 y = 6x + 11 a. ( 1, 5) c. (5, 1) b. (1, 7) d. (1, 5) 2. 2y + 8x = 58 y 5x = 11 a. (2, 21) c. (4, 20) b. (21, 2) d. (1, 21) Graph each system of equations and describe it as consistent and independent, consistent and dependent, inconsistent, or none of these. 3. 9x 8y = 15 27x 24y = 3 a. consistent and independent c. consistent and dependent b. inconsistent d. none of these 4. 5x 8y = 6 6x 6y = 6 a. inconsistent c. consistent and dependent b. consistent and independent d. none of these Solve each system of equations by using substitution. 5. 8x + 7y = 18 3x 5y = 22 a. ( 2, 4) c. (4, 2) b. (3, 2) d. (4, 0) 6. 3r + 3s = 9 3r 6s =18 a. (4, 0.5) c. (4, 1) b. (5.5, 3) d. (2, 1) Solve each system of equations by using elimination. 7. 3p + 9q = 6 5p 5q = 30 a. (6, 1) c. (5, 0.5) b. (3.75, 2) d. (5, 1) 1

2 Name: I: 8. 6a + 6b = 12 6a 5b = 12 a. (1, 0) c. (3, 0.5) b. (2, 0) d. (2, 0.25) Solve the system of inequalities by graphing. 9. x > 2 y > 8 a. c. b. d. 2

3 Name: I: 10. y > x 6 y 6 a. c. b. d. Find the coordinates of the vertices of the figure formed by each system of inequalities. 11. y + x 9 y x 7 2y + x 16 a. ( 1, 8), ( 30, 23), ( 34, 25) b. ( 1, 8), (10, 3), (34, 25) c. ( 1, 25), ( 34, 3), (10, 8) d. ( 1, 8), (10, 3), ( 34, 25) 12. y 2 2x + y 2 y 2x + 6 a. (2, 2), ( 4, 2), ( 1, 4) b. (2, 4), ( 1, 2), ( 4, 2) c. (2, 2), (4, 2), (1, 4) d. (2, 2), (4, 2), (0, 8) 3

4 Name: I: 13. Graph the system of inequalities showing the feasible region to represent the number of first visits and the number of follow-ups that can be performed. a. c. b. d. Solve the given system of equations a = 36 10a + 3c = 9 2b + 5c = 23 a. a = 12, b = 96, c = 43 c. a = 12, b = 96, c = 43 b. a = 12, b = 43, c = 96 d. a = 43, b = 12, c = a + 2c = 10 2a = 32 8b + 10c = 18 a. a = 16, b = 114, c = 93 c. a = 16, b = 93, c = 114 b. a = 16, b = 114, c = 93 d. a = 93, b = 16, c = 114 4

5 Name: I: 16. onsider the quadratic function f( x) = 2x 2 + 2x + 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 = 1 2. b. The y-intercept is 1 2. 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 = 1 2. d. The y-intercept is 1 2. The equation of the axis of symmetry is x = 2. 5

6 Name: I: 17. Graph the quadratic function f(x) = 2x 2 + 2x + 2. a. c. b. d. etermine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value of the function. 18. f(x) = x 2 2x + 2 a. The function has a maximum value. The maximum value of the function is 1. b. The function has a maximum value. The maximum value of the function is 5. c. The function has a minimum value. The minimum value of the function is 1. d. The function has a minimum value. The minimum value of the function is 5. 6

7 Name: I: 19. f(x) = x 2 + 2x + 7 a. The function has a minimum value. The minimum value of the function is 8. b. The function has a minimum value. The minimum value of the function is 4. c. The function has a maximum value. The maximum value of the function is 4. d. The function has a maximum value. The maximum value of the function is 8. Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. 20. x 2 + 5x + 4 = 0 a. c. b. The solution set is { 1, 4}. d. The solution set is { 2.5, 2.25}. The solution set is { 4, 1}. The solution set is { 1, 4}. 7

8 Name: I: 21. x 2 + 4x = 0 a. c. b. The solution set is { 0, 4}. d. The solution set is { 4, 0}. The solution set is { 4 0}. The solution set is { 2, 4}. 8

9 Name: I: 22. x 2 + 4x + 2 = 0 a. c. b. One solution is between 3 and 4, while the other solution is between 0 and 1. d. One solution is between 3 and 0, while the other solution is between 4 and 1. One solution is between 3 and 1, while the other solution is between 0 and 4. One solution is between 3 and 4, while the other solution is between 0 and 1. 9

10 Name: I: 23. 2x 2 + 3x + 4 = 0 a. c. b. One solution is between 2 and 1, while the other solution is between 0 and 3. d. One solution is between 2 and 3, while the other solution is between 0 and 1. One solution is between 2 and 0, while the other solution is between 3 and 1. One solution is between 0 and 1, while the other solution is between 2 and 3. 10

11 Name: I: 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 2 a. x 2 7x + 10 = 0 c. x 2 3x + 10 = 0 b. x 2 + 7x + 10 = 0 d. x 2 + 3x 10 = and 8 a. 4x 2 27x 40 = 0 c. x 2 27x 40 = 0 b. 4x x + 40 = 0 d. x 2 27x + 40 = 0 Solve the equation by factoring. 26. x 2 + 3x 28 = 0 a. { 4, 7} c. { 4, 7} b. { 7, 4} d. { 4, 7} 27. 2x 2 + 3x 14 = 0 a. { 4, 7 } c. { 4, 7} 2 b. { 7, 2} d. {2, 7} 2 Simplify a. 14 c b. 14 d a. b (2i)( 3i)(4i) a. 24 c. 24i b. 24i d i c. d a. i c. i b. 1 d. 1 ( 11 + i) + ( 3 15i) a i c i b i d i 11

12 Name: I: ( 11 12i) + ( 21 8i) a i c. 32 4i b i d. 29i i ( i)(5 8i) a i + 80 c i 80i 2 b i d i ( 4 + 4i)( 3 3i) a i c i b i 12i 2 d i i a i c i b i d i 6 3i 8 11i a i c i b i d i Solve the equation by using the Square Root Property x 2 48x + 36 = 49 a. { 3 } 2 c. { 13 4, 1 4 } b. { 3 2, 7} d. { 1 4, 13 4 } x 2 80x + 16 = 9 a. { 1 10, 7 10 } c. { 2 5 } b. { 7 10, 1 10 } d. { 2 5, 3} Solve the equation by completing the square. 40. x 2 + 2x 3 = 0 a. { 3, 1} c. { 6, 1} b. { 6, 2} d. { 1, 3} 41. 2x 2 + 2x = 0 a. { 2, 0} c. { 0} b. { 0, 1} d. { 1, 0} 12

13 Name: I: Find the exact solution of the following quadratic equation by using the Quadratic Formula. 42. x 2 8x = 20 a. { 10, 2} c. { 4, 20} b. { 20, 28} d. { 2, 10} 43. x 2 + 3x + 7 = 0 Ï 3 37 a., Ô Ô Ì 2 2 ÓÔ Ô Ï b. Ô Ì, Ô 2 2 ÓÔ Ô c. d. Ï Ô Ì, Ô 2 2 ÓÔ Ô Ï Ô Ì, Ô 2 2 ÓÔ Ô Find the value of the discriminant. Then describe the number and type of roots for the equation. 44. x 2 14x + 2 = 0 a. The discriminant is 196. ecause the discriminant is greater than 0 and is a perfect square, the two roots are real and rational. b. The discriminant is 204. ecause the discriminant is less than 0, the two roots are complex. c. The discriminant is 204. ecause the discriminant is greater than 0 and is not a perfect square, the two roots are real and irrational. d. The discriminant is 188. ecause the discriminant is less than 0, the two roots are complex. 45. x 2 + x + 7 = 0 a. The discriminant is 29. ecause the discriminant is less than 0, the two roots are complex. b. The discriminant is 1. ecause the discriminant is greater than 0 and is a perfect square, the two roots are real and rational. c. The discriminant is 27. ecause the discriminant is less than 0, the two roots are complex. d. The discriminant is 27. ecause the discriminant is greater than 0 and is a perfect square, the two roots are real and rational. 13

14 Name: I: Write the following quadratic function in vertex form. Then, identify the axis of symmetry. 46. y = 3x x a. The vertex form of the function is y = 3( x + 8) The equation of the axis of symmetry is x = 192. b. The vertex form of the function is y = ( x + 192) The equation of the axis of symmetry is x = 8. c. The vertex form of the function is y = 3( x 8) The equation of the axis of symmetry is x = 8. d. The vertex form of the function is y = 3 x + 8 ( ) The equation of the axis of symmetry is x =

15 Name: I: Graph the quadratic inequality. 47. y > x 2 3x + 5 a. c. b. d. 15

16 Name: I: 48. y < 2x 2 6x + 10 a. c. b. d. 49. Find the geometric mean between each pair of numbers. 28 and 7 a. 35 c. 14 b. 196 d Find the geometric mean between each pair of numbers. 256 and 841 a c. 464 b. 3 5 d

17 Name: I: 51. Find the measure of the. a c. 23 b d Find x. a. 22 c b d etermine whether QRS is a right triangle for the given vertices. Explain. 53. Q( 6, 2), R(2, 5), S( 3, 6) a. no; QR = 73, QS = 73, RS = 146; QR 2 + QS 2 RS 2 b. yes; QR = 73, QS = 73, RS = 146; QR 2 + QS 2 = RS 2 c. yes; QR = 73, QS = 73, RS = 146; RS 2 + QS 2 = RQ 2 d. no; QR = 73, QS = 73, RS = 146; RS 2 + QS 2 RQ Q(18, 13), R(17, 3), S( 18, 12) a. no; QR = 257, QS = 1297, RS = 5 58; QR 2 + QS 2 RS 2 b. yes; QR = 257, QS = 1297, RS = 5 58; RS 2 + QS 2 = RQ 2 c. yes; QR = 257, QS = 1297, RS = 5 58; QR 2 + QS 2 RS 2 d. no; QR = 257, QS = 1297, RS = 5 58; RS 2 + QS 2 = RQ 2 17

18 Name: I: 55. The length of a diagonal of a square is 24 2 millimeters. Find the perimeter of the square. a. 576 millimeters c. 96 millimeters b millimeters d millimeters 56. Find x and y. a. x = 45, y = 13.1 c. x = 30, y = b. x = 30, y = 13.1 d. x = 45, y = Find x and y. a. x = 24 3, y = 24 c. x = 24, y = 24 3 b. x = 12 3, y = 12 d. x = 12, y = Find x and y. a. x = 1.5 3, y = 1.5 c. x = 3, y = 3 3 b. x = 3 3, y = 3 d. x = 1.5, y = Find the measure of the angle to the nearest tenth of a degree. cos Y = a c b d

19 Name: I: 60. Use the figure to find the trigonometric ratio below. Express the answer as a decimal rounded to the nearest ten-thousandth. cos = 5 5, = 5, = 11, = 2, = 1 a c b d Lynn is standing at horizontal ground level with the base of the Sears Tower in hicago. The angle formed by the ground and the line segment from her position to the top of the building is The height of the Sears Tower is 1450 feet. Find her distance from the Sears Tower to the nearest foot. a. 408 ft c ft b. 7 ft d ft 62. olores is standing on a horizontal ground level with the base of the Statue of Liberty in New York ity. The angle formed by the ground and the line segment from her position to the top of the statue is The height of the Statue of Liberty is approximately 93 meters. Find her distance from the Statue of Liberty to the nearest meter. a. 188 m c. 104 m b m d. 210 m 63. rocket ship is two miles above sea level when it begins to climb at a constant angle of 3.5 for the next 40 ground miles. bout how far above sea level is the rocket ship after its climb? a. 2.4 mi c mi b. 4.4 mi d mi 64. hot air balloon is one mile above sea level when it begins to climb at a constant angle of 4 for the next 50 ground miles. bout how far above sea level is the hot air balloon after its climb? a. 2.5 mi c. 4.5 mi b. 3.5 mi d mi 60-yard long drawbridge has one end at ground level. The other end is initially at an incline of How far off the ground is the raised end of the drawbridge in its initial setting? a yd c yd b yd d yd 66. uring one stage of the drawbridge s motion, the raised end is 15 yards above the ground. What is the incline of the drawbridge to the nearest hundredth? a c b d hiker stops to rest and sees a deer in the distance. If the hiker is 48 yards lower than the deer and the angle of elevation from the hiker to the deer is 15, find the distance from the hiker to the deer. a yd c yd b yd d yd 19

20 Name: I: 68. water slide is 400 yards long with a vertical drop of 36.3 yards. Find the angle of depression of the slide. a. 5.2 c b d tubing run is 150 yards long with a vertical drop of 21.6 yards. Find the angle of depression of the run. a. 8.2 c b. 8.3 d Find each measure using the given measures of KLM. Round measures to the nearest tenth. 70. If m L = 48.4, m K = 24.5, and l = 37.9, find k. a c b d If m L = 47.1, k = 59.6, and l = 52.2, find m K. a c b. 0.8 d playground is situated on a triangular plot of land. Two sides of the plot are 175 feet long and they meet at an angle of 70. For safety reasons, a fence is to be placed along the perimeter of the property. How much fencing material is needed? a. 110 ft c ft b ft d ft 73. In, given the following measures, find the measure of the missing side to the nearest tenth.. a = 14.2, c = 13.9, m = 27.7 a. b = 6.7 c. b = 14.5 b. b = 394 d. b = In EF, given the lengths of the sides, find the measure of the stated angle to the nearest degree. d = 5.4, e = 10.5, f = 10.8; m F a c. 2.3 b. 102 d Zack, Rachel, and Maddie are unraveling a huge ball of yarn to see how long it is. s they move away from each other, they form a triangle. The distance from Zack to Rachel is 3 meters. The distance from Rachel to Maddie is 2.5 meters. The distance from Maddie to Zack is 4 meters. Find the measures of the three angles in the triangle. a. m Z = 38.6, m R = 92.9, m M = 48.5 b. m Z = 48.5, m R = 38.6, m M = 92.9 c. m Z = 92.9, m R = 48.5, m M = 38.6 d. m Z = 60, m R = 60, m M = Tomas, Ling, and aniel are experimenting with a giant rubber band. They each hold the rubber band to create a triangle. The distance from Tomas to Ling is 24 inches. The distance from Ling to aniel is 36 inches. The distance from aniel to Tomas is 20 inches. Find the measures of the three angles in the triangle. a. m L = 31.6, m T = 109.5, m = 38.9 b. m L = 38.9, m T = 31.6, m = c. m L = 109.5, m T = 38.9, m = 31.6 d. m L = 60, m T = 60, m = 60 20

21 Name: I: 77. Tiffany, Lori, and Mika are practicing for an egg-toss contest. The distance from Tiffany to Lori is 17 inches. The distance from Lori to Mika is 32 inches. The distance from Mika to Tiffany is 28 inches. Find the measures of the three angles in the triangle. a. m L = 60.9, m T = 87, m M = 32.1 b. m L = 32.1, m T = 60.9, m M = 87 c. m L = 87, m T = 32.1, m M = 60.9 d. m L = 60, m T = 60, m M = Taina, Luther, and ella are tapping a balloon to each other in the air, trying to keep it from touching the ground. The distance from Taina to Luther is 22 inches. The distance from Luther to ella is 40 inches. The distance from ella to Taina is 34 inches. Find the measures of the three angles in the triangle. a. m L = 58.1, m T = 88.5, m = 33.4 b. m L = 33.4, m T = 58.1, m = 88.5 c. m L = 88.5, m T = 33.4, m = 58.1 d. m L = 60, m T = 60, m = Luna created a trash can in the shape of a triangular prism. The sides of the triangle are 1.6 feet, 2.3 feet, and 1.2 feet. Find the measures of the angles of the triangle to the nearest tenth. a , 41.0, 29.4 c , 37.1, 41.1 b. 19.6, 49.1, 60.6 d. 60, 60, Hoshi is working on an art project in the shape of a triangular prism. The sides of the triangle are 2.4 feet, 1.5 feet, and 1.3 feet. Find the measures of the angles of the triangle to the nearest tenth. a , 33.6, 28.6 c. 25.0, 39.8, b. 27.8, 56.4, 95.8 d. 60, 60, 60 The radius, diameter, or circumference of a circle is given. Find the missing measures. Round to the nearest hundredth if necessary. 81. r = 13.1 km, d =?, =? a. d = 26.2 km, = km c. d = 6.55 km, = km b. d = 26.2 km, = km d. d = 6.55 km, = km 82. d = 22.3 km, r =?, =? a. r = 44.6 km, = km c. r = km, = km b. r = km, = km d. r = 44.6 km, = km 83. Find the exact circumference of the circle. a. 7π cm c. 10π cm b. 5π cm d. 4π cm 21

22 Name: I: 84. Find the exact circumference of the circle. a. 12π 2 mm c. 12π mm b. 24π 2 mm d. 6π 2 mm Use the diagram to find the measure of the given angle. 85. m a. 140 c. 130 b. 120 d m F a. 50 c. 130 b. 60 d m E a. 180 c. 60 b. 90 d m FE a. 50 c. 60 b. 40 d

23 Name: I: 89. m E a. 170 c. 150 b. 160 d m F a. 110 c. 130 b. 120 d. 140 Use the diagram to find the measure of the given angle. 91. PRS a. 95 c. 50 b. 20 d QRT a. 95 c. 50 b. 20 d PRQ a. 85 c. 50 b. 20 d SRT a. 85 c. 50 b. 20 d

24 Name: I: 95. In ño, E and are diameters, and O OE EOF FO. Find m arc. a. 270 c. 225 b. 90 d In ñf, F FE, m F = 7x, m FE = 5x + 12, and E and are diameters. Find m arc. a. 56 c. 50 b. 46 d

25 Name: I: 97. In ñ, F and E = 10. Find meg. a. 14 c. 10 b. 12 d In ñu, TS = 15, UQ = US. Find mpr. a. 28 c. 15 b. 30 d

26 Name: I: 99. If m = 35, m arc = 100, and m arc = 100, find m 1. a. 45 c. 35 b. 70 d If m 1 = 2x + 2, m 2 = 9x, find m 1. a. 72 c. 75 b. 19 d

27 Name: I: 101. In ñ, and m arc E = 50. Find m E. a. 85 c. 117 b. 108 d Quadrilateral is inscribed in ñz such that Ä and m Z = 84. Find m. a. 48 c. 46 b. 44 d Find x. ssume that segments that appear tangent are tangent. a. 9 c. 12 b. 7 d

28 Name: I: 104. Find x. ssume that segments that appear tangent are tangent. a. 7 c. 14 b. 6 d Find x. ssume that segments that appear tangent are tangent. a. 7 c. 9 b. 5 d Find x. ssume that segments that appear tangent are tangent. a. 11 c. 13 b. 29 d

29 Name: I: Find the measure of the numbered angle a. 230 c. 130 b. 115 d a. 55 c. 75 b. 65 d

30 Name: I: 109. a c b. 105 d a. 60 c. 80 b. 70 d a. 115 c. 120 b. 125 d

31 Name: I: 112. a. 81 c. 94 b. 90 d a. 92 c. 94 b. 95 d a. 90 c. 220 b. 180 d

32 Name: I: 115. a. 100 c. 90 b. 180 d a. 70 c. 80 b. 75 d

33 Name: I: Find x. ssume that any segment that appears to be tangent is tangent a. 15 c. 25 b. 35 d a. 50 c. 60 b. 40 d

34 Name: I: 119. a. 10 c. 12 b. 5 d a. 65 c. 68 b. 66 d a. 15 c. 20 b. 30 d

35 Name: I: 122. a. 12 c. 8 b. 14 d a. 22 c. 18 b. 9 d a. 15 c. 25 b. 20 d

36 Name: I: 125. a. 47 c. 44 b. 48 d a. 35 c. 25 b. 20 d

37 Name: I: Find x. Round to the nearest tenth if necessary a. 5 c. 3 b. 6 d a. 2 c. 3 b. 1 d. 4 37

38 Name: I: 129. a. 7 c. 9 b. 8 d a. 2 c. 2.5 b. 3 d a. 2 c. 3.2 b. 2.4 d

39 Name: I: 132. a c. 3.2 b. 2.4 d a. 4.2 c. 3.2 b. 3.8 d a. 4 c. 6 b. 5.5 d. 5 39

40 Name: I: 135. a. 6 c. 7 b. 6.5 d a. 6 c. 4 b. 5 d. 3 40

41 Name: I: Find x. Round to the nearest tenth if necessary. ssume that segments that appear to be tangent are tangent a. 5 c. 3.5 b. 2.8 d a. 9 c. 3 b. 2 d. 8 41

42 Name: I: 139. a. 7.2 c. 1.7 b. 4 d a. 2.3 c. 2.8 b. 0.9 d a. 8.7 c. 5 b. 7 d

43 Name: I: 142. a. 8 c. 3 b. 10 d a. 3 c. 2 b. 7 d a. 4 c. 6 b. 5 d. 7 43

44 Name: I: 145. a. 3.3 c. 3.1 b. 2.5 d a. 8.5 c. 9.3 b. 9.0 d Write an equation for a circle with center at ( 6, 10) and diameter 6. a. (x + 6) 2 + (y 10) 2 = 9 c. (x 6) 2 + (y + 10) 2 = 9 b. (x + 6) 2 + (y 10) 2 = 36 d. (x 6) 2 + (y + 10) 2 = Write an equation for a circle with a diameter that has endpoints at ( 10, 1) and ( 8, 5). Round to the nearest tenth if necessary. a. (x 9) 2 + (y + 3) 2 = 20 c. (x + 9) 2 + (y 3) 2 = 5 b. (x 9) 2 + (y + 3) 2 = 5 d. (x + 9) 2 + (y 3) 2 = 20 44

45 Name: I: Graph the equation x 2 + y 2 = 16 a. c. b. d. 45

46 Name: I: 150. (x + 1) 2 + (y + 3) 2 = 16 a. c. b. d. 46

47 I: ccelerated Geometry/lgebra 2 Final Exam Review 2015 nswer Section MULTIPLE HOIE 1. NS: Graph the equations and find their point of intersection. What is the x-coordinate of the intersection? id you graph both equations correctly? Write the coordinates of the intersection carefully. orrect! PTS: 1 IF: verage REF: Lesson 3-1 OJ: Solve systems of linear equations by graphing. NT: N 1 N 8 N 9 N 10 N 2 ST: TOP: Solve systems of linear equations by graphing. KEY: System of Linear Equations Graphs 2. NS: Graph the equations and find their point of intersection. orrect! id you plot the graphs correctly? id you read the intersection of the graphs correctly? What is the x-coordinate of the intersection? PTS: 1 IF: verage REF: Lesson 3-1 OJ: Solve systems of linear equations by graphing. NT: N 1 N 8 N 9 N 10 N 2 ST: TOP: Solve systems of linear equations by graphing. KEY: System of Linear Equations Graphs 3. NS: Graph the equations and check the number of solutions. id you check the number of solutions? orrect! re the y-intercepts equal? id you find the slope of each line? PTS: 1 IF: verage REF: Lesson 3-1 OJ: etermine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent. TOP: etermine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent. KEY: System of Linear Equations onsistent System Inconsistent System 1

48 I: 4. NS: Graph the equations and check the number of solutions. re the slopes equal? orrect! re the y-intercepts equal? id you plot the graphs correctly? PTS: 1 IF: verage REF: Lesson 3-1 OJ: etermine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent. TOP: etermine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent. KEY: System of Linear Equations onsistent System Inconsistent System 5. 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 the values correctly? Recalculate the value of x. orrect! Recalculate the value of y. PTS: 1 IF: verage REF: Lesson 3-2 OJ: Solve systems of linear equations by using substitution. NT: N 1 N 6 N 7 N 9 N 2 TOP: Solve systems of linear equations by using substitution. KEY: System of Linear Equations Substitution 6. 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. Recalculate the value of s. id you calculate correctly? orrect! Recalculate the value of r. PTS: 1 IF: verage REF: Lesson 3-2 OJ: Solve systems of linear equations by using substitution. NT: N 1 N 6 N 7 N 9 N 2 TOP: Solve systems of linear equations by using substitution. KEY: System of Linear Equations Substitution 2

49 I: 7. NS: Use the method of elimination to obtain the required answer. Recalculate the value of p. id you calculate the values correctly? Recalculate the value of q. orrect! PTS: 1 IF: verage REF: Lesson 3-2 OJ: Solve systems of linear equations by using elimination. NT: N 1 N 6 N 7 N 9 N 2 TOP: Solve systems of linear equations by using elimination. KEY: System of Linear Equations Elimination 8. NS: Use the method of elimination to obtain the required answer. Recalculate the value of a. orrect! id you calculate the values correctly? Recalculate the value of b. PTS: 1 IF: verage REF: Lesson 3-2 OJ: Solve systems of linear equations by using elimination. NT: N 1 N 6 N 7 N 9 N 2 TOP: Solve systems of linear equations by using elimination. KEY: System of Linear Equations Elimination 9. NS: oth the inequalities should be plotted and the region common to both should be shaded. You have plotted the first inequality incorrectly. You have plotted the second inequality incorrectly. orrect! You have plotted the inequalities incorrectly. PTS: 1 IF: verage REF: Lesson 3-3 OJ: Solve systems of inequalities by graphing. NT: N 1 N 6 N 9 N 10 N 2 TOP: Solve systems of inequalities by graphing. KEY: System of Inequalities Graphs 3

50 I: 10. NS: Plot the first inequality. Then, plot the positive and negative values of y and shade the common region. What is the y-intercept of the first related equation? id you plot the second equation correctly? id you plot all the equations? orrect! PTS: 1 IF: verage REF: Lesson 3-3 OJ: Solve systems of inequalities by graphing. NT: N 1 N 6 N 9 N 10 N 2 TOP: Solve systems of inequalities by graphing. KEY: System of Inequalities Graphs 11. 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 plot the inequalities correctly? id you check the sign of the coordinates? You have interchanged the coordinates. orrect! 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. NT: N 1 N 6 N 9 N 10 N 2 TOP: etermine the coordinates of the vertices of a region formed by the graph of a system of inequalities. KEY: System of Inequalities Graphs 12. 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. orrect! You have interchanged the coordinates. id you check the sign of the coordinates? 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. NT: N 1 N 6 N 9 N 10 N 2 TOP: etermine the coordinates of the vertices of a region formed by the graph of a system of inequalities. KEY: System of Inequalities Graphs 4

51 I: 13. NS: Write the system of inequalities and then plot the graph. orrect! id you check the values of the inequalities? id you use the correct sign in plotting the inequalities? id you check the intercept of the inequalities? PTS: 1 IF: dvanced REF: Lesson 3-4 OJ: Solve real-world problems using linear programming. NT: N 1 N 6 N 8 N 10 N 2 TOP: Solve real-world problems using linear programming. KEY: Linear Programming Real-World Problems 14. NS: Solve three equations simultaneously. orrect! heck whether the values of the variables have been interchanged. Only two of the values are correct. 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. NT: N 1 N 7 N 9 N 10 N 2 TOP: Solve systems of linear equations in three variables. KEY: System of Equations Three Variables 15. NS: Solve three equations simultaneously. orrect! Only two of the values are correct. heck whether the values of the variables have been interchanged. 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. NT: N 1 N 7 N 9 N 10 N 2 TOP: Solve systems of linear equations in three variables. KEY: System of Equations Three Variables 5

52 I: 16. 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. NT: N 2 N 6 N 8 N 10 N 3 TOP: Graph quadratic functions. KEY: Quadratic Functions Graph Quadratic Functions 17. 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. Graph ordered pairs that satisfy the function. orrect! id you plot the graph correctly? When the coefficient of x 2 is less than 0, the graphs opens down. PTS: 1 IF: dvanced REF: Lesson 5-1 OJ: Graph quadratic functions. NT: N 2 N 6 N 8 N 10 N 3 TOP: Graph quadratic functions. KEY: Quadratic Functions Graph Quadratic Functions 18. NS: The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the function. The coefficient of x 2 is greater than zero. The graph of this function opens up. orrect! What is the value of the y-coordinate of the vertex? PTS: 1 IF: verage REF: Lesson 5-1 OJ: Find and interpret the maximum and minimum values of a quadratic function. NT: N 2 N 6 N 8 N 10 N 3 TOP: Find and interpret the maximum and minimum values of a quadratic function. KEY: Maximum Values Minimum Values Quadratic Functions 6

53 I: 19. NS: The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the function. The graph of the function opens down. The coefficient of x 2 is less than zero. What is the value of the y-coordinate of the vertex? orrect! PTS: 1 IF: verage REF: Lesson 5-1 OJ: Find and interpret the maximum and minimum values of a quadratic function. NT: N 2 N 6 N 8 N 10 N 3 TOP: Find and interpret the maximum and minimum values of a quadratic function. KEY: Maximum Values Minimum Values Quadratic Functions 20. NS: The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic equation because f(x) = 0 at those points. What are the x-intercepts of the graph? orrect! Find the zeros of the function, not the vertex. The zeros of the function are the solutions of the related equation. PTS: 1 IF: dvanced REF: Lesson 5-2 OJ: Solve quadratic equations by graphing. NT: N 1 N 6 N 9 N 10 N 2 ST: TOP: Solve quadratic equations by graphing. KEY: Quadratic Equations Solve Quadratic Equations 21. NS: The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic equation because f(x) = 0 at those points. orrect! The zeros of the function are the solutions of the related equation. What are the x-intercepts of the graph? Find the zeros of the function, not the vertex. PTS: 1 IF: dvanced REF: Lesson 5-2 OJ: Solve quadratic equations by graphing. NT: N 1 N 6 N 9 N 10 N 2 ST: TOP: Solve quadratic equations by graphing. KEY: Quadratic Equations Solve Quadratic Equations 7

54 I: 22. NS: When exact roots cannot be found by graphing, you can estimate solutions by stating the consecutive integers between which the roots are located. Is the coefficient of x 2 less than zero? id you graph the function correctly? When the coefficient of x 2 is greater than 0, the graph opens up. orrect! PTS: 1 IF: dvanced REF: Lesson 5-2 OJ: Estimate solutions of quadratic equations by graphing. NT: N 1 N 6 N 9 N 10 N 2 ST: TOP: Estimate solutions of quadratic equations by graphing. KEY: Quadratic Equations Solve Quadratic Equations 23. 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? When the coefficient of x 2 is less than 0, the graph opens down. Is the coefficient of x 2 greater than 0? orrect! PTS: 1 IF: dvanced REF: Lesson 5-2 OJ: Estimate solutions of quadratic equations by graphing. NT: N 1 N 6 N 9 N 10 N 2 ST: TOP: Estimate solutions of quadratic equations by graphing. KEY: Quadratic Equations Solve Quadratic Equations 24. NS: quadratic equation with roots p and q can be written as (x p)(x q) = 0, which can be further simplified. id you verify the answer by substituting the values? id you calculate the coefficients correctly? id you check the signs of the coefficients? orrect! PTS: 1 IF: verage REF: Lesson 5-3 OJ: Write quadratic equations in intercept form. NT: N 1 N 3 N 7 N 8 N 2 TOP: Write quadratic equations in intercept form. KEY: Quadratic Equations Roots of Quadratic Equations 8

55 I: 25. NS: quadratic equation with roots p and q can be written as (x p)(x q) = 0, which can be further simplified. orrect! id you check the signs of the coefficients? id you calculate the coefficients correctly? id you verify the answer by substituting the values? PTS: 1 IF: verage REF: Lesson 5-3 OJ: Write quadratic equations in intercept form. NT: N 1 N 3 N 7 N 8 N 2 TOP: Write quadratic equations in intercept form. KEY: Quadratic Equations Roots of Quadratic Equations 26. NS: For any real numbers a and b, if ab = 0, then either a = 0, b 0, or both a and b are equal to zero. id you use the Zero Product Property correctly? orrect! id you verify the answer by substituting the values? id you factor the binomial correctly? PTS: 1 IF: verage REF: Lesson 5-3 OJ: Solve quadratic equations by factoring. NT: N 1 N 3 N 7 N 8 N 2 ST: TOP: Solve quadratic equations by factoring. KEY: Quadratic Equations Solve Quadratic Equations Factoring 27. NS: For any real numbers a and b, if ab = 0, then either a = 0, b = 0, or both a and b are equal to zero. id you use the Zero Product Property correctly? orrect! id you factor the binomial correctly? id you verify the answer by substituting the values? PTS: 1 IF: verage REF: Lesson 5-3 OJ: Solve quadratic equations by factoring. NT: N 1 N 3 N 7 N 8 N 2 ST: TOP: Solve quadratic equations by factoring. KEY: Quadratic Equations Solve Quadratic Equations Factoring 9

56 I: 28. NS: For any numbers a, b, and c, abc = a b c. lso, 1 = i 2 = i. orrect! heck for the radical sign. Take the square root of the number. heck your calculation. PTS: 1 IF: asic REF: Lesson 5-4 OJ: Find square roots. NT: N 1 N 7 N 9 N 10 N 2 TOP: Find square roots. KEY: Square Roots 29. NS: a b = a b orrect! heck the numerator. heck the square root of the numerator. heck your calculation. PTS: 1 IF: verage REF: Lesson 5-4 OJ: Find square roots. NT: N 1 N 7 N 9 N 10 N 2 TOP: Find square roots. KEY: Square Roots 30. NS: Multiply the real numbers and imaginary numbers separately. heck your calculation. heck the sign. orrect! Multiply the imaginary numbers again. PTS: 1 IF: verage REF: Lesson 5-4 OJ: Perform operations with pure imaginary numbers. NT: N 1 N 3 N 7 N 10 N 2 TOP: Perform operations with pure imaginary numbers. KEY: Imaginary Numbers 10

57 I: 31. NS: Multiply the real numbers and imaginary numbers separately. heck your calculation. heck the sign. orrect! ompute again. PTS: 1 IF: verage REF: Lesson 5-4 OJ: Perform operations with pure imaginary numbers. NT: N 1 N 3 N 7 N 10 N 2 TOP: Perform operations with pure imaginary numbers. KEY: Imaginary Numbers 32. NS: ombine the real and imaginary parts of the complex numbers to add them. orrect! ombine the real parts and then combine the imaginary parts. dd the real and imaginary parts of the two numbers separately. id you combine the similar terms correctly? PTS: 1 IF: verage REF: Lesson 5-4 OJ: Perform addition and subtraction operations with complex numbers. NT: N 1 N 3 N 7 N 10 N 2 TOP: Perform addition and subtraction operations with complex numbers. KEY: omplex Numbers dd omplex Numbers Subtract omplex Numbers 33. NS: ombine the real and imaginary parts of the complex numbers to add them. ombine the real parts and then combine the imaginary parts. orrect! ombine the similar terms correctly. dd the real and imaginary parts of the two numbers separately. PTS: 1 IF: verage REF: Lesson 5-4 OJ: Perform addition and subtraction operations with complex numbers. NT: N 1 N 3 N 7 N 10 N 2 TOP: Perform addition and subtraction operations with complex numbers. KEY: omplex Numbers dd omplex Numbers Subtract omplex Numbers 11

58 I: 34. 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. id you combine the real parts? orrect! Use the value of i 2. id you use the FOIL method to find the product? PTS: 1 IF: verage REF: Lesson 5-4 OJ: Perform multiplication operations with complex numbers. NT: N 1 N 3 N 7 N 10 N 2 TOP: Perform multiplication operations with complex numbers. KEY: omplex Numbers Multiply omplex Numbers 35. 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. Use the FOIL method to find the product. Use the value of i 2. orrect! ombine the real parts. PTS: 1 IF: verage REF: Lesson 5-4 OJ: Perform multiplication operations with complex numbers. NT: N 1 N 3 N 7 N 10 N 2 TOP: Perform multiplication operations with complex numbers. KEY: omplex Numbers Multiply omplex Numbers 36. NS: Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL method and the difference of squares to simplify the given expression. Multiply the numerator with the conjugate of the denominator. Have you multiplied the constant in the numerator with its conjugate of the denominator? id you multiply the conjugates correctly in the denominator? orrect! PTS: 1 IF: verage REF: Lesson 5-4 OJ: Perform division operations with complex numbers. NT: N 1 N 3 N 7 N 10 N 2 TOP: Perform division operations with complex numbers. KEY: omplex Numbers ivide omplex Numbers 12

59 I: 37. NS: Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL method and the difference of squares to simplify the given expression. orrect! id you multiply the conjugates correctly in the denominator? Multiply the numerator also with the conjugate of the denominator. id you combine the similar terms correctly? PTS: 1 IF: verage REF: Lesson 5-4 OJ: Perform division operations with complex numbers. NT: N 1 N 3 N 7 N 10 N 2 TOP: Perform division operations with complex numbers. KEY: omplex Numbers ivide omplex Numbers 38. NS: For any real number n, if x 2 = n, then x = ± n. id you use the Square Root Property correctly? id you verify the answer by substituting the values? id you factor the perfect square trinomial correctly? orrect! PTS: 1 IF: verage REF: Lesson 5-5 OJ: Solve quadratic equations by using the Square Root Property. NT: N 1 N 3 N 7 N 10 N 2 ST: TOP: Solve quadratic equations by using the Square Root Property. KEY: Quadratic Equations Solve Quadratic Equations Square Root Property 39. NS: For any real number n, if x 2 = n, then x = ± n. orrect! id you factor the perfect square trinomial correctly? id you use the Square Root Property correctly? id you verify the answer by substituting the values? PTS: 1 IF: verage REF: Lesson 5-5 OJ: Solve quadratic equations by using the Square Root Property. NT: N 1 N 3 N 7 N 10 N 2 ST: TOP: Solve quadratic equations by using the Square Root Property. KEY: Quadratic Equations Solve Quadratic Equations Square Root Property 13

60 I: 40. 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. orrect! id you make the quadratic expression a perfect square? id you verify the answer by substituting the values? id you check the signs of the roots? PTS: 1 IF: verage REF: Lesson 5-5 OJ: Solve quadratic equations by completing the square. NT: N 1 N 3 N 7 N 10 N 2 ST: TOP: Solve quadratic equations by completing the square. KEY: Quadratic Equations Solve Quadratic Equations ompleting the Square 41. 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 make the quadratic expression a perfect square? id you check the signs of the roots? Find both the solutions. orrect! PTS: 1 IF: verage REF: Lesson 5-5 OJ: Solve quadratic equations by completing the square. NT: N 1 N 3 N 7 N 10 N 2 ST: TOP: Solve quadratic equations by completing the square. KEY: Quadratic Equations Solve Quadratic Equations ompleting the Square 42. 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 check the signs of the solution? id you use the correct formula? id you substitute the values of a, b, and c correctly in the formula? orrect! PTS: 1 IF: verage REF: Lesson 5-6 OJ: Solve quadratic equations by using the Quadratic Formula. NT: N 1 N 6 N 8 N 9 N 2 ST: TOP: Solve quadratic equations by using the Quadratic Formula. KEY: Quadratic Equations Solve Quadratic Equations Quadratic Formula 14

61 I: 43. 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 evaluate the discriminant correctly? id you use the correct formula? orrect! PTS: 1 IF: verage REF: Lesson 5-6 OJ: Solve quadratic equations by using the Quadratic Formula. NT: N 1 N 6 N 8 N 9 N 2 ST: TOP: Solve quadratic equations by using the Quadratic Formula. KEY: Quadratic Equations Solve Quadratic Equations Quadratic Formula 44. NS: If b 2 4ac > 0 and b 2 4ac is a perfect square, then the roots are rational. If b 2 4ac > 0 and b 2 4ac is not a perfect square, then the roots are real and irrational. id you use the correct formula for the discriminant? id you check the sign of the answer? orrect! id you use the correct order of operations while evaluating the discriminant? PTS: 1 IF: asic REF: Lesson 5-6 OJ: Use the discriminant to determine the number and types of roots of a quadratic equation. NT: N 1 N 6 N 8 N 9 N 2 ST: TOP: Use the discriminant to determine the number and types of roots of a quadratic equation. KEY: Quadratic Equations Roots of Quadratic Equations iscriminates 45. NS: If b 2 4ac < 0, then the roots are complex. id you use the correct order of operations while evaluating the discriminant? id you use the correct formula for the discriminant? orrect! id you check the sign of the answer? PTS: 1 IF: asic REF: Lesson 5-6 OJ: Use the discriminant to determine the number and types of roots of a quadratic equation. NT: N 1 N 6 N 8 N 9 N 2 ST: TOP: Use the discriminant to determine the number and types of roots of a quadratic equation. KEY: Quadratic Equations Roots of Quadratic Equations iscriminates 15

62 I: 46. 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? id you check the x-coordinate of the vertex? orrect! id you identify the coordinates of the vertex correctly? PTS: 1 IF: asic REF: Lesson 5-7 OJ: nalyze quadratic functions in the form y = a(x - h)^2 + k. NT: N 2 N 7 N 8 N 10 N 6 ST: TOP: nalyze quadratic functions in the form y = a(x - h)^2 + k. KEY: Quadratic Functions xis of Symmetry 47. NS: Graph the related quadratic equation. ecause 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. orrect! What is the inequality symbol used in the equation? id you test a point inside the parabola correctly? id you shade correctly? PTS: 1 IF: dvanced REF: Lesson 5-8 OJ: Graph quadratic inequalities in two variables. NT: N 2 N 6 N 9 N 10 N 3 ST: TOP: Graph quadratic inequalities in two variables. KEY: Quadratic Inequalities Graph Quadratic Inequalities 48. 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. orrect! id you test a point inside the parabola correctly? id you shade correctly? What is the inequality symbol used in the equation? PTS: 1 IF: dvanced REF: Lesson 5-8 OJ: Graph quadratic inequalities in two variables. NT: N 2 N 6 N 9 N 10 N 3 ST: TOP: Graph quadratic inequalities in two variables. KEY: Quadratic Inequalities Graph Quadratic Inequalities 16

63 I: 49. NS: Find the product of the given numbers. Find the square root of the product. How do you find the geometric mean? Remember to take the square root of the product. orrect! This is the arithmetic mean not geometric mean. PTS: 1 IF: asic REF: Lesson 8-1 OJ: Find the geometric mean between two numbers. NT: NTM GM.1 NTM GM.1b TOP: Find the geometric mean between two numbers. KEY: Geometric Mean 50. NS: Find the product of the given numbers. Find the square root of the product. This is the arithmetic mean not geometric mean. How do you find the geometric mean? Remember to take the square root of the product. orrect! PTS: 1 IF: asic REF: Lesson 8-1 OJ: Find the geometric mean between two numbers. NT: NTM GM.1 NTM GM.1b TOP: Find the geometric mean between two numbers. KEY: Geometric Mean 51. NS: The altitude is the geometric mean between the measures of the two segments of the hypotenuse. orrect! This is the arithmetic mean not geometric mean. How do you find the geometric mean? Remember to take the square root of the product. PTS: 1 IF: verage REF: Lesson 8-1 OJ: Solve problems involving relationships between parts of a right triangle and the altitude hypotenuse. NT: NTM GM.1 NTM GM.1b ST: E.1 TOP: Solve problems involving relationships between parts of a right triangle and the altitude hypotenuse. KEY: Triangles ltitudes Hypotenuse 17

64 I: 52. NS: The sum of the squares of the two sides is equal to the square of the hypotenuse. Remember to square the numbers. orrect! Remember to find the square root. Which side is the hypotenuse? PTS: 1 IF: asic REF: Lesson 8-2 OJ: Use the Pythagorean Theorem. NT: NTM GM.1 NTM GM.1b ST: E.1 TOP: Use the Pythagorean Theorem. KEY: Pythagorean Theorem 53. NS: Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter sides is equal to the square of the third side, the triangle is a right triangle. What is the converse of the Pythagorean Theorem? orrect! heck the Pythagorean Theorem. heck the Pythagorean Theorem. PTS: 1 IF: verage REF: Lesson 8-2 OJ: Use the converse of the Pythagorean Theorem. NT: NTM GM.1 NTM GM.1b ST: E.1 TOP: Use the converse of the Pythagorean Theorem. KEY: onverse of Pythagorean Theorem 54. NS: Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter sides is equal to the square of the third side, the triangle is a right triangle. orrect! heck the Pythagorean Theorem. What is the converse of the Pythagorean Theorem? heck the Pythagorean Theorem. PTS: 1 IF: verage REF: Lesson 8-2 OJ: Use the converse of the Pythagorean Theorem. NT: NTM GM.1 NTM GM.1b ST: E.1 TOP: Use the converse of the Pythagorean Theorem. KEY: onverse of Pythagorean Theorem 18

65 I: 55. NS: To find the leg of a triangle when the hypotenuse is given, divide the hypotenuse by find the perimeter of the square, find the sum of all the sides. 2. To This is the area, not the perimeter of the square. Is the number given the length of a side or the diagonal? orrect! efore the perimeter can be found, first find the length of each side. PTS: 1 IF: verage REF: Lesson 8-3 OJ: Use properties of 45º-45º-90º triangles. NT: NTM GM.1 NTM GM.1d ST: E.1 TOP: Use properties of 45º-45º-90º triangles. KEY: Triangles Triangles 56. NS: The length of the hypotenuse is equal to the length of a leg times angle. 2. The diagonal of a square bisects the Multiply by the square root of two to find the length of the hypotenuse. heck the length of the hypotenuse and the size of the angle. The diagonal of a square bisects the angle. orrect! PTS: 1 IF: asic REF: Lesson 8-3 OJ: Use properties of 45º-45º-90º triangles. NT: NTM GM.1 NTM GM.1d ST: E.1 TOP: Use properties of 45º-45º-90º triangles. KEY: Triangles Triangles 57. NS: The shorter leg is half the length of the hypotenuse. The longer leg is 3 times the length of the shorter leg. How do you find the length of the side opposite the 60 angle? Switch the x and y values. How do you find the length of the side opposite the 30 angle? orrect! PTS: 1 IF: asic REF: Lesson 8-3 OJ: Use properties of 30º-60º-90º triangles. NT: NTM GM.1 NTM GM.1d ST: E.1 TOP: Use properties of 30º-60º-90º triangles. KEY: Triangles Triangles 19

66 I: 58. NS: The shorter leg is half the length of the hypotenuse. The longer leg is 3 times the length of the shorter leg. Switch the x and y values. How do you find the length of the side opposite the 60 angle? How do you find the length of the side opposite the 30 angle? orrect! PTS: 1 IF: verage REF: Lesson 8-3 OJ: Use properties of 30º-60º-90º triangles. NT: NTM GM.1 NTM GM.1d ST: E.1 TOP: Use properties of 30º-60º-90º triangles. KEY: Triangles Triangles 59. NS: In trigonometry, you can find the measure of an angle by using the inverse of sine, cosine, or tangent. Which trigonometric ratio should be used? orrect! This is the ratio not the angle. Which trigonometric ratio should be used? PTS: 1 IF: asic REF: Lesson 8-4 OJ: Find trigonometric ratios using right triangles. NT: NTM GM.1 NTM GM.1d ST: E.1 TOP: Find trigonometric ratios using right triangles. KEY: Trigonometric Ratios Right Triangles 60. NS: etermine the ratio associated with the given trigonometric term. ivide the numerator by the denominator. heck the setup of the ratio. Which trigonometric ratio are you asked to find? orrect! Which trigonometric ratio are you asked to find? PTS: 1 IF: verage REF: Lesson 8-4 OJ: Find trigonometric ratios using right triangles. NT: NTM GM.1 NTM GM.1d ST: E.1 TOP: Find trigonometric ratios using right triangles. KEY: Trigonometric Ratios Right Triangles 20

67 I: 61. NS: raw a picture of the situation. etermine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. heck the trigonometric ratio. Which trigonometric ratio should be used? orrect! Which trigonometric ratio should be used? PTS: 1 IF: verage REF: Lesson 8-4 OJ: Solve problems using trigonometric ratios. NT: NTM GM.1 NTM GM.1d ST: E.1 TOP: Solve problems using trigonometric ratios. KEY: Trigonometric Ratios Solve Problems 62. NS: raw a picture of the situation. etermine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. orrect! heck the trigonometric ratio. Which trigonometric ratio should be used? Which trigonometric ratio should be used? PTS: 1 IF: verage REF: Lesson 8-4 OJ: Solve problems using trigonometric ratios. NT: NTM GM.1 NTM GM.1d ST: E.1 TOP: Solve problems using trigonometric ratios. KEY: Trigonometric Ratios Solve Problems 63. NS: raw a picture of the situation. etermine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. Remember to include the initial height of two miles. orrect! Which trigonometric ratio should be used? Which trigonometric ratio should be used? PTS: 1 IF: verage REF: Lesson 8-4 OJ: Solve problems using trigonometric ratios. NT: NTM GM.1 NTM GM.1d ST: E.1 TOP: Solve problems using trigonometric ratios. KEY: Trigonometric Ratios Solve Problems 21