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Name: ________________________ Class: ___________________ Date: __________ ID: A Algebra 2: Final Exam Solve the equation. ____ 1. y − 4 = 2(y + 8) = −12 a. ____ b. =− 1 20 2. x 2 − 4x + 4 = 100 a. –8, 8 b. –12, 12 1 12 c. =− c. d. –8, 12 –12, 8 d. = −20 Use an algebraic equation to solve the problem. ____ 3. A rectangle is 5 times as long as it is wide. The perimeter is 80 cm. Find the dimensions of the rectangle. Round to the nearest tenth if necessary. a. 6.7 cm by 33.3 cm c. 13.3 cm by 33.3 cm b. 16 cm by 80 cm d. 6.7 cm by 73.3 cm Solve the inequality. Graph the solution set. ____ 4. 5r + 7 ≤ 18 a. r≥5 b. r≤2 1 5 c. r≥2 d. r≤5 1 5 Solve the absolute value equation. Graph the solution. ____ 5. What is the sum of the solutions of 2 |x − 1| − 3 = −1 ? 1 c. 1 a. 2 2 b. 0 d. 1 2 Name: ________________________ ID: A Solve the system by graphing. ____ ÏÔÔ ÔÔ −3x = y + 5 6. ÌÔ ÔÔ 2x − 4y = 6 Ó a. c. (–2, –1) (–1, –2) d. b. (–1, 2) ____ (2, –1) 7. A jet ski company charges a flat fee of $36.00 plus $1.75 per hour to rent a jet ski. Another company charges a fee of $31.00 plus $2.75 per hour to rent the same jet ski. Find the number of hours for which the costs are the same. Round your answer to the nearest whole hour. a. b. 5 9 c. d. 2 10 2 Name: ________________________ ID: A Solve the system by substitution. ____ ÏÔÔ ÔÔ −2.5x + y = 13.5 8. ÌÔ ÔÔ 2.25x − y = −12.25 Ó a. (–5, 1) b. (–1, 5) c. d. (1, –5) (5, –1) c. d. (–5, –1, 0) (–5, –1, –2) Solve the system by elimination. ____ ÔÏÔÔ x + 5y − 4z = −10 ÔÔ ÔÔ 9. ÔÔÌ 2x − y + 5z = −9 ÔÔ ÔÔÔ 2x − 10y − 5z = 0 Ó a. (5, –1, 0) b. (–5, 1, 0) ____ 10. Describe the vertical asymptote(s) and hole(s) for the graph of y = a. b. c. d. x−1 . x 2 + 6x + 8 asymptotes: x = –4, –2 and hole: x = 1 asymptote: x = 1 and no holes asymptote: x = 1 and holes: x = –4, –2 asymptotes: x = –4, –2 and no holes ____ 11. Write an explicit formula for the sequence 8, 6, 4, 2, 0, ... Then find a 14 . a. a n = −2n + 10; –16 c. a n = −2n + 8; –20 b. a n = −2n + 8; –18 d. a n = −2n + 10; –18 ____ 12. Which of the following angles is not coterminal with the other three? a. 94° b. 86° c. 454° d. –266° c. − 1 2 d. 2 2 ÊÁ 7π ˆ˜ ____ 13. Find the exact value of cos ÁÁÁÁ − radians ˜˜˜˜ . Ë 4 ¯ a. 1 2 b. 3 2 3 Name: ________________________ ID: A Graph the function in the interval from 0 to 2 π. ____ 14. y = sin (θ − 2) a. b. c. d. 4 Name: ________________________ ____ 15. y = sin (θ + 2) − 5 a. b. ID: A c. d. 5 Name: ________________________ ÁÊ π ˜ˆ ____ 16. y = 2 cos ÁÁÁÁ θ − ˜˜˜˜ + 2 6¯ Ë a. b. ID: A c. d. What are the vertex and the axis of symmetry of the equation? ____ 17. y = 2x 2 + 24x − 16 a. b. vertex: ( –6, –88) axis of symmetry: x = −6 vertex: ( –6, 88) axis of symmetry: y = −6 c. d. vertex: ( 6, –88) axis of symmetry: x = −88 vertex: ( –6, –88) axis of symmetry: x = −88 What is the maximum or minimum value of the function? What is the range? ____ 18. y = −2x 2 + 28x − 10 a. b. minimum: –88 range: y ≥ −88 minimum: 88 range: y ≥ 88 c. d. 6 maximum: 88 range: y ≤ 88 maximum: –88 range: y ≤ −88 Name: ________________________ ID: A What is the equation, in standard form, of a parabola that contains the following points? ____ 19. (–2, 18), (0, 4), (4, 24) d. y = −3x 2 + 2x + 4 y = −4x 2 − 3x − 2 ____ 20. x 2 − 6x + 8 a. (x + 4)(x + 2) b. (x − 2)(x − 4) c. d. (x − 4)(x + 2) (x − 2)(x + 4) ____ 21. −x 2 − x + 42 a. −(x − 7)(x + 6) b. (x + 7)(x + 6) c. d. (x − 6)(x − 7) −(x − 6)(x + 7) ____ 22. 3x 2 + 26x + 35 a. (x + 5)(3x + 7) b. (3x + 7)(x − 5) c. d. (3x + 5)(x − 7) (3x + 5)(x + 7) ____ 23. 9x 2 − 18x + 9 a. (3x + 3) 2 c. (3x − 3) 2 (−3x − 3) 2 a. b. y = −2x 2 + 3x − 4 y = 2x 2 − 3x + 4 c. What is the expression in factored form? What is the expression in factored form? b. (3x − 3)(−3x + 3) ____ 24. Which sum is equal to a. b. x+5 1 + x+5 x−5 1 x2 + x+5 x−5 d. x 2 + 6x − 5 ? x 2 − 25 c. d. 7 x 1 + x+5 x−5 1 x + x−5 x+5 Name: ________________________ ID: A ____ 25. The figure below shows a container that is a square prism with base area B and a hollow section (shaded region) that is a square prism with base area b. If the height h of both prisms is the same, write an expression to represent the volume of the container. Express your answer in completely factored form. a. b. h(B 2 + 2bB − b 2 ) h(B − b)(B − b) c. d. h(B + b)(B + b)(B − b)(B − b) h(B + b)(B − b) What are the solutions of the quadratic equation? ____ 26. x 2 + 11x = −28 a. –4, –7 b. –4, 7 ____ 27. 3x 2 + 25x + 42 = 0 7 1 a. − , − 3 2 1 b. 6, − 2 c. d. 4, 7 4, –7 c. –6, 3 d. –6, − 7 3 What value completes the square for the expression? ____ 28. x 2 − 18x a. b. 9 −9 c. d. 81 −81 Solve the quadratic equation by completing the square. ____ 29. −3x 2 + 7x = −5 a. 7 ± 6 b. 7 − ± 3 109 6 109 3 c. 7 ± 3 d. 7 − ± 6 8 67 3 22 6 Name: ________________________ ID: A Use the Quadratic Formula to solve the equation. ____ 30. −2x 2 − 5x + 5 = 0 a. 5 − ± 2 65 2 c. 4 − ± 5 130 4 b. 5 − ± 4 32 2 d. 5 − ± 4 65 4 ____ 31. 2x 2 + x − 4 = 0 a. 1 − ± 2 33 4 c. 1 − ± 4 33 4 b. −4 ± 66 4 d. 1 − ± 2 33 2 ____ 32. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 155 square yards. The situation is modeled by the equation h 2 + 5h = 155. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard. a. 320 yards c. 20.4 yards b. 10.2 yards d. 12.7 yards Simplify the number using the imaginary unit i. ____ 33. a. b. −144 12 −12 c. d. 12i 144i c. d. 3 + 18i (8 + 18i) Simplify the expression. ____ 34. (4 − i)(2 + 5i) a. 2(4 + 9i) b. (13 + 18i) ____ 35. −2 + i −4 − 5i a. b. 1 5 − +1 i 3 9 3 14 − i 41 41 c. d. 9 3 − 41 13 − 41 6 i 41 14 i 41 Name: ________________________ ____ 36. ID: A −2 − 3i 6i a. b. 1 − 2 1 + 2 1 i 3 1 i 3 c. d. 1 − + 2 1 − + 2 1 i 3 1 i 3 What is the solution of the quadratic system of equations? ÏÔÔ ÔÔ ÔÔ y = x 2 + 16x + 32 ____ 37. ÌÔ ÔÔ ÔÔÔ y = −x 2 + 2 Ó a. b. (–7, –3) (–23, –5) (–3, 89) (–5, 137) c. d. (–3, –7) (–5, –23) (3, –7) (5, –23) What are the zeros of the function? What are their multiplicities? ____ 38. f(x) = x 4 − 4x 3 + 3x 2 a. b. c. d. the numbers –1 and –3 are zeros of multiplicity 2; the number 0 is a zero of multiplicity 1 the number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeros of multiplicity 1 the numbers 0 and 1 are zeros of multiplicity 2; the number 3 is a zero of multiplicity 1 the number 0 is a zero of multiplicity 2; the numbers –1 and –3 are zeros of multiplicity 1 ____ 39. f(x) = 4x 3 − 12x 2 − 16x a. the numbers 1, –4, and 0 are zeros of multiplicity 2 b. the numbers –1, 4, and 0 are zeros of multiplicity 2 c. the numbers –1, 4, and 0 are zeros of multiplicity 1 d. the numbers 1, –4, and 0 are zeros of multiplicity 1 ____ 40. Divide −3x 3 − 2x 2 − x − 2 by x – 2. a. −3x 2 + 4x + 15, R 32 b. −3x 2 + 4x + 15 c. d. −3x 2 − 8x − 17 −3x 2 − 8x − 17, R –36 ____ 41. Determine which binomial is not a factor of 4x 4 − 21x 3 − 46x 2 + 219x + 180. a. x + 4 c. x – 5 b. x + 3 d. 4x + 3 10 Name: ________________________ ID: A Divide using synthetic division. ____ 42. Divide −4x 3 + 21x 2 − 23x + 6 by (x − 4). −4x 2 + 5x − 3, R –6 4x 2 − 5x + 3 a. b. c. d. −4x 2 + 37x − 43, R 18 4x 2 − 37x + 43 ____ 43. Use synthetic division to find P(–2) for P(x) = x 4 + 9x 3 − 9x + 2. a. –2 b. 0 c. –36 d. 68 d. 3x 6 Find all the zeros of the equation. ____ 44. −x 3 − x 2 = 11x + 11 a. i 11 , −i 11 , 1 i 11 , −i 11 , –1 b. d. i 11 , 1 11 , − 11 , –1 c. d. 2, −2, 5i, 0 −2, −5i c. ____ 45. 21x 2 − 100 = −x 4 a. 2, −2, 5i, −5i b. 2, 5i Use the Binomial Theorem to expand the binomial. ____ 46. What is the fourth term of (d + 4b) 3 ? a. −b 3 b. −64b 3 c. b 3 d. 64b 3 3 ____ 47. 270x 20 3 a. 5x 2x 3 3x 6 b. 3x 6 3 2x c. 3 c. 5x 3x 8 none of these 135x 19 90x 18 ____ 48. 2x a. b. 3x 8 5x 18x 17 d. What is the product of the radical expression? Ê ˆ2 ____ 49. ÁÁÁ −5 − 3 ˜˜˜ Ë ¯ a. 28 + 10 3 c. 28 − 10 3 d. b. 11 −13 + 5 3 25 − 10 3 135x Name: ________________________ ID: A Simplify. 1 1 3 ____ 50. 3 ⋅ 9 3 a. 9 b. 3 3 c. 3 c. d. –28 –18 c. 4 3 d. What is the simplest form of the number? 2 3 ____ 51. −27 a. 9 b. 57 What is the solution of the equation? ____ 52. x + 10 − 7 = −5 a. 14 b. –8 d. –6 ____ 53. The area of a circular trampoline is 112.07 square feet. What is the radius of the trampoline? Round to the nearest hundredth. a. 3.37 feet c. 5.97 feet b. 10.59 feet d. 35.67 feet ____ 54. The function d = 4.9t 2 represents the distance d, in meters, that an object falls in t seconds due to Earth’s gravity. Find the inverse of this function. How long, in seconds, does it take for a cliff diver who is 70 meters above the water to reach the water below? a. 3.8 seconds c. 8.1 seconds b. 5.9 seconds d. 13.8 seconds Write the equation in logarithmic form. ____ 55. 2 5 = 32 a. log 32 = 5 ⋅ 2 b. log 2 32 = 5 c. d. log 32 = 5 log 5 32 = 2 Evaluate the logarithm. ____ 56. log 3 243 a. 5 b. –5 c. 4 d. 3 ____ 57. log 0.01 a. –10 b. –2 c. 2 d. 10 12 Name: ________________________ ID: A Expand the logarithmic expression. ____ 58. log 3 d 12 a. log 3 d − log 3 12 c. log 3 d log 3 12 b. −d log 3 12 d. log 3 12 − log 3 d c. log3 11 + 3 log 3 p d. 11 log 3 p 3 c. 7 12 ____ 59. log 3 11p 3 a. log 3 11 ⋅ 3 log 3 p b. log 3 11 − 3 log 3 p Solve the exponential equation. ____ 60. 1 = 64 4x − 3 16 1 a. 12 b. 1 4 d. 11 12 Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary. ____ 61. Solve log(4x + 10) = 3. 7 b. a. − 4 495 2 c. 250 ____ 62. Solve ln 2 + ln x = 5. Round to the nearest tenth, if necessary. a. 50,000 b. 74.2 c. 10 d. 990 d. 3 Use natural logarithms to solve the equation. Round to the nearest thousandth. 3 4 –0.288 ____ 63. e x = a. b. –0.275 c. 13 0.275 d. 0.288 Name: ________________________ ID: A Sketch the asymptotes and graph the function. ____ 64. y = 5 −1 x−1 a. c. b. d. 3x 6 − 7x + 9 . 7x 2 + 7x + 9 c. y = 0 ____ 65. Find the horizontal asymptote of the graph of y = a. b. y=3 3 y= 7 d. −2x 3 + 3x + 2 . 2x 3 + 6x + 2 c. no horizontal asymptote d. y = 0 ____ 66. Find the horizontal asymptote of the graph of y = a. b. y=1 y = −1 no horizontal asymptote 14 Name: ________________________ ID: A What is the product in simplest form? State any restrictions on the variable. ____ 67. y2 − y − 6 y2 ⋅ y−3 y 2 + 1y a. y 2 + 2y , y ≠ 3, − 1 y+1 c. y+2 , y ≠ 3, 0, − 1 y+1 b. y 2 + 2y , y ≠ 3, 0, − 1 y+1 d. y+2 , y ≠ 3, − 1 y+1 What is the quotient in simplified form? State any restrictions on the variable. ____ 68. a+1 a+2 ÷ a − 5 a 2 − 8a + 15 (a + 2)(a − 3) , a ≠ 5, − 1, 3 a. a+1 (a + 2)(a + 1) , a ≠ 5, 3, − 1 b. (a − 5) 2 (a − 3) c. d. (a + 2)(a − 3) , a ≠ 3, − 1 a+1 (a + 2)(a + 1) , a ≠ 5, 3 (a − 5) 2 (a − 3) ____ 69. Find the least common multiple of x 3 − x 2 + x − 1 and x 2 − 1 . Write the answer in factored form. a. (x + 1) 2 (x − 1) c. (x 3 − x 2 + x − 1)(x 2 − 1) b. (x + 1)(x − 1)(x 2 + 1) d. (x + 1)(x − 1)(x 2 − 1) Simplify the sum. ____ 70. 4 5 + m + 9 m2 − 81 9 a. (m − 9)(m + 9) 4m − 31 b. (m − 9)(m + 9) c. d. 9 m + m − 72 4m + 41 (m − 9)(m + 9) 2 Simplify the difference. ____ 71. 9 n 2 − 10n + 24 − n 2 − 13n + 42 n − 7 n − 13 a. n−7 n−4 b. n−7 c. n − 13 d. n 2 − 10n + 15 n 2 − 13n + 42 15 Name: ________________________ ID: A Simplify the complex fraction. 3 1 − 3b 2b ____ 72. 4 2 + 3b 4b 10 a. 3 b. 7 15 c. 15 7 d. 3 10 Generate the first five terms in the sequence using the explicit formula. ____ 73. y n = −5n − 5 a. b. c. d. –30, –25, –20, –15, –10 30, 25, 20, 15, 10 –10, –15, –20, –25, –30 10, 15, 20, 25, 30 ____ 74. Write a recursive formula for the sequence 7, 13, 19, 25, 31, ... Then find the next term. a. a n = a n − 1 + 6, where a 1 = 7; 37 b. a n = a n − 1 + 6, where a 1 = 37; 7 c. a n = a n − 1 − 6, where a 1 = 6; –23 d. a n = a n − 1 − 6, where a 1 = 7; 37 Is the sequence arithmetic? If so, identify the common difference. ____ 75. 14, 21, 42, 77, ... a. yes; 7 b. yes; –7 c. yes; 14 ____ 76. Find the 2nd and 3rd term of the sequence –7, ___, ___, –22, –27, ... b. –17, –12 c. –10, –17 a. –12, –15 d. no d. –12, –17 d. no Is the sequence geometric? If so, identify the common ratio. ____ 77. 6, 12, 24, 48, ... a. yes; 2 b. yes; –2 c. yes; 4 ____ 78. Kaylee is painting a design on the floor of a recreation room using equilateral triangles. She begins by painting the outline of Triangle 1 measuring 50 inches on a side. Next, she paints the outline of Triangle 2 inside the first triangle. The side length of Triangle 2 is 80% of the length of Triangle 1. She continues painting triangles inside triangles using the 80% reduction factor. Which triangle will first have a side length of less than 29 inches? a. Triangle 4 c. Triangle 5 b. Triangle 3 d. Triangle 6 16 Name: ________________________ ID: A What is a possible value for the missing term of the geometric sequence? ____ 79. 1250, ___, 50, ... a. 1200 b. 650 c. 250 d. 125 ____ 80. A large asteroid crashed into a moon of a planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic sequence 26, 44, 62, 80, . . . . Find the total distance that the projectile traveled in seven seconds. a. 534 feet b. 560 feet c. 212 feet d. 426 feet 8 ____ 81. Evaluate the series ∑ 5n. n = 3 a. 125 b. 38 c. 210 d. 165 ____ 82. Justine earned $26,000 during the first year of her job at city hall. After each year she received a 3% raise. Find her total earnings during the first five years on the job. a. $138,037.53 b. $1,004,704.20 c. $4,020.51 d. $108,774.30 ____ 83. The screen below shows the graph of a sound recorded on an oscilloscope. What are the period and the amplitude? (Each unit on the t-axis equals 0.01 seconds.) a. b. 0.05 seconds; 4.5 0.05 seconds; 9 c. d. 17 0.025 seconds; 9 0.025 seconds; 4.5 Name: ________________________ ID: A Find the measure of the angle. ____ 84. a. 155° b. 315° c. 18 90° d. 205° Name: ________________________ ID: A Sketch the angle in standard position. ____ 85. –95° a. c. b. d. ____ 86. Find the cosine and sine of 180°. Round your answers to the nearest hundredth if necessary. a. 0, –1.1 b. –0.71, –0.71 c. 19 –0.71, 0.71 d. –1, 0 Name: ________________________ ID: A ____ 87. Find the cosine 315°. Round your answers to the nearest hundredth if necessary. a. 0 b. 0.71 c. 1 d. –0.78 ____ 88. Find the radian measure of an angle of –340°. 9 9π b. c. a. −17π −17 −17π 9 d. −17 9π d. − ÊÁ 3π ÊÁ 3π ˆ˜ ˆ˜ ____ 89. Find the exact values of cos ÁÁÁÁ radians ˜˜˜˜ and sin ÁÁÁÁ radians ˜˜˜˜ . Ë 4 Ë 4 ¯ ¯ a. 2 2 ,− 2 2 b. 3 1 − , 2 2 c. − 2 2 , 2 2 3 1 , 2 2 Use the given circle. Find the length s to the nearest tenth. ____ 90. a. 6.3 m b. 2.0 m c. 3.1 m d. 12.6 m a. 4.4 ft b. 70.4 ft c. 35.2 ft d. 11.2 ft ____ 91. 20 Name: ________________________ ID: A ____ 92. Find the period of the graph shown below. a. 2π b. π c. 1 π 2 d. 2 π 3 2 d. 8 ____ 93. Find the amplitude of the sine curve shown below. a. 4 π 3 b. 4 c. 21 Name: ________________________ ____ 94. y = sin 3θ a. b. ID: A c. d. Find the domain, period, range, and amplitude of the cosine function. ____ 95. y = a. b. c. d. 3 t cos 2 2 3 3 3 domain = all real numbers, period = 4π ; range: − ≤ y ≤ ; amplitude = 2 2 2 1 3 3 3 domain = all real numbers, period = ; range: − ≤ y ≤ ; amplitude = − 2 2 2 2 3 3 3 3 3 domain = − ≤ x ≤ , period = 4π ; range: − ≤ y ≤ ; amplitude = − 2 2 2 2 2 3 3 1 3 3 domain = − ≤ x ≤ , period = ; range: y ≤ ; amplitude = 2 2 2 2 2 22 Name: ________________________ ID: A What is the value of the expression? Do not use a calculator. ____ 96. tan 5π 3 3 a. b. - 3 c. 1 d. 1 3 Write an equation for the translation of the function. ____ 97. y = cos x; translated 6 units up a. y = cos (x + 6) b. y = cos (x − 6) c. d. y = cos x − 6 y = cos x + 6 Find the exact value. If the expression is undefined, write undefined. ____ 98. csc 135° a. 0 b. undefined c. 1 2 Evaluate the expression for the given value of the variable(s). 99. 4(3h − 6) 1+h ; h = −2 Solve the system using elimination. ÔÏÔÔ 7x + 2y = 11 Ô 100. ÌÔ ÔÔ 4x − 7y = −10 Ó 23 d. 2 ID: A Algebra 2: Final Exam Answer Section 1. ANS: OBJ: TOP: KEY: 2. ANS: OBJ: STA: 3. ANS: OBJ: NAT: TOP: 4. ANS: OBJ: NAT: TOP: 5. ANS: REF: OBJ: NAT: TOP: KEY: 6. ANS: REF: OBJ: NAT: STA: KEY: 7. ANS: REF: OBJ: NAT: STA: KEY: 8. ANS: OBJ: NAT: STA: KEY: 9. ANS: OBJ: NAT: TOP: KEY: D PTS: 1 DIF: L2 REF: 1-4 Solving Equations 1-4.1 To solve equations NAT: CC A.CED.1| CC A.CED.4| A.2.a| A.4.c 1-4 Problem 2 Solving a Multi-Step Equation equation | solution of an equation | inverse operations C PTS: 1 DIF: L2 REF: 4-6 Completing the Square 4-6.1 To solve equations by completing the square NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g NC 2.02a TOP: 4-6 Problem 3 Solving a Perfect Square Trinomial Equation A PTS: 1 DIF: L3 REF: 1-4 Solving Equations 1-4.2 To solve problems by writing equations CC A.CED.1| CC A.CED.4| A.2.a| A.4.c 1-4 Problem 3 Using an Equation to Solve a Problem KEY: equation | solution of an equation B PTS: 1 DIF: L2 REF: 1-5 Solving Inequalities 1-5.1 To solve and graph inequalities CC A.CED.1| A.2.a| A.3.b| A.3.d| A.4.c 1-5 Problem 2 Solving and Graphing an Inequality D PTS: 1 DIF: L2 1-6 Absolute Value Equations and Inequalities 1-6.1 To write and solve equations and inequalities involving absolute value CC A.SSE.1.b| CC A.CED.1| N.1.g| N.3.c| A.2.a| A.4.c STA: NC 2.08a| NC 2.08b 1-6 Problem 2 Solving a Multi-Step Absolute Value Equation absolute value C PTS: 1 DIF: L2 3-1 Solving Systems Using Tables and Graphs 3-1.1 To solve a linear system using a graph or a table CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d NC 2.10 TOP: 3-1 Problem 1 Using a Graph or Table to Solve a System system of linear equations | graphing | solution of a system A PTS: 1 DIF: L2 3-1 Solving Systems Using Tables and Graphs 3-1.1 To solve a linear system using a graph or a table CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d NC 2.10 TOP: 3-1 Problem 3 Using Linear Regression system of linear equations | word problem | problem solving | multi-part question A PTS: 1 DIF: L2 REF: 3-2 Solving Systems Algebraically 3-2.1 To solve linear systems algebraically CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d NC 2.10 TOP: 3-2 Problem 1 Solving by Substitution system of linear equations | substitution method C PTS: 1 DIF: L2 REF: 3-5 Systems With Three Variables 3-5.1 To solve systems in three variables using elimination CC A.REI.6| A.4.d STA: NC 2.10 3-5 Problem 2 Solving an Equivalent System system with three variables | solve by elimination 1 ID: A 10. ANS: REF: OBJ: NAT: TOP: 11. ANS: OBJ: TOP: KEY: 12. ANS: OBJ: TOP: 13. ANS: OBJ: TOP: KEY: 14. ANS: REF: OBJ: TOP: 15. ANS: REF: OBJ: TOP: 16. ANS: REF: OBJ: TOP: 17. ANS: REF: OBJ: NAT: STA: TOP: KEY: 18. ANS: REF: OBJ: NAT: STA: TOP: KEY: 19. ANS: REF: OBJ: STA: TOP: D PTS: 1 DIF: L2 8-3 Rational Functions and Their Graphs 8-3.1 To identify properties of rational functions CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h STA: NC 2.05a| NC 2.05b| NC 2.05c 8-3 Problem 2 Finding Vertical Asymptotes KEY: rational function D PTS: 1 DIF: L3 REF: 9-1 Mathematical Patterns 9-1.2 To use a formula to find the nth term of a sequence NAT: CC A.SSE.4| A.1.a 9-1 Problem 3 Writing an Explicit Formula for a Sequence sequence | explicit formula | term of a sequence B PTS: 1 DIF: L3 REF: 13-2 Angles and the Unit Circle 13-2.1 To work with angles in standard position NAT: CC F.TF.2 13-2 Problem 3 Identifying Coterminal Angles KEY: coterminal angles D PTS: 1 DIF: L3 REF: 13-3 Radian Measure 13-3.1 To use radian measure for angles NAT: CC F.TF.1| M.3.e 13-3 Problem 2 Finding Cosine and Sine of a Radian Measure central angle | intercepted arc | radian B PTS: 1 DIF: L3 13-7 Translating Sine and Cosine Functions 13-7.1 To graph translations of trigonometric functions NAT: CC F.IF.7.e| CC F.TF.5| A.2.d 13-7 Problem 2 Graphing Translations KEY: phase shift A PTS: 1 DIF: L3 13-7 Translating Sine and Cosine Functions 13-7.1 To graph translations of trigonometric functions NAT: CC F.IF.7.e| CC F.TF.5| A.2.d 13-7 Problem 3 Graphing a Combined Translation KEY: phase shift D PTS: 1 DIF: L4 13-7 Translating Sine and Cosine Functions 13-7.1 To graph translations of trigonometric functions NAT: CC F.IF.7.e| CC F.TF.5| A.2.d 13-7 Problem 4 Graphing a Translation of y = sin 2x KEY: phase shift A PTS: 1 DIF: L2 4-2 Standard Form of a Quadratic Function 4-2.1 To graph quadratic functions written in standard form CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1 NC 2.02a| NC 2.02b 4-2 Problem 1 Finding the Features of a Quadratic Function Graph functions expressed symbolically | standard form | vertex of a parabola | axis of symmetry C PTS: 1 DIF: L3 4-2 Standard Form of a Quadratic Function 4-2.1 To graph quadratic functions written in standard form CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1 NC 2.02a| NC 2.02b 4-2 Problem 1 Finding the Features of a Quadratic Function standard form | minimum value | maximum value B PTS: 1 DIF: L3 4-3 Modeling With Quadratic Functions 4-3.1 To model data with quadratic functions NAT: CC F.IF.4| CC F.IF.5| A.2.f NC 2.02a| NC 2.02b| NC 2.04a| NC 2.04b 4-3 Problem 1 Writing an Equation of a Parabola KEY: quadratic function | quadratic model 2 ID: A 20. ANS: REF: OBJ: NAT: KEY: 21. ANS: REF: OBJ: NAT: KEY: 22. ANS: REF: OBJ: NAT: KEY: 23. ANS: REF: OBJ: TOP: 24. ANS: REF: OBJ: TOP: 25. ANS: REF: OBJ: TOP: KEY: 26. ANS: OBJ: NAT: STA: KEY: 27. ANS: OBJ: NAT: STA: KEY: 28. ANS: OBJ: STA: KEY: 29. ANS: OBJ: STA: KEY: B PTS: 1 DIF: L2 4-4 Factoring Quadratic Expressions 4-4.1 To find common and binomial factors of quadratic expressions CC A.SSE.2| N.5.c| A.2.a TOP: 4-4 Problem 1 Factoring ax^2+bx+c when a=+/-1 factoring | quadratic expression D PTS: 1 DIF: L3 4-4 Factoring Quadratic Expressions 4-4.1 To find common and binomial factors of quadratic expressions CC A.SSE.2| N.5.c| A.2.a TOP: 4-4 Problem 1 Factoring ax^2+bx+c when a=+/-1 factoring | quadratic expression D PTS: 1 DIF: L3 4-4 Factoring Quadratic Expressions 4-4.1 To find common and binomial factors of quadratic expressions CC A.SSE.2| N.5.c| A.2.a TOP: 4-4 Problem 3 Factoring ax^2+bx+c when abs(a) not = 1 factoring C PTS: 1 DIF: L3 4-4 Factoring Quadratic Expressions 4-4.2 To factor special quadratic expressions NAT: CC A.SSE.2| N.5.c| A.2.a 4-4 Problem 4 Factoring a Perfect Square Trinomial KEY: factoring | perfect square trinomial C PTS: 1 DIF: L2 4-4 Factoring Quadratic Expressions 4-4.2 To factor special quadratic expressions NAT: CC A.SSE.2| N.5.c| A.2.a 4-4 Problem 5 Factoring a Difference of Two Squares KEY: identify ways to rewrite expressions D PTS: 1 DIF: L2 4-4 Factoring Quadratic Expressions 4-4.2 To factor special quadratic expressions NAT: CC A.SSE.2| N.5.c| A.2.a 4-4 Problem 5 Factoring a Difference of Two Squares factoring | identify ways to rewrite expressions A PTS: 1 DIF: L2 REF: 4-5 Quadratic Equations 4-5.1 To solve quadratic equations by factoring CC A.SSE.1.a| CC A.APR.3| CC A.CED.1| A.2.a| A.4.a| A.4.c NC 2.02a| NC 2.02b TOP: 4-5 Problem 1 Solving a Quadratic Equation by Factoring Zero-Product Property D PTS: 1 DIF: L3 REF: 4-5 Quadratic Equations 4-5.1 To solve quadratic equations by factoring CC A.SSE.1.a| CC A.APR.3| CC A.CED.1| A.2.a| A.4.a| A.4.c NC 2.02a| NC 2.02b TOP: 4-5 Problem 1 Solving a Quadratic Equation by Factoring Zero-Product Property C PTS: 1 DIF: L2 REF: 4-6 Completing the Square 4-6.2 To rewrite functions by completing the square NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g NC 2.02a TOP: 4-6 Problem 4 Completing the Square completing the square A PTS: 1 DIF: L3 REF: 4-6 Completing the Square 4-6.1 To solve equations by completing the square NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g NC 2.02a TOP: 4-6 Problem 5 Solving by Completing the Square completing the square 3 ID: A 30. ANS: OBJ: NAT: TOP: 31. ANS: OBJ: NAT: TOP: 32. ANS: OBJ: NAT: TOP: 33. ANS: OBJ: NAT: STA: KEY: 34. ANS: OBJ: NAT: STA: KEY: 35. ANS: OBJ: NAT: STA: KEY: 36. ANS: OBJ: NAT: STA: KEY: 37. ANS: OBJ: NAT: TOP: 38. ANS: REF: OBJ: NAT: TOP: 39. ANS: REF: OBJ: NAT: TOP: D PTS: 1 DIF: L3 REF: 4-7 The Quadratic Formula 4-7.1 To solve quadratic equations using the Quadratic Formula CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f STA: NC 2.02a 4-7 Problem 1 Using the Quadratic Formula KEY: Quadratic Formula C PTS: 1 DIF: L3 REF: 4-7 The Quadratic Formula 4-7.1 To solve quadratic equations using the Quadratic Formula CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f STA: NC 2.02a 4-7 Problem 1 Using the Quadratic Formula KEY: Quadratic Formula B PTS: 1 DIF: L3 REF: 4-7 The Quadratic Formula 4-7.1 To solve quadratic equations using the Quadratic Formula CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f STA: NC 2.02a 4-7 Problem 2 Applying the Quadratic Formula KEY: Quadratic Formula C PTS: 1 DIF: L2 REF: 4-8 Complex Numbers 4-8.1 To identify, graph, and perform operations with complex numbers CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g NC 1.02 TOP: 4-8 Problem 1 Simplifying a Number using i imaginary number | imaginary unit B PTS: 1 DIF: L3 REF: 4-8 Complex Numbers 4-8.1 To identify, graph, and perform operations with complex numbers CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g NC 1.02 TOP: 4-8 Problem 4 Multiplying Complex Numbers complex number B PTS: 1 DIF: L3 REF: 4-8 Complex Numbers 4-8.1 To identify, graph, and perform operations with complex numbers CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g NC 1.02 TOP: 4-8 Problem 5 Dividing Complex Numbers complex number | complex conjugates C PTS: 1 DIF: L2 REF: 4-8 Complex Numbers 4-8.1 To identify, graph, and perform operations with complex numbers CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g NC 1.02 TOP: 4-8 Problem 5 Dividing Complex Numbers complex number | complex conjugates C PTS: 1 DIF: L3 REF: 4-9 Quadratic Systems 4-9.1 To solve and graph systems of linear and quadratic equations CC A.CED.3| CC A.REI.7| A.4.a| A.4.d STA: NC 2.10 4-9 Problem 3 Solving a Quadratic System of Equations B PTS: 1 DIF: L3 5-2 Polynomials, Linear Factors, and Zeros 5-2.2 To write a polynomial function from its zeros CC A.SSE.1| CC A.APR.3| CC F.IF.7| CC F.IF.7.c| CC F.BF.1 5-2 Problem 4 Finding the Multiplicity of a Zero KEY: multiple zero | multiplicity C PTS: 1 DIF: L3 5-2 Polynomials, Linear Factors, and Zeros 5-2.2 To write a polynomial function from its zeros CC A.SSE.1| CC A.APR.3| CC F.IF.7| CC F.IF.7.c| CC F.BF.1 5-2 Problem 4 Finding the Multiplicity of a Zero KEY: multiple zero | multiplicity 4 ID: A 40. ANS: D PTS: 1 DIF: L3 REF: 5-4 Dividing Polynomials OBJ: 5-4.1 To divide polynomials using long division NAT: CC A.APR.1| CC A.APR.2| CC A.APR.6| N.1.d| A.3.c| A.3.e STA: NC 1.03 TOP: 5-4 Problem 1 Using Polynomial Long Division 41. ANS: A PTS: 1 DIF: L4 REF: 5-4 Dividing Polynomials OBJ: 5-4.1 To divide polynomials using long division NAT: CC A.APR.1| CC A.APR.2| CC A.APR.6| N.1.d| A.3.c| A.3.e STA: NC 1.03 TOP: 5-4 Problem 2 Checking Factors 42. ANS: A PTS: 1 DIF: L3 REF: 5-4 Dividing Polynomials OBJ: 5-4.2 To divide polynomials using synthetic division NAT: CC A.APR.1| CC A.APR.2| CC A.APR.6| N.1.d| A.3.c| A.3.e STA: NC 1.03 TOP: 5-4 Problem 3 Using Synthetic Division KEY: synthetic division 43. ANS: C PTS: 1 DIF: L3 REF: 5-4 Dividing Polynomials OBJ: 5-4.2 To divide polynomials using synthetic division NAT: CC A.APR.1| CC A.APR.2| CC A.APR.6| N.1.d| A.3.c| A.3.e STA: NC 1.03 TOP: 5-4 Problem 5 Evaluating a Polynomial KEY: synthetic division | remainder theorem 44. ANS: B PTS: 1 DIF: L2 REF: 5-6 The Fundamental Theorem of Algebra OBJ: 5-6.1 To use the Fundamental Theorem of Algebra to solve polynomial equations with complex solutions NAT: CC N.CN.7| CC N.CN.8| CC N.CN.9| CC A.APR.3 TOP: 5-6 Problem 2 Finding All the Zeros of a Polynomial Function KEY: Rational Root Theorem 45. ANS: A PTS: 1 DIF: L3 REF: 5-6 The Fundamental Theorem of Algebra OBJ: 5-6.1 To use the Fundamental Theorem of Algebra to solve polynomial equations with complex solutions NAT: CC N.CN.7| CC N.CN.8| CC N.CN.9| CC A.APR.3 TOP: 5-6 Problem 2 Finding All the Zeros of a Polynomial Function KEY: Fundamental Theorem of Algebra 46. ANS: D PTS: 1 DIF: L3 REF: 5-7 The Binomial Theorem OBJ: 5-7.2 To use the Binomial Theorem NAT: CC A.APR.5| D.4.k TOP: 5-7 Problem 2 Expanding a Binomial KEY: Binomial Theorem | expand 47. ANS: B PTS: 1 DIF: L3 REF: 6-2 Multiplying and Dividing Radical Expressions OBJ: 6-2.1 To multiply and divide radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e TOP: 6-2 Problem 4 Dividing Radical Expressions KEY: simplest form of a radical 48. ANS: A PTS: 1 DIF: L3 REF: 6-2 Multiplying and Dividing Radical Expressions OBJ: 6-2.1 To multiply and divide radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e TOP: 6-2 Problem 4 Dividing Radical Expressions KEY: simplest form of a radical 49. ANS: A PTS: 1 DIF: L3 REF: 6-3 Binomial Radical Expressions OBJ: 6-3.1 To add and subtract radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e TOP: 6-3 Problem 4 Multiplying Binomial Radical Expressions KEY: like radicals 5 ID: A 50. ANS: OBJ: STA: KEY: 51. ANS: OBJ: STA: KEY: 52. ANS: REF: OBJ: STA: KEY: 53. ANS: REF: OBJ: STA: KEY: 54. ANS: OBJ: STA: KEY: 55. ANS: REF: OBJ: NAT: STA: KEY: 56. ANS: REF: OBJ: NAT: STA: KEY: 57. ANS: REF: OBJ: NAT: STA: KEY: 58. ANS: OBJ: STA: 59. ANS: OBJ: STA: C PTS: 1 DIF: L3 REF: 6-4 Rational Exponents 6-4.1 To simplify expressions with rational exponents NAT: CC N.RN.1| CC N.RN.2 NC 1.01 TOP: 6-4 Problem 1 Simplifying Expressions with Rational Exponents rational exponents A PTS: 1 DIF: L3 REF: 6-4 Rational Exponents 6-4.1 To simplify expressions with rational exponents NAT: CC N.RN.1| CC N.RN.2 NC 1.01 TOP: 6-4 Problem 5 Simplifying Numbers With Rational Exponents rational exponent D PTS: 1 DIF: L2 6-5 Solving Square Root and Other Radical Equations 6-5.1 To solve square root and other radical equations NAT: CC A.CED.4| CC A.REI.2| A.2.a NC 2.07a TOP: 6-5 Problem 1 Solving a Square Root Equation square root equation C PTS: 1 DIF: L3 6-5 Solving Square Root and Other Radical Equations 6-5.1 To solve square root and other radical equations NAT: CC A.CED.4| CC A.REI.2| A.2.a NC 2.07a TOP: 6-5 Problem 3 Using Radical Equations square root equation A PTS: 1 DIF: L4 REF: 6-7 Inverse Relations and Functions 6-7.1 To find the inverse of a relation or function NAT: CC F.BF.4.a| CC F.BF.4.c| A.1.j NC 2.01 TOP: 6-7 Problem 5 Finding the Inverse of a Formula inverse function B PTS: 1 DIF: L2 7-3 Logarithmic Functions as Inverses 7-3.1 To write and evaluate logarithmic expressions CC A.SSE.1.b| CC F.IF.7.e| CC F.IF.8| CC F.IF.9| CC F.BF.4.a| G.2.c| A.2.h| A.3.h NC 1.01 TOP: 7-3 Problem 1 Writing Exponential Equations in Logarithmic Form write a function in different but equivalent forms A PTS: 1 DIF: L2 7-3 Logarithmic Functions as Inverses 7-3.1 To write and evaluate logarithmic expressions CC A.SSE.1.b| CC F.IF.7.e| CC F.IF.8| CC F.IF.9| CC F.BF.4.a| G.2.c| A.2.h| A.3.h NC 1.01 TOP: 7-3 Problem 2 Evaluating a Logarithm logarithm B PTS: 1 DIF: L4 7-3 Logarithmic Functions as Inverses 7-3.1 To write and evaluate logarithmic expressions CC A.SSE.1.b| CC F.IF.7.e| CC F.IF.8| CC F.IF.9| CC F.BF.4.a| G.2.c| A.2.h| A.3.h NC 1.01 TOP: 7-3 Problem 2 Evaluating a Logarithm logarithm A PTS: 1 DIF: L2 REF: 7-4 Properties of Logarithms 7-4.1 To use the properties of logarithms NAT: CC F.LE.4| N.1.d| A.3.h NC 1.01 TOP: 7-4 Problem 2 Expanding Logarithms C PTS: 1 DIF: L3 REF: 7-4 Properties of Logarithms 7-4.1 To use the properties of logarithms NAT: CC F.LE.4| N.1.d| A.3.h NC 1.01 TOP: 7-4 Problem 2 Expanding Logarithms 6 ID: A 60. ANS: REF: OBJ: NAT: TOP: KEY: 61. ANS: REF: OBJ: NAT: TOP: 62. ANS: OBJ: STA: KEY: 63. ANS: OBJ: STA: KEY: 64. ANS: REF: OBJ: NAT: TOP: 65. ANS: REF: OBJ: NAT: TOP: 66. ANS: REF: OBJ: NAT: TOP: 67. ANS: OBJ: NAT: STA: KEY: 68. ANS: OBJ: NAT: STA: KEY: 69. ANS: REF: OBJ: STA: C PTS: 1 DIF: L4 7-5 Exponential and Logarithmic Equations 7-5.1 To solve exponential and logarithmic equations CC A.REI.11| CC F.LE.4| A.3.h| A.4.c STA: NC 2.03a 7-5 Problem 1 Solving an Exponential Equation-Common Base exponential equation B PTS: 1 DIF: L3 7-5 Exponential and Logarithmic Equations 7-5.1 To solve exponential and logarithmic equations CC A.REI.11| CC F.LE.4| A.3.h| A.4.c STA: NC 2.03a 7-5 Problem 5 Solving a Logarithmic Equation KEY: logarithmic equation B PTS: 1 DIF: L4 REF: 7-6 Natural Logarithms 7-6.2 To solve equations using natural logarithms NAT: CC F.LE.4| A.3.h NC 1.01 TOP: 7-6 Problem 2 Solving a Natural Logarithmic Equation natural logarithmic function A PTS: 1 DIF: L2 REF: 7-6 Natural Logarithms 7-6.2 To solve equations using natural logarithms NAT: CC F.LE.4| A.3.h NC 1.01 TOP: 7-6 Problem 3 Solving an Exponential Equation natural logarithmic function C PTS: 1 DIF: L3 8-2 The Reciprocal Function Family 8-2.2 To graph translations of reciprocal functions CC A.CED.2| CC F.BF.1| CC F.BF.3| G.2.c STA: NC 1.05 8-2 Problem 3 Graphing a Translation KEY: reciprocal function D PTS: 1 DIF: L3 8-3 Rational Functions and Their Graphs 8-3.1 To identify properties of rational functions CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h STA: NC 2.05a| NC 2.05b| NC 2.05c 8-3 Problem 3 Finding Horizontal Asymptotes KEY: rational function B PTS: 1 DIF: L3 8-3 Rational Functions and Their Graphs 8-3.1 To identify properties of rational functions CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h STA: NC 2.05a| NC 2.05b| NC 2.05c 8-3 Problem 3 Finding Horizontal Asymptotes KEY: rational function B PTS: 1 DIF: L3 REF: 8-4 Rational Expressions 8-4.2 To multiply and divide rational expressions CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e NC 1.03 TOP: 8-4 Problem 2 Multiplying Rational Expressions rational expression | simplest form A PTS: 1 DIF: L3 REF: 8-4 Rational Expressions 8-4.2 To multiply and divide rational expressions CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e NC 1.03 TOP: 8-4 Problem 3 Dividing Rational Expressions rational expression | simplest form B PTS: 1 DIF: L3 8-5 Adding and Subtracting Rational Expressions 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e NC 1.03 TOP: 8-5 Problem 1 Finding the Least Common Multiple 7 ID: A 70. ANS: REF: OBJ: STA: 71. ANS: REF: OBJ: STA: 72. ANS: REF: OBJ: STA: KEY: 73. ANS: OBJ: NAT: TOP: KEY: 74. ANS: OBJ: NAT: TOP: KEY: 75. ANS: OBJ: TOP: KEY: 76. ANS: OBJ: TOP: 77. ANS: OBJ: TOP: 78. ANS: OBJ: TOP: 79. ANS: OBJ: TOP: KEY: 80. ANS: OBJ: TOP: KEY: 81. ANS: OBJ: TOP: B PTS: 1 DIF: L2 8-5 Adding and Subtracting Rational Expressions 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e NC 1.03 TOP: 8-5 Problem 2 Adding Rational Expressions A PTS: 1 DIF: L3 8-5 Adding and Subtracting Rational Expressions 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e NC 1.03 TOP: 8-5 Problem 3 Subtracting Rational Expressions D PTS: 1 DIF: L2 8-5 Adding and Subtracting Rational Expressions 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e NC 1.03 TOP: 8-5 Problem 4 Simplifying a Complex Fraction complex fraction C PTS: 1 DIF: L3 REF: 9-1 Mathematical Patterns 9-1.1 To identify mathematical patterns found in a sequence CC A.SSE.4| A.1.a 9-1 Problem 1 Generating a Sequence Using an Explicit Formula sequence | term of a sequence | explicit formula A PTS: 1 DIF: L2 REF: 9-1 Mathematical Patterns 9-1.1 To identify mathematical patterns found in a sequence CC A.SSE.4| A.1.a 9-1 Problem 2 Writing a Recursive Definition for a Sequence sequence | recursive formula | term of a sequence D PTS: 1 DIF: L2 REF: 9-2 Arithmetic Sequences 9-2.1 To define, identify, and apply arithmetic sequences NAT: CC F.IF.3| A.1.a 9-2 Problem 1 Identifying Arithmetic Sequences arithmetic sequence | common difference D PTS: 1 DIF: L3 REF: 9-2 Arithmetic Sequences 9-2.1 To define, identify, and apply arithmetic sequences NAT: CC F.IF.3| A.1.a 9-2 Problem 2 Analyzing Arithmetic Sequences KEY: arithmetic sequence A PTS: 1 DIF: L2 REF: 9-3 Geometric Sequences 9-3.1 To define, identify, and apply geometric sequences NAT: CC A.SSE.4| A.1.a 9-3 Problem 1 Identifying Geometric Sequences KEY: geometric sequence | common ratio A PTS: 1 DIF: L3 REF: 9-3 Geometric Sequences 9-3.1 To define, identify, and apply geometric sequences NAT: CC A.SSE.4| A.1.a 9-3 Problem 3 Using a Geometric Sequence KEY: geometric sequence C PTS: 1 DIF: L3 REF: 9-3 Geometric Sequences 9-3.1 To define, identify, and apply geometric sequences NAT: CC A.SSE.4| A.1.a 9-3 Problem 4 Using a Geometric Mean geometric sequence | geometric mean B PTS: 1 DIF: L3 REF: 9-4 Arithmetic Series 9-4.1 To define arithmetic series and find their sums NAT: CC F.IF.3| A.1.a| A.3.g 9-4 Problem 2 Using the Sum of a Finite Arithmetic Series series | finite series | limits D PTS: 1 DIF: L3 REF: 9-4 Arithmetic Series 9-4.1 To define arithmetic series and find their sums NAT: CC F.IF.3| A.1.a| A.3.g 9-4 Problem 4 Finding the Sum of a Series KEY: series | finite series 8 ID: A 82. ANS: OBJ: TOP: 83. ANS: OBJ: TOP: KEY: 84. ANS: OBJ: TOP: KEY: 85. ANS: OBJ: TOP: KEY: 86. ANS: OBJ: TOP: 87. ANS: OBJ: TOP: 88. ANS: OBJ: TOP: KEY: 89. ANS: OBJ: TOP: KEY: 90. ANS: OBJ: TOP: KEY: 91. ANS: OBJ: TOP: KEY: 92. ANS: OBJ: NAT: TOP: 93. ANS: OBJ: NAT: TOP: 94. ANS: OBJ: TOP: A PTS: 1 DIF: L2 REF: 9-5 Geometric Series 9-5.1 To define geometric series and find their sums NAT: CC A.SSE.4| A.1.a| A.3.g 9-5 Problem 2 Using the Geometric Series Formula KEY: geometric series A PTS: 1 DIF: L3 REF: 13-1 Exploring Periodic Data 13-1.2 To find the amplitude of periodic functions NAT: CC F.IF.4| CC F.TF.5 13-1 Problem 4 Using Periodic Functions to Solve a Problem periodic function | cycle | period | amplitude A PTS: 1 DIF: L3 REF: 13-2 Angles and the Unit Circle 13-2.1 To work with angles in standard position NAT: CC F.TF.2 13-2 Problem 1 Measuring Angles in Standard Position standard position | initial side | terminal side B PTS: 1 DIF: L3 REF: 13-2 Angles and the Unit Circle 13-2.1 To work with angles in standard position NAT: CC F.TF.2 13-2 Problem 2 Sketching Angles in Standard Position standard position | initial side | terminal side D PTS: 1 DIF: L3 REF: 13-2 Angles and the Unit Circle 13-2.2 To find coordinates of points on the unit circle NAT: CC F.TF.2 13-2 Problem 4 Finding the Cosines and Sines of Angles KEY: cosine of theta | sine of theta B PTS: 1 DIF: L3 REF: 13-2 Angles and the Unit Circle 13-2.2 To find coordinates of points on the unit circle NAT: CC F.TF.2 13-2 Problem 4 Finding the Cosines and Sines of Angles KEY: cosine of theta C PTS: 1 DIF: L3 REF: 13-3 Radian Measure 13-3.1 To use radian measure for angles NAT: CC F.TF.1| M.3.e 13-3 Problem 1 Using Dimensional Analysis central angle | intercepted arc | radian C PTS: 1 DIF: L3 REF: 13-3 Radian Measure 13-3.1 To use radian measure for angles NAT: CC F.TF.1| M.3.e 13-3 Problem 2 Finding Cosine and Sine of a Radian Measure central angle | intercepted arc | radian A PTS: 1 DIF: L3 REF: 13-3 Radian Measure 13-3.2 To find the length of an arc of a circle NAT: CC F.TF.1| M.3.e 13-3 Problem 3 Finding the Length of an Arc central angle | intercepted arc | radian C PTS: 1 DIF: L3 REF: 13-3 Radian Measure 13-3.2 To find the length of an arc of a circle NAT: CC F.TF.1| M.3.e 13-3 Problem 3 Finding the Length of an Arc central angle | intercepted arc | radian A PTS: 1 DIF: L3 REF: 13-4 The Sine Function 13-4.1 To identify properties of the sine function CC F.IF.4| CC F.IF.7.e| CC F.TF.2| CC F.TF.5| M.3.c 13-4 Problem 2 Finding the Period of a Sine Curve KEY: sine function | sine curve B PTS: 1 DIF: L3 REF: 13-4 The Sine Function 13-4.1 To identify properties of the sine function CC F.IF.4| CC F.IF.7.e| CC F.TF.2| CC F.TF.5| M.3.c 13-4 Problem 3 Finding the Amplitude of a Sine Curve KEY: sine function | sine curve A PTS: 1 DIF: L3 REF: 13-4 The Sine Function 13-4.2 To graph sine curves NAT: CC F.IF.4| CC F.IF.7.e| CC F.TF.2| CC F.TF.5| M.3.c 13-4 Problem 5 Graphing From a Function Rule KEY: sine function | sine curve 9 ID: A 95. ANS: OBJ: NAT: TOP: 96. ANS: OBJ: NAT: TOP: 97. ANS: REF: OBJ: TOP: 98. ANS: REF: OBJ: TOP: 99. ANS: 48 PTS: OBJ: NAT: TOP: 100. ANS: (1, 2) PTS: OBJ: NAT: STA: KEY: A PTS: 1 DIF: L3 13-5.1 To graph and write cosine functions CC F.IF.4| CC F.IF.7.e| CC F.TF.2| CC F.TF.5| M.3.c 13-5 Problem 1 Interpreting a Graph B PTS: 1 DIF: L3 13-6.1 To graph the tangent function CC F.IF.7.e| CC F.TF.2| CC F.TF.5| M.3.c 13-6 Problem 1 Finding Tangents Geometrically D PTS: 1 DIF: L3 13-7 Translating Sine and Cosine Functions 13-7.2 To write equations of translations 13-7 Problem 5 Writing Translations D PTS: 1 DIF: L3 13-8 Reciprocal Trigonometric Functions 13-8.1 To evaluate reciprocal trigonometric functions 13-8 Problem 1 Finding Values Geometrically REF: 13-5 The Cosine Function KEY: cosine function REF: 13-6 The Tangent Function KEY: tangent of theta | tangent function NAT: CC F.IF.7.e| CC F.TF.5| A.2.d KEY: phase shift NAT: CC F.IF.7.e KEY: cosecant 1 DIF: L4 REF: 1-3 Algebraic Expressions 1-3.1 To evaluate algebraic expressions CC A.SSE.1.a| N.1.d| N.3.a| N.3.b| A.3.b| A.3.d 1-3 Problem 3 Evaluating Algebraic Expressions KEY: evaluate 1 DIF: L2 REF: 3-2 Solving Systems Algebraically 3-2.1 To solve linear systems algebraically CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d NC 2.10 TOP: 3-2 Problem 3 Solving by Elimination system of linear equations | solve by elimination 10