Math 3 Cumulative Review Unit 1 - Weeblymisscore.weebly.com/.../84167066/cumulative_review_2016.pdf · 2018. 9. 4. · 1b. Are points on the line 2 −5 ≥10 solutions for the inequality?

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Name: ___________________________

Math 3 Cumulative Review Unit 1

Graph each of the following.

1a. 2𝑥 − 5𝑦 ≥ 10 2. { 𝑦 ≥ −3𝑥 + 2

𝑦 <3

4𝑥 − 1

1b. Are points on the line 2𝑥 − 5𝑦 ≥ 10 solutions for the inequality? Using a sentence or two, explain

why or why not.

3. {

𝒚 ≤ 𝟑−𝟒𝒙 + 𝒚 ≤ 𝟖

𝒚 ≥ 𝒙 − 𝟑

Find two solutions that work for all three inequalities.

4. Explain why a system of equations only has one solution while a system of inequalities has infinitely many solutions.

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5. Superbats Inc. Manufactures two different types of wood baseball bats, the Homer-Hitter and the Big Timber. The Homer-Hitter takes 5 hours to trim and turn on the lathe and 4 hours to finish. Each of the Homer-Hitter sold makes a profit of $19. The Big Timber takes 10 hours to trim and turn on the lathe and 6 hours to finish, and its profit is $34. The total time available for trimming and lathing is 140 hours. The total time for finishing is 90 hours. How many of each type should be produced in order to maximize their profit? What is the maximum profit? Define your variables: X= Y= Objective Function: Constraints: Graph the system:

Show ALL work to find maximum profit:

Final answer written in a full sentence:

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Unit 2 Given the following sequences, determine whether it’s arithmetic, geometric or neither. Then find the next 3 terms. 6. -25, -34, -43, -52, … 7. -2, 8, -32, 128, …

8. -58, -39, -20, -1, … 9. 5

3,

9

4,

13

5,

17

6,

21

7, …

Use the given equation to find the first 3 terms of the sequence. 10. 𝑎𝑛 = −3𝑛 + 8 11. 𝑎𝑛 = 𝑎𝑛−1 ∙ 4 𝑎1 = 3 Given the first 4 terms of the sequence, find the explicit formula and the recursive formula.

12. 22, 14, 6, -2, … 13. 2

3, 1,

3

2,

9

4,

27

8, …

Write the explicit formula for the equation. 14. 𝑎𝑛 = 𝑎𝑛−1 ∙ 5 15. 𝑎𝑛 = 𝑎𝑛−1 − 1.5 𝑎1 = −2 𝑎1 = 7 Write the recursive formula for the equation. 16. 𝑎𝑛 = −3𝑛 + 1.7 17. 𝑎𝑛 = −3(4)𝑛−1

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Use formulas for sequences and series to solve each of the following. Show ALL work for full credit. Write your final answer in a sentence. 18. Hector gets better and better at a video game every time he plays. He scores 20 points in the first game, 25 in the second, 30 in the third, and so on. How many points will he score in his 27th game? How many points total did he score? Write your sentences here: 19. Samantha decides that she is going to save $500 of her paycheck each month. As hard as she tries, each month she only saves 80% of the previous month. What does she save on the 11th month? How much did she save total in those 11 months? How much would she save if she continued the pattern forever? Write your sentence here: Unit 3

Write the equation of a line parallel to each of the following. Show ALL work for full credit.

20. 7𝑥 + 3𝑦 = 33 21.

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22. Parallel to 𝑦 = 3𝑥 + 1 through (−7, 4)

Write the equation of a line perpendicular to each of the following. Show ALL work for full credit.

23. 𝑦 = −2𝑥 + 13 24.

Find the missing angles given that a ∥ b, m∠1= 𝟗𝟒°, and m∠2= 𝟓𝟑°.

25. m∠3= _______ 26. m∠4= _______ 27. m∠5= _______

28. m∠6= _______ 29. m∠7= _______ 30. m∠8= _______

31. m∠9= _______ 32. m∠10= _______

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Use what you know about two parallel lines and a transversal to solve for x. Show ALL work for full

credit.

33. 34.

Use what you know about parallelograms to find the missing information.

35. 𝐶𝐷 = _______ 36. 𝐴𝐷 = _______ 37. 𝐴𝐶 = _______

38. 𝐷𝐵 = _______ 39. 𝐷𝐸 = _______ 40. 𝐶𝐸 = _______

41. m∠𝐴 = _______ 42. m∠𝐷 = _______ 43. m∠𝐵 = _______

44. m∠𝐵𝐷𝐶 = _______ 45. m∠𝐷𝐸𝐶 = _______ 46. m∠𝐷𝐸𝐴 = _____

(11𝑥 − 80)° (5𝑥 + 46)°

(−8𝑥 + 67)°

(15𝑥 + 85)°

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Unit 4

Evaluate each of the following.

47. 𝑓(𝑥) = −14𝑥2 + 𝑥 − 6 for 𝑓(−8) 48. 𝑓(𝑛) =3𝑛−10

𝑛+6 for 𝑓(4)

Factor the following.

49. 3𝑦2 + 21𝑦 + 24 50. 4𝑥2 − 49

Factor to solve the following. Show all work for full credit.

51. 4𝑥2 + 14𝑥 = −10 52. 8𝑥2 + 56𝑥 = 0

Use the quadratic formula to solve for x. Write the exact solution and the approximate solution.

Round answers to the nearest thousandth (3 decimal places). Don’t forget to check your answer!

Show all work for full credit.

53. 7𝑥2 = 22 + 7𝑥 54. 3𝑥2 − 42 = 11𝑥

55. Draw a picture of a quadratic that has 2 imaginary, complex roots

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Complete the square on the following equations to put them into vertex form. Show all work for full

credit.

56. 𝑦 = 𝑥2 − 8𝑥 + 21 57. 𝑦 = 4𝑥2 − 16𝑥 + 11

58. Write the transformations for 𝒚 = −𝟏

𝟑(𝒙 − 𝟐)𝟐 + 𝟓

Unit 5

Find all real and complex roots of the polynomial function.

59. 𝑓(𝑥) = 𝑥4 + 𝑥3 − 33𝑥2 + 9𝑥 − 378 60. 𝑓(𝑥) = 2𝑥3 + 6𝑥2 + 5𝑥 + 15

Write the equation of the polynomial function that satisfies the following conditions. Write your

equation in standard form.

61. 62. Quadratic with a root of 2 − 5𝑖

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63. Degree: 3, Roots: -3 with multiplicity of 2 and 8 with a multiplicity of 1

Find the x- and y-intercepts. 3 decimals! Find the local max and min. 3 decimals!

64. 𝑓(𝑥) = −𝑥4 + 2𝑥2 − 𝑥 + 4 65. 𝑓(𝑥) = 𝑥3 − 7𝑥2 + 11𝑥 + 1

Find the domain and range. 3 decimals!

66. 𝑓(𝑥) = −𝑥3 − 2𝑥2 + 4𝑥 + 5 67. 𝑓(𝑥) = −𝑥4 + 2𝑥2 + 2𝑥 + 4

Find the maximum and minimum, then find the increasing and decreasing intervals. Draw a picture to

show your work.

68. 𝑓(𝑥) = 𝑥4 − 4𝑥3 + 3𝑥2 + 2𝑥 − 2

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At a carnival there was a potato launching contest. On one launch, the height of the potato (in feet)

above the ground after t seconds is modeled by the equation 𝒉(𝒕) = −𝟏𝟔𝒕𝟐 + 𝟒𝟖𝒕 + 𝟕. Round all

decimal answers to the nearest tenth (one decimal place).

69. At what height was the potato launched? Write your answer in a sentence.

70. What is the maximum height the potato reached? Write your answer in a sentence.

71. How long did it take the potato to reach that maximum height? Write your answer in a sentence.

72. At what time did the potato hit the ground? Write your answer in a sentence.

73. How high was the potato at 3 seconds? Write your answer in a sentence.

74. When was the potato 28 feet off the ground? Write your answer in a sentence.

Unit 6

Simplify. Show all of your work.

75. 𝑥2−9

𝑥2−7𝑥+12 76.

𝑥

3𝑥+9+

5

𝑥+3

77. 𝑥+4

6𝑥−2÷

𝑥2+2𝑥−8

3𝑥−1 78.

𝑥2+6𝑥+7

𝑥2+2𝑥−15∙

2𝑥−10

𝑥2+6𝑥+7

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Solve the following equations. Show all of your work.

79. 6

7=

2

7𝑥−

4

𝑥 80.

𝑥+5

𝑥2+6𝑥−

1

𝑥+6=

3

𝑥

81. Write the standard or general form of each equation under the graph that would be an example

of that equation.

02 cbxax 023 dcxbxax CByAx

cx cy )(

)()(

xq

xpxf , 0)( xq

Unit 7

Find the inverse of each function.

82. 𝑦 = (𝑥 − 3)2 + 1 83. 𝑦 =1

2𝑥 − 5 84. { (-3, 7), (0, 19), (6, -12) }

12

Solve for x.

85. 162𝑥+1 = (1

8)

−𝑥+3 86. 35𝑥−1 = 276 87. (

1

625)

𝑥+4= 252−𝑥

Unit 8

Solve for x. Show ALL WORK for full credit. All decimals should be rounded to the nearest hundredth

(two decimal places).

88. log6(3𝑥 − 4) = 2 89. log4(𝑥 + 6) − log4 𝑥 = log4 57

90. 7𝑥 = 19 91. log5 48 = 𝑥

92. 5𝑥+11 = 19.4 93. 6 + 2𝑒7𝑥 = 32

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Complete each of the following word problems. Show ALL WORK for full credit. Round decimal

answers to the nearest hundredth (two decimal places) and be sure to include units for full credit!

94. James purchased a truck for $24,300. The value of the truck decreases by 11% per year. What will

be the approximate value 15 years after the purchase? 𝑦 = 𝑃(1 ± 𝑟)𝑡

95. The half-life of a radioactive isotope is 9 years. Initially, there are 140 grams of the isotope. How

long will it take for there to be 15 grams of the isotope? 𝑦 = 𝑃 (1

2)

𝑡ℎ⁄

96. Isabella invested $900 at 4.5% annual interest, compounded quarterly. The value, A, of an investment can be

calculated using the equation 𝑦 = 𝑃 (1 +𝑟

𝑛)

𝑛𝑡. Exactly how long will it take for her investment to be worth four

times as much (quadruple) in value?

Find the inverse of each function. Show ALL WORK for full credit.

97. 𝑦 = 3(𝑥 + 1)3 − 5 98.

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Graph each function. Show the transformation of the characteristic points by filling out the table.

Then find the domain and range, increasing and decreasing intervals, and intercepts.

99. 𝑓(𝑥) = −𝑙𝑜𝑔4(𝑥 + 2) − 1 100. 𝑓(𝑥) = 2(3)𝑥−4 + 1

Domain: ____________ Domain: ___________

Range: ____________ Range: ___________

Increasing Int: ____________ Increasing Int: ____________

Decreasing Int: ____________ Decreasing Int: ____________

x-int: ____________ x-int: ____________

y-int: ____________ y-int: ____________

Unit 9

Find the missing side length. Show all work for full credit.

101. 102.

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Find the center and radius of each circle. Show all applicable work for full credit.

103. (𝑥 − 8)2 + (𝑦 + 6)2 = 19 104. 𝑥2 + 𝑦2 + 22𝑥 − 8𝑦 + 100 = 0

Center:

Radius:

Center: Radius:

Draw a picture for each of the following in relationship to a circle (each drawing should include a

circle).

105. tangent line 106. chord 107. secant line

108. inscribed angle 109. intercepted arc 110. central angle

Find the unknown value. Assume that lines that appear to be diameters are actually diameters. Show

all applicable work for full credit.

111. 112.

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113. Find each angle.

a) m1 = __________

b) m2 = __________

c) m3 = __________

d) m4 = __________

e) m5 = __________

f) m6 = __________

g) m7 = __________

h) m8 = __________

Unit 10

Name the quadrant that the following angles are in. Then convert radians to degrees and degrees to

radians.

114. 3𝜋

7 115. −118° 116. 520° 117. −

𝜋

13

42

128

100 70

1

F

E D

C

B

A

O

2

3 4

5 6

7

8

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Match each of the following angles with their graphs.

118. 160° ______

119. 𝜋

5 ______

120. 230° ______

121. 13𝜋

7 ______

Find the six trig ratios for the angle of interest.

122.

sin θ = csc 𝜃 =

cos 𝜃 = sec 𝜃 =

tan θ = cot 𝜃 =

123. Complete the chart.

Degrees Radians (𝑥, 𝑦) Quadrant sin 𝜃 cos 𝜃 tan 𝜃

𝜋

6

120°

7𝜋

4

210°

Graph each of the following.

124. 𝑦 = −2 sin(3𝜃)

Amplitude: Period: Domain: Range:

𝜃

4

1

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125. 𝑦 = 3 cos(𝜃) + 2

Amplitude: Period: Domain: Range: