CP Algebra 1 Final Exam Review 2015-16 Equation...

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CP Alg 1 Final Exam Review

CP Algebra 1 Final Exam Review 2015-16

Equation Review 1. Solve the equations.

a. 3𝑥 + 6 = 12 b. 2(𝑥 − 4) = 20

c. −4(𝑥 − 5) + 2𝑥 = 40 d. 3𝑥 + 4 − 5(𝑥 − 2) = 10

2. Find the slope of the line from the graph.

x

y



Review Questions for Unit 5 3. A local ice cream shop keeps track of how much ice cream they sell versus the temperature

on that day. The following table shows the

temperature and ice cream sales for 12 days.

Make scatterplot of the data and then draw a

trend line that you feel best fits the data

points. Label and scale the axes appropriately.

a. What is the independent variable in the problem? _____________________________

b. What is the dependent variable in the problem? _____________________________

c. Find an equation in slope intercept form for the trend line using the points (12, 180) and

(16, 300).

d. Find the equation of the regression line using your graphing calculator. Round the

parameters to the nearest tenth.

Temperature

(° C)

Ice Cream Sales

($)

14.2 215

16.4 325

11.9 185

15.2 332

18.5 406

22.1 522

19.4 412

25.1 614

23.4 544

18.1 421

22.6 445

17.2 408



e. What is the slope of the trend line? What does the slope represent in the context of the

problem?

f. What is the y-intercept of the trend line? What does the y-intercept represent in the

context of the problem?

g. Describe the strength and direction of the correlation in the scatterplot.

h. Use the equation of your regression line to predict the total ice cream sales when the

temperature is 21.3 °C.

i. Use the equation of your regression line to determine the temperature if the sales were

$450.

4. The following data represent the number of text messages sent in one day by a group of

students:

[3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56 ]

a. To the nearest tenth what is the mean number of text messages sent by the students?

b. What is the mode number of text messages sent by the students?

c. What is the median number of text messages sent by the students?

d. What is the range in the number of text messages sent by the students?

e. What is the interquartile range (IQR) for the number of text messages sent by the

students?

f. Which number text messages appears to be an outlier?

g. If the outlier is eliminated which statistic will change more, the mean or median?

Explain.



5. What is the median? _______ What is the smallest number? _____ What is the Range? _______ What is Q3? ____

What is the inter-quartile range? ____

6. The following table shows the speeds of different ocean animals. Find the five-number

summary, range, and mean. Then draw a box-and-whisker plot above the axis below.

Box-and-whisker plot:

Marine Animals Speed (mph)

Albacore, leaping 40

Killer Whale 35

Shortfin Mako 31

Blue Whale 30

Barracuda 27

Fin Whale 25

California Sea Lion 25

Common Dolphin 24

Leatherback Turtle 22

Mahi Mahi 20

Gentoo Penguin 17

Bottlenose Dolphin 17

Mackerel 12

Pacific Salmon 8

Sea Trout 5

min Q1 med Q3 max range mean

Speed(mph)

9 15 17

12

21 25

CP Algebra 1 Page 5 of 19

Final Exam Review Packet 2015-2016

Final Examination Review Questions Unit 7 CP Algebra 1

7. The following table shows the cost of airfare based on distance in miles.

Destination Distance (Miles) Airfare

Atlanta 576 $164

Boston 370 $124

Chicago 612 $143

Dallas 1,216 $216

Detroit 409 $161

Denver 1,502 $216

Miami 946 $180

New York 189 $108

St. Louis 737 $180

a. Using the points (946, 180) and (576, 164), find the equation of the trend line.

b. Use your graphing calculator to find the equation of the regression line. Round to the

nearest tenth.

c. Using the equation from the calculator, find the cost of a trip that is 800 miles.

d. Using the equation from the calculator, find the distance of a trip that cost $200.




Review Questions for Unit 6 Solve by using graphing.

8.

4

39

2

y x

y x

____________ 9.

3

4 2

y x

y x

____________

Solve using substitution.

10. 3 6

2

x y

y x

____________ 11.

3 3

2 9 11

x y

x y

____________

Solve using Elimination

12. 5 8

3 2

x y

x y

____________ 13.

2 5 13

4 3 13

x y

x y

____________




Solve using whichever method seems best to you. Identify your method of choice. (If you choose to use graphing, help yourself to grid paper and attach it your review packet.)

14. 2 4

5

y x

y x

____________ 15.

3 5 16

3 2 2

x y

x y

____________

16. 9 3 5

1

x y

y x

____________ 17.

3 2 0

4 4 5

x y

x y

____________

18. 8

10

x y

x y

____________ 19.

3 5

10 2

x y

y x

____________

20. Find two numbers whose sum is 52 and whose difference is 8.




21. Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket? 22. The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry? 23. You want to join a gym. There is a $100 start-up fee for Planet Fitness, and then it is $10 a month. At the Fitness Edge, you need to put $50 down, and then pay $15 a month. If you just want to work out for this summer (3 months) which gym should you join? After how many months will the gym costs be equal?




Review Questions for Unit 7 24. 15 6 7( )( )x y x y 25. 5 2(9 )g 26. 3 2 2 5(5 )( 6 )( )c t ct c t

27. 15

2

42

6

x

x 28.

12 7

5 4

12

24

a b

a b 29.

15 13 2

4 2

x y z

xy z

30. 2

11 1510x y z 31. 7 11 3 4( )( )a a b c 32.

0

4 3

40

2

xyz

a b xdewf

33. 12 15x y 34. 14 10 8 12x y x y 35. 4 5 7

2 4 9

21

7

a b c

a b c

36. 7 8 3(4 )y y 37. 7

2 6 10

60

10

xyz

x y z




38. Identify if the table is linear, exponential function, or neither.

Explain your reasoning. If it is linear or exponential write the equation.

a.

x y 0 20 3 13 6 6 9 –1

b.

x y 0 0 2 2 4 6 6 12

c.

x y 0 40 1 20 2 10 3 5


CP Algebra 1 – Final Exam Review 2015-16

Each table of values represents an exponential function of the form 𝑓(𝑥) = 𝑎𝑏𝑥 . Find the values of the parameters a and b and explain your reasoning. 39.

x y 0 100 1 50 2 25 3 12.50 4 6.25

a = _______________ b = _______________ Explanation: 40.

x y 0 2 1 10 2 50 3 250 4 1250

a = _______________ b = _______________ Explanation: 41. Sketch the graph the following exponential functions:

a. 3(4)xy b. 1

64

x

y



Use for #’s 41 – 43: The mice population after t years can be modeled with the function

𝑓(𝑡) = 100(4)𝑡. 41. What is the growth factor?

42. What is the initial value of the population of mice?

43. How many mice will there be after 7 years?

44. In the year 1990, the population of Dreamville started with 6,500 residents. The population

is increasing by 11% each year. The growth factor is 1.11.

a. Write an equation that models the growth of Dreamville’s population.

b. Fill in the table. Round the population to the nearest whole number.

Year Years since 1990 Population 1990 0 6,500 1991 1992 1993

c. Is this growth linear or exponential? Explain.

45. A business discovered that their kitchen has been infested with fruit flies! The owner keeps a record of the number of flies and finds they are growing exponentially, doubling every week. Here are the data he has collected.

Number of weeks since flies were

discovered

Number of fruit flies in the

kitchen 0 10 1 20 2 40 3 80

How many flies will there be in 6 weeks? In 7.5 weeks?



46. Identifying Graphs

In the graph above, each curve represents a function of the form 𝑦 = 𝑎 ∙ 𝑏𝑥. The parameter a takes on one of these values: 2 or 4. The parameter b takes on one of these values: 0.5, 0.8, 1.25, or 2. For each graph, identify the values of a and b:

Graph #1 a = ________ b = ________ Graph #2 a = ________ b = ________ Graph #3 a = ________ b = ________ Graph #4 a = ________ b = ________



Review Questions for Unit 8 For these questions you may use the quadratic formula.

Quadratic Formula

Solutions to the equation 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0 are given by the formula: 𝑥 = −𝑏±√𝑏2−4𝑎𝑐

2𝑎.

Add or Subtract:

47. ( )13107()121219 22 xxxx 48. ( )181519()764 22 xxxx

49. )51719()131520( 22 xxxx 50. )141510()49( 4556 xxxx

51. ( )13107()129 22 xxx 52. )6209()695( 2636 xxxxxx

53. (17x2 + 7x - 14) - (-6x2 - 5x - 18) 54. (-18x2 + 4x - 16) - (15x2 + 4x - 13) Multiply:

55. )4(2 2xx 56. )2(17 52 xx 57. )4(3 23 xx

58. )2(12 2 xx 59. )2(4 x 60. )12(3 2 x



61. )72(6 2 xx 62. )1(4 xx 63. )5(2 xx

64. 3x²(4x³ – 5x + 10) 65. 35 aa 66. 13 nn

67. 36 bb 68. 118 yy 69. 16 xx

70. 123 xx 71. 5213 aa 72. 4615 xx

73. 532 xx 74. yy 512 75. 232 a

76. 24x 77. 243 x 78. 132 xx

79. 1233 xx 80. xx 423 81. yxyx 52

81. nmnm 23



Factor:

82. 34 17a 83. 28 4a a 84. 211 44x x y

85. 216 8y y 86. 214 18xz xz 87. 2 2 325 30a b ab

88. 2 236 12p q pq 89. 3 23 9 36x y xy xy 90. 12 20 32ax bx cx

91. 2 5 6x x 92. 2 12 35x x 93. 2 8 15x x

94. 2 24 144x x 95. 2 16 55x x 96. 2 5 24x x

97. 2 7 30x x 98. 2 12 36x x 99. 2 16 36x x

100. 2 6 16x x Solve: 101. ( 8)( 8) 0x x 102. ( 6)( 10) 0x x 103. ( 5)( 11) 0x x

104. (3 4)( 5) 0x x 105. ( 12)( 7) 0x x 106. (2 5)(3 7) 0x x



Solve by factoring:

107. 2 3 40 0x x 108. 2 13 42 0x x 109. 2 22 105 0x x

110. 2 7 10 0x x 111. 2 6 16 0x x Solve by using the quadratic formula:

2 4

2x

b b ac

a

112. 2 3 2 0x x 113. 24 8 1 0x x 114. 2 11 18 0x x

115. 2 2 14 0x x 116. 2 10 25 0x x 117. 2 3 7 0x x Solve each equation any way you want. Show your work.

118. 2 3 2 0x x 119. 2 5 4 0x x



Miscellaneous Review

120. 121. Rajeev has $175 that he earned from his summer job. He puts the money in an account that yields 4% interest compounded annually. Assume that Rajeev does not make any other deposits or withdrawals from his account. After how many years from the time he deposited the money will Rajeev have at least $200 in his account?



Multiple-Choice --- Select the answer that best answers the question. 122. Ricardo has two types of assignments for his class. The number of mini assignments, m, he has is 1 fewer than twice the number of long assignments, L, he has. If he has 46 assignments in total, which of the following systems of equations can be used to correctly solve for m and L?

a. 2 1

46

m L

m L

b.

2 1

46

m L

m L

c. 2 1

46

L m

m L

d.

2 1

46

L m

m L

123. What is the sum of 3 ( 4)b b and 6( 8)b ?

a. 3 (1 2 16)b b b. 3 ( 2 16)b b

c. 23( 2 16)b b d. 23( 2 16 )b b

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