Math Models Final Exam Review
Final Exam Review, Page 1 of 16
Name
Date
Period ________
Math Models Final Exam Review A box contains 4 opals, 5 garnets, and 6 pearls. A jewel is selected at random from the box. Find each probability. 1. P(the jewel is a garnet)
2. P(the jewel is either a pearl or a garnet)
3. P(the jewel is a emerald)
4. The scores on the Unit 1 Exam are listed below. What is the probability that a student picked at random scored 75% or above? 61
74
60
70
83 90
90
80
100
102
28
75
98
21
49
5. A manager of a sporting goods store was analyzing a frequency table identifying the number of shoes sold during the last 6 months. Which measure of data describes the most popular shoe sold?
6. Frank rolled a die 7 times and recorded his results in the tally chart below. What is the experimental probability of rolling a 2? 1 2 3 4 5 6
| | | ||| |
7. Using the tally chart in problem #6, what is the experimental probability of rolling a 5?
8.
The vertex of f ( x) x 2 is A. (0, 2) B. (2, 0)
9. Define the median of a list of data:
C. (-2, 0)
D. (0, -2)
Final Exam Review, Page 2 of 16
10. For the information in the table below, circle the correlation between the elbow-hand length in cm and the height in cm of high-school students. Elbow-hand length 25 28 30 35
Height 97 111 120 139 negative
positive
no correlation
Use this work bank for problems #11 – 14 Word Bank Negative
Opposite Reciprocal
Same
Positive
Zero
No Slope
One
Horizontal
Vertical
11. Lines that are parallel have slopes that are the ___________________. 12. Lines that are perpendicular have slopes that are _________________. 13. Horizontal lines have a slope of ___________________. 14. Vertical lines have a slope of __________________.
15. Which pair of variables is most likely modeled by the following scatterplot? A The amount of calories burned and the person’s height
80 60
B The amount of calories burned and the amount of time resting after a run.
40 20 0 0
2
4
6
C The amount of calories burned and the amount of time spent exercising D The amount of calories burned and the amount of time spent sleeping
Final Exam Review, Page 3 of 16
16. Write the correlation for each graph? Word Bank: No Correlation, Positive, Negative, Quadratic Correlation 7 6 5 4 3 2 1 0
12 10 8 6 4 2 0
0
2
4
6
80
0
2
4
6
8
10
0
2
4
6
8
10
12 10
60
8
40
6 4
20
2
0
0 0
2
4
6
2x² + 3x = 15 – 4x
17. What are the solutions to
18. Mrs. Williamson asked each of her students what color car they drove. The results are recorded in the table below. What is the central angle of the sector that represents the black cars? Record your answer in the chart below and fill in the bubbles. Color Number
White
Red
Silver
Blue
Black
Other
19
28
7
9
18
9
. 0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
Final Exam Review, Page 4 of 16
19. Events C and B are dependent events. The probability of event C is 0.5 and the probability of event B, given that event C has occurred, is 0. 25. What is the probability of C and B? Record your answer and fill in the bubbles on the grid below. . 0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
(This problem was copied from the 2003 TAKS test.) 20. The graph shows the price of a share of Compuco stock at the close of each day during a 1week period.
Price Per Share
25 20 15 10 5 0 8/24
8/25
8/26
8/27
8/28
8/29
8/30
Date
Based on the data in the graph, which conclusion is most accurate? F The closing price remained constant throughout the week G The closing price increased at the beginning of the week and then leveled off at the end of the week. H J
The closing price decreased at the beginning of the week and the increased at the end of the week. The closing price each day was lower than the closing price on the previous day.
21. Ashley rolls a die, flips a quarter, and then rolls the die again. What is the probability that he will roll two odd numbers and that the coin will land on heads?
Final Exam Review, Page 5 of 16
22. The distance on a map from Dallas to New Jersey measured with a centimeter ruler is 5, and the map scale is 1centimeter = 450 kilometers. What is the actual distance in kilometers? Record you answer on the grid below. (Hint use a proportion.) . 0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
Given the following equation, plug into the quadratic formula and solve. 23. x 2 4 x 3 0
x = __________________
24. The following solution for this inequality is incorrect. Put a star by the step that is incorrect and then work the problem correctly. 2 x 3 5x 6 3x 9 x 3
25. Leslie earns $400 per week if she works exactly 40 hours. She earns $15 for each additional hour beyond 40 hours. Write the inequality that describes h, the number of additional hours she must work in order to earn at least $500 in 1 week? DO NOT SOLVE!
Final Exam Review, Page 6 of 16
26. Normal tire pressure in an automobile tire is 30 psi (pounds per square inch). It is safe for the normal pressure to vary by 5 psi in either direction. Which number line shows the range of safe tire pressure?
A. 25
30
35
B. 25
30
35
25
30
35
25
30
35
C.
D.
Matching Problems #27-29 Match the following descriptions to their graphs. _______ 27. You pull the plug out of the bathtub. The amount of water remaining in the tub and the number of seconds since you pulled the plug. _______ 28. As you play with a yo-yo, the number of seconds that have passed and the yo-yo’s distance from the floor are related. _______ 29. Your height depends on your age.
A
B
C
D
Final Exam Review, Page 7 of 16
30. Dorcus Carter’s family owns a pecan orchard. Each pecan tree produces from 20 to 30 pounds of pecans each year. There are 220 pecan trees. What is the highest and lowest number of pounds that could be produced per year?
31. Richard has 2 grasshoppers of the same species. The corresponding parts of the grasshoppers bodies are proportional. The larger grasshopper has an 8-centimeter body and a 1.5 –centimeter forelimb. The smaller grasshopper has a 1.2 – centimeter forelimb. How long is the body of the smaller grasshopper?
32. In order for a student to be considered for a certain college grant, the combined income of the student’s parents must be less than $25,000. If F is the father’s income and M is the mother’s income, which sentence represents the conditions of the grant? A. B. C. D. E.
F + M > $25,000 2F < $25,000 2F + M > $25,000 F + M < $25,000 F x M < $25,000
33. What is the equation that describes the data in the table? X
-4
-1
1
4
7
Y
-1
2
4
7
10
Final Exam Review, Page 8 of 16
34. Which of the following situations would produce the graph shown?
S p e e d Time A. Amber began walking, rested for a while, and then began to run. B. Amber started sprinting, stopped to rest and then started sprinting again. C. Amber was running, started to sprint, then slowed down to rest. After a while she started to walk. D. Amber started at a slow jog, then gradually increased to a sprint.
Use the equations below to answer questions #35 and #36 7 x+1 2
I
y=-
II
y = 7x + 3
III
y=
IV
y=-
2 x+2 7
V
y=-
1 x 7
7 x 2
35. Which equations represent lines that are parallel? A. I and II
B. I and III
C. I and IV
D. III and IV
E. Not Here
J. II and V
K. Not Here
36. Which equations represent lines that are perpendicular? F. I and III
G. I and V
H. II and III
Final Exam Review, Page 9 of 16
37. Write the equation of the function that includes all the ordered pairs in the table? x y
-2 5
0 3
2 1
4 -1
6 -3
38. Joseph was riding his scooter to school, when he ran out of gas. He stopped to check the scooter, then he walked the rest of the way. Which of the following graphs best models this situation?
F.
H. D i s t a n c e
D i s t a n c e
Time
Time
G.
J.
Not Here
D i s t a n c e
Time 39. Jim has a $30 gift certificate for a movie theater. Each time that he sees a movie, m, $5 is deducted from his gift-certificate balance, b. Write an equation that describes b in terms of m?
Final Exam Review, Page 10 of 16
40. Employees receive a bonus of $75 plus $16 per hour, h, for working on New Year’s Eve. If an employee earned no more than $203, write and inequality that represents this situation? DO NOT SOLVE.
41. If 8 pens and 7 pencils cost $3.37 while 5 pens and 11 pencils cost $3.10, how much does each pen and pencil cost?
42. A rectangle has a perimeter of 18 cm. Its length is 5 cm more than its width. Find the dimensions.
43. Jimmy had $5.25 in nickels and quarters. If he had 15 more nickels than quarters, how many coins of each type did he have?
Final Exam Review, Page 11 of 16
44. Tickets for a school football game cost $1.00 each if purchased before the day of the game. They cost $1.50 each if bought at the gate. For a particular game, 600 tickets were sold, with receipts of $700. Write a system of equations that could be used to determine the number of pre-game tickets, P, and tickets sold at the gate, G? DO NOT SOLVE – JUST WRITE THE SYSTEM
45. Timmy has 180 marbles, some plain (P) and some colored (C). If there are 32 more plain marbles than colored marbles, write a system of equations that could be used to determine the number of colored marbles. DO NOT SOLVE – JUST WRITE THE EQUATIONS
46. The sum of two numbers is 32. One number is 4 more than the other. WRITE a system of equations that could be used to find the numbers.
47. Solve.
x–y=6 2x + y = 0
48. Solve.
3 1 x4 7 x 4 2
Final Exam Review, Page 12 of 16
49. Write the system of linear inequalities for the given graph?
50. The owner of a plant nursery knows that the color red will occur in a certain plant once out of every 15 seedlings. If the nursery wants to have about 200 red plants of this variety to sell, what equation could be used to determine the total number of seeds that should be planted?
A.
15 x 14 200
B.
14 200 15 x
C.
1 x 15 200
D.
1 200 15 x
51. Write the equation of each line with slope 0, and passes through (-5,4)
Final Exam Review, Page 13 of 16
52. Write the equation of each line that passes through (-1, -2) and (0,3)
The table below shows the life expectancy of people born in the US between 1920 and 1970. Year 1920 1930 1940 1950 1960 1970
Life Expectancy (years) 54.1 59.7 62.9 68.2 69.7 70.8
53. What is the independent variable?
54. What is the dependent variable?
55. Write the equation for the line of best fit.
56. What is the slope of the line?
57. What is the y-intercept?
58. What will be the life expectancy of a person born in the year 2010?
59.
What is the solution to the system:
3x + 2y = 4 -x + 3y = -5
r=
Final Exam Review, Page 14 of 16
60. Which graph represents the solution to –7 < 3x + 2 < 14 A. B.
-4 -3 -2 -1 0 1 2
3 4 5
-4 -3 -2 -1 0 1 2
3 4 5
-4 -3 -2 -1 0 1 2
3 4 5
-4 -3 -2 -1 0 1 2
3 4 5
C. D.
61. Find the equation of the line that passes through (-1, -2) and (0,3)
MATCH THE GRAPH TO THE EQUATION. A.
B.
C.
D.
______62. y = -x²
______63. y = x² ______64. y = x² - 2 ______65. y = -4x² ______66. y = -x² + 3 ______67. y = (x – 2)² - 3
E.
F.
______68. y = (x + 2)² - 1 ______69. y =
1 x² 4
G.
H.
I.
J.
______70. y = (x + 1)² + 1 ______71. y = -(x – 1)² + 2
Final Exam Review, Page 15 of 16
72. Two lines have the following equations: 4x + 3y = 7 x + 2y = -2 At what point do they intersect?
73. Beth bought 15 tickets to a movie, where adult tickets cost $6.00 and senior citzen tickets cost $4.00. She spent a total of $76. Write a system of equations that will determine the number of adult tickets, a, and the number of senior citzen tickets, s, Beth purchased? DO NOT SOLVE.
74. Solve
5x – ( x – 8 ) = 9 + 3( 2x – 3 )
75. Find the vertex of the given equation to the nearest tenth. y = 3x² + 4x – 1 vertex 76. At which points does the graph of f(x) = 2x² + 6x + 4 intersect the x-axis ? (hint: roots)
77. Which ordered pair represents one of the roots of the function? f(x) = 2x2 + 3x - 20 A. ( -4,0 ) B. ( -5,0 ) C. ( -20,0 ) 5 D. ( ,0 ) 2
Final Exam Review, Page 16 of 16
Write the name and the equation of each parent function. You may use your pink/blue sheet on the review, but you will not be able to use the blue/pink sheet on the final exam. You will have to recognize the parent functions on your own.
78.
79.
5 4 3 2 1
-5 -4 -3 -2 -1
1 2 -1 -2 -3 -4
80.
5 4 3 2
5 4 3 2 1
1 3
4 5
-5 -4 -3 -2 -1
-5
1 2 -1 -2 -3 -4 -5
3
-5 -4 -3 -2 -1
4 5
Function:
Function:
Equation:
Equation:
Equation:
5 4 3 2
82.
1 2 -1 -2 -3 -4 -5
5 4 3 2
83.
1
1 -5 -4 -3 -2 -1
3
4 5
-5 -4 -3 -2 -1
1 2 -1 -2 -3 -4 -5
3
4 5
-5
Function:
81.
1 2 -1 -2 -3 -4
5 4 3 2 1
3
4 5
-5 -4 -3 -2 -1
Function:
Function:
Equation:
Equation:
1 2 -1 -2 -3 -4 -5
3
4 5
Your final exam is 70 questions. Each question on the exam is on this review sheet. You need to complete this review sheet and bring it the day of the exam for 5 points bonus on the final exam. You must show work on every single problem. I will not give you the 5 points if you do not have enough work shown. If you do not know how to show work on a problem then write a sentence telling me how you figured out the answer without showing any work. You will be allowed to use your calculator and the TAKS formula sheet on the final exam. You will not be able to use any other study aids (i.e. pink/blue sheet).
Name
Date
Period ________
Math Models Final Exam Review A box contains 4 opals, 5 garnets, and 6 pearls. A jewel is selected at random from the box. Find each probability. 1. P(the jewel is a garnet)
2. P(the jewel is either a pearl or a garnet)
3. P(the jewel is a emerald)
4. The scores on the Unit 1 Exam are listed below. What is the probability that a student picked at random scored 75% or above? 61
74
60
70
83 90
90
80
100
102
28
75
98
21
49
5. A manager of a sporting goods store was analyzing a frequency table identifying the number of shoes sold during the last 6 months. Which measure of data describes the most popular shoe sold?
6. Frank rolled a die 7 times and recorded his results in the tally chart below. What is the experimental probability of rolling a 2? 1 2 3 4 5 6
| | | ||| |
7. Using the tally chart in problem #6, what is the experimental probability of rolling a 5?
8.
The vertex of f ( x) x 2 is A. (0, 2) B. (2, 0)
9. Define the median of a list of data:
C. (-2, 0)
D. (0, -2)
Final Exam Review, Page 2 of 16
10. For the information in the table below, circle the correlation between the elbow-hand length in cm and the height in cm of high-school students. Elbow-hand length 25 28 30 35
Height 97 111 120 139 negative
positive
no correlation
Use this work bank for problems #11 – 14 Word Bank Negative
Opposite Reciprocal
Same
Positive
Zero
No Slope
One
Horizontal
Vertical
11. Lines that are parallel have slopes that are the ___________________. 12. Lines that are perpendicular have slopes that are _________________. 13. Horizontal lines have a slope of ___________________. 14. Vertical lines have a slope of __________________.
15. Which pair of variables is most likely modeled by the following scatterplot? A The amount of calories burned and the person’s height
80 60
B The amount of calories burned and the amount of time resting after a run.
40 20 0 0
2
4
6
C The amount of calories burned and the amount of time spent exercising D The amount of calories burned and the amount of time spent sleeping
Final Exam Review, Page 3 of 16
16. Write the correlation for each graph? Word Bank: No Correlation, Positive, Negative, Quadratic Correlation 7 6 5 4 3 2 1 0
12 10 8 6 4 2 0
0
2
4
6
80
0
2
4
6
8
10
0
2
4
6
8
10
12 10
60
8
40
6 4
20
2
0
0 0
2
4
6
2x² + 3x = 15 – 4x
17. What are the solutions to
18. Mrs. Williamson asked each of her students what color car they drove. The results are recorded in the table below. What is the central angle of the sector that represents the black cars? Record your answer in the chart below and fill in the bubbles. Color Number
White
Red
Silver
Blue
Black
Other
19
28
7
9
18
9
. 0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
Final Exam Review, Page 4 of 16
19. Events C and B are dependent events. The probability of event C is 0.5 and the probability of event B, given that event C has occurred, is 0. 25. What is the probability of C and B? Record your answer and fill in the bubbles on the grid below. . 0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
(This problem was copied from the 2003 TAKS test.) 20. The graph shows the price of a share of Compuco stock at the close of each day during a 1week period.
Price Per Share
25 20 15 10 5 0 8/24
8/25
8/26
8/27
8/28
8/29
8/30
Date
Based on the data in the graph, which conclusion is most accurate? F The closing price remained constant throughout the week G The closing price increased at the beginning of the week and then leveled off at the end of the week. H J
The closing price decreased at the beginning of the week and the increased at the end of the week. The closing price each day was lower than the closing price on the previous day.
21. Ashley rolls a die, flips a quarter, and then rolls the die again. What is the probability that he will roll two odd numbers and that the coin will land on heads?
Final Exam Review, Page 5 of 16
22. The distance on a map from Dallas to New Jersey measured with a centimeter ruler is 5, and the map scale is 1centimeter = 450 kilometers. What is the actual distance in kilometers? Record you answer on the grid below. (Hint use a proportion.) . 0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
Given the following equation, plug into the quadratic formula and solve. 23. x 2 4 x 3 0
x = __________________
24. The following solution for this inequality is incorrect. Put a star by the step that is incorrect and then work the problem correctly. 2 x 3 5x 6 3x 9 x 3
25. Leslie earns $400 per week if she works exactly 40 hours. She earns $15 for each additional hour beyond 40 hours. Write the inequality that describes h, the number of additional hours she must work in order to earn at least $500 in 1 week? DO NOT SOLVE!
Final Exam Review, Page 6 of 16
26. Normal tire pressure in an automobile tire is 30 psi (pounds per square inch). It is safe for the normal pressure to vary by 5 psi in either direction. Which number line shows the range of safe tire pressure?
A. 25
30
35
B. 25
30
35
25
30
35
25
30
35
C.
D.
Matching Problems #27-29 Match the following descriptions to their graphs. _______ 27. You pull the plug out of the bathtub. The amount of water remaining in the tub and the number of seconds since you pulled the plug. _______ 28. As you play with a yo-yo, the number of seconds that have passed and the yo-yo’s distance from the floor are related. _______ 29. Your height depends on your age.
A
B
C
D
Final Exam Review, Page 7 of 16
30. Dorcus Carter’s family owns a pecan orchard. Each pecan tree produces from 20 to 30 pounds of pecans each year. There are 220 pecan trees. What is the highest and lowest number of pounds that could be produced per year?
31. Richard has 2 grasshoppers of the same species. The corresponding parts of the grasshoppers bodies are proportional. The larger grasshopper has an 8-centimeter body and a 1.5 –centimeter forelimb. The smaller grasshopper has a 1.2 – centimeter forelimb. How long is the body of the smaller grasshopper?
32. In order for a student to be considered for a certain college grant, the combined income of the student’s parents must be less than $25,000. If F is the father’s income and M is the mother’s income, which sentence represents the conditions of the grant? A. B. C. D. E.
F + M > $25,000 2F < $25,000 2F + M > $25,000 F + M < $25,000 F x M < $25,000
33. What is the equation that describes the data in the table? X
-4
-1
1
4
7
Y
-1
2
4
7
10
Final Exam Review, Page 8 of 16
34. Which of the following situations would produce the graph shown?
S p e e d Time A. Amber began walking, rested for a while, and then began to run. B. Amber started sprinting, stopped to rest and then started sprinting again. C. Amber was running, started to sprint, then slowed down to rest. After a while she started to walk. D. Amber started at a slow jog, then gradually increased to a sprint.
Use the equations below to answer questions #35 and #36 7 x+1 2
I
y=-
II
y = 7x + 3
III
y=
IV
y=-
2 x+2 7
V
y=-
1 x 7
7 x 2
35. Which equations represent lines that are parallel? A. I and II
B. I and III
C. I and IV
D. III and IV
E. Not Here
J. II and V
K. Not Here
36. Which equations represent lines that are perpendicular? F. I and III
G. I and V
H. II and III
Final Exam Review, Page 9 of 16
37. Write the equation of the function that includes all the ordered pairs in the table? x y
-2 5
0 3
2 1
4 -1
6 -3
38. Joseph was riding his scooter to school, when he ran out of gas. He stopped to check the scooter, then he walked the rest of the way. Which of the following graphs best models this situation?
F.
H. D i s t a n c e
D i s t a n c e
Time
Time
G.
J.
Not Here
D i s t a n c e
Time 39. Jim has a $30 gift certificate for a movie theater. Each time that he sees a movie, m, $5 is deducted from his gift-certificate balance, b. Write an equation that describes b in terms of m?
Final Exam Review, Page 10 of 16
40. Employees receive a bonus of $75 plus $16 per hour, h, for working on New Year’s Eve. If an employee earned no more than $203, write and inequality that represents this situation? DO NOT SOLVE.
41. If 8 pens and 7 pencils cost $3.37 while 5 pens and 11 pencils cost $3.10, how much does each pen and pencil cost?
42. A rectangle has a perimeter of 18 cm. Its length is 5 cm more than its width. Find the dimensions.
43. Jimmy had $5.25 in nickels and quarters. If he had 15 more nickels than quarters, how many coins of each type did he have?
Final Exam Review, Page 11 of 16
44. Tickets for a school football game cost $1.00 each if purchased before the day of the game. They cost $1.50 each if bought at the gate. For a particular game, 600 tickets were sold, with receipts of $700. Write a system of equations that could be used to determine the number of pre-game tickets, P, and tickets sold at the gate, G? DO NOT SOLVE – JUST WRITE THE SYSTEM
45. Timmy has 180 marbles, some plain (P) and some colored (C). If there are 32 more plain marbles than colored marbles, write a system of equations that could be used to determine the number of colored marbles. DO NOT SOLVE – JUST WRITE THE EQUATIONS
46. The sum of two numbers is 32. One number is 4 more than the other. WRITE a system of equations that could be used to find the numbers.
47. Solve.
x–y=6 2x + y = 0
48. Solve.
3 1 x4 7 x 4 2
Final Exam Review, Page 12 of 16
49. Write the system of linear inequalities for the given graph?
50. The owner of a plant nursery knows that the color red will occur in a certain plant once out of every 15 seedlings. If the nursery wants to have about 200 red plants of this variety to sell, what equation could be used to determine the total number of seeds that should be planted?
A.
15 x 14 200
B.
14 200 15 x
C.
1 x 15 200
D.
1 200 15 x
51. Write the equation of each line with slope 0, and passes through (-5,4)
Final Exam Review, Page 13 of 16
52. Write the equation of each line that passes through (-1, -2) and (0,3)
The table below shows the life expectancy of people born in the US between 1920 and 1970. Year 1920 1930 1940 1950 1960 1970
Life Expectancy (years) 54.1 59.7 62.9 68.2 69.7 70.8
53. What is the independent variable?
54. What is the dependent variable?
55. Write the equation for the line of best fit.
56. What is the slope of the line?
57. What is the y-intercept?
58. What will be the life expectancy of a person born in the year 2010?
59.
What is the solution to the system:
3x + 2y = 4 -x + 3y = -5
r=
Final Exam Review, Page 14 of 16
60. Which graph represents the solution to –7 < 3x + 2 < 14 A. B.
-4 -3 -2 -1 0 1 2
3 4 5
-4 -3 -2 -1 0 1 2
3 4 5
-4 -3 -2 -1 0 1 2
3 4 5
-4 -3 -2 -1 0 1 2
3 4 5
C. D.
61. Find the equation of the line that passes through (-1, -2) and (0,3)
MATCH THE GRAPH TO THE EQUATION. A.
B.
C.
D.
______62. y = -x²
______63. y = x² ______64. y = x² - 2 ______65. y = -4x² ______66. y = -x² + 3 ______67. y = (x – 2)² - 3
E.
F.
______68. y = (x + 2)² - 1 ______69. y =
1 x² 4
G.
H.
I.
J.
______70. y = (x + 1)² + 1 ______71. y = -(x – 1)² + 2
Final Exam Review, Page 15 of 16
72. Two lines have the following equations: 4x + 3y = 7 x + 2y = -2 At what point do they intersect?
73. Beth bought 15 tickets to a movie, where adult tickets cost $6.00 and senior citzen tickets cost $4.00. She spent a total of $76. Write a system of equations that will determine the number of adult tickets, a, and the number of senior citzen tickets, s, Beth purchased? DO NOT SOLVE.
74. Solve
5x – ( x – 8 ) = 9 + 3( 2x – 3 )
75. Find the vertex of the given equation to the nearest tenth. y = 3x² + 4x – 1 vertex 76. At which points does the graph of f(x) = 2x² + 6x + 4 intersect the x-axis ? (hint: roots)
77. Which ordered pair represents one of the roots of the function? f(x) = 2x2 + 3x - 20 A. ( -4,0 ) B. ( -5,0 ) C. ( -20,0 ) 5 D. ( ,0 ) 2
Final Exam Review, Page 16 of 16
Write the name and the equation of each parent function. You may use your pink/blue sheet on the review, but you will not be able to use the blue/pink sheet on the final exam. You will have to recognize the parent functions on your own.
78.
79.
5 4 3 2 1
-5 -4 -3 -2 -1
1 2 -1 -2 -3 -4
80.
5 4 3 2
5 4 3 2 1
1 3
4 5
-5 -4 -3 -2 -1
-5
1 2 -1 -2 -3 -4 -5
3
-5 -4 -3 -2 -1
4 5
Function:
Function:
Equation:
Equation:
Equation:
5 4 3 2
82.
1 2 -1 -2 -3 -4 -5
5 4 3 2
83.
1
1 -5 -4 -3 -2 -1
3
4 5
-5 -4 -3 -2 -1
1 2 -1 -2 -3 -4 -5
3
4 5
-5
Function:
81.
1 2 -1 -2 -3 -4
5 4 3 2 1
3
4 5
-5 -4 -3 -2 -1
Function:
Function:
Equation:
Equation:
1 2 -1 -2 -3 -4 -5
3
4 5
Your final exam is 70 questions. Each question on the exam is on this review sheet. You need to complete this review sheet and bring it the day of the exam for 5 points bonus on the final exam. You must show work on every single problem. I will not give you the 5 points if you do not have enough work shown. If you do not know how to show work on a problem then write a sentence telling me how you figured out the answer without showing any work. You will be allowed to use your calculator and the TAKS formula sheet on the final exam. You will not be able to use any other study aids (i.e. pink/blue sheet).
