Student Name: Teacher: Date: District: Miami-Dade County Public Schools. Assessment: 9_12 Mathematics Algebra II Exam 2. Form: 201

Transcription

1 Student Name: Teacher: Date: District: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Algebra II Exam 2 Description: Algebra 2 Topic 6 Test Form: A college entrance exam has a verbal section and a math section. A student can score a maximum of 800 points in each. To qualify, a student has to score at least 600 points in math and a minimum total of 1100 points. Which ordered pair represents a combination of math scores, x, and verbal scores, y, of a student who qualifies? 2. A farmer has 12 acres of land. He plans to plant w acres of wheat and b acres of barley on his land. If he plans to plant wheat in no more than 3 acres of land, which system of inequalities represents the possible values for b and w?

2 3. If the complex expression has no real part, which statement is correct? 4. The table represents the values of and for different values of What are the solutions of the equation

3 5. Bella is solving a system of equations. She evaluates the equations and decides to solve them by the graphing method. The graph she constructed to solve the system of equations is shown below. Which of these is the best approximated solution for this system of equations?

4 6. Peyton makes bracelets of two kinds: those with beads and those with stones. She can make at most 25 bracelets in one week. Peyton makes at most 8 bracelets with beads per week, which she sells for $35 each. The bracelets with stones sell for $45 each. Peyton wants to sell at least $1,000 in bracelets this week. Use b to represent the number of bracelets with beads and s to represent the number of bracelets with stones. Which set of inequalities bounds the acceptable region for Peyton's sales?

5 7. Which graph shows the solutions of the system of equations

6 8. Flash Air Conditioning charges $65 for a service call on Monday through Thursday, plus $45 per hour for labor. $75 for a service call on Friday through Sunday, plus $50 per hour for labor. Perfect Air Conditioning charges $40 for a service call on Monday through Thursday, plus $30 per hour for labor. $60 for a service call on Friday through Sunday, plus $30 per hour for labor. Flash advertises they will complete the same quality service in half the time it takes any company to complete the same job. The McCartney family had their air conditioner serviced last Saturday by Perfect Air Conditioning. According to a Flash advertisement, Flash would have finished the job (done by Perfect Air Conditioning) in half the time and charged the same total price for this service. How long did it actually take Perfect Air Conditioning to complete this service? 1 hour 30 minutes 3 hours 3 hours 20 minutes 5 hours 9. Manny is buying wood blinds for 35 windows in his home. He needs to purchase two different sizes: 36 inches that costs $44.95 and 24 inches that costs $ He may spend up to $1, for the blinds. Which system of inequalities would best represent this situation, where "x" represents the number of 35 inch blinds and "y" represents the number of 24 inch blinds he can purchase?

7 10. The table below shows the corn production of four corn-producing countries of the world and their individual populations. A reporter analyzes these data and comes to the following conclusion: Brazil produces about 3 times the amount of corn per person per year as Mexico produces. Which statement best describes why the reporter's conclusion is correct or incorrect? The reporter is correct because Brazil produces about 3 tons of corn per person per year. The reporter is correct because Brazil produces about 3 times as much corn as Mexico produces per year. The reporter is incorrect because Brazil only produces about 40% more corn per person per year than Mexico produces. The reporter is incorrect because Mexico produces about 1 more ton of corn per person per year than Brazil produces. 11. At what points do the graphs of and intersect? Please use the following passage for this question. The Mathematics of Beanbag Toss What Is Beanbag Toss? In the past few years, a lawn game commonly called beanbag toss has seen a growth in popularity and recognition across the United States. In beanbag toss, players throw beanbags at an inclined platform in an attempt to get the beanbags to land on the platform

8 or go through a hole in the platform. The game is typically played by four players at a time, with two teams of two players each, and continues until one of the teams reaches a certain score. The rules of the game are easy to learn, but tossing a beanbag so that it lands in the right spot can be challenging. The beanbag often slides off the slanted platform, so players practice tossing the beanbag into a high parabola. If the beanbag is thrown with too much velocity, it can land on the platform but then continue moving and slide off the top. Beanbag Toss Setup To play beanbag toss, two platforms and two different-colored sets of beanbags are needed. Many companies sell pre-made game sets that include all necessary materials. Instead of buying a set, a lot of people make their own platforms out of wood and paint them in their favorite colors or add logos representing their college or favorite sports team. Beanbag toss platforms are 2 feet (ft) wide by 4 feet long and are angled so that the top is higher than the base. Each platform has a hole that is 6 inches (in.) in diameter. The center of the hole is 9 inches from the top of the platform and 12 inches from each edge. The platforms are typically 2 inches thick and have legs that fold out to make the top of the platform 12 inches tall. There are four beanbags in each set, and two sets are needed for each game. The beanbags are filled with beans, corn kernels, or other similar materials. Each is a square that is 5 to 6 inches wide and weighs between 12 and 16 ounces.

9 A typical beanbag toss court is set up so that the bases of the platforms are 27 feet apart and the holes are 33 feet apart at their closest point. The pitcher s boxes are the areas next to each platform;; the players stand in their pitcher s box area when it is their turn to toss a beanbag, or pitch, onto the opposite platform. When pitching, players must stay behind the foul line formed by the base of the platform. Rules and Scoring Each team has two players who stand across from each other instead of next to each other. Members of opposing teams stand next to the same platform. In each round, the first player tosses a beanbag at the opposite platform;; the opposing team s member then tosses a beanbag at that same platform. These two players alternate until they have each tossed all four of their beanbags. The score for the round is totaled;; the next round begins when the other two players pick up the beanbags and toss them in the same alternating fashion. Depending on where it lands, each beanbag can earn 3, 1, or 0 points. Every beanbag that goes through the hole by the end of the round is worth 3 points. These points are awarded no matter how the beanbag falls into the hole;; it can be tossed directly into the hole, land on the platform and slide into the hole, or land on the platform and be pushed into the hole by another beanbag that lands on the platform. If a beanbag lands on the platform but does

10 not fall through the hole or slide off the platform by the end of the round, it is worth 1 point. No points are awarded for any beanbag that touches the ground before reaching the platform, that never reaches the platform, or that is thrown from closer than the foul line. To play a faster game, the point values can be added together until one team reaches 21 points. A longer and more common version of the game involves using cancellation scoring until one team reaches 21 points. In this version of the game, only one team can earn points in each round, and the team with the higher score is awarded the difference in the scores for that round. For example, if Team 1 had two beanbags on the platform and one in the hole and Team 2 had one beanbag on the platform and none in the hole, Team 1 would earn 4 points. In that same round in the faster version of the game, Team 1 would earn 5 points and Team 2 would earn 1 point. There are many other scoring variations that can be used, such as playing to 25 points, requiring that a team wins by at least 2 points, or requiring a winning score of exactly 21 points and being penalized for going over 21 points. Beanbag toss can be played anywhere and by people of all ages. The combination of outdoor fun, competition with friends, and versatility is what attracts people to the game. Start a game of beanbag toss with your friends or family this weekend and find out which variation of the game you prefer. 12. Read "The Mathematics of Beanbag Toss" and answer the question. If is a quadratic function that represents the vertical location of a beanbag based on its horizontal location, and represents the equation of the line formed by the slanted platform at which the the beanbag is thrown, what does the solution to the system of equations containing and represent? the maximum height of the beanbag in the air the path of the beanbag as it slides on the board the location of the beanbag when it hits the ground the location of the beanbag when it hits the platform

11 13. The graphs of functions and are shown below. Which statement is true about the real solutions of the equation It has only one real solution,. It has two real solutions, It has two real solutions, It has three real solutions,

12 14. Challi has a dojo and teaches karate classes on Saturday mornings and afternoons. His morning class started with 15 students, and three new students joined the class every two weeks. The afternoon class started with 10 students, and two new students joined the class every week. Which graph shows the enrollment for the two classes?

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14 15. What are the solutions of the system of equations 16. What is the solution of the system of equations that contains the equation and the equation of the line shown on the graph below? no solution infinitely many solutions

15 17. Rashad is the manager of a shoe store at the mall. He earns a commission of 30% on any sales he makes, a commission of 8% on sales that other salespeople make, and a base salary of $ a week. Last week Rashad sold $4, worth of merchandise, Luis sold a total of $1,385.00, Sylvia's sales were $1,862.00, and Tomas sold a total of $2, Which formula can be used to calculate Rashad's earnings for the week? R = ( )/2 * ( ) R = 0.3 (4548) ( ) R = 0.3 (4548) ( ) R = 0.3 (4548) ( ) 18. Four students attempt to represent in a + bi form. Who represented it correctly? Aden Ella Jose Noami 19. An amusement park charges $17 for each adult ticket and $6 for each child ticket. One day, the park earned $3,640 in ticket sales. Let x represent the number of adult tickets sold. Let y represent the number of child tickets sold. If 400 tickets were sold on this day, which system of equations can be used to find the number of each type of ticket sold?

16 20. On Saturday, Carrie went to the store and bought 4 loaves of bread and 1 gallon of milk for a total of $ The next weekend, she went to the same store and spent $11.50 on 2 loaves of bread and 2 gallons of milk. The prices had not changed. What is the price for one gallon of milk? $2.25 $2.50 $3.50 $ The graph below shows the function f. A linear function g is such that the solutions of the equation are Which function correctly represents g? 22. A sample of 250 students were asked for the average amount of money they spend in a day. The data resulted in a mean of $5.50 with a standard deviation of $2.45. If the mean amount of money that all students spend in a day is between $5.10 and $5.90, approximately which confidence level does the range represent? 99% 93% 45% 32%

17 23. Sunrise High School's tennis club needs to rent a van for travel to a tournament. Company A charges a flat rate of $50 plus $15 per day. Company B charges a flat rate of $30 plus $25 per day. Assuming the tennis club will spend y dollars on the van rental, which method could they use to determine the number of days where the cost of renting a van from either Company A or from Company B would be the same? Let y represent the total cost and x represent the number of days. Company A: Company B: Graph both lines and note where they intersect. The x-coordinate of the intersection point is the number of days. Company A: Company B: Graph both lines and note where they intersect. The y-coordinate of the intersection point is the number of days. Company A: Company B: Graph both lines and note where they intersect. The x-coordinate of the intersection point is the number of days. Company A: Company B: Graph both lines and note where they intersect. The y-coordinate of the intersection point is the number of days.

18 24. Which graph represents the solutions to the system of equations below?

19 25. When 865 voters in a state are randomly selected and surveyed, it is found that 70% of the voters support the current elected official. For a 95% confidence level, the margin of error for the population mean is 3.05%. Which statement explains how this survey could be adjusted so that the population mean can be reported with a 99% confidence level? If the margin of error is fixed at 3.05% and the sample size is decreased to 500, the survey could be reported with a 99% confidence level. If the margin of error is fixed at 3.05% and the sample size is increased to 1,200, the survey could be reported with a 99% confidence level. If the sample size remains 865 and the margin of error is adjusted to 4.02%, this would result in a survey that could be reported with a 99% confidence level. If the sample size remains 865 and the margin of error is adjusted to 2.08%, this would result in a survey that could be reported with a 99% confidence level.

20 Student Name: Teacher: Date: District: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Algebra II Exam 2 Description: Algebra 2 Topic 6 Test Form: A college entrance exam has a verbal section and a math section. A student can score a maximum of 800 points in each. To qualify, a student has to score at least 600 points in math and a minimum total of 1100 points. Which ordered pair represents a combination of math scores, x, and verbal scores, y, of a student who qualifies? MAFS.912.A-CE1.3 Webb: 2 2. A farmer has 12 acres of land. He plans to plant w acres of wheat and b acres of barley on his land. If he plans to plant wheat in no more than 3 acres of land, which system of inequalities represents the possible values for b and w? MAFS.912.A-CE1.3 Webb: 2

21 3. If the complex expression has no real part, which statement is correct? MAFS.912.N-CN.1.1 Webb: 2 4. The table represents the values of and for different values of What are the solutions of the equation MAFS.912.A-REI.4.11 Webb: 1

22 5. Bella is solving a system of equations. She evaluates the equations and decides to solve them by the graphing method. The graph she constructed to solve the system of equations is shown below. Which of these is the best approximated solution for this system of equations? MAFS.912.A-REI.3.6 Webb: 1

23 6. Peyton makes bracelets of two kinds: those with beads and those with stones. She can make at most 25 bracelets in one week. Peyton makes at most 8 bracelets with beads per week, which she sells for $35 each. The bracelets with stones sell for $45 each. Peyton wants to sell at least $1,000 in bracelets this week. Use b to represent the number of bracelets with beads and s to represent the number of bracelets with stones. Which set of inequalities bounds the acceptable region for Peyton's sales? MAFS.912.A-CE1.3 Webb: 2

24 7. Which graph shows the solutions of the system of equations MAFS.912.A-REI.3.7 Webb: 2

25 8. Flash Air Conditioning charges $65 for a service call on Monday through Thursday, plus $45 per hour for labor. $75 for a service call on Friday through Sunday, plus $50 per hour for labor. Perfect Air Conditioning charges $40 for a service call on Monday through Thursday, plus $30 per hour for labor. $60 for a service call on Friday through Sunday, plus $30 per hour for labor. Flash advertises they will complete the same quality service in half the time it takes any company to complete the same job. The McCartney family had their air conditioner serviced last Saturday by Perfect Air Conditioning. According to a Flash advertisement, Flash would have finished the job (done by Perfect Air Conditioning) in half the time and charged the same total price for this service. How long did it actually take Perfect Air Conditioning to complete this service? MAFS.912.A-CE1.2 Webb: 2 1 hour 30 minutes 3 hours 3 hours 20 minutes 5 hours 9. Manny is buying wood blinds for 35 windows in his home. He needs to purchase two different sizes: 36 inches that costs $44.95 and 24 inches that costs $ He may spend up to $1, for the blinds. Which system of inequalities would best represent this situation, where "x" represents the number of 35 inch blinds and "y" represents the number of 24 inch blinds he can purchase? MAFS.912.A-CE1.3 Webb: 2

26 10. The table below shows the corn production of four corn-producing countries of the world and their individual populations. A reporter analyzes these data and comes to the following conclusion: Brazil produces about 3 times the amount of corn per person per year as Mexico produces. Which statement best describes why the reporter's conclusion is correct or incorrect? MAFS.912.S-I2.6 Webb: 3 The reporter is correct because Brazil produces about 3 tons of corn per person per year. The reporter is correct because Brazil produces about 3 times as much corn as Mexico produces per year. The reporter is incorrect because Brazil only produces about 40% more corn per person per year than Mexico produces. The reporter is incorrect because Mexico produces about 1 more ton of corn per person per year than Brazil produces. 11. At what points do the graphs of and intersect? MAFS.912.A-REI.3.7 Webb: 3 Please use the following passage for this question. The Mathematics of Beanbag Toss

27 What Is Beanbag Toss? In the past few years, a lawn game commonly called beanbag toss has seen a growth in popularity and recognition across the United States. In beanbag toss, players throw beanbags at an inclined platform in an attempt to get the beanbags to land on the platform or go through a hole in the platform. The game is typically played by four players at a time, with two teams of two players each, and continues until one of the teams reaches a certain score. The rules of the game are easy to learn, but tossing a beanbag so that it lands in the right spot can be challenging. The beanbag often slides off the slanted platform, so players practice tossing the beanbag into a high parabola. If the beanbag is thrown with too much velocity, it can land on the platform but then continue moving and slide off the top. Beanbag Toss Setup To play beanbag toss, two platforms and two different-colored sets of beanbags are needed. Many companies sell pre-made game sets that include all necessary materials. Instead of buying a set, a lot of people make their own platforms out of wood and paint them in their favorite colors or add logos representing their college or favorite sports team. Beanbag toss platforms are 2 feet (ft) wide by 4 feet long and are angled so that the top is higher than the base. Each platform has a hole that is 6 inches (in.) in diameter. The center of the hole is 9 inches from the top of the platform and 12 inches from each edge. The platforms are typically 2 inches thick and have legs that fold out to make the top of the platform 12 inches tall. There are four beanbags in each set, and two sets are needed for each game. The beanbags are filled with beans, corn kernels, or other similar materials. Each is a square that is 5 to 6 inches wide and weighs between 12 and 16 ounces.

28 A typical beanbag toss court is set up so that the bases of the platforms are 27 feet apart and the holes are 33 feet apart at their closest point. The pitcher s boxes are the areas next to each platform;; the players stand in their pitcher s box area when it is their turn to toss a beanbag, or pitch, onto the opposite platform. When pitching, players must stay behind the foul line formed by the base of the platform. Rules and Scoring Each team has two players who stand across from each other instead of next to each other. Members of opposing teams stand next to the same platform. In each round, the first player tosses a beanbag at the opposite platform;; the opposing team s member then tosses a beanbag at that same platform. These two players alternate until they have each tossed all four of their beanbags. The score for the round is totaled;; the next round begins when the other two players pick up the beanbags and toss them in the same alternating fashion.

29 Depending on where it lands, each beanbag can earn 3, 1, or 0 points. Every beanbag that goes through the hole by the end of the round is worth 3 points. These points are awarded no matter how the beanbag falls into the hole;; it can be tossed directly into the hole, land on the platform and slide into the hole, or land on the platform and be pushed into the hole by another beanbag that lands on the platform. If a beanbag lands on the platform but does not fall through the hole or slide off the platform by the end of the round, it is worth 1 point. No points are awarded for any beanbag that touches the ground before reaching the platform, that never reaches the platform, or that is thrown from closer than the foul line. To play a faster game, the point values can be added together until one team reaches 21 points. A longer and more common version of the game involves using cancellation scoring until one team reaches 21 points. In this version of the game, only one team can earn points in each round, and the team with the higher score is awarded the difference in the scores for that round. For example, if Team 1 had two beanbags on the platform and one in the hole and Team 2 had one beanbag on the platform and none in the hole, Team 1 would earn 4 points. In that same round in the faster version of the game, Team 1 would earn 5 points and Team 2 would earn 1 point. There are many other scoring variations that can be used, such as playing to 25 points, requiring that a team wins by at least 2 points, or requiring a winning score of exactly 21 points and being penalized for going over 21 points. Beanbag toss can be played anywhere and by people of all ages. The combination of outdoor fun, competition with friends, and versatility is what attracts people to the game. Start a game of beanbag toss with your friends or family this weekend and find out which variation of the game you prefer. 12. Read "The Mathematics of Beanbag Toss" and answer the question. If is a quadratic function that represents the vertical location of a beanbag based on its horizontal location, and represents the equation of the line formed by the slanted platform at which the the beanbag is thrown, what does the solution to the system of equations containing and represent? MAFS.912.A-REI.4.11 Webb: 1 the maximum height of the beanbag in the air the path of the beanbag as it slides on the board the location of the beanbag when it hits the ground the location of the beanbag when it hits the platform

30 13. The graphs of functions and are shown below. Which statement is true about the real solutions of the equation MAFS.912.A-REI.4.11 Webb: 1 It has only one real solution,. It has two real solutions, It has two real solutions, It has three real solutions,

31 14. Challi has a dojo and teaches karate classes on Saturday mornings and afternoons. His morning class started with 15 students, and three new students joined the class every two weeks. The afternoon class started with 10 students, and two new students joined the class every week. Which graph shows the enrollment for the two classes? MAFS.912.A-CE1.2 Webb: 2

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33 15. What are the solutions of the system of equations MAFS.912.A-REI.3.7 Webb: What is the solution of the system of equations that contains the equation and the equation of the line shown on the graph below? MAFS.912.A-REI.3.6 Webb: 1 no solution infinitely many solutions

34 17. Rashad is the manager of a shoe store at the mall. He earns a commission of 30% on any sales he makes, a commission of 8% on sales that other salespeople make, and a base salary of $ a week. Last week Rashad sold $4, worth of merchandise, Luis sold a total of $1,385.00, Sylvia's sales were $1,862.00, and Tomas sold a total of $2, Which formula can be used to calculate Rashad's earnings for the week? MAFS.912.A-CE1.2 Webb: 2 R = ( )/2 * ( ) R = 0.3 (4548) ( ) R = 0.3 (4548) ( ) R = 0.3 (4548) ( ) 18. Four students attempt to represent in a + bi form. Who represented it correctly? MAFS.912.N-CN.1.1 Webb: 2 Aden Ella Jose Noami

35 19. An amusement park charges $17 for each adult ticket and $6 for each child ticket. One day, the park earned $3,640 in ticket sales. Let x represent the number of adult tickets sold. Let y represent the number of child tickets sold. If 400 tickets were sold on this day, which system of equations can be used to find the number of each type of ticket sold? MAFS.912.A-CE1.3 Webb: On Saturday, Carrie went to the store and bought 4 loaves of bread and 1 gallon of milk for a total of $ The next weekend, she went to the same store and spent $11.50 on 2 loaves of bread and 2 gallons of milk. The prices had not changed. What is the price for one gallon of milk? MAFS.912.A-REI.3.6 Webb: 2 $2.25 $2.50 $3.50 $4.80

36 21. The graph below shows the function f. A linear function g is such that the solutions of the equation are Which function correctly represents g? MAFS.912.A-REI.4.11 Webb: A sample of 250 students were asked for the average amount of money they spend in a day. The data resulted in a mean of $5.50 with a standard deviation of $2.45. If the mean amount of money that all students spend in a day is between $5.10 and $5.90, approximately which confidence level does the range represent? MAFS.912.S-I2.4 Webb: 3 99% 93% 45% 32%

37 23. Sunrise High School's tennis club needs to rent a van for travel to a tournament. Company A charges a flat rate of $50 plus $15 per day. Company B charges a flat rate of $30 plus $25 per day. Assuming the tennis club will spend y dollars on the van rental, which method could they use to determine the number of days where the cost of renting a van from either Company A or from Company B would be the same? Let y represent the total cost and x represent the number of days. MAFS.912.A-REI.4.11 Webb: 2 Company A: Company B: Graph both lines and note where they intersect. The x-coordinate of the intersection point is the number of days. Company A: Company B: Graph both lines and note where they intersect. The y-coordinate of the intersection point is the number of days. Company A: Company B: Graph both lines and note where they intersect. The x-coordinate of the intersection point is the number of days. Company A: Company B: Graph both lines and note where they intersect. The y-coordinate of the intersection point is the number of days.

38 24. Which graph represents the solutions to the system of equations below? MAFS.912.A-REI.3.7 Webb: 1

39 25. When 865 voters in a state are randomly selected and surveyed, it is found that 70% of the voters support the current elected official. For a 95% confidence level, the margin of error for the population mean is 3.05%. Which statement explains how this survey could be adjusted so that the population mean can be reported with a 99% confidence level? MAFS.912.S-I2.4 Webb: 2 If the margin of error is fixed at 3.05% and the sample size is decreased to 500, the survey could be reported with a 99% confidence level. If the margin of error is fixed at 3.05% and the sample size is increased to 1,200, the survey could be reported with a 99% confidence level. If the sample size remains 865 and the margin of error is adjusted to 4.02%, this would result in a survey that could be reported with a 99% confidence level. If the sample size remains 865 and the margin of error is adjusted to 2.08%, this would result in a survey that could be reported with a 99% confidence level.