Math 092 Essex County College Syllabus Assignments

Transcription

1 Student Name: Teacher: District: Date: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Algebra II Interim 2 Description: Mid-Year Algebra II Form: During a physics experiment, a ball is tossed and its height in feet, y, after x seconds is recorded. In the graph created from these data, the function is parabolic in shape and has a y-intercept at an x-intercept at and a vertex at Which statement is true of the ball in this experiment? The ball is in the air more than 5 seconds. The ball is thrown from a height of about 21 feet. The ball reaches a minimum height of about 21 feet. The ball reaches a maximum height after about 1 second. 2. The system of equations has the solutions What is the value of

2 3. The steps used to solve the equation are shown below. Which property is incorrectly used? distributive property division property of equality addition property of equality subtraction property of equality 4. John has two garden hoses, A and B, to fill a pool. He estimates that hose A alone can fill the pool 1.5 times faster than hose Working together, both hoses take 6 hours to fill the pool. How long will it take to fill the pool if only hose A is used? 2.4 hours 3.6 hours 10 hours 15 hours

3 5. Use the function graphed on the coordinate plane below. What are the intervals where the function is decreasing and increasing? The function decreases from and increases from The function decreases from and increases from The function decreases from and increases from The function decreases from and increases from

4 6. 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 7. A store sells two types of speakers, A and B; x represents the number of type A speakers sold daily, and y represents the number of type B speakers sold daily. The system of inequalities below represents the possible values of x and y for this situation. If the store s daily profit is represented by the function maximum daily profit for the store? what is the $700 $740 $760 $800

5 8. Solve the equation below. 9. The path of a roller coaster over a particular length of track can be represented by a quadratic function f, where f(x) represents the vertical displacement above or below a support bar (in meters), and x represents the horizontal displacement to the left or right of a flagpole (in meters). The roller coaster dips below the support bar for values of x between and 1. Which function could represent f?

6 10. Craig works at an appliance store. He earns a fixed salary of $1,000 every 2 weeks. He also earns a $50 commission on each appliance he sells. Craig's earnings in dollars, y, can be represented as a function of the number of appliances he sells, x. Which graph represents Craig's earnings during a two week period in which he sells no more than 20 appliances?

7 11. The members of the Drama Club sold their old costumes in a booth at the school craft fair. Their profit was the difference between the amount of money they made selling the costumes and the cost of the booth. The cost of the booth was $50 and each of the costumes was sold for the same price. After the members of the Drama Club had sold 9 costumes, they had made a profit of $ The function p represents the Drama Club's profit as a function of c, the number of costumes they sold. What does the c-intercept of the function represent? The c-intercept represents a profit of $0 when 4 costumes are sold. The c-intercept represents a profit of $0 when 5 costumes are sold. The c-intercept represents a loss of $50 when no costumes are sold. The c-intercept represents a loss of $37.50 when 1 costume is sold. 12. What are the solutions of the system of equations 13. The height in feet, a kangaroo reaches seconds after it has jumped in the air is modeled by the quadratic function Which equation shows the correctly factored version of the function and the number of seconds it takes for the kangaroo to return to the ground? 8 seconds 1.5 seconds 8 seconds 1.5 seconds

8 14. Which function is both an equivalent form of and reveals the minimum of the function? 15. The graph of the function f(x) and the transformed function are shown below. Which values are the best estimates for the values of a and k? and and and and

9 16. At how many points do the graphs and intersect? The graph below represents the closing price of a stock over a period of two weeks. What is the average rate of change in the closing price between November 5 and November 7?

10 18. If the quadratic equation is rewritten in the form what is the value of? 19. The function is restricted to a specific domain. Under this restriction, its range is What is the largest possible domain for 20. What is the equation of the parabola with a focus at and a directrix of

11 21. 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?

12 22. Which graph represents the function

13 23. Which of these quadratic equations has non-real solutions? 24. What is the equation of a parabola with a focus at and a directrix of

14 25. Which graph shows the solutions of the system of equations

15 26. 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? 27. The dollar price-per-share of a certain stock over the first half of 2013 is modeled by the function where t is the number of months after January 1. What is the minimum price-per-share the stock reaches during this time? $0.66 $3.00 $6.00 $12.00

16 28. How is the graph of related to the graph of The graph of is reflected across the y-axis and translated up 2 units. The graph of is reflected across the x-axis and translated up 2 units. The graph of is reflected across the y-axis and translated down 2 units. The graph of is reflected across the x-axis and translated down 2 units.

17 29. Which graph below shows the graph of an absolute value function that is decreasing over the interval and increasing over the interval

18 30. The height, in feet, of an arrow shot from a bow in an upwards direction, is modeled by the function where represents the time in minutes. During which interval is the arrow going up? 31. Jessie thinks that the first step in solving the equation shown below could be to use the addition property of equality. His friend Robin thinks that the multiplication property of equality could be used first. Who is correct and why? Jessie is correct because can first be added to both sides of the equation. Robin is correct because both sides of the equation can first be multiplied by 10. Both are correct because the first step can be either to add or to multiply by 10 on both sides of the equation. Neither is correct because neither adding nor multiplying by 10 on both sides of the equation is a valid first step. 32. Which values of x represent the solutions of the equation

19 33. The value of a certain house is modeled by the function where x represents the number of years since it was bought. Which statement is true? The initial cost of the house is $2,500. The value of the house will increase to $126,000 over a period of time. The initial cost of the house is $126,000, and the value is decreasing by $2,500 every year. The initial cost of the house is $126,000, and the value is increasing by $2,500 every year. 34. Which statement describes the solutions to the equation There are two distinct real solutions and no non-real, complex solutions. There is one real solution and one non-real, complex solution. There is one real solution and no non-real, complex solutions. There are no real solutions and two non-real, complex solutions. 35. Henry examined the table that represents values satisfying the function shown below. Based on the information in the table, which one of these key features is incorrect? The y-intercept of the graph of the function is at The maximum value of the function is 4. A local minimum is located within the interval A local maximum is located within the interval

20 36. Robin has a collection of dimes, nickels and quarters. He has 4 times as many dimes as nickels. He has 20 more quarters than nickels. The ratio of the number of dimes to the number of quarters is 3:2. Which equation can be used to calculate the number of nickels, n, Robin has? 37. Jon throws a ball into the air off a platform. The height of the ball is given by where y is the height, in feet, above the ground when the ball has traveled a horizontal distance of x feet. What is the factored form of the expression that could be used to find out how far the ball has traveled horizontally when it hits the ground? 38. If which expression represents the average rate of change of the function between the points and

21 39. Which expression is equivalent to the expression 40. What is the equation of a parabola with a focus at and a directrix 41. In the function what values of h and k ensure that the vertex of the graph of the function appears in the 3rd quadrant? 42. Which function represents the function below in vertex form and gives the correct minimum value of and has a minimum value of and has a minimum value of and has a minimum value of and has a minimum value of

22 43. How can the following expression be rewritten so it is equal to where a and b are binomials? 44. Frederick works in a grocery store and also mows lawns. He earns $10 per hour at the grocery store and $8.50 per hour mowing lawns. He worked a total of 35 hours last week, of which he spent x hours mowing lawns. Which is the simplified equation that represents the relationship between his earnings, y, in dollars and the number of hours he spent working last week? 45. Which of the following is equivalent to the expression below?

23 46. All the rectangular public-information signs in a shopping center are built such that, for some integer x, they are feet high and feet wide. In order for painters to paint a sign, they must first calculate the area. Which expression represents the area, in square feet, of each sign? 47. The heights and bases of two geometric shapes are modeled by the expressions shown. Triangle: Parallelogram: What expression represents the number of units by which the area of the parallelogram is greater than the area of the triangle?

24 48. A student is finding the value of the variable x in the equation where and are integer constants, none of which are 0. Which statement describes and justifies steps the student can take to find the value of the variable? The student can multiply both sides of the equation by and then add to both sides of the equation because of the Multiplication and Addition Properties of Equality. The student can add to both sides of the equation and then multiply by because of the Addition and Multiplication Properties of Equality. The student can divide by its coefficient and then subtract from the left side of the equation because of the Division and Subtraction Properties of Equality. The student can subtract from the left side of the equation and then divide both sides of the equation by Equality. because of the Subtraction and Division Properties of 49. Two boats start traveling from opposite directions at the same time and meet each other after 2 hours. One boat is traveling upstream, and the other is traveling downstream. In still water, both boats have the same speed of 15 mph. The speed of the boat traveling upstream is 12 mph. Which equation represents the initial distance, d, between the boats?

25 50. Michael buys a car and agrees to pay $1,500 up front and $450 each month for the next 2 years. Which graph shows the total amount, y, in dollars that will be paid at the end of x months?

26

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