I can graph the solutions to a linear inequality in two variables as a half-plane.

Transcription

1 1 Algebra II Chapter 3 Test Review Standards/Goals: (Algebra I): A.1.d./A.CED.1.: o I can solve and graph a linear inequality/equation. o I can solve a single step or multi-step linear inequality that has only one variable. D.1.a.: I can solve compound inequalities containing the words or and and. D.1.a./A.CED.1.: I can create and solve absolute value equations and graph their solutions. D.1.b.: I can solve and graph compound inequalities that involve both or and and. (Algebra I): A.REI.12.: I can graph the solution of a linear inequality in a half-plane. D.2.a./A.REI.12: o o I can graph the solutions to a linear inequality in two variables as a half-plane. I can graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. D.2.a./A.REI.12: o I can graph the solutions to a linear inequality in two variables as a half-plane. o I can graph a system of linear inequalities in two variables with and without technology to find the solution set to the system. D.2.b./A.CED.3.: o I can solve linear programming problems by finding maximum and minimum values of a function over a region defined by linear inequalities. o I can use linear inequalities to represent constraints in problem solving. #1. A factory wants to make ball bearings that have a standard diameter, d of mm. Ball bearings that are deemed to be acceptable measure within ±0.155 mm of this standard. Determine the solution set for the diameter of these ball bearings. Graphing linear inequalities. #2. What is the area of the figure determined by this system of inequalities? Use the graph provided below, if you wish. {

2 2 Solve AND graph the following. Write answers in set and interval forms.: #3. 4x + 8 < 12 OR 5 8x -35 #4. #5. #6. #7. #8.

3 3 #9. #10. #11. #12. #13. #14. Write an absolute value inequality or equation for each number line shown: #15. #16. #17. #18. Write an absolute value inequality for each situation below: #19. On the real number line, x is less than 6 units away from 10. #20. On the real number line, x is more than 6 units away from 11. #21. On the real number line, x is within 5 units of 17. #22. On the real number line, x is within 10 units of 37, (non inclusive).

4 4 #23. Graph this system of constraints and show its feasible region. Write the vertices down, and the point that achieves the maximum and minimum for the objective function: P(x, y) = 4x + 2y. { #24. The cost C is given by: C = 0.12x y. Find the minimum and maximum values.

5 5 #25. For the following, graph the system of constraints. Name ALL vertices and then find the values of x and y that maximize or minimize the objective function. Use the graph provided. { Maximum for P = x + 3y #26. Write a set of constraints and an objective function for the situation described above.

6 6 #27. Write a set of constraints and an objective function for the situation described above. What systems of inequalities are shown in the graphs? #28. #29. #30.

7 7 MULTIPLE CHOICE QUESTIONS: #31. What is the solution of 1 < 2x + 3 < 9? a. -1 > x < 2 b. 2 < x < 3 c. -1 < x < 2 d. -1 < x < 3 #32. The hourly rate of a waiter is $4 plus tips. On a particular day, the waiter worked 8 hours and received more than $150 in pay. Which could be the amount of tips the waiter received? a. $18.75 b. $32 c. $118 d. $ #32. Which expression best represents a simpler form of 4m + 3(m + n)? a. 7m + 3n b. 4m + 3mn c. 3m + 4n d. #33. Throwback Topic: Boxplots Twenty-six samples of Romano-British pottery were found at four different kiln sites. The percentage of oxides of two metals, magnesium and iron, measured by atomic absorption spectrophotometry, are displayed in the given boxplots. a. Between what two values do the higher 75% of data approximately lie for the Iron distribution? b. Between what two values do the middle 50% of the data approximately lie for the Magnesium distribution? c. Between what two values do the lower 75% of the data approximately lie for the Magnesium distribution? #34. Solve the system of equations using any method you choose: {

8 8 Consider an equation with a slope of -1/2 and passes through the point (-12, 10). #35. Write the equation of the line in point-slope form. #36. What would be the slope of a line parallel to this line? #37. What would be the slope of a line perpendicular to this line? #38. Write the equation of the line in slope-intercept form. #39. Write an example of an equation of a line that would be parallel to the line you just wrote an equation for. #40. Write an example of an equation of a line that would be perpendicular to the line you just wrote an equation for. #41. Write the equation of the line in standard form. #42. Write an example of an equation of a line that would be parallel to the line you just wrote an equation for. #43. Write an example of an equation of a line that would be perpendicular to the line you just wrote an equation for.

9 9 #44. Free Response Practice The table and scatterplot below show the relationship between student enrollment (in thousands) and total number of property crimes (burglary and theft) in 2006 for eight colleges and universities in a certain U.S. state. a. Is the slope of the LSRL positive or negative? b. Use the line to predict approximately the number of crimes when the enrollment is 15,000 students. c. Use the equation to predict the number of crimes when the enrollment is 15,000 students. Show your work. d. Comment on the difference between your answers to part b and part c. e. From the equation written in part c, which number is the slope? f. From the equation written in part c, which number is the intercept? g. From the equation written in part c, what does x represent? h. From the equation written in part c, what does represent?

10 10 #45. You have 7 books to place onto a shelf. In how many ways can you arrange these books? #46. You have a friend with 4 books to place on a shelf. In how many ways can your friend arrange these books? #47. In how many more ways can you arrange the books on the shelf than can your friend? #48. You have 10 friends that you plan to take on a weekend trip to the beach. You need one friend to plan the meals for the trip. You need another friend to make the hotel reservations. You need a third friend to take your car to the mechanic to get serviced before the trip. Finally, you need a fourth friend to help you pack your car for the trip. In how many ways can you select 4 friends? #49. Find the 300 th term from the sequence written below: 10, 17, 24, #50. Find the 60 th term from the sequence written below: -9, -21, -33,