Math 11 Final Exam Review Part 3 #1

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1 Math 11 Final Exam Review Part 3 #1 College Algebra / Math 11 RCC Fall 2011 #48794 (Prof. Chiek) Student Name/ID: 1. For each point in the table below, decide whether it is on Line 1, Line 2, both, or neither. Line 1: Line 2: 2. Hong bought a desktop computer and a laptop computer. Before finance charges, the laptop cost less than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was per year, and for the laptop it was per year. The total finance charges for one year were. How much did each computer cost before finance charges? 3. A cyclist travels in hours going against the wind. She travels with the wind in the same amount of time. What is the rate of the cyclist in still air and what is the rate of the wind? Rate of the cyclist in still air: Rate of the wind: 4. Use substitution to solve the system. ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 1/23

2 5. Graph the system below and write its solution. Note that you can also answer "No solution" or "Infinitely many solutions." 6. For each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, answer the question about its solutions. L1: ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 2/23

3 L2: This system of equations is: - consistent dependent - consistent independent - inconsistent This means the system has: - a unique solution: Solution: L1: L2: - no solution - infinitely many solutions This system of equations is: - consistent dependent - consistent independent - inconsistent This means the system has: - a unique solution: Solution: L1: L2: - no solution - infinitely many solutions ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 3/23

4 This system of equations is: - consistent dependent - consistent independent - inconsistent This means the system has: - a unique solution: Solution: - no solution - infinitely many solutions 7. Two rainstorms occurred in one week in a certain area. In the first storm, of rain fell per hour, and in the second storm, of rain fell per hour. Rain lasted for a total of hours, resulting in a total rainfall of. How long was each storm? First storm: Second storm: 8. Solve the system. 9. The sum of three numbers is. The third number is times the second. The second number is less than the first. What are the numbers? ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 4/23

5 10. Karen, Goran, and Ryan sent a total of text messages over their cell phones during the weekend. Goran sent times as many messages as Ryan. Ryan sent fewer messages than Karen. How many messages did they each send? 11. Solve the system. 12. The sum of three numbers is. The first number is more than the second. The third number is times the first. What are the numbers? 13. Solve the system. 14. Solve the system. 15. A gardener has up to square feet available for planting flowers and vegetables. The gardener wants the space used for vegetables to be at least twice the space used for flowers. In addition, at least square feet is to ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 5/23

6 be used for flowers. Let denote the area in square feet used for flowers, and let denote the area in square feet used for vegetables. Shade the region of the plane that represents all allocations of space satisfying these requirements. 16. Graph the solution to the following system of inequalities. 17. A store has two types of animal feed available. Type A contains pounds of oats and pound of corn per bag. Type B contains pounds of oats and pounds of corn per bag. A farmer wants to combine the two types so that the resulting mixture has at least pounds of oats and at least pounds of corn. The store only has bags of type A feed and bags of type B feed in stock. Type A costs per bag, and type B costs per bag. How many bags of each type should the farmer buy to minimize his cost? ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 6/23

7 18. Find the maximum value of the function subject to the following constraints. 19. Graph the inequality in the coordinate plane. 20. Graph the inequality. ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 7/23

8 21. Graph the inequality. 22. Evaluate. Simplify your answer as much as possible. ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 8/23

9 23. Find the first four terms of the sequence given by the following. 24. Evaluate. Simplify your answer as much as possible. 25. Evaluate. Simplify your answer as much as possible. 26. Find the first four terms of the sequence given by the following. 27. Find the first four terms of the sequence given by the following. ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 9/23

10 28. Find the first four terms of the sequence given by the following. 29. For a given arithmetic sequence, the nd term,, is equal to, and the th term,, is equal to. Find the value of the rd term,. 30. Compute the sums below. (Assume that the terms in the first sum are consecutive terms of an arithmetic sequence.) (a) 31. Compute the sums below. (Assume that the terms in the first sum are consecutive terms of an arithmetic sequence.) (a) 32. Compute the sums below. (Assume that the terms in the first sum are consecutive terms of an arithmetic sequence.) (a) ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 10/23

11 33. For a given arithmetic sequence, the st term,, is equal to, and the th term,, is equal to. Find the value of the th term,. 34. For a given arithmetic sequence, the th term,, is equal to, and the th term,, is equal to. Find the value of the th term,. 35. For a given arithmetic sequence, the st term,, is equal to, and the th term,, is equal to. Find the value of the th term,. 36. Compute each sum below. If applicable, write your answer as a fraction. (a) ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 11/23

12 37. Compute each sum below. If applicable, write your answer as a fraction. (a) 38. The sequences below are either arithmetic or geometric. For each sequence, determine whether it is arithmetic or geometric, and write the formula for the th term of that sequence. 39. For a given geometric sequence, the th term,, is equal to, and the th term,, is equal to. Find the value of the th term,. If applicable, write your answer as a fraction. 40. For a given geometric sequence, the th term,, is equal to, and the th term,, is equal to. Find the value of the th term,. If applicable, write your answer as a fraction. 41. Compute each sum below. Give exact values, not decimal approximations. If the sum does not exist, click on "No sum". ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 12/23

13 (a) 42. The sequences below are either arithmetic or geometric. For each sequence, determine whether it is arithmetic or geometric, and write the formula for the th term of that sequence. 43. How many ways are there of choosing letters, without replacement, from distinct letters, if the order of the choices does not matter? the order of the choices matters? 44. How many ways are there of choosing objects, without replacement, from distinct objects, if the order of the choices is not relevant? the order of the choices is relevant? 45. How many ways are there of choosing objects, without replacement, from the objects pencil, eraser, desk, and chair, if the order of the choices is taken into consideration? the order of the choices is not taken into consideration? ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 13/23

14 46. A catering service offers appetizers, main courses, and desserts. A banquet chairperson is to select appetizers, main courses, and desserts for a banquet. In how many ways can this be done? 47. How many ways are there of choosing colors, without replacement, from the colors red, blue, green, and purple, if the order of the choices matters? the order of the choices does not matter? 48. (a) athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the medals be distributed? From a collection of store customers, are to be chosen to receive a special gift. How many groups of customers are possible? 49. (a) A company that makes crayons is trying to decide which colors to include in a promotional mini-box of crayons. The company can choose the mini-box colors from its collection of colors. How many mini-boxes are possible? A company has salespeople. A board member at the company asks for a list of the top salespeople, ranked in order of effectiveness. How many such rankings are possible? 50. Use the binomial formula to find the coefficient of the term in the expansion of. 51. ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 14/23

15 Use the binomial formula to find the coefficient of the term in the expansion of. 52. Use the binomial formula to find the coefficient of the term in the expansion of. 53. Use the binomial formula to find the coefficient of the term in the expansion of. 54. Use the binomial formula to find the coefficient of the term in the expansion of. 55. Use the binomial formula to find the coefficient of the term in the expansion of. 56. Use the binomial formula to find the coefficient of the term in the expansion of. ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 15/23

16 Math 11 Final Exam Review Part 3 #1 Answers for class College Algebra / Math 11 RCC Fall 2011 # Desktop: Laptop: 3. Rate of the cyclist in still air: Rate of the wind: Solution: 6. L1: L2: ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 16/23

17 This system of equations is: - inconsistent This means the system has: - no solution L1: L2: This system of equations is: - consistent independent This means the system has: - a unique solution: Solution: L1: L2: ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 17/23

18 This system of equations is: - consistent dependent This means the system has: - infinitely many solutions 7. First storm: hours Second storm: hours First number: Second number: Third number: 10. Number of text messages Karen sent: Number of text messages Goran sent: Number of text messages Ryan sent: First number: Second number: Third number: 13. ALEKS Math 11 Final Exam Review Part 3 #1-11/30/2011 4:06:25 PM PST -Copyright 2011 UC Regents and ALEKS Corporation. P. 18/23

Midterm Review Part 1 #4

Midterm Review Part 1 #4 Intermediate Algebra / MAT135 S2014 sec 042 (Prof. Fleischner) Student Name/ID: 1. Solve for. 2. Solve for. 3. A Web music store offers two versions of a popular song. The size