math 11 final exam review part 3 #1 -...

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

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.


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," "consistentindependent," or "inconsistent." Then, answer the question about its solutions.

L1:


L2:

This system of equations is:

- consistent dependent - consistent independent - inconsistent

This means the system has:

- a unique solution:

Solution: - no solution - infinitely many solutions

L1:

L2:






L1:

L2:







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?


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?


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?



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


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 theserequirements.

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?


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.


21. Graph the inequality.

22. Evaluate.

Simplify your answer as much as possible.


23. Find the first four terms of the sequence given by the following.

24. Evaluate.


25. Evaluate.






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 arithmeticsequence.)

(a)

(b)


(a)

(b)


(a)


(b)


st term, , is equal to , and the

th term, , is equal to

.

Find the value of the th

term, .


th term, , is equal to , and the



term, .


st term, , is equal to , and the


.


term, .

36. Compute each sum below. If applicable, write your answer as a fraction.

(a)

(b)


37. Compute each sum below. If applicable, write your answer as a fraction.

(a)

(b)

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




term, . If applicable, write your answer as a fraction.

40. For a given geometric sequence, the



. 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".


(a)

(b)

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?


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?

(b) 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?

(b) 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.


Use the binomial formula to find the coefficient of the term in the expansion of .







Math 11 Final Exam Review Part 3 #1 Answers for class College Algebra / Math

11 RCC Fall 2011 – #48794

1.

2. Desktop:

Laptop:

3. Rate of the cyclist in still air:

Rate of the wind:

4.

5.

Solution:

6.

L1:

L2:



- inconsistent


- no solution

L1:

L2:


- consistent independent



Solution:

L1:

L2:



- consistent dependent


- infinitely many solutions

7. First storm: hours

Second storm: hours

8.

9. 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:

11.

12. First number:

Second number:

Third number:

13.


14.

15.

16.

17. Type A feed: bag(s)

Type B feed: bag(s)

18.

19.


20.

21.

22.

23.

, , ,

24.


25.

26. , , ,

27.

, , ,

28.

, , ,

29.

30. (a)

(b) .

31. (a)

(b) .

32. (a)

(b) .

33.

34.

35.

36.

(a)


(b) .

37.

(a)

(b) .

38.

39.

40.

41.

(a)

(b) No sum

42.

43. (a)

(b)

44. (a)

(b)


45. (a)

(b)

46.

47. (a)

(b)

48. (a)

(b)

49. (a)

(b)

50.

51.

52.

53.

54.

55.

56.

math 11 final exam review part 3 #1 -...

Documents