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

ALEKS Math 11 Final Exam Review Part 1 #1 - 11/30/2011 3:50:14 PM PST -Copyright © 2011 UC Regents and ALEKS Corporation. P. 1/29

Math 11 Final Exam Review Part 1 #1

College Algebra / Math 11 RCC Fall 2011 – #48794 (Prof. Chiek)

Student Name/ID:

1. Two trains leave stations miles apart at the same time and travel toward each other. One train travels at

miles per hour while the other travels at miles per hour. How long will it take for the two trains to meet?

Do not do any rounding.

hours

2. Solve the following equation for .

3. Solve for .

Simplify your answer as much as possible.

4. Rueben rented a truck for one day. There was a base fee of , and there was an additional charge of

cents for each mile driven. Rueben had to pay when he returned the truck. For how many miles did he

drive the truck?

5. Solve the inequality for .



6. Solve the inequality for .


7. Keith is going to rent a truck for one day. There are two companies he can choose from, and they have the followingprices.

Company A has no initial fee but charges cents for every mile driven.

Company B charges an initial fee of and an additional cents for every mile driven.

For what mileages will Company A charge more than Company B?

Use for the number of miles driven, and solve your inequality for .

8. Lamar has scored , , , and on his previous four tests. What score does he need on his next test so

that his average (mean) is ?

9. Multiply.

Write your answer as a complex number in standard form.

10. Simplify the complex number as much as possible.


11. Write in terms of .


12. Add.

Write your answer as a complex number in standard form.

13. Simplify the expressions below as much as possible.

Leave no negative numbers under radicals and no radicals in denominators.

14. Solve the equation

for .

15. Solve.


(If there is more than one solution, separate them with commas.)

16. Solve for .

17. Solve for .

18. A model rocket is launched with an initial upward velocity of . The rocket's height (in feet) after

seconds is given by the following.

Find all values of for which the rocket's height is feet.

Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

19. Solve for , where is a real number.


20. Solve for .

21. Solve.

If there is more than one solution, separate them with commas.

22. Solve for .


23. Using the pencil, plot the point .


24. Suppose that the relation is defined as follows.

Give the domain and range of .

Write your answers using set notation.

25. Graph the circle .

26. Graph the line.


27. Calculate the distance between the points and in the Cartesian plane.

Write the exact answer in radical form.

28. Find the -intercept and -intercept of the line given by the equation.

x-intercept

y-intercept

29. Graph the line.


30. Find the slope of the line graphed below.

31. Write equations for the horizontal and vertical lines passing through the point .

horizontal line:

vertical line:

32. Graph the line .


33. Consider the line .

What is the slope of a line perpendicular to this line?

What is the slope of a line parallel to this line?

34. A line passes through the point and has a slope of . Write an equation for this line.

35. For each scenario below, choose the graph that gives the best representation.


36. Find an equation for the line below.

37. Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in

minutes). When graphed, the function gives a line with a slope of . See the figure below.

There is in credit remaining on the card after minutes of calls. How much credit was there after

minutes of calls?

38. Suppose that the relation is defined as follows.

Give the domain and range of .

Write your answers using set notation.


39. The functions and are defined as follows.

Find and .

Simplify your answers as much as possible.

40. Pablo will rent a car for a day. The rental company offers two pricing options: Option A and Option B. For eachpricing option, cost (in dollars) depends on miles driven, as shown below.

If Pablo drives the rental car miles, which option costs more? How much more does it cost than the other

option?

a.

For what number of miles driven do the two options cost the same? If Pablo drives less than this amount, which option costs less?

b.

41.

Find the difference quotient , where , for the function below.



42. Four functions are depicted below. For each function, either the function is defined explicitly, or the entire graph ofthe function is shown.

For each, decide whether it is an even function, an odd function, or neither.

the function r

- even - odd - neither

the function s





43. Use the graph of the function below to find the following.

All values at which has a local minimum

All local minimum values of

If there is more than one answer, separate them with commas.

44. Determine the interval(s) on which the function is (strictly) increasing.

Write your answer as an interval or union of intervals.

45. The graph of a function is given below.

Give all -intercepts and -intercepts shown.


If there is more than one answer, separate them with commas.

-intercept(s):

-intercept(s):

46. The graph of is shown below.

Graph .

47. Below is the graph of .

Graph .


48. Graph the function .

49. Graph

.


50. Below is the graph of .

Translate it to make it the graph of .

51. Suppose that the function is defined , for all real numbers, as follows.

Graph the function .



Find the following.

53. Suppose that the function is defined on the interval as follows.

Graph the function .


54. Suppose that the function is defined on the interval as follows.

Find the following.


Find the following.


56. Suppose that the functions and are defined as follows.

Find and . Then, give their domains using interval notation.

Domain of :

Domain of :

57. Suppose .

Find two functions and such that .

Neither function can be the identity function.(There may be more than one correct answer.)

58. Let and be two functions defined by

for any real number .

Find and then find all values that are NOT in the domain of . If there is more than one value, separate


them with commas.

59. Suppose that the functions and are defined for all real numbers as follows.

Write the expressions for and and evaluate .

60. Suppose that the functions and are defined as follows:

.

Find the following:


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

11 RCC Fall 2011 – #48794

1. hours

2.

3.

4. miles

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

,


16. ,

17. ,

18. seconds

or seconds

19.

20.

21.

22.

23.

24. domain

range

25.


26.

27.

Distance =

28.

-intercept

-intercept

29.

30.


31. horizontal line:

vertical line:

32.

33.

34.

35.

36.

37.

38. domain

range

39.


40.

(a) If Pablo drives the rental car miles, which option costs more?

Option B

How much more does it cost than the other option?

(b) For what number of miles driven do the two options cost the same?

miles

If Pablo drives less than this amount, which option costs less?Option A

41.

42. the function r

- even

the function s


- neither

- even

- odd

43. All values at which has a local minimum: ,

All local minimum values of : ,

44.

45.

-intercept(s): ,

-intercept(s):

46.

47.


48.

49.

50.


51.

52.

53.

54.


55.

56.

Domain of :

Domain of :

57.

58.

Values that are NOT in the domain of :

59.

60.

.

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