Download Comprehensive Review Show All Your Work! 1. Evaluate the

Comprehensive Review
Show All Your Work!
1. Evaluate the following expressions: a.
9  8  2  14
(10  6) 2  4
b. (3x) 2  8x when x  3.
Simplify.
3.  4 x 2  3x  8  7 x  6 x 2  13  x
4.
 2(3x  5)  x(4 x  3)  9  x 2
5. Calculate the simple interest on $200 that was invested at an annual interest rate of 2.5% for
3 years.
Order the following numbers and expressions from least to greatest.
1
23
6. 8 , 2.75,  3.2 , 3 , 2.7,
8
11
7. Solve:
3
y  12  0
11
8. Solve: 5n – 2(n – 2) = –11+ 4n
9. Solve:
2 y  16
5
2
10. The triangle below has a perimeter of 20. Solve for x.
9
11. The Fahrenheit and Celsius scales are related by the equation F  C  32 . What temperature Celsius
5
would give the body Temperature of 41 o F?
12. Solve. 4x = –2(–2x + 3)
For exercises 13- 16. write and solve an equation for each problem.
13. What is the length of a rectangular solid if the volume is 480m3, the width is 5m, and the
height is 12m?
14. A parking garage charges $3 plus $1.50 per hour. You have $12 to spend for parking. Find the number of
hours that you can park. (hint let x = number of hours parked)
15. Three consecutive integers have a sum of 228. What are the three integers?
16. The mean of 5 numbers is 84. Four of the numbers are 90, 73, 92, and 80. What is the 5th number?
17. Write the equation that describes the function containing all the points shown
in the table.
Input (x)
Output (y)
0
7
1
15
2
23
3
31
4
39
5
47
18. In 2001, a video store had 23,500 rentals. In 2007, the store had 28,540 rentals. Find the average rate of
change of the store’s rentals in rentals per year.
19. What is the y-intercept of 3x + 2y = 21?
20. What is the equation of the line shown?
21. Given 3x + 4y = -12. What is the slope of the line parallel to the graph of this equation?
22. Graph the equation using Slope-Intercept Form:
4x + 2y = 8
Find the slope of the line with the following points:
23. (2, -4) & (5, 6)
24. Evaluate the following when f(x) = x2 + 7x – 1 and g(x) =
a) f(-4)
b) g(3)
1
x–6
2
25. Is this a function? How do you know?
26. Use the following table to help you answer the questions below.
x
y
a) Is this a function?
1
1
3
4
6
–2
b) State the domain.
8
0
c) State the range.
27. Given the following arithmetic sequence 32, 47, 62, 77,…
a) What is the common difference? ______
b) List the next three terms. _______________________
c) Write an equation for the nth term ______________________
d) Determine
_______
e) Which term of the arithmetic sequence is 467?
28. Find the second, fourth and eleventh terms of the sequence:
Write an equation in slope-intercept form of the line that passes through the point and has the given slope.
29.
(1, -3) m = -4
Write an equation in slope-intercept form of the line that passes through the given points.
30.
(5, 3), (4, -3)
31. Write an equation that is written correctly in point-slope form that passes through the given point (4, -2)
and slope = -3.
32. Rewrite the following equation given in Standard Form into Slope-Intercept Form:
3x + 4y = -12
33. Write an equation that has a graph that is parallel to the graph of y = 3x + 4 and would pass through the
point (-2, 5)?
34. What is the slope of a line that would be perpendicular to the graph that passes through the following points
(9, -2) and (1, 2)?
Use any method to solve each linear system.
35.
2x + 3y = 31
y=x+7
37.
y = -2x + 3
y=x-3
36.
m + 2n = 1
5m + 3n = -23
Write a system of linear equations for each of the following word problems. Then solve the linear system
to find the solution to the problems. Make sure to state your solution.
38. A shoe store sold 28 pairs of cross-trainer shoes for a total of $2220. Style A sold for $70 per pair and
Style B sold for $90 per pair. How many of each style were sold?
39. Jen and Lori left on a motorcycle trip along the same route across the U.S.A. from Florida to California.
Jen got a 63 mile head start and averaged 70 miles per hour. Lori averaged 76 miles per hour. If their breaks
were equal in time, how long will it take for Lori to catch Jen?
Graph the following systems of inequalities.
40.
y  x5
yx
41.
y6
y  2x  2
42. At what point do the lines 2x – 4y = 6 and 3x +4y = 4 intersect?
43. In the system of linear equations, if -x + y = 5 and x +y = 17, then xy = _______?
44. Which system of linear equations would not have a solution?
a. y = 4x – 5
y = 2x + 3
b. 8x + y = 19
2y – 16x = 10
c. y = 12 - 2x
y + 2x = -13
d. -4x + y = 5
3y + 12x = 7
SOLVE.
45.
 7  3x  11  2
49. x  12  18
46. 4  10 x  24
47. x  21
48.  1  x  4  18
50. 15  2 x  8  25
Write an inequality for each of the following. THEN, graph each inequality on a number line.
51. All real numbers less than 8.
52. All real numbers greater than or equal to 15 and less than 32.
Solve the following.
53. A car rental company charges an initial fee of $50 plus $0.20 per mile to rent a car.
a. Write and solve an inequality that represents the possible number of miles
that a person could drive the car for $130.
b. What is the maximum number of miles that could be driven?
54. Starting a home business can be quite expensive. The costs for running a certain business are $5000 for
equipment and $8.50 for materials to make each item that is sold. The revenue made from each item sold is
$10.50. Write an inequality to represent the least number of items that must be sold in order to generate profit
for the business.
Simplify
55. (2 x y)
4
 10 x 3 y 2
59. 
4 7
 5x y
 x2 y8 
57.  10 
 xy 
56. (4 x y )  (3xy )
2
2



3 2
5 2
2
60.
5x 2 y 4 x 2 y 3

3xy 2 7 x 4 y 2
Write the following in scientific notation.
61. 98,000,000
62. 0.000000478
Write the following in decimal form.
64. 6.12  10 3
63. 3.53  10 4
Simplify the following. Answers must be in scientific notation.

65. (4.2  10 )  3  10
4
6

1
15  10 9
66.
0.3  1015
58.
5x 3 y 4  10 x 5 y 6