MATH 0406 Review for Final Exam
1. Simplify.
13  3(2)4
3  (6  10)
2. Find the perimeter of the following rectangle.
x4
x
3. Find the length of the missing side of the right triangle. (Round to the nearest tenth.)
x
36 cm
45 cm
4. 50% of what number is 60?
5. Solve. 12  5 x  6( x  2)
6. Solve. 2( x  2)  5 x  17
7
3
7. Solve. x  2  x
8
4
8. Solve.
x
x
2 4
3
5
9. Solve for x.
x
9

14 21
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10. Solve for x.
5 15

12 x
11. Solve for z. PR 
x yz
w
12. Graph the points on the grid. (–4, 6), (5, 0), (0, –7), (8, –4)
Is this relation a function?
y
x
13. There are 76 milligrams of cholesterol in a 3.4 ounce serving of lobster. How much
cholesterol is in 7 ounce serving of lobster?
A. 156.5 milligrams
D. 20.3 milligrams
B. 155 milligrams
E. 532 milligrams
C. 36.9 milligrams
14. The standard dose of medicine for a cat is 2 grams for every 15 pounds of body weight.
What is the standard dose for a cat that weighs 20 pounds?
15. Solve the inequality and write your solution in interval notation.
x  6  2( x  1)
16. Solve the inequality and write your solution in interval notation. 7 x 15  13x  51
17.A gallon of paint covers 400 square feet. How many gallons of paint will be needed to cover
the side of a building that measures 120 feet by 80 feet?
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18. 95% of 400 is what number?
19. 15% of what number is 90?
20. Before taking a typing course, Jana could type 36 words per minute. By the end of the
course she was able to type 97 words per minute. Find the percent of increase. Round to the
nearest tenth of a percent.
21. After 8 months, Joellen has lost 75 pounds. This is a 30% decrease in her starting weight.
Find her starting weight.
22. If
A = {11, 12, 13, 14, 15, 17, 19, 20}, B = {13, 15, 16, 17}, then
a. List the elements of A B
b. List the elements of A∩B
Translate each sentence to an equation. Then solve the equation.
23. Fifteen subtracted from a number is –23.
24. Twice the difference of a number and 7 is equal to –8.
25. Evaluate 5 x 2  x  1 for x  2 .
26. Evaluate
2x  y
for x  3 , y  1 and z  4 .
3z
27. Evaluate if x = –2, y = 3, and z = –6.
A)
3x  2 y  z 2
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B)
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28. The difference of three times a number and five times the same number is four. Find the
number.
29. During a 258 mile trip, a car used 10.75 gallons of gas. How many miles would we expect
the car to travel on 1 gallon of gas?
30. Find the slope of the line passing through  3,  1 and  4, 2  .
31. State the slope of a line perpendicular to the line 2 x  5 y  8 .
2
5
2
5
8
A) 
B) 
C)
D)
E) 
5
2
5
2
5
32. For the graph:


a. state the
coordinates
of the y- intercept
b. state the slope
y
a _______________________


b________________________
x










c________________________

c. find the domain
d. find the range
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d________________________


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33. a. Graph x  3
b. Graph y  2
y

y







x








x
















34. Solve the system of equations by graphing
y

2 x  3 y  6

2

 y   3 x  2



x














Solve the following systems of equations.
5 y  12  x
35. 
2 x  10 y  5
4 x  3 y  1
36. 
3x  5 y  13
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



37. Write the systems of equations. Then solve.
Retail orders. The St. Andrew’s Community Barbecue served 175 dinners. A child’s
plate cost$3.50 and an adult plate cost $7.00. A total of $875 was collected. How many of each
type of plate were sold?
Equations: _______________
_______________
Solutions: _______________


38. Simplify. 7 p 8  2 p 2

39. Simplify. 4b 
0
40. Combine Like Terms. 7r  12r 6  3r 6  12r
41. Subtract. (16 x  9)  (6 x 2  8x  9)
42. Multiply. (5 p  2)(5 p  2)
2 p 4
43. Simplify. Write with positive exponents.
3 p9
44. Divide.
 9 x 5  3x 4  12
3x 3
45. Divide.
x 2  15 x  56
x 8
46. Factor Completely. 5x 2  20 x
47. Factor Completely. 2x 3  4x 2  6x  12
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48. Factor Completely: t 2  14t  48
49. Find the vertex of the quadratic function. f ( x)  x 2  12 x  2
50. If the sides of a square are increased by 2 meters, the area becomes 25 square meters. Find
the length of a side of the original square.
A) 3m
B) 7 m
C) 2m
D) 5m
E) 4m
51.
Identify the function values from the graph.

a) f  3 
y


b) f  0  


  


x






52. Solve. t 2  13t  30 = 0
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MATH 0406 Review
**Answer Key**
1. -5
16.
2. 4x-8
3. 57.6
17. 24 gallons
4. 120
18. 380
5. x = 0
19. 600
6. x = -7
20. 169.4%
7. x = -16
21. 250 lbs.
8. x = 15
22. a.
b.
9. x = 6
10. x = 36
23
11. z  PRw  x
y
12. Yes, it is a function.
24.
25. 23
26.
27. a. -36
b. -19
13. A
28. -2
14.
29. 24 miles
15.
30.
31.
32. a. (0,1)
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b.
43.
c.
44.
d.
45.
33. a.





    




46.
y
47.
48.
49. (-6,-38)
x
    
50. A.
51. a. 1
b. -2
52. 3,10
b.





    




34.
y
x
    
 x, y  | 2x  3 y  6
35. No solution
36. (4,-5)
37.
100 child plates and 75 adult plates
38.
39. 1
40.
41.
42.
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