Math 125 Review Final Exam
1. Solve:
a.
x 6  9
b. 2 x  3  6  24
2. Solve the following inequalities. Write your answer in interval notation.
a. x 2  7 x  30
b. 2x 2  7 x  4
3. Factor completely: 3 x 2  5ax  3 xy  5ay
4. Divide 3 x 3  10 x 2  9 x  4 by x  2 using the long division. State the quotient and the remainder
clearly.
5. Subtract. Simplify if possible.
9
2

x x x
2
3
5
6. Simplify:
 32
7. Evaluate:
3 45  2 20  80
8. Solve: a.

x  8  16
b.
x 8  x  2
9. Solve the linear system by any method.
 x  2y  3z  11

 2x  3y  z  7
3 x  5 y  7z  14

10. Solve:
a. 23 x 1  16 .
b. log7 x  2 .
11. Solve: log2 x +log2 (x  4) = 5
f (a  h )  f (a )
. Simplify you answer.
h
13.Use completing the square to write the equation f ( x )  x 2  2x  1 in the form
12.If f ( x )  x 2  2x  1 , find
f ( x )  a  x  h   k and sketch the graph.
2
14. If f ( x )  3 x  5 and g ( x ) 
a. find f ( 3)
x6 ,
b. find  g f  ( x )
c. find f 1( x )
15. A box contains $7.80 in nickels, dimes, and quarters. There are 6 more dimes than nickels and
three times as many quarters as nickels. Find the number of quarters.
1
16. Divide and write your answer in (a + bi) form:
3
2i
17. Graph the solution set on the grid below:
y  2x  1


2
 y  3 x  3
18. Graph
x2
 y2  1
9
19. Use completing the square to write x 2  4 x  y 2  6y  4  0 in standard form. Then graph.
20. Does the function y  2x 2  5 have a maximum or minimum value? __________________
What is that value? __________
21. Graph f  x  
x  1  2 using the transformation. Describe how the graph can be obtained
from the graph of the generic curve.
22. Given the two points:  3,  2 and
5,  6 , find the distance between the two points. (simplify your
radical)
23. Determine log5 632 to four decimal places.
24. Write the equation of the line through the two points in standard form ( Ax  By  C ).
25. Suppose that the present population of a city is 50,000. Use the equation P (t )  P0 e 0.02t , where P0
represents an initial population, to answer the following questions.
26. Find P (20) . Round your answer to the nearest whole number.
27. Find how many years it will take a population of 50,000 to double itself? Express the answer to the
nearest tenth of a year.
28. Evaluate the functions below. Simplify your answers.
a. Let f ( x )  x  7 . Find f (32).
b. Let f ( x )  2x  3 . Find f ( -15).
29. Find the domain for each function.
a.  1,4  ,  2,7 


1
5x
c. f ( x )  x  3
b. f ( x ) 
2
30. Let f ( x )  x 2  2 and g ( x )  x  1.
a. Find the difference function (f – g)(x).
b. Find the composition function (f g)(x). [This is the same as f (g(x)) .]
31. Find the inverse function f 1( x ) for:
b. f ( x )  3 x
a. f ( x )  2 x  3
32. Simplify. Variables represent non-negative real numbers.
a
3
b
24
33. Rationalize the denominator:
3
12x 6
4
x
34. Evaluate the following logarithms:
 1 

 100 
a. log2 8
b. log 
35. Solve using the quadratic formula:
3x 2  8x  2  0
36. Find all real solutions: x 4  6 x 2  8  0
37. Use row operations (matrix) to solve the system.
xy z 2
x  y  2z  3
2x  y  z  7
38. Write your solution set in interval notation:
39. Graph f  x  
x 5  2
x 3
40. Graph f  x   x  1
41. Graph f ( x )  ( x  3)2  2
42.Graph f ( x )  2x and g ( x )  log2 x on the same grid below.
3
43. Graph 4 x 2  9y 2  36
44.Use completing the square to write x 2  4 x  y 2  6y  4  0 in standard form. Then graph.
45.Two trains leave the same depot at the same time, one traveling east and the other traveling west. At the
end of 4 1 hours, they are 639 miles apart. If the rate of the train traveling east is 10 miles per hour
2
greater than that of the other train, find their rates. ( Hint: Rate Time = Distance)
46.How long will it take $100 to triple itself if it is invested at 8% interest compounded continuously?
( Hint: A  pe rt )
 x 2  y 2  29
47. Solve 
. Sketch the graphs in the same grid.
x  y  3
48. Simplify the expression using the properties of exponents. Answer with positive exponents.
 3x 3 y 
 3 
 y 
49. Solve
3
x3
0
x5
50. Solve the linear equation
 2  4 8n  1   5n  3  5
4