Math 125 Review Final Exam
1. Solve: a. b.
2. Solve the following inequalities. Write your answer in interval notation.
a. b.
3. Factor completely:
4. Divide by using the long division. State the quotient and the remainder
clearly.
5. Subtract. Simplify if possible.
6. Simplify:
7. Evaluate:
8. Solve: a. b.
9. Solve the linear system by any method.
10. Solve: a. .
b. .
11. Solve:
12.If , find . Simplify you answer.
13.Use completing the square to write the equation in the form
and sketch the graph.
14. If ,
a. find
b. find
c. find
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.
16. Divide and write your answer in (a + bi) form:
17. Graph the solution set on the grid below:
18. Graph
19. Use completing the square to write in standard form. Then graph.
20. Does the function have a maximum or minimum value? ______
What is that value? ______
21. Graph using the transformation. Describe how the graph can be obtained
from the graph of the generic curve.
22. Given the two points: , find the distance between the two points. (simplify your radical)
23. Determine to four decimal places.
24. Write the equation of the line through the two points in standard form ().
25. Suppose that the present population of a city is 50,000. Use the equation , where
represents an initial population, to answer the following questions.
26. Find . 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 . Find f (32).
b. Let . Find f ( -15).
29. Find the domain for each function.
a.
b.
c.
30. Let .
a. Find the difference function (f – g)(x).
b. Find the composition function (fg)(x). [This is the same as f (g(x)) .]
31. Find the inverse function for:
a. b.
32. Simplify. Variables represent non-negative real numbers.
a b
33. Rationalize the denominator:
34. Evaluate the following logarithms:
a. b.
35. Solve using the quadratic formula:
36. Find all real solutions:
37. Use row operations (matrix) to solve the system.
38. Write your solution set in interval notation:
39. Graph
40. Graph
41. Graph
42.Graph on the same grid below.
43. Graph
44.Use completing the square to write 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 hours, they are 639 miles apart. If the rate of the train traveling east is 10 miles per hour greater than that of the other train, find their rates. ( Hint: RateTime = Distance)
46.How long will it take $100 to triple itself if it is invested at 8% interest compounded continuously?
( Hint: )
47. Solve . Sketch the graphs in the same grid.
48. Simplify the expression using the properties of exponents. Answer with positive exponents.
49. Solve
50. Solve the linear equation
4