Semester 1 Final ReviewDec. 2014
College Algebra (DC)
Integer/Rational Exponents:
1. Simplify: 2. Simplify:
Radical Expressions: (Assume all variables are nonnegative.)
3. Simplify. 4. Simplify:
Polynomials: Perform the indicated operation and simplify.
5. 6.
Factoring: Factor each polynomial completely.
7. 8. 9.
10. 11.12.
Rational Expressions: Perform the indicated operation and simplify. Also, state all numbers which must be excluded from the domain.
13. 14.
15. 16.
Linear Equations: Solve for x.
17. 18.
Rational Equations: Solve for x. Check that the solution is not excluded from the domain.
19. 20.
Models and Applications:
21. Solve for h. 22. Solve for r.
23. A car rental agency charges $225 per week plus $0.20 per mile to rent a car. How many miles can you travel in one week for $245?
24. You inherit $10,000 with the stipulation that for the first year the money must be invested in two stocks paying 6% and 11% annual interest, respectively. How much should be invested at each rate if the total interest earned for the year is to be $700?
25. Inclusive of a 6.8% sales tax, a diamond ring sold for $2029.20. Find the price of the ring before the tax was added.
26. The president of a certain university makes three times as much money as one of the department heads. If the total of their salaries is $270,000, find each worker’s salary.
Complex Numbers: Perform the indicated operation and simplify.
27. 28.
29. 30.
Quadratic Equations:
31. Solve by factoring.
32. Solve using the square root property.
33. Solve using quadratic formula.
34. Use the discriminant to determine the number and type of solutions.
Polynomial Equations: Solve for x.
35. 36.
Radical Equations: Solve.
37. 38.
Equations with Rational Exponents: Solve.
39. 40.
Absolute Value Equations: Solve.
41. 42.
Linear and Absolute Value Inequalities: Solve. Graph the solution set on a number line and write it in interval notation.
43.
44. A certain store has a fax machine available for use by its customers. The store charges $2.25 to send the first page and $0.60 for each subsequent page. Use an inequality to find the number of pages that can be faxed for $5.25.
45. 46.
47. 48.
Functions and Function Notation:
49. If , then
50. If , then
Determine whether the graph represents y as a function of x.
51. 52.
Determine the domain and range of the function.
53. 54.
55. Find the intervals on which the function is increasing, decreasing, and constant. Also, find (estimate), the zerosrelative maximums, and relative minimums.
56. Let . Find and sketch the graph.
Determine whether the functions are even, odd, or neither.
57. 58.
Slope and Equations of Lines:
59. Find the equation of the line passing through and . Write the answer in slope intercept form and sketch the graph.
60. Sketch the graph of the lines and . Be sure to label each of them.
61. Find the slope and y-intercept of the graph of the equation. Also, sketch the graph.
62. Find an equation of the line passing through the point and parallel to the line whose equation is . Write the answer in slope-intercept form and standard form.
63. Find an equation of the line passing through the point and perpendicular to the line whose equation is . Write the answer in slope-intercept form and standard form.