## Final Exam - Study Guide

1. Find the intersection and union of two sets.
2. Solve an equation involving absolute value.
3. Solve a story problem (coin) with one variable.
4. Expand an expression.
5. Factor an expression.
6. Factor an expression.
7. Solve an equation. Pay attention to those with x^3.
8. Solve a geometry problem (Know Pythagorean theorem).
9. Divide two rational expressions.
10. Simplify a compound fraction.
11. Solve a rational equation.
12. Solve a work problem.
13. Find the equation of a line passing through a point and having a given slope.
14. Find the equation of a line passing through two points.
15. Solve a variation problem.
16. Simplify an expression involving rational exponents.
18. Solve a quadratic by completing the square.
19. Graph a linear inequality.
20. Graph a non-linear inequality.
21. Solve a rational equation.
22. Determine the equation that has the given solutions.
25. Solve using substitution.
26. Evaluate a 3x3 determinant.
27. Solve a 2x2 system of equations using Cramer's Rule.
28. State the domain and range of the given relation and indicate whether or not it is also a function.
29. Evaluate a function at a specific value.
30. Find the inverse of a function.
31. Write the equation of a circle with given center and radius.
32. Simplify a logarithm.
33. Graph a conic section (ellipse or hyperbola).
34. Complete the square and then give the center and radius of a circle.
35. Graph a logarithmic and exponential curve on the same axes.
36. Solve an exponential equation. Leave answers in terms of logs, do not use the calculator.
37. Rewrite a single logarithm as the sum, difference, and multiples of simple logarithms.
38. Rewrite the sum, difference, and multiples of simple logarithms as a single logarithm.
39. Give the domain, range, and equation for a relation by looking at the graph. Concentrate on ellipses and hyperbolas.
40. Find the vertex, x-intercept, y-intercept, and axis of symmetry for a parabola. Then sketch the parabola
The testing time will be broken up as follows.
• 10:00 - 11:00 alone, no notes.
• 11:00 - 11:30 alone with notes.
• 11:30 - 11:50 either continue to work alone and use notes, or surrender notes and work with up to two other persons. If you get into a group, you cannot later decide to exit the group and go back to your notes.