Study Guide - Final 2

Math 098

1. Match the definition, property, or theorem with the statement described. You should know the following terms (15 of these are on the exam). Absolute value, Associative property, Chord, Circle, Closure property, Commutative property, Contrapositive, Converse, Degree, Determinant, Diameter, Discriminant, Ellipse, Function, Fundamental Theorem of Arithmetic, Greatest common factor, Hyperbola, Identity property, Intersection, Inverse, Inverse property, Least common multiple, One-to-one function, Parabola, Pythagorean theorem, Radius, Relation, Secant line, Slope, Squaring property of equality, Tangent line, Union. Matching, 15 parts.
2. Sketch a line with each of the four possible types of slope (0, undefined, positive, and negative).
3. Complete the mathematical sentence in its melodic form. Concentrate on the properties of radicals and logarithms. Fill in the blank, 6 parts.
4. Finish the eight properties of logarithms. Half of the property is given.
5. Explain the ac method of factoring. Are there two factors of ______ whose ______ is ______?. Fill in the blanks, 2 parts.
6. List the steps to factoring polynomials.
7. When is completing the square the nicest? When is it necessary to complete the square vs just extracting the roots?
8. Use synthetic division to evaluate a polynomial function.
9. Complete the square to put an ellipse into standard form.
10. Use Cramer's rule to solve a 2x2 system of linear equations.
11. Solve and graph a rational inequality.
12. Solve a logarithmic equation for a variable in the exponent. Concentrate on the formula for compound interest.
13. Use Tartaglia's formula to solve a cubic equation. Tartaglia's formula is given on the test. This is a question to make sure you can work your calculator. Review the challenge problem on page 433.
14. Find the equation of the perpendicular bisector between two points. This involves four steps: Finding the midpoint between two points (section 9.1), finding the slope between the points (section 2.2), finding the slope of the perpendicular line (opposite reciprocal) (section 2.2), and finding the equation of the line passing through a given point (the midpoint) with the given slope (of the perpendicular line) (section 2.3).
15. Use your calculator to evaluate an exponential (involving base e) function. This is a logistics function, but you don't need to worry about that. Just be able to evaluate a function using the e^x key on your calculator.