In addition to studying this review packet, you should
also go over the review sheets for
the first and second midterms, and old quizzes and midterms. Then you should go
over notes
and homework problems. If you get that far, you should take a quick break, and
then do it all
again!
Below is a list of topics required by the UO Math
department to be covered on the Final Exam.
• The definition of absolute value and/or absolute
value equations
• Solving Quadratics
• Circles
• Lines
• The definition of a function
• Finding the domain of a function
• The difference quotient
• Drawing graphs and/or graph reading
• Graph transformations
• Even and odd functions
• Function composition
• Inverse functions
• Finding the domain of a composite and/or inverse function
• Roots /factors of polynomials
• Rational functions
• Definitions and properties of logarithms and exponents
• Solving equations for a variable in the exponent
• Solving logarithmic equations
• Word problems
Chapter 1
Make sure that you understand the definition of absolute
value (remember, we had two definitions of
absolute value). Interval notation is important, though there will not be any
questions explicitly on interval
notation.
1. True/False.
2. True/False.
has two solutions.
1.2: Solving Equations Algebraically and 1.2A, Solving
Absolute Value Equations, 1.2B Variation
From 1.2: Completing the square is crucial - you need to
be able to do this in your sleep. You should
be able to solve a quadratic equation using the quadratic formula as well. You
should know the
discriminant and how to use it.
3. Solve x^2 + x = 4 by completing the square
4. For what values of m will the equation 3x^2 + mx + 5 =
0 have exactly one solution?
From 1.2A: Solving simple absolute value equations - don’t
forget to check your answers!
5. Solve |3x + 2| = x + 1 for x.
The most important topics from this section are circles
and x- and y-intercepts. You should know the
midpoint formula and distance formula too, though.
6. Find the center and radius of the following circle.
7. True/False. The radius of the circle given by the
equation
is 7.
1.4: Lines
You need to know the slope- intercept form , the point-slope
form, the formulas for vertical and horizontal
lines, how to determine whether two lines are perpendicular or parallel, and how
to determine an
equation for a line given particular data.
8. Find the equation of a line perpendicular to the line
3x + 8y = 4 and through the point (3, 1).
9. True/False. The lines x = 2 and y = 0 are perpendicular
Chapter 2
2.3: Applications of Equations
10. A 10 gallon radiator is filled with a solution that is
65% radiator fluid. How much of this solution
should be drained and replaced with a solution that is 95% radiator fluid so
that the resulting solution
in the radiator is 80% radiator fluid?
