# Math 1010-3 Exam #3 Review Guide

***This is only a guide, for your benefit, and it in no
way replaces class notes, homework, or studying***

**General Tips for Studying:**

1. Review this guide, class notes, the text, and rework examples done in class

2. Review comments on quizzes and rework ALL quiz problems

3. Review (assuming you have already completed it) ALL homework assigned for
6.69.2

4. Complete ALL suggested problems for the exam review given in class

5. Start studying early enough to ask questions!

Chapter 6: Rational Expressions, Equations, and Functions

6.6 Solving Rational Equations** (This WILL be
on the Exam):**

• Be able to solve rational equations with constant or variable denominators

• Remember! The first step is to multiply each term by the LCD of ALL fractions
involved

(NOT the LCD/LCD)

We are not trying to get a common denominator, we are trying to eliminate all

denominators (so the resulting equation is either linear or quadratic)

• Remember! You MUST check for extraneous solutions. In these problems, that
means we

must check if our answer(s) give a zero denominator in the ORIGINAL equation. If
an

answer does, then it is not a solution of the equation.

Chapter 7: Radicals and Complex Numbers

7.1 Radicals and Rational Exponents:

• Know how to evaluate the nth roots of numbers and evaluate radical expressions

Remember! In this book we usually use the principle square root (the nth root

that has the same sign as the radicand)

• Know properties 1 and 2 on page 447 (Because we covered 7.6, we can now take
even

roots of negative numbers, so rule 3 no longer applies)

• Know properties 1 and 2 on page 448 (Remember the absolute value if n is
even!)

a

If n is odd, then
. If n is even, then

• Understand how to change exponents to radicals and radicals to exponents

AND

Remember! Either method gives you the same result, but sometimes one is easier

to compute than the other

• Be able to use our previous exponent rules (see table page 449) with rational
exponents

• Be able to find the domain of a radical function

If n is odd, the domain of
is all real numbers

If n is even, the domain of
is the set of all nonnegative real
numbers

(we must still restrict this because we only plug in real numbers)

7.2 Simplifying Radical Expressions:

• Use the product and quotient rules to simplify radical expressions

If the nth roots of u and v are real, then

AND

• Be able to rationalize the denominators (to remove any radicals) of radical
expressions

7.3 Adding and Subtracting Radical Expressions:

• Be able to combine like radical terms to add or subtract radical expressions

7.4 Multiplying and Dividing Radical Expressions:

• Know how to use the distributive property and FOIL to multiply radical
expressions

• Know what conjugates are and be able to use conjugates to rationalize two term

denominators of radical expressions

The idea here is that
so our middle term cancels out

7.5 Radical Equations and Applications **(This WILL be on the Exam)**:

• Be able to solve radical equations

** For single radical equations:** isolate the radical and then raise each side of
the

equation to the appropriate nth power (2 for square roots, 3 for cube roots).

Then, solve the resulting equation.

**For multiple radical equations: **try to isolate a radical on each side, then
follow

the steps as above. If you cannot isolate the radicals then raise each side to
the

nth power, but notice that there will be a radical in the resulting equation.
You

must then isolate this new radical and do the process again.

• Remember! You MUST check for extraneous solutions. In these types of problems,

extraneous solutions are ones that simply do not solve the ORIGINAL equation.
Raising

to the nth power sometimes introduces these extra "solutions."

ALWAYS check the solutions in the original equation, do NOT raise both sides
to

the nth power while you are checking!!!

7.6 Complex Numbers:

• Be able to write numbers in i-form

and perform operations with these numbers

so that

This means that

• Know how to add, subtract, and multiply complex numbers

• Understand what complex conjugates are and be able to use them to write the
quotient

of two complex numbers in standard form

(pay special attention the the + sign here)

**
Chapter 8: Quadratic Equations, Functions, and Inequalities**

**Remember! If the directions of a problem ask you to use a certain method, you MUST use that

method or you will receive no credit.**

8.1 Solving Quadratic Equations: Factoring and Special Forms:

• Solve quadratic equations by factoring (already tested on Exam 2)

• Solve quadratic equations by using the Square Root Property (both real and complex)

If u

^{2}=d where d>0 then and

If u

^{2}=d where d<0 then and

8.2 Completing the Square:

• Rewrite quadratic expressions in completed square form and be able to solve quadratic

equations by completing the square

To complete the square for add

Note that

Remember! If the leading coefficient is NOT 1, you must make it one by dividing

the entire equation by that coefficient BEFORE completing the square

8.3 The Quadratic Formula:

• Use the quadratic formula to solve quadratic equations

The solutions of
are given by

Remember! If
the equation has 2 real solutions. If b^{2}−4ac=0 the

equation has one repeated real solution. If the equation has no real

solutions (two complex solutions)

8.4 Graphs of Quadratic Functions (See my handout from class):

• Be able to sketch parabolas, , using the following
information:

The vertex of a parabola is (You can complete the square to find

the vertex, but I suggest memorizing this formula)

The parabola opens up if
and down if

The x intercept(s) (let y=0 and solve for x) and the y intercept (let x=0 and
solve

for y...notice this always gives you y=c) (You can just plug in random points,
but I

suggest the intercepts...they are easy to find and graph)

**Chapter 9:Exponential and Logarithmic Functions
**

9.1 Exponential Functions:

• Be able to evaluate exponential functions

• Know how to build a table of values to graph exponential functions

• Know how to use transformations and reflections to graph exponential functions

•

**Note :**On the exam you will only be required to simplify as much as possible without a

calculator, you will not be expected to get decimal approximations. Numbers will be

reasonable to work with without a calculator.

9.2 Composite and Inverse Functions:

• Understand function composition:

This is read f“ of g of x”

Remember! Function composition is NOT multiplication!

•

**Note :**Finding inverse functions will be covered on Quiz 10 and the Final Exam

Just a Reminder...

Just a Reminder...

You are responsible for knowing and applying all material covered on Exam 1 and Exam 2

as it relates to the current material being tested.