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Final Exam Review_ Unit 1

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					    Make sure you know the
day and time of the final exam for
    this section of Math 110:
   Day: ______ Date:______
   Time: ______ to _______
   • All Math 110 finals will be given in
     your regular classroom.
   • Final exam schedules for all sections
     are posted on the bulletin board and in
     your course syllabus.
          Math 110 Final Exam:
• Comprehensive – covers the whole semester
• Worth 200 points (20% of course grade)
• 47 questions
• Test period is one hour and 50 minutes
• Practice Final is worth 10 points and also has 47 questions
  and unlimited tries.
• Your best score on the practice final will also earn up to
  20 extra credit points on the final.
• The practice final is due at the scheduled start time of this
  section’s final exam.
• IMPORTANT NOTE!!! To get access to the practice final, you
  must have submitted all four final exam review homework
  assignments and have scored at least 80% on each one.
   Final Exam Review Materials:
1. Four review homework assignments:                         These are each
    worth 10 points, vs. the usual homework assignment of 6 points.


• Unit 1 review homework (Chapters 1, 2, 3).
• Unit 2 review homework (Chapters 4, 5, 8):
                   Due today.
• Unit 3 review homework (Chapter 6):
   NOTE: You must get at least 80% on the Unit 2 Review before you can
start the Unit 3 review. Check with your teacher for due date & time.
•Unit 4 review homework (Chapter 7):
   NOTE: You must get at least 80% on the Unit 3 Review before you can
start the Unit 4 review. Check with your teacher for due date and time.
Comprehensive Practice Final:

Once you finish the Unit 4 Final Review homework with at least
an 80% score, you will have access to the practice final, with as
many attempts as you want.

The practice final is worth 10 points, plus a possible bonus of
up to 20 extra credit points on the final exam. Your best
percentage score on the practice final will earn that percent of
10 points toward your course grade, plus that best score percent
times 20 extra credit points will be added on to your final exam
point score before partial credit points are added.

This makes it extremely important for you to make sure you work
to get at least 80% on each of the four final exam review
homework assignments so that you can get access to the
practice final.
 Math TLC Open Lab Hours:
     Room 203 Jarvis Hall Science Wing
Regular hours through last day of classes
          (8:00 AM – 7:30 PM)
    Finals week open lab hours:
        Check bulletin boards
        in JHSW 214 and 203
Now please
CLOSE
YOUR LAPTOPS
and turn off and put
away your cell phones.
Any questions on the Unit 2
   Review Homework?
Final Exam Review,
    Units 3 & 4
Units 3 & 4 Cover:
Chapter 6
 (Rational expressions)
Chapter 7
(Radicals, rational exponents, rationalizing radical
denominators)
          Unit 3:Chapter 6
             (Rational Expressions)
Don’t forget to review the application
 problems from section 6.6 homework and
 your work on the offline worksheet.
(Remember those fun problems about planes and cars, and three
   people doing a job at different rates?)
These were a common source of trouble for many
  students in previous semesters, so make sure
  you study the application problems on the
  Practice Test, and then review the section 6.6
  homework if you need more work on those
  problems.
           IMPORTANT:
Almost all problems in Chapter 6 on rational
  expressions require you to use one or
  more techniques for factoring polynomials.

  DON’T FORGET TO REVIEW THESE
   FACTORING METHODS AND KNOW
  HOW AND WHEN TO USE EACH ONE!

Two methods that students often have trouble with
         are factoring by grouping and
  sums/differences of cubes, so make sure you
     review problems using these methods.
  Domain example:
 Find the domain of the expression x 2  3x  4
                                   x 2  x  20
Solution: Set the denominator equal to zero and
solve for x. (Notice that this boils down to a
factoring problem.)
x2 – x – 20 = 0
(x – 5)(x + 4) = 0
(x – 5) = 0 gives x = 5,
and (x + 4) = 0 gives x = -4

Therefore the domain is {x | x ≠ 5 and x ≠ -4}
Example Multiply the following rational expressions.

             a a bab
               3      2
                           6a                 2
                         3
                a a
                 3
                         2a  2b 3


Solution: Factor each polynomial completely,
then cancel all factors that appear on both the top
and the bottom.
                             NOTE: This problem uses
                          factoring by grouping, factoring
             3a             out a GCF (twice!), and the
 ANSWER : 2
         a  ab  b 2          sum of cubes formula.
                                       Whew!
Example

   Add the following rational expressions.
                    4          x
                          , 2
                 x  x  6 x  5x  6
                  2


   4          x              4                 x
          2                                          
x  x  6 x  5 x  6 ( x  3)( x  2) ( x  3)( x  2)
 2


             4( x  3)                  x( x  3)
                                                         
     ( x  3)( x  2)( x  3) ( x  3)( x  2)( x  3)
         4 x  12  x 2  3 x           x 2  x  12
                                
       ( x  2)( x  3)( x  3)   ( x  2)( x  3)( x  3)
Dividing a polynomial by a monomial:
  Divide each term of the polynomial separately by the
   monomial.




Example

       12 a 3  36 a  15    12 a 3 36 a 15
                                         
               3a              3a      3a 3a
                                         5
                            4a  12 
                                 2

                                         a
 Example    Dividing a trinomial by a binomial:


                  4x  5       Divide 7x into 28x2.
                               Multiply 4x times 7x+3.
7 x  3 28 x  23 x  15
            2
                               Subtract 28x2 + 12x from 28x2 – 23x.

        28x  12x
            2                  Bring down -15.
                               Divide 7x into –35x.

               35 x  15      Multiply -5 times 7x+3.
                               Subtract –35x–15 from –35x–15.
               35x 15        Nothing to bring down.



           So our answer is 4x – 5.
HOW WOULD YOU CHECK THIS ANSWER???
Example of a complex fraction:

10
3x                  .
 5
6x

Solution: view as a division problem:

  10 ÷ 5 = 10 · 6x = 4
  3x   6x  3x 5
Example: Solving a rational equation:
Solve     2x + 1 = 1                     .
        2x – 1 x 2x – 1
Solution:
1. Multiply both sides by the LCD x(2x – 1).
      This gives 2x(x) + 1(2x – 1) = 1(x)
2. Now simplify this equation:
           2x2 + 2x – 1 = x
           2x2 + x – 1 = 0
3. Solve either by factoring or by using the
  quadratic formula.
Answers: x = -1, x = 1/2
Example (continued):
NOW CHECK BOTH ANSWERS in original
   equation:
   Note that when you plug in x = 1, everything
   checks out OK ( you get -1/3 = -1/3)
   BUT when you plug in x = 1/2, you get zeroes in
   some denominators, so this number is NOT a
   solution. (it gives 1 + 1 = 1
                       0 ½ 0
So the final answer is just x = -1
(if you write x = -1, 1/2, you’ll get ZERO credit.)
     To Review Unit 4 (Ch. 7)
Make sure you look over your graded Test 4
  worksheet and go over the problems you
  missed with a teacher or TA to make sure
  you understand how to do them.
Since we just reviewed this material for Test
  4, we won’t be doing a formal review of
  this material in class today.
REMINDER: Comprehensive Practice Final:

Once you finish the Unit 3 and 4 Final Review homework
assignments with at least an 80% score, you will have access to
the practice final, with as many attempts as you want.

The practice final is worth 10 points, plus a possible bonus of
up to 20 extra credit points on the final exam. Your best
percentage score on the practice final will earn that percent of
10 points toward your course grade, plus that best score percent
times 20 extra credit points will be added on to your final exam
point score before partial credit points are added.

This makes it extremely important for you to make sure you work
to get at least 80% on each of the four final exam review
homework assignments so that you can get access to the
practice final.
 Math TLC Open Lab Hours:
     Room 203 Jarvis Hall Science Wing
Regular hours through last day of classes
          (8:00 AM – 7:30 PM)
    Finals week open lab hours:
        Check bulletin boards
        in JHSW 214 and 203