Transcript Final Exam Review, Unit 1

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 15 points, vs. the usual homework assignment of 4 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. Due at the start of the next class session.
•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
(next Tuesday, May 10):
Monday–Thursday: 8:00 a.m. - 6:30 p.m.
Study Day and finals week:
Wednesday, 5/9:
Thursday, 5/10:
Friday, 5/11:
Monday, 5/14:
Tuesday, 5/15:
10:00 a.m. - 4:00 p.m.
8:00 a.m. - 6:00 p.m.
8:00 a.m. - 6:00 p.m.
8:00 a.m. - 6:00 p.m.
8:00 a.m. - 2:00 p.m.
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,
Unit 3
Unit 3 Covers:
Chapter 6
(Rational expressions)
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:
2
x
 3x  4
Find the domain of the expression
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
6a
 3
3
3
a a
2a  2b
3
2
2
Solution: Factor each polynomial completely,
then cancel all factors that appear on both the top
and the bottom.
3a
ANSWER : 2
2
a  ab  b
NOTE: This problem uses
factoring by grouping, factoring
out a GCF (twice!), and the
sum of cubes formula.
Whew!
Example
Add the following rational expressions.
4
x
, 2
2
x  x  6 x  5x  6
4
x
4
x
 2



2
x  x  6 x  5 x  6 ( x  3)(x  2) ( x  3)(x  2)
4( x  3)
x( x  3)


( x  3)(x  2)(x  3) ( x  3)(x  2)(x  3)
4 x  12  x 2  3x
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
 12a 3  36a  15
 12a 3 36a 15



3a
3a
3a 3a
5
2
 4a  12 
a
Example
Dividing a trinomial by a binomial:
4x  5
2
7 x  3 28x  23x  15
2
28x  12x
 35 x  15
 35 x  15
Divide 7x into 28x2.
Multiply 4x times 7x+3.
Subtract 28x2 + 12x from 28x2 – 23x.
Bring down -15.
Divide 7x into –35x.
Multiply -5 times 7x+3.
Subtract –35x–15 from –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.)
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
(next Tuesday, May 10):
Monday–Thursday: 8:00 a.m. - 6:30 p.m.
Study Day and finals week:
Wednesday, 5/9:
Thursday, 5/10:
Friday, 5/11:
Monday, 5/14:
Tuesday, 5/15:
10:00 a.m. - 4:00 p.m.
8:00 a.m. - 6:00 p.m.
8:00 a.m. - 6:00 p.m.
8:00 a.m. - 6:00 p.m.
8:00 a.m. - 2:00 p.m.