Transcript Final Exam Review, Unit 1

Test 4 Results:
If you got less than 70% on Test 4, make sure to go over
your test with me or a TA sometime this week. (This
material will also be covered again on the final exam.)
•Average class score after partial credit: __________
•Commonly missed questions: #_________________
Grade
A
A-
B+
B
B-
C+
C
C-
F
Points
≥ 920 ≥ 890 ≥ 860
≥ 830
≥ 800
≥ 750
≥ 700 ≥ 670 < 670
% Score
≥ 92
≥ 83
≥ 80
≥ 75
≥ 70
≥ 89
≥ 86
≥ 67
< 67
Now please
CLOSE
YOUR LAPTOPS
and turn off and put
away your cell phones.
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).
Due at the start of the next class session..
• Unit 2 review homework (Chapters 4, 5, 8):
NOTE: You must get at least 80% on the Unit 1 Review before you can start
the Unit 2 review. Due at the start of the second to last class session.
• 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 last 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.
Final Exam Review Materials:
2. Comprehensive Practice Final
NOTE: You must get at least 80% on the Unit 4 Review Homework before
you can start the comprehensive practice final.
•
•
The practice final has 47 questions, as does the regular
final exam. The questions will NOT be exactly the same as
those on the regular final, but they will be similar in content
and are distributed across sections the same way as on the
regular final.
Each time you take the practice final you will get a different
set of questions, AND your highest score will earn you that
percentage of 20 extra credit points on the final, so it will
pay off if you can find the time to take it more than once.
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, 5/11:
Thursday, 5/12:
Friday, 5/13:
Monday, 5/16:
Tuesday, 5/17:
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.
Final Exam Review,
Unit 1
Unit 1 covers the material from Test 1:
Chapter 1 (Real numbers)
Chapter 2 (Linear equations/
inequalities)
Chapter 3 (Graphs, functions,
domains/ranges,
lines/slopes/intercepts)
Sets of numbers:
• Natural (counting) numbers :
N = {1, 2, 3, 4, 5, 6 . . .}
• Whole numbers :
W = {0, 1, 2, 3, 4 . . .}
• Integers :
Z = {. . . -3, -2, -1, 0, 1, 2, 3 . . .}
More Sets of numbers:
• Rational numbers : the set (Q) of all numbers that
can be expressed as a quotient of integers, with
denominator  0
• Irrational numbers : the set (I) of all numbers that
can NOT be expressed as a quotient of integers
• Real numbers : the set (R) of all rational and
irrational numbers combined
NOTE: Q is a subset of R
I is a subset of R
but Q and I have NO members in common
• Commutative property
• of addition: a + b = b + a
• of multiplication: a · b = b · a
• Associative property
• of addition: (a + b) + c = a + (b + c)
• of multiplication: (a · b) · c = a · (b · c)
• Distributive property of multiplication over addition
• a(b + c) = ab + ac
Applications of Linear
Equations:
Sections 2.2 and 2.3 contained many types
of word problems. You should review
these two homework assignments using
the online Gradebook sometime before
your final (in addition to the review
homework problems for this unit.)
Don’t forget that if both sides of an
inequality are multiplied or
divided by a negative number, the
direction of the inequality sign
MUST BE REVERSED.
Example:
-7(x – 2) - x < 4(5 – x) + 12
-7x + 14 - x < 20 - 4x + 12
- 8x + 14 < - 4x + 32
(simplify both sides)
- 8x + 4x + 14 < - 4x + 4x + 32
- 4x + 14 < 32
- 4x – 14 + 14 < 32 - 14
(use distributive property)
(add 4x to both sides)
(simplify both sides)
(subtract 14 from both sides)
- 4x < 18
(simplify both sides)
9
x
2
(divide both sides by -4 and
simplify)
Graph of solution ( -9
,)
2
(
-9
2
Highlights from Chapter 3:
Slope of a line
Informally, slope is the tilt of a line.
It is the ratio of vertical change to horizontal
change, or
rise y change y2  y1
m


run x change x2  x1
x2  x1
Slope-intercept form of a line
• y = mx + b has a slope of m and has a y-intercept
of (0, b).
• This form is useful for graphing, since you have a
point and the slope readily visible.
Example
Find the slope and y-intercept of the line 2x – 6y = 12.
• First, we need to solve the linear equation for y.
-6y = -2x + 12
(subtract 2x from both sides)
y=
1
3
x–2
(divide both sides by –6)
•Since the equation is now in the form of y = mx + b,
 slope is 1/3
 y-intercept is (0,-2)
The slope-intercept form uses, specifically,
the y-intercept in the equation.
The point-slope form allows you to use ANY
point, together with the slope, to form the
equation of the line.
y  y1  m( x  x1 )
m is the slope
(x1, y1) is a point on the line
Example
Find an equation of a line with slope –2, through
the point (-11,-12). Write the final equation in
slope-intercept form. (Note: it’s always a
good idea to graph the line first.)
First, substitute the slope and point into the pointslope form of an equation:
y – (-12) = -2(x – (-11))
y + 12 = -2x – 22 (use distributive property)
y = -2x - 34 (subtract 12 from both sides)
So the slope is -2, and the y-intercept is -34.
• Any questions on the Unit 1 Review
Homework from those who have started it
already?
• If no further questions, you may open your
laptops and work on this assignment from
now till the end of class.
• Remember, this assignment is due at the
start of next session, AND you need to
score at least 80% on this to get access to
the next one.
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, 5/11:
Thursday, 5/12:
Friday, 5/13:
Monday, 5/16:
Tuesday, 5/17:
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.