1/8/2014
Fri, 12/20
I can’t pass the tests back until the
last person finishes the test.
You Need:
Fancy calculators
Pencil
Graph paper (depending on which problems you get today)
Planner to write down important dates
Grades are posted, though, so feel
free to ask to see your grade
during independent work today.
5th Period: Enter silently as ALWAYS
Remember that the last day to
complete the online quiz is the 23rd!
Semester Exam:
50 Multiple Choice Questions
45 with only a four function
calculator
5 with the fancy calculator
Semester Exam Review
There are approximately 135
problems.
Day 1
This works out to about 20 problems
per day between the 6th and the 13th.
The Review Questions are due on the
13th.
1
1/8/2014
Sunday
Monday
Tuesday
Wednesday Thursday
Friday
Saturday
5
6
Work on
Review in
class
7
Benchmark
Exam on
computers
8
Work on
Review in
class
2nd period
9
Work on
Review in
class
5th and 7th
10
Benchmark
Exam on
computers
11
12
13
Exam
Review
DUE! I will
take
questions
in class.
14
Begin
Semester
Exam
No more
time for
questions!
15
Semester
Exam 2nd
period
16
Semester
Exam 5th
and 7th
period
17
Teacher
Work Day
18
19
20
21
22
23
24
25
I will start by letting you work with
the person sitting next to you. How
much you can accomplish will
determine if you will work with
partners when we come back from
break.
Monday, 1/6/14
You Need:
Fancy calculators
Blue calculators
Pencil
Graph paper (depending on which problems you get today)
Planner to write down important dates
5th Period: Enter silently as ALWAYS
Chapter 4 Test Averages
2nd Period:
5th Period:
7th Period:
84%
88.9%
88.9%
Ch. 4 Test Re-take: Remember that you must complete with
100% accuracy the extra assignments that I have posted on
the website.
You will bring those with you when you are scheduled to take
the re-take. If you answer any one question incorrectly you
will not be allowed to take the re-take…the answers are
posted online so this shouldn’t be a problem.
You should also show your work as usual and do the graphs on
graph paper.
This Friday is the last day to re-take the Chapter 4 Test. It is
not multiple choice and will include graphing.
2
1/8/2014
Disciplinary stuff:
Disciplinary stuff:
-ONE warning
5th Period: Now is your opportunity to
show that you can re-join your peers
and NOT have silent entry!
-Essay detention with parent signature
-After school detention with parent
signature, phone call home
-Referral
When we begin the second semester on
January 21st you will need a new 5 or 3 subject
notebook.
Sunday
Monday
Tuesday
Wednesday Thursday
Friday
Saturday
5
6
Work on
Review in
class
7
Benchmark
Exam on
computers
ROOM 667
8
Work on
Review in
class
2nd period
9
Work on
Review in
class
5th and 7th
10
Benchmark
Exam on
computers
ROOM 667
11
Last day
for late
work and
ch. 4 test
re-take
We will start a new table of contents. You will
need to tear out Assignments 1-5 from your old
notebook for us to glue into the new one.
12
13
Exam Review
DUE! I will
take
questions in
class.
14
Begin
Semester
Exam
No more
time for
questions!
15
Semester
Exam 2nd
period
16
Semester
Exam 5th
and 7th
period
17
Teacher
work day
18
19
20
Holiday
21
22
23
24
25
Let your parents know NOW that you need it so
you have it on time!
Go DIRECTLY to room 667 tomorrow and
Friday. You will need to turn off cell
phones and put them in your backpack
(they can not be in your pockets or
anywhere on your person) and backpacks
will be placed in a corner of the room.
You will need a pencil and scratch paper.
Grade Breakdown:
1st Quarter:
2nd Quarter:
Semester Exam:
3rd Quarter:
4th Quarter:
EOC Final Exam:
20%
20%
10%
20%
20%
10%
3
1/8/2014
Semester Exam Review
There are approximately 135
problems.
Day 2
This works out to about 20 problems
per day between the 6th and the 13th.
The Review Questions are due on the
13th.
Wednesday, 1/8 and Thursday, 1/9
For the review in class:
You may use a fancy pants device to
check your answers on my website as
you go.
Anyone want to tutor Algebra or PreAlgebra in the mornings with Ludick?
You Need:
Fancy calculators
Blue calculators
Pencil
Graph paper (depending on which problems you get today)
HW that I can’t actually check but
I’m still assigning:
Read through ALL topics posted in
the notes.
4
1/8/2014
Studying in math…
Studying in math…
Preparing for a math exam does NOT mean only completing the
review problems assigned by the teacher.
To adequately prepare for the semester exam you should
1) Skim through every section in the textbook that the exam will
be on. As you go, look for concepts that you don’t remember.
ESPECIALLY look for concepts that you need to have
memorized.
2) Make flash cards as you go through the textbook. You are
responsible for EVERYTHING from each section that we have
covered, as well as the Algebra 1 review from Chapter 1.
3) If there is a topic that you don’t feel comfortable with, work
through extra problems from the textbook (preferably ones
with answers in the back so you can check your work).
Studying in math…
Studying in math…
Preparing for a math exam does NOT mean only completing the
review problems assigned by the teacher.
Preparing for a math exam does NOT mean only completing the
review problems assigned by the teacher.
To adequately prepare for the semester exam you should
1) Skim through every section in the textbook that the exam will
be on. As you go, look for concepts that you don’t remember.
ESPECIALLY look for concepts that you need to have
memorized.
2) Make flash cards as you go through the textbook. You are
responsible for EVERYTHING from each section that we have
covered, as well as the Algebra 1 review from Chapter 1.
3) If there is a topic that you don’t feel comfortable with, work
through extra problems from the textbook (preferably ones
with answers in the back so you can check your work).
To adequately prepare for the semester exam you should
1) Skim through every section in the textbook that the exam will
be on. As you go, look for concepts that you don’t remember.
ESPECIALLY look for concepts that you need to have
memorized.
2) Make flash cards as you go through the textbook. You are
responsible for EVERYTHING from each section that we have
covered, as well as the Algebra 1 review from Chapter 1.
3) If there is a topic that you don’t feel comfortable with, work
through extra problems from the textbook (preferably ones
with answers in the back so you can check your work).
Studying in math…
Preparing for a math exam does NOT mean only completing the
review problems assigned by the teacher.
To adequately prepare for the semester exam you should
1) Skim through every section in the textbook that the exam
will be on. As you go, look for concepts that you don’t
remember. ESPECIALLY look for concepts that you need to
have memorized.
2) Make flash cards as you go through the textbook. You are
responsible for EVERYTHING from each section that we have
covered, as well as the Algebra 1 review from Chapter 1.
3) If there is a topic that you don’t feel comfortable with, work
through extra problems from the textbook (preferably ones
with answers in the back so you can check your work).
Semester Exam Review
Day 3
5
1/8/2014
Sets of Numbers and Their Notation
Maximum or Minimum – x or y-value?
Sets of Numbers and Their Notation
ℝ: Real Numbers
ℕ: Natural Numbers – Also called counting numbers.
Positive whole numbers. Does NOT include zero.
Factoring Four Terms
ℚ: Rational Numbers - Can be written as a fraction
Identifying Graphs
: Whole Numbers – Positive whole numbers, but
DOES include zero.
3 Variable System from a Word Problem, Solving by Hand
ℤ: Integers – Positive and negative whole numbers
Square Roots
Scientific Notation
: Irrational – CANNOT be written as a fraction. , 2,
etc.
If we ask you to find the maximum or
minimum but only provide one
number answers, should you choose
the y-value or the x-value?
If we ask you to find the maximum or
minimum but only provide one
number answers, should you choose
the y-value or the x-value?
Factoring Four Terms
Factoring Four Terms
+ 5 + 10 + 50
+ 5 + 10 + 50
Factor out the GCF of
each pair like we
usually do!
6
1/8/2014
Factoring Four Terms
+ 5 + 10 + 50
Factor out the GCF of
each pair like we
usually do!
+ 5 + 10 + 50
+ 5 + 10 + 50
Factor out the GCF of
each pair like we
usually do!
+ 5 + 10( + 5)
Factoring Four Terms
+ 5 + 10 + 50
Factoring Four Terms
Identifying Graphs
Factor out the GCF of
each pair like we
usually do!
+ 5 + 10( + 5)
+ 10 ( + 5)
Piecewise Functions
Identifying Graphs
Identifying Graphs
Constant Functions
Step Functions
7
1/8/2014
Identifying Graphs
Identifying Graphs
Absolute Value Functions
Identity Function
3 Variable System from a Word Problem
In triangle PQR, the measure of angle Q is three times
the measure of angle P. The measure of angle R is 20˚
more than the measure of angle P. Remember that the
sum of the three angles in any triangle will add to 180˚ .
In triangle PQR, the measure of angle Q is three times the
measure of angle P. The measure of angle R is 20˚ more than
the measure of angle P. Remember that the sum of the three
angles in any triangle will add to 180˚ .
= 3
In triangle PQR, the measure of angle Q is three times the
measure of angle P. The measure of angle R is 20˚ more than
the measure of angle P. Remember that the sum of the three
angles in any triangle will add to 180˚ .
= 3
In triangle PQR, the measure of angle Q is three times the
measure of angle P. The measure of angle R is 20˚ more than
the measure of angle P. Remember that the sum of the three
angles in any triangle will add to 180˚ .
= 3
= 20 + = 20 + + + = 180
8
1/8/2014
In triangle PQR, the measure of angle Q is three times the
measure of angle P. The measure of angle R is 20˚ more than
the measure of angle P. Remember that the sum of the three
angles in any triangle will add to 180˚ .
1
= 3
2
= 20 + 3
+ + = 180
1
3
= 3
+ + = 180
2
3
= 20 + + + = 180
Make two pairs of
equations. Remember
that you can pair them
any way you want.
We want to make two new equations from each of
these pairs. Our new equations should only have two
variables. They must be the same two variables in
each.
1
3
= 3
+ + = 180
2
3
= 20 + 1
+ + = 180
Let’s use substitution to get rid of P. Remember that
you can also use elimination.
3
=
3
+ + = 180
2
3
3
1
=
3
+ + = 180
− 20 = + + = 180
Let’s use substitution to get rid of P. Remember that
you can also use elimination.
1
+ + = 180
3
3
=
3
+ + = 180
+ + = 180
3
+ 3 + 3 = 540
Let’s use substitution to get rid of P. Remember that
you can also use elimination.
Multiply through by 3 to clear the fraction.
9
1/8/2014
1
3
=
3
1
+ + = 180
3
+ + = 180
=
3
− 20 = 2
3
3
+ + = 180
4
4 + 3 = 540
+ + = 180
+ 3 + 3 = 540
4
4 + 3 = 540
We have one new equation with only two variables.
We eliminated P.
2
−20 + + 2 = 180
2
3
( − 20) + + = 180
+ + = 180
3
( − 20) + + = 180
− 20 = Let’s use substitution to get rid of P. Remember that
you can also use elimination.
− 20 = + + = 180
2
+ + = 180
3
( − 20) + + = 180
−20 + + 2 = 180
2
3
− 20 = − 20 = + + = 180
+ 2 = 200
10
1/8/2014
( − 20) + + = 180
−20 + + 2 = 180
5
2
3
=
3
1
− 20 = + + = 180
3
+ 2 = 200
− 20 = 2
3
+ + = 180
4
4 + 3 = 540
+ + = 180
+ 2 = 200
5
We have our second new equation with only two
variables. We eliminated P.
5
+ 2 = 200
5
4 + 3 = 540
4
4
Solve our new system with the two new equations.
5
4
− + 2 = 200
4 + 3 = 540
+ 2 = 200
4 + 3 = 540
Let’s use elimination this time!
5
−4 − 8 = −800
4
4 + 3 = 540
5
4
+ 2 = 200
4 + 3 = 540
Let’s use elimination this time!
Let’s use elimination this time!
11
1/8/2014
5
−4 − 8 = −800
4
4 + 3 = 540
5
4
+ 2 = 200
5
−4 − 8 = −800
4 + 3 = 540
4
4 + 3 = 540
−5 = −260
−5 = −260
= 52˚
= 52˚
Let’s use elimination this time!
= 52˚
5
+ 2 = 200
5
4
+ 2 = 200
4 + 3 = 540
5
4
+ 2 = 200
4 + 3 = 540
Plug R back in to one of these two equations to solve
for Q.
= 52˚
5
+ 2 = 200
5
4
+ 2 = 200
4 + 3 = 540
+ 2(52) = 200
Plug R back in to one of these two equations to solve
for Q.
= 52˚
5
+ 2 = 200
5
4
+ 2 = 200
4 + 3 = 540
Plug R back in to one of these two equations to solve
for Q.
= 52˚
5
+ 2 = 200
+ 2(52) = 200
+ 2(52) = 200
+ 104 = 200
+ 104 = 200
5
4
+ 2 = 200
4 + 3 = 540
= 96˚
Plug R back in to one of these two equations to solve
for Q.
Plug R back in to one of these two equations to solve
for Q.
12
1/8/2014
1
= 3
2
= 20 + 3
+ + = 180
We now know two
variables. Pick an
equation that includes
P to solve for P.
1
= 3
2
= 20 + 3
+ + = 180
We now know two
variables. Pick an
equation that includes
P to solve for P.
= 52˚
= 52˚
= 96˚
1
= 3
2
= 20 + 3
+ + = 180
We now know two
variables. Pick an
equation that includes
P to solve for P.
1
1
= 96˚
= 3
= 3
2
= 20 + 3
+ + = 180
We now know two
variables. Pick an
equation that includes
P to solve for P.
= 52˚
1
96 = 3
= 96˚
= 52˚
1
= 96˚
96 = 3
32˚ = In triangle PQR, the measure of angle Q is three times the
measure of angle P. The measure of angle R is 20˚ more than
the measure of angle P. Remember that the sum of the three
angles in any triangle will add to 180˚ .
Square Roots
When thinking about adding and subtracting square roots,
treat them like variables.
3 5 + 7 5 = 10 5
∠ = 32˚
∠ = 52˚
∠ = 96˚
3 5+7 7=3 5+7 7
They are not “like terms” since they do not have the same
number under the radical. Since we also can’t simplify the
square root of 5 or 7, this is as simplified as we can get it.
13
1/8/2014
Square Roots
When thinking about adding and subtracting square roots,
treat them like variables.
3 20 + 7 20
Square Roots
When thinking about adding and subtracting square roots,
treat them like variables.
3 20 + 7 20
10 20
Square Roots
When thinking about adding and subtracting square roots,
treat them like variables.
Square Roots
Make sure you ALWAYS simplify the radical.
3 20 + 7 20
3 20 + 7 20
10 20
10 20
10 4 ∙ 5
10 4 ∙ 5
20 5
Square Roots
Make sure you ALWAYS simplify the radical.
3 20 − 14 100 + 4 5 + 32
Square Roots
Make sure you ALWAYS simplify the radical.
3 20 − 14 100 + 4 5 + 32
3 4 ∙ 5 − 14 100 + 4 5 + 32
14
1/8/2014
Square Roots
Make sure you ALWAYS simplify the radical.
Square Roots
Make sure you ALWAYS simplify the radical.
3 20 − 14 100 + 4 5 + 32
3 20 − 14 100 + 4 5 + 32
3 4 ∙ 5 − 14 100 + 4 5 + 32
3 4 ∙ 5 − 14 100 + 4 5 + 32
6 5 − 14 100 + 4 5 + 32
6 5 − 140 + 4 5 + 32
Square Roots
Make sure you ALWAYS simplify the radical.
3 20 − 14 100 + 4 5 + 32
Scientific Notation
Write the following numbers in scientific notation:
.00000005238
3 4 ∙ 5 − 14 100 + 4 5 + 32
6 5 − 140 + 4 5 + 32
856328541359200
10 5 − 108
Scientific Notation
Write the following numbers in scientific notation:
.00000005238 = 5.2 × 10?
856328541359200
Scientific Notation
Write the following numbers in scientific notation:
.00000005238 = 5.2 × 10%&
856328541359200
15
1/8/2014
Scientific Notation
Write the following numbers in scientific notation:
.00000005238 = 5.2 × 10%&
856328541359200 = 8.5 × 10?
Scientific Notation
Write the following numbers in scientific notation:
.00000005238 = 5.2 × 10%&
856328541359200 = 8.6 × 10'(
Scientific Notation
Multiply:
Scientific Notation
Multiply:
3.0215 × 10%&
and
4.17 × 10%')
3.0215 × 10%&
4.17 × 10%')
It can be helpful to think of the 10 as a variable, then change
it back at the end.
(3.0215 × * %& ) (4.17 × * %') )
Scientific Notation
Multiply:
3.0215 × 10%&
Scientific Notation
Multiply:
4.17 × 10%')
It can be helpful to think of the 10 as a variable, then change
it back at the end.
3.0215 × 10%&
4.17 × 10%')
They have the same base, so we can use our exponent
rules.
(3.0215 × * %& ) (4.17 × * %') )
(3.0215 × * %& ) (4.17 × * %') )
3.0215* %& ∙ 4.17* %')
3.0215* %& ∙ 4.17* %')
16
1/8/2014
Scientific Notation
Multiply:
Scientific Notation
Multiply:
3.0215 × 10%&
4.17 × 10%')
They have the same base, so we can use our exponent rules.
Multiply the coefficients and add the exponents.
(3.0215 × * %& ) (4.17 × * %') )
3.0215* %& ∙ 4.17* %')
3.0215 × 10%&
They have the same base, so we can use our exponent rules.
Multiply the coefficients and add the exponents.
3.0215* %& ∙ 4.17* %') =
12.599655* %'&
Scientific Notation
Multiply:
3.0215 × 10%&
4.17 × 10%')
Scientific Notation
Multiply:
4.17 × 10%')
Usually we round our answer to make it shorter, but on a
multiple choice test look to see what matches.
3.0215* %& ∙ 4.17* %') =
3.0215 × 10%&
4.17 × 10%')
Usually we round our answer to make it shorter, but on a
multiple choice test look to see what matches.
3.0215* %& ∙ 4.17* %') =
12.599655* %'&
12.599655* %'&
1.2599655* %'+
1.2599655* %'+ = 1.3 × 10%'+
17