Transcript 1-15 Final Review - Amundsen High School

Bell Ringer
 On a sheet of paper, write the following.
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Your name
Date
All of your classes (1st period – 8th period)
Teacher’s Names
Current grade in that class (if you don’t know
your grade, write the grade you think you have)
 If you have any grades below a C, also
write what you can do to do better in that
class in the second semester.
Good Morning
Friday, January 15
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Bell Ringer
Uniform & ID Check
Debrief
Bell Ringer Review
Homework Turn in HW
Chapter 1 Review
Chapter 2 Review
Chapter 3 Review
Chapter 4 Review
Break @ Bell
Debrief
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The end of the semester is coming
Monday-No School
Tuesday-Chapter 2 and 3 Review
Wednesday-Chapter 4 Review
Thursday-Final Exam
Other
Turn in Homework
Final Exam Review
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Chapter
Chapter
Chapter
Chapter
1
2
3
4
Test Review – Chapter 1
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Adding numbers with the same sign
Adding numbers with different signs
Subtracting numbers
Multiply/Dividing numbers with same sign
Multiply/Divide numbers with different signs
Order of Operations
Test Review – Chapter 1
 Adding numbers with the
same sign
 Add the numbers
together
 Keep the sign
 Questions to think about:
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Will the sum of two
positive numbers be
positive or negative?
Will the sum of two
negative numbers be
positive or negative?
Examples
1. 3 + 4 =
2. -7 + -12 =
3. 25 + 82 =
4. -12 + -17 =
5. 10 + 28 =
Test Review – Chapter 1
 Adding numbers with
different signs
 Subtract the absolute
values of the numbers.
 Keep the sign of the
number with the
greatest absolute value.
 Question to think about:
 Why isn’t the sum of a
positive number and a
negative number
always negative?
Examples
1. 4 + -2 =
2. -18 + 35
3. 18 + -18
4. -12 + 18
5. -10 + 13
=
=
=
=
Test Review – Chapter 1
 Subtracting numbers
 Change subtraction to
adding the opposite.
 Follow the rules for
addition.
 Questions to think
about:
 Why can we write
subtraction as
addition of the
opposite?
 What is the opposite
of a number?
Examples
1. 28 – 37 =
2. -18 – 10 =
3. -45 - -17 =
4. 12 - -12 =
5. 10 – 8 =
Test Review – Chapter 1
 Multiply/Dividing
numbers
 If the signs are the
same the answer is
always positive.
 If the signs are
different the answer
is always negative.
 Questions to think
about:
Examples
1. -2 x 4 =
2. -9 x -6 =
3. 5 x -99 =
4. 84 x 98 =
5. -12 / -6 =
6. 55 / 11 =
7. -27 / 9 =
8. 64 / -16 =
Test Review – Chapter 1
 Order of Operations
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Parenthesis – Symbols of
inclusion
Exponents
Multiplication and Division
from left to right
Addition and Subtraction
from left to right
 Questions to think about:
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Why are mult. and div. in
the same step?
Why are addition and
subtraction in the same
step?
Examples
1. 3[8-3*2+4(5-2)]
2. [7+3*2+8]/7
3. (20+22)/6+1
4. 5+3*4-8+2*7
5. 18/(9-15/5)
6. 2*8-62
7. 2*27-13*2
8. 18/9-15/5
9. 2*(8-62)
* means multiplication
/ means division
Test Review – Chapter 2
 Simplifying expressions
 Distribute
 Combine Like Terms
 Solving linear equations
 Writing equations from word
problems (Guess Check Generalize)
 Solving word problems
Test Review – Chapter 2
 Simplifying
expressions
 Distribute
 Combine Like Terms
 Questions to think
about:
 What are like terms?
 Why do we distribute
before combining like
terms?
Examples
1. 2(5x+4)
2. (2x-4)3
3. -(14x-3)
4. ¼ (12x-8)
5. 6(5-3x)
6. 7b-b-x+5-2x-7b
7. 4a+3-2y-5a-7+4y
8. 2x-5+3a-5x+10a
9. -6m+3t+4-4m-2t
10. 4-p-2x+3p-7x
Test Review – Chapter 2
 Solving linear
equations
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Backtracking
Number Tricks
Flowcharts
5 Steps
 Question to think
about:
 What is your favorite
method for solving
equations?
 Why do you like it?
Examples
1. 17 = -8 + x
2. 5.2 + h = 0.3
3. -2 = d / 4
4. 6x = 15
5. 3x + 4 = 10
6. f/6 – 5 = -8
7. -4 = 8 - 3x
8. 3 - 4d = 6d – 17
9. 5e + 13 = 7e – 21
10. 3k + 5 = 2(k + 1)
Test Review – Chapter 2
 Writing equations from
word problems
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Guess a correct answer
Check to see if it works
Make your third guess a
variable; generalize to
make an equation
 Questions to think about:
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Why should you make the
third guess a variable?
Why is it so important
that you write all your
steps and organize your
work when you guess?
Examples
 It takes Trevon ten hours to
clean an attic. Cody can
clean the same attic in
seven hours. Find how long
it would take them if they
worked together.
 A cattle train left Miami and
traveled toward new York.
14 hours later a diesel train
left traveling at 45m/h in an
effort to catch up to the
cattle train. After traveling
for four hours the diesel
train finally caught up. What
was the cattle train’s
average speed.
Test Review – Chapter 2
 Solving word
problems
 Solve the equation
that you created
when you GuessChecked-Generalized.
 Question to think
about:
 Why should you
check your answer
again?
 What should you
check for?
Examples
 A passenger plane made a
trip to Las Vegas and back.
On the trip there it flew
432mph and on the return
trip it went 480 mph. How
long did the trip there take if
the return trip took nine
hours?
 An aircraft carrier made a trip
to Guam and back. The trip
there took three hours and
the trip back took four hours.
It averaged 12m/h on the
return trip. Find the average
speed of the trip there.
Test Review – Chapter 3
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Absolute value equations
Using equations as point testers
Graphing equations using (x,y) table
Solving for a variable
Test Review – Chapter 3
 Absolute value
equations
 Create two equations
 Solve both equations
 Questions to think
about:
 What does absolute
value represent?
 Why do we create
two equations?
 Why can absolute
value not = 0?
Examples
1. |6m| = 42
2. |k – 10| = 3
3. |7 + p| = 7
4. |n| + 1 = 2
5. |-3p| = 15
6. |h| = 5
7. |6x + 2| + 3 = 4
8. |8y – 2| + 12 = 8
Test Review – Chapter 3
 Using equations as point
testers
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Substitute the x value
and y value into the
equation
Simplify to see if it
comes out true
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What does it mean for a
point to make an
equation true?
What does it mean if a
point does not make an
equation true?
 Example
Find 5 points on each graph
and 5 points not on each
graph.
1.
2.
3.
4.
5.
4x + 2y = 20
7 + 3x = y
10y + x = 30
2x + 3y = 8
x+y=4
Test Review – Chapter 3
 Graphing equations using
(x,y) table
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Make a table for your
points
Choose values for x
Solve for y
Write your points into
the table
Plot your points
Connect the points
 Questions to think about:
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Why do we make a
table?
How do we know what
values to choose for x?
Examples
1. y = -5x – 1
2. y = -7x + 3
3. y = 5
4. x = -3
5. y – 2x = -5
6. y – 1 = -6x
7. y = -5/2 x + 5
Test Review – Chapter 3
 Solving for a variable
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Identify the variable
that you are solving for.
Move everything else to
the other side of the
equation
 Questions to think about:
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Why is it helpful to
solve for a variable?
When is the answer
going to be just a
number and when will
the answer be an
expression?
Examples
1. 5x + 3 = y; solve for x
2. 2x + 3y = 8; solve for y
3. x = 3(y + 2); solve for y
4. 2x + 8y = 0; solve for x
Test Review – Chapter 4
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Find slope between two points
Determine if points are collinear
Find a collinear point
Use slope to determine if line goes up
to the right, down to the right,
horizontal or vertical.
Test Review – Chapter 4
 Find slope between two
points
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m(A,B) = rise
run
Rise = y2 – y1
run
x 2 – x1
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What happens to the
slope when you change
the order of the points?
When is it easier to find
the slope using rise/run
and when is it easier to
use the slope formula?
 Examples
1. (19,-16) and (-7,-15)
2. (1,-19) and (-2,-7)
3. (12,-18) and (-15,-18)
4. (-4,7) and (-6,-4)
5. (20,8) and (9,16)
6. (17,-13) and (17,8)
7. (3,0) and (-11,-15)
8. (19,3) and (20,3)
9. (-2,6) and (-2,15)
10. (6,-12) and (15,-3)
Test Review – Chapter 4
 Use slope to
determine how a
line looks.
 Positive slope—line
goes up to the right
 Negative slope—
line goes down
 Slope = 0  line is
horizontal
 Slope is undefined
 line is vertical
 Examples
Which directions do these
lines go in?
1. (19,-16) and (-7,-15)
2. (1,-19) and (-2,-7)
3. (12,-18) and (-15,-18)
4. (-4,7) and (-6,-4)
5. (20,8) and (9,16)
6. (17,-13) and (17,8)
7. (3,0) and (-11,-15)
8. (19,3) and (20,3)
9. (-2,6) and (-2,15)
10. (6,-12) and (15,-3)
Test Review – Chapter 4
 Use slope to determine how a line
looks.
 Questions to think about:
 When is the slope of a line undefined?
 When is the slope of a line = 0?
 What is another way of determining what
the line looks like without using slope?
Test Review – Chapter 4
 Determine if points
are collinear
 In order for points
A,B, and C to be
collinear:
m(A,B)=m(B,C)
 Questions to think
about:
Test Review – Chapter 4
 Find a collinear
point
 Graph the two
points and find
another point on
the line
 Use the slope to
create a point
tester
 Questions to think
about:
 Examples
Find a point C, collinear with
these points.
1. (19,-16) and (-7,-15)
2. (1,-19) and (-2,-7)
3. (12,-18) and (-15,-18)
4. (-4,7) and (-6,-4)
5. (20,8) and (9,16)
6. (17,-13) and (17,8)
7. (3,0) and (-11,-15)
8. (19,3) and (20,3)
9. (-2,6) and (-2,15)
10. (6,-12) and (15,-3)
Test Review – Chapter 4
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Find slope between two points
Determine if points are collinear
Find a collinear point
Use slope to determine if line goes up
to the right, down to the right,
horizontal or vertical.
Homework