Transcript Algebra I - Denise Kapler

Math Review May 12, 2014
Solve
1a. 10 = lx – 2l
2. Distribute to
solve for y
(x + 6) (x + 12) = y
3. Graph:
y = x2
1b. 10 = 2(y+2)
1c. 6 =
36
x
Solve for the
unknown number.
Distribute – give
one to
everyone.
• Wind and
Wave
• FOIL
m
y 2  y1
x2  x1
y= mx + b
defines linear
Math Review May 13, 2014
Solve
1a. 4 = lx – 6l
2. Distribute to
solve for y
(x + 4) (x + 3) = y
3. Graph:
y = 2x2
1b. 9 = 3(y+4)
1c. 4 =
24
x
Solve for the
unknown number.
Distribute – give
one to
everyone.
• Wind and
Wave
• FOIL
m
y 2  y1
x2  x1
y= mx + b
defines linear
Math Review May 14, 2014
Solve
1a. 14 = lx – 7l
2. Distribute to
solve for y
(x + 5) (x + 5) = y
3. Graph:
y = -x2
1b. 12 = 4(y+4)
1c. 8 =
72
x
Solve for the
unknown number.
Distribute – give
one to
everyone.
• Wind and
Wave
• FOIL
m
y 2  y1
x2  x1
y= mx + b
defines linear
Math Review May 15, 2014
Solve
1a. 4 = l2x + 6l
2. Distribute to
solve for y
(x + 3) (x + 3) = y
3. Graph:
y = -2x2
1b. 9 = -(y+4)
1c. 7 =
28
2x
Solve for the
unknown number.
Distribute – give
one to
everyone.
• Wind and
Wave
• FOIL
m
y 2  y1
x2  x1
y= mx + b
defines linear
Math Review May 19, 2014
Solve
1a. 2 = l4x - 6l
2. Distribute to
solve for y
(x + 3)2 = y
1b. 9 > -(y-4)
1c. 3 =
27
3x
Solve for the
unknown number.
Distribute – give
one to
everyone.
• Wind and
Wave
• FOIL
3. Graph:
1
y=
x
m
y 2  y1
x2  x1
y= mx + b
defines linear
Math Review May 20, 2014
Solve
1a. 9 = l-x - 6l
2. Distribute to
solve for y
(x + 7)2 = y
1b. 16 > -2(y-4)
1c. 7 =
49
7x
Solve for the
unknown number.
Distribute – give
one to
everyone.
• Wind and
Wave
• FOIL
3. Graph:
1
y=
2x
m
y 2  y1
x2  x1
y= mx + b
defines linear
Math Review May 21, 2014
Solve
2. Distribute to
1a. 12 = 2 lx + 2l
solve for y
(x + 4)2 = y
1b. -2 > -4(y+1)
1c. 4 =
36
3x
Solve for the
unknown number.
Distribute – give
one to
everyone.
• Wind and
Wave
• FOIL
3. Graph:
1
y=
x
m
y 2  y1
x2  x1
y= mx + b
defines linear
Math Review May 22, 2014
Solve
2. Distribute to
1a. 12 = 2 lx + 2l
solve for y
(x + 9)2 = y
1b. 16 > -2(y+4)
1c. 8 =
64
2x
Solve for the
unknown number.
Distribute – give
one to
everyone.
• Wind and
Wave
• FOIL
3. Graph:
1
y =
2x
m
y 2  y1
x2  x1
y= mx + b
defines linear
Agenda
I know
?
Algebra
That a point is defined by two
coordinates (x, y).
Why is a point defined by two
coordinates?
Word
Point
4-2-2013
Math Review April 7, 2014
1a. 8x+(x+3)=
(8x+x)+3
2. Find the
distance
1b.
between (-2,
3a+b+2a=
12) and (5, b+3a+2a
12)
3. Plot the points
and find the
slope defined
by:
(2, -6) and (-1, 0)
1c.
9 = -2 (y+2)
m
Distance Formula
Properties of Real
numbers:
Associative,
Commutative and
Distributive.
d
 y  y  x  x 
2
2
1
2
1
y 2  y1
x2  x1
2
y= mx + b
defines linear
Agenda
I know
Algebra
That a system of equation’s
solution is found at the point of
intersection.
?
How do you know if two lines are
parallel, perpendicular or neither?
Word Parallel
Perpendicular
4-1-2013
1a.
Math Review April 8, 2014
3. Plot the points
2. Find the
and find the
distance
slope defined
between (-5, 24)
by:
and (2, 0)
0 = - (y+2)
1b.
a+b+a=
b+a+a
1c.
(2, -4) and (-1, 2)
y 2  y1
m
x2  x1
x+(x+7)=
(x+x)+7
Properties of Real
numbers:
Associative,
Commutative and
Distributive.
d
 y  y  x  x 
2
2
1
2
1
2
y= mx + b
defines linear
Agenda
I
Algebra
That the Pythagorean Theorem
know
works when I have a right triangle.
?
How do you find a right angle
in the real world?
Word Right angle = 90°
3-20-2013
1a.
Math Review April 9, 2014
2. Find the
distance
between (-6, 0)
and (1,0)
-6 (2x+1)= 2x
1b.
2a+(3a+9)=
(2a+3a)+9
1c.
-3+v+9=
v+-3+ 9
Properties
of Real
1c.
numbers:
Associative,
Commutative and
Distributive.
3. Plot the points
Find the slope
defined by:
(-2, 1) and (3,0)
m
d
 y  y  x  x 
2
2
1
2
1
y 2  y1
x2  x1
2
y= mx + b
defines linear
Agenda
I know
?
Algebra
That the Pythagorean Theorem is
used to solve real life problems.
When can I assume a right
angles exists?
Word
2-dimension
3-19-2013
1a.
Math Review April 10, 2014
2. Find the
distance
between (-6, 0)
and (1,0)
-6 (2x+1)= 2x
1b.
-u+v+12u=
v+12u+ -u
1c.
3. Plot the points
and find the
slope defined
by:
(0, 2) and (2,0)
x+(9x+1)=
(x+9x)+1
Properties of Real
numbers:
Associative,
Commutative and
Distributive.
m
d
 y  y  x  x 
2
2
1
2
1
2
y 2  y1
x2  x1
y= mx + b
defines linear
Agenda
I know
?
Algebra
That the Pythagorean Theorem can
be used to find the side length of a
right triangle.
How can you tell if a triangle is
a right triangle?
Word
a^2 + b^2 = c^2
3-18-2013
1a.
Math Review April 14, 2014
2. Find the
distance
between (-5, 2)
and (1,-2)
-4 = - (3m+1)
1b.
2u+2v+u=
2v+2u+u
1c.
3. Plot the points
and find the
slope defined
by:
Line 1
(0, 2) and (2,-2)
Line 2
(10, 2) and (2,-2)
-x+(3x+2)=
(-x+3x)+2
Properties of Real
numbers:
Associative,
Commutative and
Distributive.
d
y
2
y
1

2
  x 2  x1 
2
m
y 2  y1
x2  x1
y= mx + b
defines linear
Agenda
I know
?
Algebra
That the Line of Best Fit for a
scatterplot has the same number
of points above as below it.
Why is the Line of Best Fit an
average?
Word
points
3-13-2013
1a.
Math Review April 15, 2014
2. Find the
distance
between (-5, 3)
and (10,-5)
-11 = - (5m+1)
1b.
u+v+10u=
v+u+10u
1c.
3. Plot the points
and find the
slope defined
by:
Line 1:
(2, 2) and (2,-2)
Line 2:
(2, 2) and (-2,2)
-2x+(x+2)=
(-2x+x)+2
Properties of Real
numbers:
Associative,
Commutative and
Distributive.
d
 y  y  x  x 
2
2
1
2
1
2
m
y 2  y1
x2  x1
y= mx + b
defines linear
1a.
Math Review April 16, 2014
3. Plot the points
2. Find the
and find the
distance
slope defined
between (-5, 33)
by:
and (4,-7)
8 = - (3y+9)
1b.
2a+2b+a=
2b+2a+a
1c.
6x+(4x+8)=
(6x+4x)+8
Properties of Real
numbers:
Associative,
Commutative and
Distributive.
d
 y  y  x  x 
2
2
1
2
1
2
Line 1
(7, -2) and (-1,-2)
Line 2
(-1,-2) and (7, -2)
y 2  y1
m
x2  x1
y= mx + b
defines linear
Agenda
I know
?
Algebra
That a scatterplot has a line of best
that is linear when the data has an
average a constant rate of change.
Why is the Line of Best Fit a
straight line?
Word
Average
3-12-2013
1a.
Math Review April 17, 2014
3. Plot the points
2. Find the
and find the
distance
slope defined
between (-5, 33)
by:
and (4,-7)
8 = - (3y+9)
1b.
2a+2b+a=
2b+2a+a
1c.
Line 1
(1, 0) and (-2,6)
Line 2
(0, 0) and (3,-6)
6x+(4x+8)=
(6x+4x)+8
Properties of Real
numbers:
Associative,
Commutative and
Distributive.
d
 y  y  x  x 
2
2
1
2
1
2
m
y 2  y1
x2  x1
y= mx + b
defines linear
Agenda
Algebra
I know That a scatterplot provides a
summary of the data points.
?
How do you draw a
Line of Best Fit?
Word
Line of Best Fit
3-4-2013
Agenda
Geometry
I know How to analyze the pattern in an
algebraic relationship using:
tables, graphs and equations.
?
How do you find the common
ratio in a geometric sequence?
Word
3-4-2013
Agenda
I know
?
Geometry
How to analyze the pattern in an
algebraic relationship using:
changes in y.
How do you find the common
difference/slope in an algebraic
sequence?
Word m =
3-5-2013
Agenda
Geometry
I know the distance formula will find the
distance between two points.
?
How do you find the distance
between two points?
Word
d
x  x 
2
1
2

y  y 
2
1
2
3-6-2013
d
 y  y x  x 
2
1
2
1
Math Review April
1a.
a+(b+c)=(a+b)+c 2a. Find the
distance
between (3, 4)
and (0,0)
1b.
a+b +c=b+a+c
1c.
21, 2014
2b. Solve for c.
a=4 and b=3
3. Plot the points,
draw the line
and find the
equation
defined by:
(-3, 5) and (0, 2)
2(x+1)=10
Properties of
2
2 y= mx + b
Real numbers:
d  y  y   x 2  x1 
2
1
defines linear
Associative,
Commutative
a2+b2=c2
and Distributive.


Math Review April 22, 2014
1a.
-(2x+2)=16
3. Plot the points,
draw the line
and find the
equation
defined by:
2. Find the
distance
between (-4, 3)
and (0,0)
1b.
9x+y+3x=
y+9x+3x
2b. Solve for c.
1c.
(-2, 4) and (1, 1)
a=3 and b=4
5x+(4x+3)=
(5x+4x)+3
Properties of Real
numbers:
Associative,
Commutative and
Distributive.
d
 y  y  x  x 
2
2
a2+b2=c2
1
2
1
2
y= mx + b
defines linear
Math Review April 23, 2014
1a.
3(2x+2)=18
2. Find the
distance
1b.
between (2, 3)
x+3y+5x=
and (-6, 9)
3y+x+5x
2b. Solve for c.
1c.
a=6 and b=8
7x+(3x+1)=
(7x+3x)+1
Properties of Real
numbers:
Associative,
Commutative and
Distributive.
d
3. Plot the points,
draw the line
and find the
equation
defined by:
(-2, -4) and (2, 4)
 y  y  x  x 
2
2
a2+b2=c2
1
2
1
2
y= mx + b
defines linear
Math Review April 24, 2014
1a.
-7(2x+2)=28
1b.
7x+y+x=
y+7x+x
1c.
2a+(a+9)=
(2a+a)+9
Properties of Real
numbers:
Associative,
Commutative and
Distributive.
2a. Find the
distance between
(-6, 3) and (6,-2)
3. Plot the points,
draw the line
and find the
equation
defined by:
2b. Solve for c.
a=5 and b=12
d
(5, 3) and (-1, -3)
 y  y  x  x 
2
2
1
a2+b2=c2
2
1
2
y= mx + b
defines linear
Solve Steps
Word Problems
1.
2.
3.
4.
5.
6.
Draw – picture, graph, table
Known- from inside and outside the problem
Unknown – what are you being asked to find
Relationship – between known and unknown
Solve
Answer: Does it make sense? Plug it back in
Solve Steps
1.
2.
3.
Use GEMDAS - work one side then the
other
Isolate the variable - when there is
nothing left to do on either side
Use one variable to solve for the other(s)
- for a system
Solve Steps
1.
2.
3.
Read and write down the problem
Ask yourself - What do I do next?
Think - about what you know
2y=4x+6
y=2x+3
Agenda
Linear Functions
I know the slope intercept form
defines linear.
?
Word
Why do linear equations graph a
straight line?
Change in y
Change in x
11-14-2012
Number
Theory
Real
Irrational
Rational
a
form b
positive, negative and zero
Integers
Whole
positive
zero
Real Numbers
Agenda
Real Number Operations
I know Multiplication is repeated addition;
Division repeated subtraction
?
What are the four things you can
do to a number?
Word
Inverse
9-10-2012
Decimal – place value
Y-intercept
X-intercept
•Find the y-intercept by setting x to
zero and solving for y.
•Find the x-intercept by setting y to
zero and solving for x
Notebook
Organizer Notes from class
Notes from class
Date
Title
Happy Mole Day!!!!