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© 2006 Doug Clarke
Algebra I
To take the square root, you need how
Many to pull out?
Two
To take the cube root, you need how
Many to pull out?
Three
X to the third times x to the sixth
Add the exponents
X to the 9th
When raising a power to a power
___ the exponents.
Multiply the exponents
A negative exponent means to place
That part of the answer where?
In the bottom
(denom.)
When dividing polynomials,
____ the exponents.
Subtract
Any term raised to the zero
Power = ?
One
To find perimeter
…
Add all sides
To add polynomials
…
Combine like terms
To subtract polynomials
…
1. Change subtraction to addition
2. 2.Change 2nd polynomial to its opposite
Area = ?
Length x width
A = lw
(2x + 3)(x – 2)
2 x squared – x - 6
When factoring, look for the
____ first.
GCF
Sum, Difference
Product, Quotient
Mean to ____.
+ - X divide
X squared -2x-24 divided by
X+4
X-6
A rectangle has a width of 2x + 3 and
An area of 2x squared – 5x -12.
What is the length?
X-4
Plus, more than, increased by,
Additional, sum are
____ indicators
Addition
Times, twice, of, product, per are
____ indicators.
Multiplication
Less, less than, fewer than,
Decreased by, difference are
____ indicators.
Subtraction
Which subtraction word indicators
Switch the order?
Less than
Quotient, share equally, separate into
Equal groups are ___ indicators.
Division
To solve equations in the calculator:
Y1
Y2
Y1=left side
Y2=right side
Zoom 6, 2nd calc 5 enter 3 times
The opposite of squaring is to
_______
Take the square root.
Two things side by side with no sign in
Middle is what operation?
Multiplication
A line that has a positive slope
Looks like…
Rises up and to the right
A line that has a negative slope
Looks like….
Falls to the right
A horizontal line has what slope?
Zero
A vertical line has what slope?
Undefined
Slope given two points
M=
M=y–y/x-x
Slope of (3,0) & (3,2)
Undefined
No slope
Slope is what direction over
What direction?
Rise / Run
Parallel lines have what type
Of slopes?
Same slope
Perpendicular lines have ___
____ slopes?
Opposite Reciprocal slopes
The product of the slopes of
Two perpendicular lines is
Always ___.
-1
X intercept
Where the graph crosses or
Touches the x axis.
Y intercept
Where the graph crosses or
Touches the y axis.
Slope Intercept
Form Equation
Y = mx + b
Standard Form
Plain number by itself
X term is positive
No fractions or decimals
Calc steps for graphing, slope int form
Equation, predictions:
Stat/enter
X #’s into L1,Y #’s into L2
stat => calc,4, enter twice
Y=vars 5=>EQ enter
2nd graph to predict
Point Slope Form
Equation
Y – Y1 = m ( X – X1)
The equation of a horizontal
Line…
Y=
The equation of a vertical line
…
X=
Systems of Equations:
Two intersecting lines:
One solution
Consistent
Independent system
Systems of Equations:
Parallel lines:
No solution
Inconsistent system
System of Equations:
Only one line:
(The two lines coincide)
Infinitely Many Solutions
Consistent
Dependent system
Inequality signs:
Greater than
Less than
Not equal to
> <
< > have what type of
Circles when graphing?
Open circles
Greater than or equal to,
Less than or equal to have what
Type of circles when graphing?
Closed circles
When does the inequality sign
Reverse?
If you multiply or divide BOTH
Sides by a Negative.
Solve inequalities so that the letter
Is on the ___ side.
Left
Three ( =)
Three inequalities
Two insides are the same:
What property?
Transitive Property
Two variable inequalities:
What type of line?
Greater than or
Less than?
Broken line
Two variable inequalities:
Greater than or equal to
Less than or equal to have what
Type of line?
Solid
To graph equations and inequalities
In the calculator,
Solve for ___ first.
Y=
To put > or < in the calculator,
Go where?
Left of Y1
And left of Y2.
When solving inequalities by graphing,
Where are the solutions?
The region with the darker shading
Is the solution.
___, ___, ___, ___ are all where
The graph crosses or touches the
X axis.
Real roots, zeros, x intercepts,
Solutions.
How many real solutions does a
Quadratic have if it touches the
X axis once?
One real solution
How many real solutions does a
Quadratic have if it touches the
X axis twice?
Two real solutions
How many real solutions does a
Quadratic have if it does not
touch the
X axis?
No real solutions
The solutions to solving Quadratic
Equations using a table are
Y or f(x) = ____ ?
When Y = 0
F(x) = 0
Property Justification:
-3(2x+5) = 9 Given
-6x -15 = 9 ____
-6x=24 ____
X = -4____
Distributive
Addition Property of equality
Division Property of Equality
How do you tell if a relation is
A function?
If the x coordinates repeat => No
If the x coordinates are all different
=> Yes
Is y = -5 a function?
Yes
Is x = 3 a function?
No
How do you tell if a graph is a
Function?
Use the vertical line test.
Touches once => Yes
Touches more than once => No
What is a linear function?
When graphed, it is a straight line.
Graph x = y squared.
Is it a function?
Solve for y first and graph.
No, it is not a function.
Write an equation to represent the
Function: f(x) is 3 less than 4 times the
Square of x.
F(x) = 4x - 3
What is an arithmetic sequence?
Adding the same number to get
The next number.
The number being added each
Time in an arithmetic sequence is
The ___.
Common difference
How do you find the Common
Difference?
D = a2 – a1
(second term – first term)
A(n) = a1 + (n – 1) d
Identify each term.
A (n) = last term
A1 = first term
N = # of terms
D = # being added
-2,3,8,13,…
Write a formula for finding the nth term
Find the 15th term in the sequence.
A(n) = 5n – 7
A (15) = 68
What is the domain of a relation?
Domain is the x coordinates.
What is the range of a relation?
The range is the y coordinates.
Which is the dependent variable
Domain or Range?
Range. The y answer depends on the
Value of x.
Describe the domain and range for
function(-4,4)(-3,5)(-1,0)(1,-1)(5,3)
(Connected)
Domain => -4<x<5 (or equal to)
Range => -1<y<5 (or equal to)
Describe the domain and range for
F(x) = 4x -4.
Domain: all real numbers
Range : all real numbers
Describe the domain and range
For f(x) = 3.
Domain : all real numbers
Range: f(x) = 3 or y = 3
To describe the domain of a graph,
Stretch which way?
Left and right to see how wide it is.
To describe the range, stretch which
Way?
Up and down to see how tall it is.
In direct variation,
y is directly proportional to x.
Write the formula or equation,
Y = kx
How does a direct variation graph
Look?
It goes DIRECTLY to and or through
The origin.
For a direct variation graph, what is
The constant of proportionality?
Y intercept?
K = slope
Y intercept = (0,0)
Write the formula for inverse variation.
Y = k/x
Direct variation proportion:
x1 over x2 = y1 over y2
(proportion)
Inverse Variation Proportion:
X1 over x2 = y2 over y1
To solve proportions
…
Cross multiply and divide.
How do you find the:
Mean:
Mean Abs. Dev.
Stat/enter
Key #’s into L1
2nd 0 (down to Mean, 2nd L1)
M.A.D. => Stat=>Calc enter twice
Variance = ????
Variance = standard deviation
Squared.
Z – score =
Z – score = # - mean/ st. dev
Box-&-Whisker Plots: identify: lower
Extreme, LQ,whisker,median,UQ,
Upper extreme
Draw a bow-&-whisker plot
Range =
IQ Range =
Range = highest # - smallest #
IQ = UQ - LQ
To graph quadratics:
Stat/enter
#’s into L1 & L2
Y = clear & unhighlight
2nd y=
Enter/On
Zoom 9 to graph,stat,calc,5enter
3 times, 2nd graph to predict
Factor 4x squared -2x-2.
2 (2x squared – x – 1)
2 ( 2x+1)(x-1)
Which property?
10a + -10a = 0
10a + 0 = 10a
A+10= 10+a
Inverse for addition
Identity of addition
Commutative of addition
Which property?
9x + (3x + 8) = (9x+3x) + 8
8(3x-2) = 24x - 16
Associative of addition
Distributive