Download File - Mr. McCarthy

Standard Form
Y-Intercept Form
Ax+By+C
Rise Run
intercept
Y-
Forms of a Line
Point Slope Form
Parallel–Slopes
Same
PerpendicularSlopes
Negative Reciprocals
Slope
m=
Slope
Properties of
Addition
Additive Inverse
Property
Properties of
Multiplication
Distributive Property of Multiplication:
Inverse Property of Multiplication:
Multiplying the sum of two numbers by If you multiply a number by its
reciprocal (multiplicative inverse) the
a third number is the same as
multiplying each of the two numbers by product is 1.
that third number and adding the
9 x 1/9 = 1
product.
a x (b+c) = (axb) + (axc)
1/9 x 9 = 1
3 x (6+4) = (3x6) + (3x4)
a x 1/a = 1
6 x (20 x 4) = (6 x 20) + (6 x 4)
Properties of
Multiplication
1/a x a = 1
1/0 is undefined
Laws of
Exponents
With ( )
Laws of
Exponents
(-2)2 = (-2) × (-2) = 4
Without ( )
-22 = -(22) = - (2 × 2) = -4
With ( )
(ab)2 = ab × ab
Without ( )
ab2 = a × (b)2 = a × b × b
Laws of
Exponents
Addition:
Subtraction:
If a = b then a + c = b + c
If -3+a=7
Then, -3+a+3=7+3
a=10
If a = b then a – c = b– c
If 8+a=24
Then, 8+a-8=24-8
a=16
Multiplication:
Properties of
Equality
If a = b then ac = bc
If a/3=9
Then, 3(a)=9(3)
a=27
Division:
If a = b and c ≠ 0 then a/c = b/c
If 3(a) = 9
Then, a/3=9/3
a=3
Leg
Hypotenuse
Leg
Pythagorean Triples
Pythagorean
Theorem
Distance Formula
Special
Triangles
Functions
function
not a
function
Special Binomials
(Z is for the German "Zahlen", meaning
numbers, because I is used for the set of
imaginary numbers).
Number Sets
Irrational Numbers
The numbers you can make by dividing
one integer by another (but not dividing
by zero).
In other words fractions.
Q is for "quotient" (because R is used for
the set of real numbers).
Examples: 3/2 (=1.5), 8/4 (=2), 136/100
Any real number that
is not a Rational Number.
Transcendental Numbers
Any number that is a solution to a
polynomial equation with rational
coefficients.
Any number that is
not an Algebraic Number
Examples of transcendental
numbers include π and e.
Includes all Rational Numbers, and
some Irrational Numbers.
Number Sets
Numbers that when squared give a
All Rational and Irrational numbers.
negative result.
A simple way to think about the Real
“Imaginary" numbers can seem
Numbers is: any point anywhere on the
impossible, but they are still useful!
number line (not just the whole
Examples: √(-9) (=3i), 6i, -5.2i
numbers).
The "unit" imaginary numbers is √(Examples: 1.5, -12.3, 99, √2, π
1)
(the square root of minus one),
They are called "Real" numbers because and its symbol is i, or sometimes j.
A combination of a real and an
imaginary number in the form a + bi,
where a and b are real, and i is
imaginary.
The values a and b can be zero, so the
set of real numbers and the set of
imaginary numbers are subsets of the
set of complex numbers.
Examples:
1 + i, 2 - 6i, -5.2i, 4
# Sets
Natural numbers are a subset of Integers
Integers are a subset of Rational
Numbers
Rational Numbers are a subset of the
Real Numbers
Combinations of Real and Imaginary
numbers make up the Complex
Numbers.
Absolute Value
The distance between a number and zero
|5| = 5
|-5| =
5
5 units
5 units
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Polynomials
Add and
Subtract
Polynomials
Binomials
Factor Binomials
Factor Squares
Zeros - Roots
Quadratic
Exponent Laws
Exponent Laws
Addition
Plus
And
Total of
Increased by
Add
More than
Together
Gain
Greater
Added to
All together
In all
Make
Sum
Combine
Later
Perimeter
Multiplication
Times
Double
Multiplied by
Of
Increased by
Factor
Twice
Multiple
Each
Area
Array
Area
Volume
Squared
Cubed
Power
Exponent
Radical
Radicand
Base
Subtraction
Subtract
Decreased by
Shared
Gave
Fewer than
Minus
Less than
Difference
Less
Loss
Parentheses
Times the sum of
The quantity of
Times the difference of
Plus the difference of
Key Math Problem Solving
Words
Division
Is
Quotient
Are
Reduced
Percent
Was
Simplest form Were
Split
Divided by
Will be
Per
Yields
Divisor
Sold for
Half
Root
Zeros of x
Equal
Percent
Formulas
2
x
1
2
3
4
5
6
7
8
9
10
11
12
8
1
2
3
4
5
6
7
8
9
10
11
12
x
Double
the
number
x5
+
x3
Or
Double
Double
Double
3
x
1
2
3
4
5
6
7
8
9
10
11
12
Triple 4
the
1
number 2
x
Double
Double
3
4
5
6
7
8
9
10
11
12
9
1
2
3
4
5
6
7
8
9
10
11
12
x
- 1
+
=9
11
1
2
3
4
5
6
7
8
9
10
11
12
x
6
1
2
3
4
5
6
7
8
9
10
11
12
x
x5
+ group
Double Digit
or
Front, back,
add the middle
12
1
2
3
4
5
6
7
8
9
10
11
12
7
1
2
3
4
5
6
7
8
9
10
11
12
x
x5
+
x2
x DISTRIBUTE
x 10
+
x ones