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43 Cards in this Set
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Real Numbers

Any number on the number line (3 2 1 0 1 2 3) Can be a rational or irrational number.


Rational Numbers

Real number that can be written as a fraction, terminating decimal (eg 0.25), or repeating decimal (eg 0.212121...)


Irrational Numbers

Numbers that cannot be written as a fraction. (Square roots, cube roots, and pi, though not ALL square roots are irrational)


Percent Increase
(eg: An amount goes up from 20 to 45... What is the % increase?) 
(New Value  Original Value / Original Value ) Multiplied by 100
( 45  20 = 25 / 20 = 1.25 x 100 = 12.5% Increase ) 

Percent Decrease
(eg: An amount of 50 decreases by 5.. What is the %I Decrease?) 
(Original Value  New Value / Original Value) Multiplied by 100
( 50  45 = 5 / 50 = 0.1 x 100 = 10% decrease) 

Convert Fractions to Decimals
(Eg: 3/125) 
Divide 3.00 by 125
0.024 

Fractions with power of 10 denominators to decimal

1/10 = 0.1
1/100 = 0.01 1/1000 = 0.001 1/10000 = 0.0001 1/100000 = 0.00001 

Convert 1/5 to decimal

1/5 > 2/10 = 0.2


Convert Decimals to Fractions

eg: 0.025 = 25 / 1000
0.25 = 25 / 100 0.0025 = 25 / 10000 Rewrite in simplest form: 25 / 25 = 1 1000 / 25 = 40 = 1/40 

Convert Fractions to Percents

eg 5/8 to percents
1) Convert to decimal = 0.625 2) Multiply by 100 and add % sign = 62.5% 

Convert % to Fractions

1) Remove % symbol
2) Write # over 100 3) Simplify eg: 35% = 35/100 35 divided by 5 = 7 100 divided by 5 = 20 = 7/20 

Convert % to Decimals

eg: 78% = 0.78


Roman Numerals

M = 1000
D= 500 C = 100 L= 50 X = 10 V = 5 I = 1 

Convert Roman Numeral to Arabic (1)

Begin with largest value then write from left to right.
When I, X, or C is used to to the left of larger value, Subtract it from that value. eg: IV = 4 

Convert Roman Numerals to Arabic (2)

eg: DCCCXXV =
500 + 300 + 20 +5 = 825 MCCXXXIV = 1000 

Metric System Prefixes

10^3 = 1000  kilo (k)
10^2 = 100  hecto (h) 10^1 = 10  deka (da) 10^0 = 1 10^1 = 1/10  deci (d) 10^2 = 1/100  centi (c) 10^3 = 1/1000  milli (m) 

Dependent and Independent Variables

Independent = data put into the set of data  input
Dependent = output based on input 

Algebraic Applications (1)

Addition, Subtraction, Multiplication, and division of polynomial terms.


Constant

A quantity that does not change


Coefficient

The numerical part of a term; the number that is being multiplied to the variable.


Expression

One or more terms consisting of any combination of constants and/or variables.


Algebraic Applications (1)

Addition, Subtraction, Multiplication, and division of polynomial terms.


Constant

A quantity that does not change


Coefficient

The numerical part of a term; the number that is being multiplied to the variable.


Expression

One or more terms consisting of any combination of constants and/or variables.


Variable

An unknown quantity in an expression, usually in the form of x, y, or z.


Like Terms

Terms that have the same variable and with the same exponent.


Degree

The exponent or sum of exponents of the variables of a term.


Divisor

The denominator in a division problem (eg 4/2 . 2 is the divisor)


Dividend

The numerator in a division problem
(eg 14/2 , 14 is the dividend) 

Quotient

The answer to the division problem; for example in 14/2 , 7 is the quotient.


Term

A term is a constant, variable, or product of a constant and a variable.
(Terms in an expression are separated by a + or  sign) 

Polynomial

Term or combination of terms.
(Monomial or Binomial) 

Monomial

Polynomial with 1 term


Binomial

Polynomial with 2 terms


(3x1) (2x+5)

(3x)(2x) + (3x)(5)  (1)(2x)  1 (5)
6x^2 +13x  5 

Equations with 1 unknown

Addition principle and Multiplication principle


Addition Principle

Rule that makes it possible to move terms from one side of an equation to the other by adding opposites to each expression.


Multiplication Principle

Rule that makes it possible to isolate the variable in an equation by multiplying both expressions by the reciprocal of the variables coefficient.


Equations with 1 unknown (pt2)
eg: 2(3x 1) = 4x  14 
1) Distributive property to remove parenthesis
2) If there are fractions, remove by multiplying each term by least common denominator 3) Use addition principle to move like terms together on both sides of equation 4) Use multiplication principle to isolate the variable by multiplying both sides of the equation by the reciprocal of the coefficient of the variable 5) Check solution. Substitute the answer into the original equation to make sure both result in the same value. 

eg: 2(3x 1) = 4x  14

2(3x 1) = 4x  14
6x  2 = 4x  14 6x2 +2 = 4x  14 +2 6x = 4x  12 6x  4x = 4x  4x  12 2x = 12 divide both sides by 2 x =  6 

Absolute Value of n = n

The distance between the number n and zero on the number line.
n = n when n is a positive number n = (n) when n is a negative number xn = xn when xn is a positive number xn = (xn) when xn is a negative number 

Absolute Value Equations

1) xn = a  xn = a or xn= a
2) xn < a  a < xn < a 3) xn <_ a  a <_ xn <_ a 4) xn > a  xn > a or xn < a 5) xn >_ a  xn _> a or xn _> a 