Numbers and algebra

integers

Any positive or negative whole number, including zero, but not fractions, decimals, or mixed numbers

Prime number

any whole number greater than one that has only two factors, itself and 1 ( can divide evenly with just itself and 1 )

composite number

Any whole number greater than 1 that has more than two different factors; in other words, any whole number that is not a prime number

ex. has 1,2,4,6,,8

rational numbers

Include all integers, decimals, and fractions. Any terminating or repeating decimal number is a rational number

Irrational numbers

Cannot be written as fractions or decimals because the number of decimal places is infinite, and there is no recurring pattern of digits within the number. For example, pi begins with 3.14

Real number

are the set of all rational and irrational numbers

Common factor

a number that divides exactly into two or more other numbers, for example, the factors of 12 are 12 are 1, 2, 3, 4, 6, and 12, while the factors of 15 are 1, 3, 5, 15. the ___ of 12 and 15 are 1 and 3.

the greatest common factor

the largest number that is a factor of two or more numbers

the least common multiple

The smallest number that is a multiple of two or more numbers

exponents divide by each other and contain the same base, causing the exponents to subtract from one another

b^m / bⁿ = b^m-n

improper fractions

Translating mathematical phrases

Dividing fractions

Two fractions can be divided by flipping the numerator and denominator of the second fraction and then multiplying it

converting decimals into fractions

move two decimal places to the left, then put it over a hundred, and then keep simplifying until you get the smallest possible fraction

adding and subtracting decimals

When adding or subtracting decimals, always make sure to line up the decimal places, and then if there is any empty space, just add a zero to fill up the space then do the problem normally

multiplying decimals

When multiplying decimals, forget the decimal point in the beginning and multiply it regularly, then at the end, you count how many numbers are behind the original factors and move the decimal to the left that many times

dividing decimals

When dividing decimals, you multiply both factors by 10 as many times as needed to get rid of the decimal, then you just have to do long division

rational numbers

numbers that an be expressed as a ration or fraction

irrational numbers

numbers that basically go on forever like pie

how to find a percent of a number

To find a percent of a number, just turn the percent into a decimal and multiply it by the whole ( in this instance, you have a calculator; if you don’t, there is another process for this )

How to find a percent increase

slope formula

Y₂ - Y₁ over X₂ - X₁ = M ( slope)

Perimeter of triangle formula

P = A + b+ C

Area of triangle formula

A = (Bh) 1/2

Area ot trapezoid formula

A = ½ h (b₁ + b₂)

perimeter of a trapezoid formula

P = a + b₁ + C + b₂

area of a parallelogram formula

A= bh

perimeter of a parallelogram

P = 2( a + b)

area of a rectangle

A = lw

perimeter of a rectangle

P = 2 (l +w)

area of a rhombus

A = ½ (d₁ + d₂)

Perimeter of a rhombus

area of a circle

perimeter of a circle

volume of a prism

volume of cube

volume of sphere

volume of cylinder

volume of pyramid

volume of cone

What does a weighted mean

What does it mean when there is a large standard deviation

A lot of the data is away from the mean

If the mean is skewed to the right of the median, it’s …

positive skewed

If the mean is skewed to the left of the median …

negatively skewed

unimodal

When a distribution has a single peak

bimodal

When a distribution has 2 peaks

uniform distribution

When a distribution has no distinct peaks

compound event

an event that involves two or more independent events ( rolling a pair of dice and taking the sum )

desired outcome

( success) - an outcome that meets a particular set of criteria ( a roll of 1 or 2 if we are looking for numbers less than 3)

independent events

two or more events whose outcomes don’t affect one another ( two cards drawn consecutively)

dependent events

two or more events whose outcomes do affect one another ( two cards drawn consecutively from the same deck)

certain outcome

probability of the outcome is 100% or 1

impossible outcome

probability of outcome 0% or 0

mutually exclusive outcomes

two or more outcomes whose criteria cannot all be satisfied in a single event ( a coin coming up head and tail on the same toss )

random variable

refers to all possible outcomes of a single event, which may be discrete or continuous

theoretical probability

P(A) = # of acceptable outcomes/ # of possible outcomes

probability of a compound event

P ( A or B ) = P(A) + P(B) - P ( A+B)

conditional probability

the probability that event A will occur, given that event B has occurred

probability of two independent events

P ( A and B) = P(A) x P(B)