Math formulas + def

What is common factor

a number that divides into 2 or more numbers

ex. common factor of 12 is 1,2,3,4,6,12

What is the greatest common factor

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

ex. the GCF of 12 and 15 is 3, because this is the largest number both parties can be factored too

prime factor

a prime number cannot be divided by any other numbers except 1 and themselves

ex. prime numbers of 12 is 2 and 3

composite number

a positive integer greater than 1 that has more than two factors

ex. 4 , 1,2,4

least common multuple

smallest # that is muluple of two or more numbers

ex. 3 and 5 leaste commmon multiple is 15

irrational # vs rational #

numbers that cant be written as fractions or decimals > ex. pi

rational= integers, decimals, fractions

EXPONENT RULES

1. Product of Powers
aᵐ · aⁿ =

2. Quotient of Powers
aᵐ / aⁿ =

3. Power of a Power
(aᵐ)ⁿ =

4. Power of a Product
(ab)ⁿ =

5. Power of a Quotient
(a/b)ⁿ =

6. Zero Exponent
a⁰ =

7. Negative Exponent
a⁻ⁿ =

11. One Raised to Any Power
1ⁿ = 1

EXPONENT RULES

1. Product of Powers
aᵐ · aⁿ = aᵐ⁺ⁿ

2. Quotient of Powers
aᵐ / aⁿ = aᵐ⁻ⁿ

3. Power of a Power
(aᵐ)ⁿ = aᵐⁿ

4. Power of a Product
(ab)ⁿ = aⁿ · bⁿ

5. Power of a Quotient
(a/b)ⁿ = aⁿ / bⁿ

6. Zero Exponent
a⁰ = 1 (a ≠ 0)

7. Negative Exponent
a⁻ⁿ = 1/aⁿ

11. One Raised to Any Power
1ⁿ = 1

PEMDAS

• P: Parentheses (or Grouping Symbols)

• E: Exponents

• MD: Multiplication and Division (LEFT TO RIGHT)

• AS: Addition and Subtraction (LEFT TO RIGHT)

what percentage of 40 is 8

40x=8 > 0.2 = 0.20

what # is 20% of 40

0.20 × 40 = 8

what # is 8 20%

0.20 times x = 8 > 40

decimal to % ex. 2.15

move two places to the right > 215

% to decimal ex. 66.7%

move two places to the left > 0.667

% to fraction 0.1%

write it over 100 then multiple depending on the number of decimal places in the % ex. 1/1000 0.1 has one decimal places to multiple by 10

decimal to fraction > ex. 2.55

write it over 1 then mulitple depending on the # of decimal places in the decimal ex. 2.55 has two decimal places so 2.55/1 times 100 top and bottom

what is the equation of standard form

Ax+By= C

slope intercept form

y=mx+b

point slope form

y-y1=m(x-x1)

two point form

y2-y1/x2-x1

average rate of change

f(b)-f(a)/b-a

f(b) you plug in the bigger number (x) to the givene f(x) equation and the place it on the numerator

F(a) you plug in the smaller number (x) to the given f(x) equation and then place it on the numerator f(a)

when working with inequalities…

change the sign when multiplying or dividing with negative # you must flip the inequality

relative error formula

|Measured value - known value|

known value

relative error with no known value

|greatest possible error| / measured value

absolute error formula is

|measured value - known value|

possible error formula ex. 12.35

you look at the given number and see how many places it has then divide by 2

ex. 12.35 has two decimal places so it becomes the hundredths = 0.01/2 = 0.005

the formula for the sum of the interior angles of a polygon is

(n-2)180

what is the sum of the interior angles of a hexagon

(6-2)180= 720

the sum of the interior angles of a polygon is 1,080. How many sides does the polygon have?

(n-2)180=1080 > n=8

we are given the sum of the interior agnles just need to find how many sides.

the measure of one interior angles of a regular polygon is 150 degree. how many sides does the polygon have

we are givene only one interior angles so we have to use the the formula

one interior angles of a regulat polygon = (n-2)180/n > (n-2)180 / n = 150

the measure of one exterior angle of a regular polygon is 72. how many sides does this regualt polygon have

one exterior angle = 360/n > 360/n = 72

volume and surface area of prism

volume = BH (b=area of base)

SA= 2B + PH (b= area of base / p= perimeter of base)

use mean when…

When the data has no extreme outliers and you want the overall average

ex. Test scores: 80, 82, 85, 88, 90

use median when…

When there are outliers or skewed data. It gives the middle value.

Incomes: $30k, $35k, $40k, $45k, $1,000k

use mode when…

When you want the most common value. Useful for categories or repeated values.

use range when..

When you want to describe how spread out the data is.

Small SD

describe the data values with the mean

type of variations

location data points

shape

• Data values are close to the mean.

• Very little variation.

• The data points are clustered together.

• PEAKS HIGH IN THE MIDDLE AND IS NARROW

large SD

describe the data values with the mean

type of variations

location data points

shape

• Data values are far from the mean.

• Lots of variation.

• The data points are spread out.

• peak is very low and more spread out

normal SD

• Data values are somewhat spread out, but not extremely.

• There is a reasonable amount of variation.

• BELL CURVE AKA SYMETRICAL AKA UNMODAL