sum calm sat review type shi

yeah im going test optional lol

Isoceles triangles

AB = AC
<B = <C

Equilateral Triangles

All slides equal n all angles equal

Right triangles

Pythagorean theorem + B is 90 duh

Pythagorean triplets

3/4/5 & 5/12/13 will follow the pythagorean theorem

Triangles are the same if

• 2 angles that are the same

• ratio of sides and perimeters are equal

The sum of the lengths of 2 sides of a triangle must be

greater than the length of the third side

Polygon angle equation

180(number of sides) -2

For data analysis, it must

• have a well defined population

• randomly selected participants

• everybody has a chance of being chosen

• assigned to treatment group @ random

Data analysis terms

Representative: reflects attributes of the population

Treatment: Measuring if something will change a condition

How to calculate margins of error

• Take the average they give u and then add or subtract the margin of error
  ex: 1.4 hours of x per day with a margin of error of 0.2 → 1.4 +- 0.2
  
  ^ to calculate total numbers its the same process but move your decimal point so its 0 point your number and then multiply by the pop

How to generate a function from a table

• Start with f(x) = a x b^x - make sure your x value is 0 so it turns into b=1

• plug the y value into the fx

• solve for a

• recreate equation again with a

• plug in a different x value from the table into the (x)

• solve for b

• final equation yes

Slope

y2-y1 / x2-x1

point slope form

y-y1=m(x-x1)

intercept slope form tip

if u need to solve for b u can take a random y value u were given and plug it in

quadratic equations

y = ax² + bx + c
x int form - y = x+- p and x +- 1
vertex form
y=(ax-h)² + k
h is the x coordinate of the vertex, k is the y

Non linear functions

• when f(x) = 0 find x int,

• if f(0) fine y int

Mean

the average of a set of numbers

Median

The middle of a let of numbers (must be ordered L→ G or vice versa)

Mode

Most common # in a set of numbers

Range

Difference between the largest and greatest in a set

arc length if its in radians

s = theta r

arc length if its in degrees

s =θ/360×2 π r

circumference

2 π r

arithmetic sequence

adding or subtracting consistent diff between numbers

arithmetic sequence equation

term u want to solve for = 1st term + difference (what u have to add or subtract) (term # + or - 1)
nth term = a1 + d (n+1)

Geometric sequences

Result from multiplying or dividing rather than subtracting or adding

Geometric sequences equation

An = a1 x r ^ n-1

Nth term = first term x the number its being multiplied or divided by to the power of term # -1

Infinite solutions

4 = 4

No solution

4 = 5

How to solve absolute value equations

graph the left side of the equation as y = left side and y = right side in a different collumn, and then where they intersect is the answer

Absolute value tricky stuff

anything = 0 only has 1 SOLUTION

any expression + any positive number = 0 is a NO SOLUTION

if any equation is equal to a negative number IT IS NO SOLUTION

exponent multiplying rule

u add them tg instead of multiplying (x² o x³ = x^5)

When multiplying polynomials

list them by coefficients and then variables in alphabetical order

exponent rule - a^0 = ?

1

adding exponents rule

x^m + x^n = m - n

power of a power exponent rules

(a^m)^n = a^mn

neagtive exponents…

get split up into 1/a^positive of whatever number it was to the power of

for function problems

you can graph one line as the equation - f(x) = the equation you are given and the other as f(x) = the value you are solving for

min faces the

left

max faces the

right

for inequalities

graph the equation & the point its asking u,

how to make linear functions

subtract your smallest x value from your biggest on the bottom
same thing for y but on the top
put into slope intercept form

plug in y and x’s of your choice

solve for b

remake equation (if that is what its asking you)

acute

less than 90

obtuse

above 90

However & Nevertheless…

always follow a comma when used as a transition word and are (usually) preceded by a semi colon

IDP clause

sub & a v that form a complete thought

Dependent clause

idp clauses but do NOT form a complete thought

Usually start with “maker words” like because

Colons and single dashes

Must come after an IDP clause
make sure it is a complete thought. anything that makes you expect a continuation is not a complete thought.

double dashes

go around an interruption

does NOT need to follow an IDP
in the first part before the interruption and the part after how to make an IDP

commas in a list

• commons go in between each item, before the and (noun)

• they also go in between two adjectives that do not fit together

commas not in a list

can follow an IDP to add additional info but the additional info CANNOT be an IDP
can also be seperating additional info interrupting an IDP

conjunctions remembering trick

fanboys

for and not but or yet so

commas w/ conjunctions

go inbetween 2 IDPS

has to be fanboys

false conjuctions

cannot be used w/ a comma to connect idps - HAD TO BE USED W/ A SEMI COLON

thus, furthermore, however, moreover, therefore,