sat math formulas/tips

“than” and “of” means that is the denominator in the %

(A is what % of B = (a/b)*100) (A is what % more than B (a-b/b)*100)

“B must increase” or “A must decrease”

whatever is changing is in the denominator ((a-b/b)*100) or ((a-b/a)*100)

% change formula

((FV-IV)/IV) * 100

directly proportional

ratios stay the same (x1/y1=x2/y2)

inversely proportional

product stays the same (x1*y1=x2*y2)

distance

speed*time

work

rate*time

total cost

unit cost*quantity

net rate

rate1+rate2+rate3…

when plugging in from options

always start w middle options bcz youll see if it has to be less or more

median (odd) (n=total number of terms)

((n+1)/2)th term

median (even) (n=total number of terms)

((n/2)th term+(next term))/2

mode

max repeated value/highest frequency

frequency

 # times repeated

total # terms

add all frequencys

SD

deviation from data to the mean value

small SD

data is closer to the mean, small variation in the data, higher concentration in data

large SD

data is far from mean, more variation in the data, low concentration in data

concentration

how close together data is

if u are given a data set with a lot of values

make ur own data set with less values (3-4) and solve the question w ur new set

can always be found on box whiskers plot

min n max value, lower n upper quartile, median

range

max-min value

interquartile range

upper quartile-lower quartile

(box whiskers) 1

min value

(box whiskers) 2

lower quartile

(box whiskers) 3

median

(box whiskers) 4

upper quartile

(box whiskers) 5

max value

(box whiskers) median can be

anywhere on the box

(box whiskers) always 25%

min-low qrt , low qrt - med , med-up qrt , up qrt-max

if its not marked on box whiskers graph then

you dont know it

if a side/extention of a triangle is produced, the exterior angle formed is equal to

the sum of the two interior opposite angles to it

45, 45, 90

x,x,x(sqrt(2))

30, 60, 90

x, x(sqrt(3)), 2x

similar triangles

same shape diff size, cooresponding angles are equal, cooresponding sides in same ratios

for any closed shape

(area of triangle 1/ area of triangle 2 ) = (ratio of sides) = (perimiter of triangle 1/ perimeter of triangle 2)

area of regular hexagon

(3(sqrt(3))/2) * x²

area of equalitaral triangle

(sqrt(3)/4)*x²

circumference circle

2*pi*r

area circle

pi*r²

arc length

(x/360)*(2pi*r)

chord

line that joins any two points in the circumference of circle

segment

default means minor segment

minor segment

part under a chord (smaller part)

diameter

longest chord of the circle

sector

area between 2 radii and arc (default means minor sector) (there is minor n major sector)

area of sector

(x/360)*(pi*r²)

angle between a tangent and radius

90

angle in a semi circle

always 90

angles drawn in same segment

are equal to eachother

angle at center of cirlce is

twice the angle at the circumference

length of arc in radians

(x/2pi)*(2pi*r)

2pi radians is the same as

360 deg

area of sector in radians

(x/2pi)*(pi*r²)

tangents drawn from an external point to a circle are

equal in length

pythagoream theorem for 3d shapes

sqrt(l²+b²+h²)

if u have pi while solving smthn

never multiply it in

trig ratios

only apply to right triangles

csc

sin^-1

sec

cos^-1

cot

tan^-1

when u have a side of a triangle in decimal

make it into decimal/1 so its a fraction

cos(x)

sin(90-x)

sin(x)

cos(90-x)

in a right triangle ur angles are

90, x, 90-x

pi radians

180 deg

deg to radians

x* (pi/180)

radians to deg

x* (180/pi)

random sample

unbiased result , can b generalized

selected sample

biased result, cant b generalized

if cos(x)=sin(y)

x+y are complementary angles

complementary angles

add up to 90

(sinx)²+(cosx)²=

1

large sample size

less margin of error

small sample size

more margin of error

solution in system of eqs

pt of intersection

eq w one solution

x-int

for complex eqs

use desmos

if data is symmetrically distributed from middle

the middle is the median

data is concentrated

small SD

data is not v concentrated

high SD

surface area

all faces added

surface area of cube (l=length)

6*l²

volume of cube

l³

(discriminant)>0

2 solutions

(discriminant)=0

1 solution

(discriminant)<0

no solutions

always start math sections

w easy questions

after doing ez questions

do medium questions (1-1min 30s)

mid pt formula

(x1+x1)/2

sum of roots

-b/a

product of roots

c/a

x coordinate of vertex

-b/(2a)

slant height eq

s = √(r² + h²)

slant height

NOT same as normal height (vertical) it is like the hypotenous