DAT QR

Rational numbers

a number that can be writen as a ratio/fraction of two integers

irational numbers

a number that cannot be writen as a ratio/fraction of two integers

You have an irrational love of pi

Prime numbers

a whole nuber that is greater than one and is only divisible by one and itself

Factors

whole numbers that multiply togehter to get another whole number

prime factorization

Factoring out until the result leaves prime numbers

Log rules

Log_x (a) + Log_x (b) =Log_x (ab)

Log_x (a) - Log_x (b) =Log_x (a/b)

Log_x (a²) = 2Log_x (ab)

Factorials

!

product of all integers equal or less than a given positive integer

5! = 5×4×3×2×1

Principal square root

unique positive square root of a non negative real number (When finding the square root, it can be both positive or negative.

the principal square root is always positive

elimination method

substitution method

composite functions

when do you flip the inequality?

when you divide by a negative number

Quadrratic equations

Ax² +bx + c

where X is the solution as long as y=0

X,0

Foling shortcuts

(x+y)² =(X²+2xy+y²)

(x-y)² =(X²-2xy+y²)

(x+y)(x-y)=(x²-y²)

Product of roots

c/a

sum of roots

-b/a

The discriminant

determines how many solutions the quadratic has

B²-4ac

>0, 2 solutions

=0 1 solution

< 0 0 solutions

what slope is perpendicular to a line

its negative reciprocal

how to calculate slope

(Y₂ -Y₁)/(X₂ -X₁)

what does a parabola’s a value affect

a=+ (facing up)

a=- (facing down)

what does a parabola’s b value affect

-b=right

+b=left

what does a parabola’s c value affect

-c=down

+c=up

parabola root

X intercepts of parabola

y=0, x=0

how to calculate vertex

-b/2a

When graphing inequalities, what will the < or > sign result in?

< bellow

> above

Absolute value functions

f(x) = a |x-h|+k

square root functions

f(x) = a Sqrt(x-h) +k

cubic functions

ax³+bx²+cx +d

Distance formula

Sqrt ((x₂-x₁)² + (y₂-y₁)²)

Midpoint formula

(x₂+x₁)/2 , (y₂+y₁)/2

Horizontal velocity equation

time = horizontal distnace/horizontal velocity

Area of a circle

2Pi R²

Circumfrencce of a circle

2pir

Area of a rectangle

A=lw

rectangle area equation

A=lw

Rectangle Perimeter equation

P=2l+2w

area of a triangle

a=bh

what do the interior angles of a triangle add up to

180

what do the complementary angles of a triangle add up to

90

what do the supplementary angles of a triangle add up to

180

combined work formula

1/t1 + 1/t2 = 1/ttotal

Average speed formula

Average = total distance traveled / total time

DIRT formula

Distance = rate * time

Compound interest formula

FV = PV(1 + r/n)^nt

FV = future value

PV= present value

r = rate

n = times compounded

t = time period

Concentration increase formula

C1V1 + C2V2 = CfVf

Dilution formula

C1V1 = (W+V1)Ctotal

Combinations

Order does not matter,

permutations

order matters

Combination formula

n!/r!(n-r)!

n= number of objects, r = number of objects selected

select

permutation formula

n!/(n-r)!

arrange

how much cards are in a standard deck

52, half red, half black

how much suits are in a deck of cards

4

spades and clubs are black

diamonds and hearts are red

No repeating letters

letter # !

repeating letters

letter # ! / repeat #!

and probability

mulitply

or probaility

add chances

at least one probablility for independent events

P (at least one) = 1- (p none)^# of trials

at least one probablility for dependent events

P (at least one) = 1- (p none)^# of trials

P none decreases numerator and denomenator minus one for each trial

union

includes all data points except duplicate values

intersections

shared values within data Sets

Mode

most occuring number in a data set

Standard deviation formula

STDDEV = Sqrt ( (sum of all (values - average)²)/N)

Normal distribution curve

68 95 99.7 rule

Z scores

how far a data point is from the mean in terms of standard deviation

- = below the mean

+ = above the mean

for example, -1 z score means one STD bellow the mean

stem and leaf plot

Z score formula