SAT MATH PREP

standard form

ax + by = c

slope-intercept form

y=mx+b

vertex form

y=a(x-h)^2+k

vertex

(h,k)

What shape do even-exponent graphs have?

Parabola

What shape do odd-exponent graphs have?

S-shape

what shape do exponential equations have?

curves

what are exponential equations?

equations where the variable is the exponent

what shape do absolute-value function graphs have?

v-shape

Slope key words

each
per
rate
increase
decrease of

Y-intercept key words

starting point
beginning
initial number
flat fees
x=0
have/had

random sampling key words that are never the answer

all
any
ever
never
everyone
always
anybody

percentages divide into

mark-up and discount

equation for mark-up

NP=P+IP

key words for mark-up

tax, margins, profits, tips

equation for discount

NP=P-IP

What do NP, P and I mean in a percentage equation

New price, original price, and rate %

equarion for percentages

x%= new - old /old x100

What do we use when we have two totals?

system of equations

how do we solve a system of equations?

elimination or substitution

how many rules in "algebra rules"

5

algebra rule 1

If lines intersect at one point, the system has one solution. If they intersect at n points, it has n solutions

algebra rule 2

if lines are parallel, the system has infinitely many solutions

algebra rule 3

If the system has infinitely many solutions, equations are multiples of each other and the same line when graphed

algebra rule 4

if slopes are the same, lines are parallel

algebra rule 5

if lines are perpendicular, they are opposite reciprocals

what does opposite reciprocal mean?

flip number and change the sign

what is a line of best fit?

a line that predicts the future behavior of y

equation for probability of x

# of occurences of x / # number of possibilities

p(x) AND p(y)

multiply: p(x)*p(y)

p(x) OR p(y)

add: p(x)+p(y)

to get the mean, median, mode and range, in what order should the data be?

ascending order

mean

average= sum/total

mode

most repetitive number

median

central value

range

highest - lowest

if data is clustered together, what kind of standard deviation does it have?

low standard deviation

if data is spread apart, what kind of standard deviation does it have?

high standard deviation

difference of two squares rule formula

a^2 - b^2 = (a + b)(a - b)

perfect squares rule formula

(a+b)^2= a^2 + 2ab + b^2

negative perfect squares rule formula

(a-b)^2= a^2 - 2ab + b^2

if a^2 = b^2 then

a=b and a=-b

how many exponent rules are there?

5

product rule of exponents

when multiplying, add exponents

quotient rule of exponents

when dividing, subtract exponents

power rule of exponents

when theres a power to a power, multiply exponents

when theres a -n exponent

position change / reciprocal

fraction exponents

goes into a root with numerator inside and denominator outside.

important example for fraction exponents

√x = x^1/2

answers in factoring key words

x-intercepts
solutions
zeros
roots

0 as an exponent equals

1

factoring sign rules: ax^2 + bx + c

(+)(+)

factoring sign rules: ax^2 - bx + c

(-)(-)

factoring sign rules: ax^2 + bx - c

(+)(-)

factoring sign rules: ax^2 - bx - c

(+)(-)

quadratic formula

x = -b ± √(b² - 4ac)/2a

if b^2 - 4a > 0

2 real solutions

if b^2 - 4a < 0

2 imaginary solutions

if b^2 - 4a = 0

1 real solution

if |a| = b

then a=b and a=-b

what measures population of living organisms?

exponential growth or decay

exponential growth formula

y=a(1+r)^t

exponential decay formula

y=a(1-r)^t

what do a, r and t represent in an exponential growth or decay equation?

initial population, percentage and time

in a vertex form equation, if a is +

then k is the minimum value of y

in a vertex form equation, if a is -

then k is the maximum value of y

in what 2 ways can we go from standard form to vertex form?

using the equation h=-b/2a or finding a new C

equation to go from standard form to vertex form

h=-b/2a

rule for finding a new C when going from standard form to vertex form

a must = 1

steps to find a new C when going from standard form to vertex form

get rid of c
calculate a new c
add new c to equation
factor
compress

how many steps to find a new C when going from standard form to vertex form?

5

equation to find a new C when going from standard form to vertex form

c = (b/2)^2

perimeter of a rectangle

P=2b+2h

Area and perimeter of a square

A=s^2
P=4s

all interior angles in a quadrilateral add up to

360º

Area of a triangle

A=bh/2

area of trapezoid

a = (b1 + b2)h/2

area of a parallelogram

A=bh

rules for parallelograms

opposite sides are parallel and equal
opposite angles are congruent
adjacent angles are supplementary

supplementary angles

add up to 180º

complementary angles

add up to 90º

tangent of a circle

line that touches a circle in exactly one point that is perpendicular to its center

how do you find the length of an arc?

xº/360º =

how do you find the area of an arc?

xº/360º = arc/πr^2 and cross multiply

isoceles triangle

has two equal sides and two congruent angles

scalene triangle

all sides and angles are different

equilateral triangle

all angles and sides are equal, angles=60º

acute

angle is less than 90º

obtuse

angle is greater that 90º

right angle

angle measures 90º

pythagorean theorem

c^2 = a^2 + b^2

what do you need to apply pythagorean theorem?

two sides of a triangle

Types of special right triangles

45-45-90 and 30-60-90

45-45-90

two equal sides and hyp = x√2

30-60-90

s1 = x, s2 = x√x, and hyp = 2x

similar triangles

have same shape, congruent angles , but sides are proportional

two parallel lines and a transversal

if angles looks alike, they are congruent. If angles lokk different, they are supplementary

sine xº

opp/hyp

cosine xº

adj/hyp

tangent xº

opp/adj