SAT Math

increase/decrease by a percent formula

P (1 ± %/100)

solutions to a linear equation

1 solution: m1 ≠ m2, b1 = b2

no solution: m1 = m2, b1 ≠ b2

infinite solutions: m1=m1, b1=b1

(m1 is slope 1, and b1 is the y-intercept)

transformation formula

y = ± a(x-h)+k

(h = x-axis)

(k = y-axis

systems of equations

1) ___x + y = ____ (total)

2) ___x + ___y = ______ (value $)

3) y = mx + b

biology/chem questions usually equal?

growth/decay formula:

y = a⋅b^x/c

(a = start symbol/y-intercept)

(b = growth: b>1, decay: 0

what formula would you use when taxes are involved?

increase % formula -> P (1 ± %/100)

what formula would you use when a sale is involved?

decrease % formula -> P (1 ± %/100)

what formula would you use for a no increase/decrease question?

(is)/(of) = %/100

x^a/x^b =

x^a-b

x^a⋅x^b =

x^a+b

(x^a)^b

x^ab

What is a quadratic equation?

ax² + bx + c = 0, where a ≠ 0

quadratic equation in standard form

ax² + bx + c = 0

Slope from Standard Form

m = -A/B

X-Intercept/Standard Form

c/a

Y-intercept standard form

C/B

y-intercept formula

y=mx+b

sliders on desmos trick

for 2 or more variables, add the sliders for the variables and make sure the number theyre on are NOT 0,1, OR 2. the equation will generate a magical number, afterwards, plug in the equations from the answer choices and find the one that matches!

parabola equation

y=ax^2+bx+c

special right triangle rules/theorem

30: x = ?

60: x√3 = ?

90: 2x = ?

what is an integer?

A whole number (NOT A FRACTION) that can be positive, negative, or zero

What is a constant?

a variable/number that you cannot change or substitute

key words to pay attention to in a question:

total, product, sum, difference, quotient (division)

Prime numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

prime numbers are?

numbers that are divisible only 1 and itself

cube formula

Volume = side x side x side

Volume = s^3

square formula

s^2 (and obviously side x side)

Parabola

either 2 solution, 1 solution, or no solution

what should i think of when there is a function with 2 solutions

parabola that has 2 points crossing the x-axis

vertex

vertex form (quadratic)

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

standard formula (quadratic)

y=ax² + bx + c

Quadratic Formula

x = -b ± √(b² - 4ac)/2a

Factor Formula (quadratic)

a (x-m) (x-h)

what should i think of when i read the word "average"

slope

for functions like g(x) -> how would i solve it?

using desmos, replace g(x) into y and locate intersections

onion method

c = 23/d + 11 (make it d =___) -> c = 23/d - 11 -> (c-11) = 23/d ->

d = 23/c-11

midpoint formula

(x₁+x₂)/2, (y₁+y₂)/2, which finds y=mx+b

Probability questions?

want/total (and when it asks for a percentage, incorporate %/100)

Surface area of a cube formula

6s^2

Surface area of a rectangular prism formula

SA=2lw+2lh+2wh

Exterior Angle Theorem

a+b=c (for a triangle)

always order angles on a triangle clockwise!!!

always order angles on a triangle clockwise!!!

pythagoreom theorem

a^2+b^2=c^2

pythagoreom theorem for triangles

hypotenuse - leg -> a = √c^2 - b^2

leg + leg -> c = √a^2 + b^2

Volume of a Cone Formula

V=1/3πr²h

volume of a pyramid formula

V=1/3Bh

Area of a circle formula

A=πr²

Triangle postulates

SSS, SAS, ASA, AAS (not really used), HL

[proves that a triangle is congruent]

Theorem/rules for isosceles right triangle

45: x

90: x√2

Inscribed Angle Theorem

x -> 2x

ex: x=27 -> 2x=54

cylinder volume formula

v=πr^2-h

length of arc formula

x/360 * 2(pi)r

radian to degrees conversion

d/180π=r

Area of a square/rectangle

A=lw/bh

pythagoreom triples

3-4-5

5-12-13

6-8-10

7-24-25

9-12-15

11-60-61

Volume of a rectangular prism

V=lwh

where is the y-intercept in y=mx+b?

b = y-intercept

f(x)/f(0) = ?

y - intercept

what should i do anytime i see a graph?

make a table with the values -> x | f(x)

Distance Formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

tips for the pythagoreom theorem

a = small

b = med

c = large / hypotenuse

Probability Formula

want (#)/total #