SAT math formulas to Memorize

memorize these for the math SAT

Slope-Intercept form

y=mx+b

Slope Formula

Slope = (y2-y1) / (x2-x1)

Distance formula

distance= rate x time

Parallel lines

same slope

Perpendicular Lines

opposite, reciprocals slope

Factoring patterns

(x+y)(x+y)= x²+2xy+y²
(x-y)(x-y)= x²-2xy+y²
(x+y)(x-y)= x²-y²

Exponent rules: product rule

x²x³= x^(2×3) = x^6
when multiplying two expressions with the same base, add the exponents

Exponent rules: Quotient rule

When dividing two expressions with the same base, subtract the exponents.
ex) (x^7)/(x³)= x^(7-3) = x^4

exponent rules: power rule

When raising an exponent to another exponent, multiply the exponents.
ex) (x²)³ = x^(2×3) = x^4

exponent rules: zero rule

Any non-zero number raised to the power of zero is equal to 1.
ex) x^0 = 1

exponent rules: negative exponent

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent.
ex) x^-5 = 1/x^5

Exponent rules: power of product

When raising a product to a power, apply the exponent to each factor in the product.
(3x)³ = 3³ x³

exponent rules: power of quotient rule

When raising a quotient to a power, apply the exponent to both the numerator and the denominator.
(5/x)³ = (5³/x³)

exponent rules: fractional exponent to radical

the denominator of the fractional exponent represents the root of the radical, while the numerator represents the power of the value under the radical.
x^(2/3) = 3rd radical x²

Quadratic Formula

x= (-b± radical b²-4ac)/ 2a

Vertex form of parabola

y= a(x-h)² +k
(h,k) is the vertex of the parabola. if a is positive, the parabola opens upward and it a is negative, it’ll open downwards.

Vertex of parabola

for a parabola of the form y=ax² +bx+c
the x coordinate of the vertex is equal to -(b/2a)

Mean

mean = (sum of all terms) / (number of terms)

median

middle term when terms are in order from least to greated

Mode

most frequent term

Range

Different between least to greatest values

Standard deviation

The greater the standard deviation, the greater the dispersal of data.
the lower the standard deviation, the lower the dispersal of data.
ex) Set (8,9,10,11,13) has a lower SD than set (1,5,10,16,20).

Percentages

% = (part/whole) x 100
30 is what percent of 40? Solution: (30/40) x100 = 75%

Exponential Growth & Decay

f(x)= a(1± r)^x
f(x)= exponential growth/decay function
a= initial amount

r= growth rate expressed as a decimal (ex: 4% growth is 0.04)
Add r is there is growth and subtract r if there is decay.
x= number of time intervals

Supplementary angles

when added they equal 180 degrees

Vertical angles

opposite angles are equal to each other

Alternate interior/exterior angles

when two PARALLEL lines are cut by a transversal, the alt. int. angles are equal, and the alt. ext. angles are equal

Equilateral and Isoceles Triangles

equilateral: all same sides & angles
isosceles: two sides are the same, two angles are the same

Trigonometry

SOH-CAH-TOA

O= opposite
H= hypotenuse
A= adjacent

Imaginary Numbers: i

i = radical (-1)

imaginary numbers: i²

i² = -1

Circle formula

(x-h)² + (y-k)² = r²
vertex is (h,k)
radius is r

Equilateral Triangle Area

Area = (radical 3)/ 4 (side length)²

Complementary Angles

when added, they equal 90 degrees
The sine and cosine of 2 complementary angles (ones that add up to 90 degrees) are equal
ex) Sin(30) = Cos(60)