SAT main concepts

Arc length formula

2πr x (angle)/360

Sector area formula

πr² x (angle) / 360

Quadratic formula

(-b±√(b²-4ac))/(2a)

Sum of the roots formula

-b / a

Product of roots formula

c / a

Discriminant formula

b² - 4ac

Complementary rules

• sin(x) = cos(90-x)

• cos(x) = sin(90-x)

x = degree of angle

Sin(x)

opposite / hypot. (SOH)

Cos(x)

adjacent / hypot (CAH)

Tan(x)

opposite / adjacent (TOA)

probability

Target (center event happening) / total (all possibilities)

total angle

180(n-2)

n = # of sides

20% less than

total x 0.8

20% of

total x 0.2

Lines tangent to a circle:

forms a right angle

Radius

r = C / 2π

tangent line + radius

forms right angle

Equation of a circle

(x - h)² + (y - k)² = r²

h = x cor. of center

k = y cor. of center

what does the discriminant tell us?

the number of roots / solutions

how many roots are there if the discriminant is less than 0?

0

Formula to find the x vertex

-b / 2a

What does the average of two roots tell us?

the x vertex

Vertex form

y = a(x - h) ² + k

(h, k) = x, y corrdinants

In vertex form, what is the (x, y)?

(h, k)

Steps to finding the remainder in synthetic division (equation / equation)

• find the number that makes the denominator 0

• plug it into the top numerator

What is 3 ^(2 / 3) in root form?

∛3²

Exponent on exponent

Multiply them

If there are no solutions to the system…

the ratio of coefficient for x & y must be equal

Triangles: direct relationship between…

angle and the opposite side

Bigger the angle…

longer the opposite side

Special right triangles

• 60, 30, 90

• 45, 45, 90

Side length rations for a 60, 30, 90 triangle

• 60: x√3

• 30: x

• 90: 2x

Side length ratio for a 45, 45, 90 triangle

• 45: x

• 45: x

• 90: x√2

What is the standard deviation of a bell curve graph

low

What is the standard deviation of a skewed graph?

Medium

What is the standard deviation for a DT

high

Finding a side of similar triangles

short / long

Slope formula

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

Slope of a perpendicular line

the negative reciprocal

cycle of i starting at i^1

• i

• -1

• -i

• 1

i^0

1

i^1

i

i²

-1

i³

-i

i^4

1

slope intercept form

y = mx + b

m: slope

b: y-intercept when x is 0