SAT Math Equations and Tips - Junior and Senior Year 2024 Digital SAT

Quadratic Formula

Quadratic Formula

The Discriminant

b^2-4ac

Arc Formula

s = r θ

Negative Exponents (x^-n?)

1/x^n

(x-y)^2

x^2-2xy+y^2

Pyramid Volume Formula

V = 1/3(lwh)

Percent Change Formula

% change = difference/original x 100

Rectangular Prism Volume Formula

V = lwh

X - Intercept for Standard Equation

c / a

If the Quadratic has a Positive Discriminant...

The Quadratic has 2 real solutions

Distance Formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

Solving Strategies for Quadratic Equations

Distribution, Factor, Expand, Simplify, Foil

Average Formula

T = AN (A - Average, T = Total, N - Number of things)

Sum of the Roots (y=ax^2+bx+c)

-b/a

Product of the Roots (y=ax^2+bx+c)

c/a

Mean

The average of the data set.

Median

The middle number in the data set.

Mode

The value that occurs most frequently in a given data set.

Arc Length Formula

θ/360 x 2πd

Standard Form of a Line Equation

Ax + By = C

Sphere Volume Formula

V = 4 / 3πr³

Slope Formula for Standard Equation

-A/B

Sector Area Formula

θ/360 x πr²

Quadratic Standard Equation

y = ax² + bx + c

Sum of Degrees Formula

180(n-2)

Cone Volume Formula

V = (1/3)π r^(2) h

When the Discriminant equals Zero...

The Quadratic has 1 Solution

When the Discriminant is Positive...

The Quadratic has 2 Real Solution

When the Discriminant is Negative...

The Quadratic has No Real Solutions (2 Imaginary)

Circle Equation

r² = (x-h)² + (y-k)²

Are square roots allowed to be in the denominator of a fraction?

No

PEMDAS

Parentheses, Exponents, Multiplication or Division, Addition, Subtraction

i = ?

√-1

i^2 = ?

-1

30 - 60 - 90 Triangle

45 - 45 - 90 Triangle

Similar Triangles have...

Identical Angles, Proportional Sides, and The Same Trigonometric Functions

(x + y)(x - y) = ?

x² - y²

Fractional Exponents: x^(y/z)

z√(x^y)

When a negative number is raised to an odd exponent, the number becomes...

Negative

when a negative number is raised to an even exponent, the number becomes...

Positive

√(x/y) = ?

√x / √y

Direct Proportions Formula

x1 / y1 = x2 / y2

Similar Triangle's Angles are always...

Congruent

Y - intercept of Standard Equation

C/B

Growth Formula

y = a(1+r)^t

Decay Formula

y = a(1-r)^t

Inverse Proportions Formula

x1 y1 = x2 y2

Quadratic Vertex Formula

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

Cylinder Volume Formula

y = π r^2 h

Quadratic Factored Form

y = a (x-r1)(x-r2)

Pythagorean Triples

Midpoint Formula

[ (x₁+x₂) / 2, (y₁+y₂) / 2 ]

Soh Cah Toa

sin= opposite/hypo; cos= adjacent/hypo; and tan= opposite/ adjacent

Rate Formulas

D=RT and W=RT

MADSPM

Multiply
Add
Divide
Subtract
Power
Multiply

Slope Formula

m = (y₂- y₁) / (x₂- x₁)

Arcs

Proportions of the circumference

Sectors

Portions of the area

Radians to Degrees Formula

(radians) x (180°/π)

Degrees to Radians Formula

(degrees) x (π/180°)

Total Amount of Radians in a Circle

2π

Complex Conjugate

(a+bi) and (a-bi)

Y - Coordinate of Vertex in a Quadratic Formula

Standard Equation for a Line

y = mx + b

Exponent and Root Rule

Point-Slope Formula

y - y₁ = m (x - x₁)

Density Formula

D= m / v

D = Density
M = Mass
V = Volume

Volume Formula for a Cube

V = s^3

Percent Formula

% = Part/Whole x 100