ACT Math Equations

Basic snd Advanced Equations

Standard Form

Ax + By = C

Slope-Intercept Form

y = mx+b

Point Slope Form

y2 - y1 = m(x2 - x1)

Slope

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

General Form

Ax + Bx + C = 0

Quadratic Formula

x = (-B ± √(B² - 4AC)) / 2A

Midpoint

((x1 + x2) / 2, (y1 + y2) / 2)

Distance Point to Point

d = √((x2 - x1)² + (y2 - y1)²)

Area of Triangle

A = ½ * base * height

Area of Parallelogram

A = base * height

Area of a Trapezoid

A = ½ (base1 + base2) * height

Area of Regular Polygon

A = ½ * perimeter * apothem

Volume of Prism

V = area of base * height

Surface Area of Right Prism

SA = 2 * area of base + perimeter * height

Volume of Circular Cylinder

V = π * radius² * height

Surface Area of Right Circular Cylinder

SA = 2 * π * radius² + 2 * π * radius * height

Volume of Pyramid

V = (1/3) * base area * height

Surface Area of Right Pyramid

SA = base area + 1/2 * perimeter * slant height

Volume of Circular Cone

V = (1/3) * π * radius² * height

Surface Area of Right Circular Cone

SA = π*radius² + (π * radius * slant height)

Volume of Sphere

V = 4/3 * π * radius³

Surface Area of Sphere

SA = 4 * π * radius²

Center - Radius Form

(x - h)² + (y - k)² = r² (center is h,k)

Area of a Circle

A = πr²

Circumference of a Circle

C = 2πr or C = πd

Area of a Sector

A = (theta / 360)* π * radius²

Pythagorean Theorem

a² + b² = c²

Trigonometric Ratios

Soh - Cah -Toa

Arithmetic Sequence

a_n = a₁ + (n - 1) * d

Sum of Arithmetic Series

s_n = n/2 (a₁ + a_n)

Simple Interest

is calculated using the formula I = PRT, where I is the interest earned, P is the principal amount, R is the rate of interest, and T is the time in years.

Compound Interest n times per year

A = p(1 + r/n)^n*t

Interest Compound Annually

A = P(1 + r)^t

Percent Increase or Decrease

(|old - new| / old) *100%

Difference between Squares

a² - b² = (a + b)(a - b)

Sum of Cubes

a³ + b³ = (a + b)(a² - ab + b²)

Difference of Cubes

a³ - b³ = (a - b)(a² + ab + b²)

Perfect Square Trinomial

a² + 2ab + b² = (a + b)² or a² - 2ab + b² = (a - b)².

Completing Square

x² + bx + (b/2)² or (x + b/2)²

Average

sum of item / number of items

Median

middle number of data

Mode

most frequent number in data

Range

maximum - minimum

Probability

desired outcomes / possible outcomes

Angles of any polygon including triangles add up to

(n-2)*180

Degree vs Length

arc measure / 360 = arc length / dπ

Central Angle

equal to the arc measure

Inscribed Angle

arc/2

Interior Angle

(arc + arc) / angle

Exterior Angle

(big arc - small arc) / 2

Distance Point to Line

|Ax + By + C| / √(A² + B²)

Pythagorean Triples

(9,40,41) , (3,4,5) , (8,15,17) , (5,12,13) , (7,24,25)

Law of Sines

a/sinA = b/sinB = c/sinC

Law of Cosines

a² = b² + c² - 2bc*cos(A)

Geometric Sequence

a_n = a₁ * r^n-1

Sum of Geometric Series

S_n = a₁(1 - rⁿ) / (1 - r)

Determinant of

(a b)

(c d)

is ad - bc

Parallel Lines

Have the same slope

Perpendicular Lines

Have the negative reciprocal slope