ACT Math Formulas

Must need to know math formulas for the ACT.

A = lw

Area of a rectangle

Area of a Triangle

A = πr²

Area of a circle

C = πd or C = 2πr

Circumference of a circle

d = 2r

Diameter and radius of a circle

V = Bh

Volume of rectangular prism

90°

Right angle

180°

straight line

180°

triangle

180°

circle

When a line intersects to parallel lines

2 kinds of angles form: big and small

big angle = big angle

little angle = little angle

big angle + little angle = 180°

a² + b² = c²

Pythagorean theorem

sin(θ) =

opposite/hypotenuse

cos(θ)=

adjacent/hypotenuse

tan(θ)=

opposite/adjacent

A = s²

Area of a square

A = bh

Area of a parallelogram

Area of a trapezoid

v = s³

Volume of a cube

v = lwh

volume of a rectangle

v = πr²h

Volume of a cylinder

90°, 45°, 45° triangle

x√2 (hypotenuse), x, x(other 2 sides)

30°, 60°, 90° triangle

2x (hypotenuse), x (near 60°), x√3 (near 30°)

(n-2)180°

Sum of angles in an n-sides polygon

Angle measure of each angle in a regular n -sided polygon

S = 2(lw + lh + wh)

Surface area of a rectangular solid

S = 6s²

Surface area of a cube

Surface area of a right circular cylinder

S = 2πr² + 2πrh

law of sines

S = 4πr²

Surface area of a Sphere

Volume of a sphere

Slope

y = mx + b

Slope-intercept form of a line

Distance formula

Midpoint formula

Ax + By = C

Standard form

Ax + By = C

Standard form: slope

Ax + By = C

Standard form: y-intercept

x² + y² = r²

Center of circle at (0,0)

(x – h)² + (y – k)² = r²

Center of a circle at (h,k)

x/a + y/b = 1

Standard equation of an ellipse with center (0,0)

(x - h)²/a + (y - k)²/b = 1

Standard equation of an ellipse with center (h,k)

Quadratic formula

D = b² - 4ac

Discriminant

D > 0

there will be two distinct, real solutions

D = 0

there will be one distinct real solution

D < 0

there will be no real solutions. Instead, there will be two complex solutions

The sum of the roots

The product of the roots

The midpoint of the roots and the
x -coordinate of the vertex

nth term = original term + (n - 1)d [d = constant difference between terms]

Arithmetic sequence

or y = kx [k is a constant]

Direct variation

[k is a constant] or x ₁ y ₁ = x ₂ y ₂

Inverse variation

nth term = (Original Term)r^{( n – 1)} [r = constant ratio between terms]

Geometric sequence

Total = Group 1 + Group 2 - Both + Neither

Group Formula

Average x Number of things

Average (Arithmetic mean) or Total

Probability

Permutations (the number of ways to arrange or order a group of things)

_n P _r =

n = number of elements available

r = number of elements chosen

Combinations (the number of ways make different groups out of a group of things)

_n C _r =

n = number of elements available

r = number of elements chosen

(probability of each occurrence) x (value of that occurrence) then add the sums

Expected vaule