ACT Math Formula Sheet

Arithmetic Sequence

a_n = a₁+ d(n-1)

Geometric Sequence

a_n = a₁ x r^n-1

Sum of arithmetic sequence

S_n= n(a₁ + a_n)/2

Sum of finite geometric sequence

S_n= a₁ (1-r_n/1-r)

Mean

Sum of terms / number of terms

Median

Middle number

Mode

Most common number

Range

Biggest-smallest

Probability

Number of desired terms / total number of terms

Multiple Probabilities

P(A and B) = P(A) × P(B)

Distance Formula

√[(y1 – y2)² + (x1 – x2)²]

Midpoint Formula

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

Area of Triangle

A= ½ x b x h

45:45:90 Triangle Ratio

x : x : x√2

30:60:90 Triangle Ratio

x : x√3 : 2x

Area of Trapezoid

(b1 + b2 )/2 × h

Sum of angles in n-sided figure

(n – 2) × 180°

Area of Rectangle

Length × width

Area of parallelogram

Base x height

Circle Arc Length

Central angle / 360° × circumference

Circle Sector Area

Central angle / 360° × area

Area of Circle

πr²

Circumference of Circle

2πr

Diameter of Circle

2r

Equation of a circle graph

(x – h)² + (y – k)² = r²

Surface Area of Rectangular Prism

2(length × width + length × height + width × height)

Volume of Rectangular Prism

lwh

Volume of Right Cylinder

V = πr²h