ACT MATH FORMULA REVIEW

Ellipses:

# of diagonals

= ½*N(N-3)

Sum of angles in a regular

polygon with n sides:

180 (n-2)

Pythagorean

Theory:

𝑎2 + 𝑏2 = 𝑐2

3, 4, 5

5, 12, 13

6, 8, 10

7, 24, 25

8, 15, 17

Averages

Roots, Powers and Exponents

Prime numbers First ten primes: 2,3,5,7,11,13,17,19,23,29

Perfect squares

Commonly used on the ACT:

112=121; 122=144; 132=169;

142=196; 152=225; 162=256; 252=625

Irrational numbers

Cannot be written as a ratio of

two integers: Examples π, √2, √3, etc.

Imaginary Numbers

When squared, gives a negative result

𝑖 ∗ 𝑖 = −1 𝑖 = √−1 √(−𝑥) = 𝑖√𝑥

𝑖1 = 𝑖; 𝑖2 = −1; 𝑖3 = −𝑖 ; 𝑖4 = 1; 𝑖5 = 𝑖1

Mean: Average ǁ Median: Middle number

Mode: Most frequent number

Weighted average: Add

the values for each

occurrence; divide

by total occurrences.

CYLINDER:

Area: πr2 + πr2 + h*2πr

Volume: 𝜋𝑟2 ∗ ℎ

A0 = 1

A1 = A

√𝑎

𝑏=

√𝑎

√𝑏

√𝑎𝑏 = √𝑎√𝑏

AmAn = Am+n

(𝐴𝑚)𝑛 = 𝐴𝑚𝑛

𝐴𝑚

𝐴𝑛= 𝐴𝑚−𝑛

𝐴−𝑚 = 1

𝐴𝑚

𝐴𝑚𝑛 = √𝐴𝑚𝑛

logaax = x (log28 = log223 = 3)

loga(xy) = logax + logay

loga (x

y) = logax − logay

Quadratic Formula

𝐴𝑥2 + 𝑏𝑥 + 𝑐 = 0

𝑥 = −𝑏±√𝑏2−4𝑎𝑐

2𝑎

Distance Time Formula

Speed (v) = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝑑)

𝑇𝑖𝑚𝑒 (𝑡) v =

𝑑

𝑡

CIRCLE Area = 𝜋𝑟2 Perimeter = 2𝜋𝑟

Formula: x2 + y2 = r2

(x-a)2 + (y-b)2 = r2

Midpoint = (a,b); radius = r

For interactive formulas visit www.myclass101.com

Equilateral

triangle:

Volume: Cube: V = s3 Cone: V = 1/3 πr2 h

Pyramid: V = 1/3 lwh Sphere: V= 4/3 π r3

TRIGONOMETRY: SOH-CAH-TOA

Sin ʘ = 𝑂𝑝𝑝

𝐻𝑦𝑝 Csc ʘ =

𝐻𝑦𝑝

𝑂𝑝𝑝=

1

𝑆𝑖𝑛

Cos ʘ = 𝐴𝑑𝑗

𝐻𝑦𝑝 Sec ʘ =

𝐻𝑦𝑝

𝐴𝑑𝑗=

1

𝐶𝑜𝑠

Tan ʘ = 𝑂𝑝𝑝

𝐴𝑑𝑗 Cot ʘ =

𝐴𝑑𝑗

𝑂𝑝𝑝=

1

𝑇𝑎𝑛

Triangles

𝑡𝑎𝑛ʘ =𝑠𝑖𝑛ʘ

𝑐𝑜𝑠ʘ

Isosceles triangle

≅ Congruent (shape and size)

~ Similar (shape)

Area of a trapezoid: Half-point line: (A+B)/2 * h

Area of a parallelogram: L*H

Linear Equations 𝑦 = 𝑚𝑥 + 𝑏

y intercept is b (x=0)

X intercept is 𝑚𝑥 + 𝑏 = 0 (y=0) = −𝑏

𝑚

The slope is 𝑚 =𝑟𝑖𝑠𝑒

𝑟𝑢𝑛=

𝑦2−𝑦1

𝑥2−𝑥1

A line with a perpendicular slope has an

opposite reciprocal of m: −1

𝑚

Distance Formula 𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2

Midpoint Formula (𝑥1+𝑥2

2,

𝑦1+𝑦2

2)

ACT MATH FORMULA REVIEW

Ellipses

# of diagonals

= _______

Averages

Roots, Powers and Exponents

Prime numbers First ten primes: _______________

Perfect squares

Commonly used on the ACT:

112=____; 122=____; 132=____;

142= ___; 152=____; 162=____; 252=___

Irrational numbers

Definition: _____________________

Examples: _____________________

Imaginary Number,

Definition: ___________ _________

𝑖1 =___; 𝑖2 = ___; 𝑖3 = ___; 𝑖4 =___

Mean: __________

Median: __________

Mode: __________

Weighted average: _____________

Triangles

A0 = ___

A1 = ___

√𝑎

𝑏= ___

√𝑎𝑏 = ___

AmAn = ___

(𝐴𝑚)𝑛 = ___ 𝐴𝑚

𝐴𝑛 = ___

𝐴−𝑚 = ___

𝐴𝑚

𝑛 = ___

logaax = ___ loga(xy) = ___

loga (x

y) = ___

Quadratic Formula 𝐴𝑥2 + 𝑏𝑥 + 𝑐 = 0

𝑥 =

Distance-Time Formula

D = ___*___ T= ?

?

t

Linear Equations

𝒚 = 𝒎𝒙 + 𝒃

y intercept is ______

X intercept is ______

The slope 𝑚 =?

? ______

The line with a perpendicular slope

has a slope of ______

Distance Formula 𝑑 = _______________

Midpoint Formula ___________

CIRCLE:

Area

= _______

Perimeter

= ______

Formula:

(___) (___) = __

Midpoint = __ , __

CYLINDER:

Area: ________

Volume: ________

Isosceles triangle

For interactive formulas visit www.myclass101.com

Equilateral triangle

TRIGONOMETRY:

Sin ʘ = _c_ /_b_

Sec ʘ= __ /__

Cos ʘ= __ /__

Cot ʘ= __ /__

Csc ʘ= __ /__

Tan ʘ = __ /__

Area of a trapezoid:

______________

Sum of angles in a

regular polygon with n sides:

_____

Volume: Cube: V = Cone: V =

Pyramid: V = Sphere: V=

° °

𝑡𝑎𝑛ʘ =____ʘ

____ʘ

≅ ________

~ ________

Area of a parallelogram:

_____

L*H

Pythagorean Theory:

Formula: __________

Examples:

3, ___ , ___

5, ___ , ___

6, ___ , ___

7, ___ , ___

8, ___ , ___