ACT math

Sum of interior angles of a polygon

180(n-2) where n is the number of sides

Area of a triangle

A=1/2bh

Area of a parallelogram

A=bh

Area of a trapezoid

A=(b1+b2/2)h

30-60-90 triangle

45-45-90 triangle

Volume of a cylinder

V=πr²h

Volume of rectangular solid

V=lwh

Surface area of a rectangular solid

SA=2lw + 2lh + 2wh

Pythagorean triples formula

Pythagorean triples

(3,4,5), (6,8,10), (9,12,15), (5,12,13)

Circumference of a circle

C=2πr

Area of a circle

A=πr²

Length of an arc

Length of arc/2πr=Angle/360°

Area of a sector

Area of sector/πr²=Angle/360°

Inscribed angle theorum

Cross multiplication

Least common multiple (LCM)

The lowest multiple that is common to two or more numbers

Integers

Any whole number

Prime numbers

2,3,5,7,11,13,17,19, 23,29,31,37,41,43,47,53,59,61

Scientific notation

A number between 1 and 10 multiplied by 10 to the power of something. (Ex: 7.1×10¹⁴)

Positive exponent in scientific notation

Move decimal point to the left by how much the exponent is

Negative exponent in scientific notation

Move decimal point to the right by how much the exponent is

Rational number

A number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. Examples include integers, fractions, and terminating or repeating decimals.

Irrational number

A number that cannot be expressed as a simple fraction or quotient of two integers. Examples include non-repeating, non-terminating decimals such as pi and the square root of 2.

Real numbers

Numbers on the number line

Complex/imaginary numbers

Numbers that are not on the number line (Ex: √-1)

Digits places

Consecutive numbers

Numbers that follow each other in order, such as 1, 2, 3 or 5, 6, 7.

Average speed

Distance/time

Distance

Rate(time)

Slope formula

Slope of a horizontal line

m=0

Slope of a vertical line

m=undefined

What are the slopes of parallel lines?

The same

What are the slopes of perpendicular lines?

Negative reciprocal slopes (Ex: 2 and -1/2)

Midpoint formula

Distance formula

Equation of a circle on a coordinate plane

(x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.

Direct relationship

If x increases, y increases

Indirect/inverse relationship

If x increases, y decreases, etc

Reflection of point (x,y) across x axis

(x, -y)

Reflection of point (x,y) across y axis

(-x, y)

Reflection of point (x,y) across origin

(-x, -y)

Perfect square: (x+y)²=

x² + 2xy + y²

Difference of squares: (x-y)²=

x² - 2xy + y²

Quadratic formula

a⁰⁼

1

a^−m =

1/a^m

(a^m)ⁿ

a^mn

(ab)^m

a^mb^m

a^m × aⁿ =

a^m+n

a^m / aⁿ =

a^m−n

(a/b)^m =

a^m/b^m

a^m/n =

ⁿ√(x^m)

nth term in an arithmetic sequence

a_n= a₁ + (n - 1)d where d is the common difference

Sum of n terms

Sn = (a₁+a_n)n/2

nth term in a geometric sequence

a_n = a₁ * r^(n-1) where r is the common ratio

Standard deviation

Measurement of how spread out numbers are from the middle of the set

Expected value

The expected value is the weighted average of all possible values of a random variable

How to calculate expected value

Multiply each possible value by its probability and sum the results.

What to do when you reverse a squared number? (Ex; (x+1)²=21)

Add ± to your solution

Sum of a finite sequence

S_n= a₁(1-rⁿ ) / (1-r) if r ≠ 1

Sum of an infinite sequence

S_n = a₁ / (1 - r) when |r| < 1

How to find the value of θ in x=sinθ?

Multiply by sin^-1

Tanx=

sinx / cosx

sin²+cos²=

1

When to use law of sine?

When the triangle is AAS, ASA, or ASS (ambiguous)

When is a triangle ambiguous?

ASS

Law of sines

Law of cosines

Area of SAS triangle

1/2 * a * b * sin(C)

Area of SSS triangle

Union (∪)

All numbers together

Intersection (∩)

Only numbers that overlap in both sets

Probability

Wanted outcomes/total possible outcomes

What to do if a problem uses the word or between two possible outcomes?

Add the probabilities together

What to do if a problem uses the word and between two possible outcomes?

Multiply the probabilities

When to use permutation?

When order matters in arrangements

When to use combination?

When order does not matter in arrangements

Super pythagorean theorem

√-1=

i

i²=

-1

i³⁼

-i

i⁴=

1

What is the exponential form of log_ab=x

a^x=b

log_ab=

log_b/log_a

log_ab^x=

x log_ab

log_ab+log_ac=

log_a(bc)

log_ab-log_ac=

log_a(b/c)

Area of a rhombus

A=(d1*d2)/2

Surface area of a cube

SA=6s²

Volume of a cube

V=s³

Volume of a sphere

V=(4/3)πr³

Surface area of a sphere

SA=4πr²

Volume of a cone

V=(1/3)πr²h

Surface area of a cone

SA=2πr²+2πrh

Surface area of a cylinder

SA=2πrh+2πr²

√a*√b=

√(ab)

What transformation is this? y=(x-a)²

It represents a shift of the parabola to the right by 'a' units