Act Math Formulas

Vertical angles are..

Equal

Adjacent angles are supplementary

(x+y = 180)

Sum of Interior angles of a Polygon

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

Triangle area

½ bh

Rectangle Area

A = LxW

Rectangle perimeter

P = 2L + 2W

Square Area

A = s squared

Square Perimeter

4s

Parallelogram Area

A = bh

Circle area and circumference

A= π x radius squared. C = 2π × radius

Trapezoid Area

A = ½ (b1 +b2)h

Kite Area

A= ½ x d1 x d2 (diagonals)

Rectangular Prism Volume

V = lwh

Cube Volume

V = s cubed

Right Cylinder Volume

V = πr squared x h

Volumes of Other Three-Dimensional Solids: V= BxH

(where b is the area of the base and h is the height)

Pythagorean Theorem

a squared + b squared = c squared

Pythagorean Triples

3, 4, 5 Right Triangle; 5, 12, 13 Right Triangle

45 - 45 - 90

X, X, X square root 2

30 - 60 -90

x, x square root 3, 2x

Area of an Equilateral Triangle

A = s squared root 3 / 4

Third Side of a Triangle Rule

The sum of the two shorter sides of a triangle, a and b, must be greater than the longest side of a triangle, c (a + b > c)

Time is equal to

distance/speed

square inches is for

area

cubic inches is for

volume

Kite perimeter

p = 2a +2b

Slope formula

y2-y1/x2-x1

Midpoint formula

(x1+x2 divided by 2), (y1 +y2 divided by 2)

Point-Slope form

y-y1 = m(x-x1)

Distance formula

square root (x1-x2) squared + (y1-y2) squared

Integers are…

whole numbers (1,2, -2)

Prime numbers are…

numbers that are only divisible by one and itself (9= 2, 3, 5)

Rational numbers are…

Any number that can be expressed as a fraction (2/3)

Irrational numbers

any numbers that cannot be expressed as a fraction

Undefined numbers

Zero in the denominator

Imaginary Numbers

real numbers multiplied by the imaginary unit i

Greatest Common Factor

Largest positive number that divides evenly into all numbers in the set.

Least common multiple

Smallest positive integer that is divisible by all numbers in the set.

is/of

%/100

Percentage change

final value - initial value / initial value x 100

Percentage greater than

new/original = 100 + %/100

Percentage less than

new/original = 100 - %/100

Direct proportions (More and More in wording)

y=kx (where k is constant)

Indirect proportion

y=k/x (k is constant - solve for k and decide what x and y is)

Average

average = sum/number of items

weighted average

(average 1)(weight 1) + (average 2) (weight 2) / weight 1 + weight 2

Absolute value

make 2 equations and change sign on the other side of =

a^x x a^y

a^x+y

a^x / a^y

a^x-y

(a^x)^y

a^xy

a^x/y

^y√a^x

a^-1

1/a^x

a⁰

1

n√xy

ⁿ√x (ⁿ√y)

ⁿ√x/y

ⁿ√x/√y

log_ab =c is the same as

a^c =b

Change of Base Rule

log_ba = log(a)/log(b)

log_a(xy)

log_ax+log_ay

log_{a (x/y)}

log_ax-log_ay

log_a1

0

log_ax^y

ylog_ax

In b =c is the same as

e^c =b

Quadratic Formula

-b+- √b² -4ac/2a

Discriminant (under square root in QF can tell you)

positive - 2 real solutions, 0 - one real solution, and negative- 0 solutions (2 complex solutions)

Vertex form

y = a(x-h)² +k

cscx

hyp./opp.

secx

hyp./adj.

cotx

adj./opp

sin^-1

(opposite/hypotenuse)

cos^-1

(adjacent/hypotenuse)

tan^-1

(opposite/adjacent)

When do you use inverse trigonometry?

When you need to find angle and have the sides

sin² 0 + cos² 0

1

Period for sine, cosine, secant and cosecant

2π/b

Period for tangent and cotangent

π/b

Law of sines

sin(A)/a = sin(B)/b = sin(C)/c

Law of Cosines

a² = b² +c² - 2bc cos (A)

For a (2 × 2) matrix {a. b c. d}, the determinant is

ad - bc

det(A)=ab-bc

Matrices formula (find trinomial and solve for roots)

number of successes

divided by total possible outcomes (probability)