ACT Math Formulas

distance formula

distance formula

sqrt((x1-x2)^2 + (y1-y2)^2

Volume of a rectangular prism

v=lwh

volume cyl

pi r^2 h

graphing a circle

(x-h)^2 + (y-k)^2 = r^2

exponent rules

X^3 * X^5 = X^8 (multiply=add exponents)
X5/X3 = x2 (divide=subract exponents)
(x3)5= X15 (raised to that power=multiply)

area of a trapezoid

1/2 (b1 + b2)h

45, 45, 90

x, x, xSqrt2

30, 60, 90

30= x, 60 =xSqrt3, 90=2x

degrees in circle

360 degrees

complimentary angles

add to =90

supplementary angles

add to =180

sequence sum

sn= n/2 (2a + (n-1) d)

tangent means

touching

slope

m=y2-y1/x2-x1 (rise/run)

slope intercept form

y=mx+b
m=slope
b=y-intercept

midpoint

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

area of a square or rectangles

A=base <b> height (b</b>h)

area of a parallelogram

A=bh

area of circle

pi r ^2

circumference (perimeter of a circle)

2πr

circumference of an arc (outside edge piece of circle)

2πr* (degree measure center of arc/360)

Area of a triangle

A=1/2bh

Perimeter of a triangle

P=a+b+c

Perimeter of a quadrilateral

P = 2(length) + 2(width) OR P=s+s+s+s

degrees in a quadrilateral

360 degrees

degrees in triangle

180 degrees

central angle of a circle

an angle whose vertex is the center of the circle

Area of a section of a circle

pi r ^2 * (degree measure center of arc/360)

probablility

# wanted/total

odds

# wanted/# total - # wanted

Pythagorean Theorem

a²+b²=c²

sinx

SOH (opp/hyp)

cosx

CAH (adj/hyp)

tanx

TOA (opp/adj)

perfect right triangles

3-4-5,
5-12-13,
7-24-25,
8-15-17

FOIL

First, Outer, Inner, Last

Factoring

the opposite of FOIL

difference of squares

a^2 -b^2 = (a+b)(a-b)

to quickly find the distance between two points

make the distance the hypotenuse of a right triangle and use a²+b²=c²

2 parallel lines cut by a transversal

corresponding angles=congruent
alternate interior angles=congruent
alternate exterior angles=congruent
consecutive interior angles=supplementary
consecutive exterior angles=supplementary

solving f(x) problems

plug in the number given for x and solve

solving f(g(x)) problems

plug the number given for x into the G equation first and solve. Then take the solution from the G equation and plug it into the F equation.

2 step problems

always REREAD the instructions to make sure you have solved the problem all the way through

Arthmetic sequence

ADD to get the next term (same number)

Geometric sequence

MULTIPLY to get the next term (same number)

reciprocal

a "flipped over" fraction

mean

average (add all up and divide by # of terms)

mode

value that occurs most

median

middle number (must be in order smallest to largest) (if two in middle, average them together)

range

largest number minus the smallest number

prime number

can only be divided by 1 and itself

per

divide

perfect of OR fraction of

_______ of _______ is ________
a x b = c

parallel lines slope

same slope

perpendicular lines slope

opposite reciprocal (or negative reciprocal) (flip and change sign)