Math Formulas Flashcards
distance formula
d = rt
time formula
t = d/r
rate formula
r = d/t
(rate = speed, so this is the same as s = d/t)
the quadratic formula
radical rule of exponents
n√x = x1/n
area of a trapezoid
A = ([a+b]/2)h
area of a rhombus
A = 1/2(D1)(D2)
surface area of a rectangular prism
SA = 2LW + 2WH +2LH
area of a circle
A = πr2
circumference of a circle
C = 2πr = πd
a central angle has the same measure as
the intercepted angle
any inscribed angle in a semi-circle is
a right angle
an inscribed angle is ___ the measure of the intercepted arc
half
what are the most common triangles on the ACT?
3-4-5
6-8-10
5-12-13
7-24-25
8-15-17
what are the measurements of the 30-60-90 special right triangle?
- the side opposite the right angle is 2x
- the side opposite the 30˙ is x
- the side opposite the 60˙ is x√3
what are the measurements of the 45-45-90 special right triangle?
- the side opposite the right angle is x√2
- the two sides opposite 45˙ angles are x
sum of interior angles of a polygon
sum of interior angles = (N-2)180˙
where N = the number of sides
number of diagonals in a polygon
number of diagonals = (N[N-3])/2
where N = the number of sides
slope-intercept form
y = mx + b
standard form
Ax + By = C
(on the ACT, convert this to slope-intercept form to solve for y)
slope formula
midpoint formula
distance formula
equation of a circle
(x-h)2 + (y-k)2 = r2
multiplication principle
- if there are n ways to select one item and m ways to select another, then there are nm ways to select one of each type*
- ex: if there are 3 shirts, 4 pants, and 5 shoes, 3x4x5 = 60 outfits are possible
ordering of objects
there are n! ways to order n different objects
- n! = n(n-1)(n-2)(n-3) . . .
- ex: 5 different books can be arranged 5! = 120 different ways
- evaluate on TI-83/84 by typing the number you would like to find the factorial of, then click ‘math’ and go to PRB and select 4. Hit enter on the main screen and it will calculate the factorial.
properties of logs
- logbx = y if and only if by = x
- logb(xy) = logbx + logby
- logb(x/y) = logbx - logby
- logbxn = nlogbx
- logbx = (logx) / (log b)
pythagorean identities
sin2θ + cos2θ = 1
1 + tan2θ = sec2θ
1 + cot2θ = csc2θ
tangent pythagorean identity
tan2θ + 1 = sec2θ
cotangent pythagorean identity
1 + cot2θ = csc2θ
for a quadratic equation ax2 + bx + c = 0, the sum of the roots is
-b/a
for a quadratic equation ax2 + bx + c = 0, the product of the roots is
c/a
what is the discriminant?
b2 - 4ac
- if it is greater than zero there are 2 real solutions
- if it is equal to zero there is 1 real solution
- if it is less than zero there are no real solutions, but 2 complex solutions
what is the vertek form of a parabola?
y = a(x - h)2 + k
- vertex = (h,k)
- if a > 0 the parabola opens up
- if a < 0 the parabola opens down
difference of squares
x2 - y2 = (x-y)(x+y)
given standard form Ax + By = C, what is the slope and y-intercept?
slope = -A/B
y-intercept = C/B
the exterior angle of a triangle is equal to
the sum of the two opposite internal angles
the sum of the exterior angles of a triangle are
360˙
what is the generic formula for volume?
the area of the base times the height
arc length formula
s = (θ/360˙)(2πr) if θ is in degrees
s = rθ if θ is in radians
properties of trig graphs
y = Asin(Bx) or y = Acos(Bx)
- amplitude = |A|
- period = 2π/|B| or 360˙/|B|
degrees to radians
multiply by π/180˙
radians to degrees
multiply by 180˙/π
if an is the nth term and d is the common difference, then
an = a1 + (n-1)d
the sum of the first n terms (Sn) is
Sn = (n/2)(a1 + an)
mean
mean = (sum of the terms) / (number of terms or amount of different terms)
probability formula
probability of outcome happening = (number of desired outcomes) / (total possible outcomes)
probability of two events both happening
probability of event = (event A)(event B)
area of an arc
area of arc = (πr2)(degree measure of center of arc / 360)
circumference of an arc
circumference of arc = (2πr)(degree measure of center of arc / 360)
