Math Review Flashcards
Geometric sequence
General: tn =a(r)^n-1
recursive: tn = a; tn - rtn-1
geometric series
Sn = a(r^n-1)/r-1
Sn = tn-1 - t1/r-1
arithmetic series
Sn = n(t1 +tn)/2
Sn = n[2a + (n=1)d]
arithmetic sequence
general: tn = a + (n-1)d
recursive: t1= a; tn = tn-1 + d
Trig Ratios
sin = csc
cos = sec
tan = cot
quotient identities
tan = sin/cos
cot = cos/sin
pythagorean identities
sin^2 + cos^2 = 1
1 + tan^2 = sec^2
1 + cot^2 = csc^2
Sine law
a/sinA = b/sinB = c/sinC
SSA
ASA or AAS
cosine law
c^2 = a^2 +b^2 - 2abcosC
SAS
SSS
transformation notation
f(x) = af[k(x-d)]+c
quadratic standard equation
y = ax^2 + bx + c
Quadratic Vertex form
y = a(x-h)^2 + k
quadratic factor form
y = a(x-r)(x-s)
finding vertex, x-coordinates
vertex = r+s/2
vertex = -b/2a
quadratic formula
x = -b (+/-) square root b^2 - 4ac/2a
exponential function
f(x) - aB^x
a= initial value
B = Decay factor (1-r/100)
r = Decay in %
exponential growth
f(x) = a(1+growth rate)^x
exponential decay
f(x) = a(1-decay rate)^x
profit and loss equations
profit = r-c
loss = c-r
r = revenue
c = cost
of zeros/solutions
b^2-4ac >0: 2 zeros
b^2 - 4ac = 0: 1 zero
b^2 - 4ac <0: 0 zeros
half life equation
m(t) = a(1/2)^ t/t^1/2
sinusoidal transformation notation
f(x) = asin[k(x-d)]+c
f(x) = acos[k(x-d)]+c
what does variable c mean in sinusoidal function
- vertical translation
affects: - y = x
- max & min
- range
what does variable d mean in sinusoidal function
- horizontal translation
what does variable a mean in sinusoidal function
- vertical stretch or compression
affects: - max & min
- amplitude
- range
what does variable k mean in sinusoidal function
- horizontal stretch or compression
affects: - period changing it to 360/absolute value of k
period
how long something is
cycle
how many times it gets repeated
equation of axis
y = max+min/2
amplitude
y = max - min/2
what is the equation for speed
speed = circumference/period
