ALGEBRA Flashcards
5 ways on how two (or more) variables can relate to each other.
Direct Variation, where one variable is a constant multiple of another
x=ky
Inverse or Indirect Variation, where when one of the variables increases, the other one decreases (their product is constant)
x=k/y
Joint Variation, where more than two variables are related directly
x=kzy
Combined Variation, which involves a combination of direct or joint variation, and indirect variation
x=kz/y
Partial Variation, where two variables are related by a formula, such as the formula for a straight line (with a non-zero y-intercept)
x=ky+c
Exponent of imaginary numbers (i) with remainder of; 0=? 1= ? 2=? 3= ?
0= 1 1= i 2= -1 3= -i
whatt is the degree of a polynomial with multiple variables
the term with the greatest sum of its exponents
6 rules in determining significant numbers :)
- non zeroes= S
- zeroes betwe non zeroes = S
- Trailing zeroes w/i decimal = S
- Leading Zeroes = InS
- Trailing Zeroes w/o decimal = InS
- Mulipliers does not matter such as. X10^n
5 available coins in the US & 6 available coinds in the PH
PH:
.01/.05/.25/1/5/10PHP
US:
half: .5$
quarter: .25$
dime: .10$
nickel: .05$
penny: .01$
how many decimal places should you follow when adding/subtracting
follow the least no. of decimal places
how many decimal places should you follow when multiplying/dividing
follow the least number Significant numbers.
in a clock problem, if X is the distance of the minute hand then the distance of the hour hand is?
X/12
when the minute hand moves by a min, the degree of elevation/depression equates to ?
6°
is a progression formed by taking the reciprocals of an arithmetic progression.
harmonic PROGRESSION
how do you geat the mean of each algebraic progressions?
A.M= sum of of terms/ number of terms G.M= nth rooth of the product of n terms = Nthrt(product of n terms) H.M= number of terms/ sum of reciprocal terms
how does the mean of the 3 algebraic progression relate to each other?
H.M = G.M^2/A.M
shortcut to get LCM ON CALCU
LCM (a,b)
- put a/b on calcu, preferrably a being the lesser number
- calcu will simplify and will yield c/d.
- LCM = bXc = aXd
shortcut for GCM, gre8est common factor.
LCM (a,b)
- put a/b on calcu, preferrably a being the lesser number
- calcu will simplify and will yield c/d.
- LCM = a/c = b/d
formula to get the Rth term of a BINOMIAL EXPANSION
given (a+b)^n
rth term = nC(r-1) a^(n-r+1) b^(r-1)
r= rth term duh!?!
formula to get the sum of coefficient in trinomial/binomial expansion
given (ax +by + C)^n
Sum= (a+b)^n - C^n
formula to get the sum of exponents in a polynomial
SoE = SoE(inside) [(n+r-1)Cr]
where r= number of terms inside
Formula to solve the number of terms inside a polynomial
of terms = (n+r-1)C(r-1)
r= number of terms insides n= exponent
HOw to solve the nth term in an ARITHMETIC PROGRESSION
NTH term
nth term= a1 + (n-1)d
where d = an -(an-1)
HOw to solve the sum of n terms in an ARITHMETIC progression
Sn= n/2(a1+an)
for Geometric progression, what is the equivalent of difference from arithmetic progression, or what is the pattern
we have the COMMON RATION where
r= an / an-1
how to solve for the nth term in geometric progression
an= a1 r^(n-1)
n= nth term a1= 1st term r= common ratio
how to solve for the sum of nth terms for geometric progressions
Sn = [a1(1-r^n)]/ (1-r)
what is the difference between an arithmetic progression and a geometric progression in terms of a graph
AP = LINEAR GP = EXPONENTIAL
IN AN INFINITE GEOMETRIC PROGRESSION,
how do you know if it is convergent or divergent, what are they even?
if |r| > 1, it is considered as divergent therefore it increases
if |r| < 1, it is considered as convergent therefore it keeps decreasing infinitely.
how do you solve for the S∞ or the approximate sum of all ∞ terms in an convergent series
S∞ = a1 / (1-r)
What is the pattern in a harmonic PROGreSsIoN
there is a arithmetic progression within the reciprocal of the terms
how to solve for the nth term in a harmonic progression
an= 1/ (a1 + (n-1) d)
how to solve for the sum of first n terms in a harmonic progressions
Sn = nΣ(x=1) [1/ (a1 + (x-1)d) ]
in a clock problem, how do you solve for θ between the hr and minute hand if the hr hand is leadin and vice versa
θ = 30h - 11m/2 - hr hand is leading
θ = 11m/2 - 30h - min hand is leading
how to solve for the GEOMETRIC MEAN
G.M = n^√(product of n terms)
*nth rooth of the product of n terms
how to solve for arithmetic mean
sum of terms/ number of terms
-average lang
how to solve for the harmonic MEAN
number of terms / sum of reciprocal of terms
in a work problem, if the rate of work is equal then you can express the equation as. _________ given the following factors
#of jobs don ( J ) # of workers (W) and time to finish the job (T)
number of worker (W) α number of job done(J) / time to finish (T)
w = kJ/T
WT/K = k
then
W1T1/J1 = W2T2/J2
VIETA’S THEOREM, THE SUM OF ROOTS
r1 + r1 +r3 +…. = -b/a
r1r2 + r2r3 + r1r3 + …. = c/a
r1r2r3 + …… = -d/a
.. and so on,,,
