ALGEBRA

Question 1

5 ways on how two (or more) variables can relate to each other.

Answer 1

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

Question 2

Exponent of imaginary numbers (i) with remainder of;
0=?
1=  ?
2=?
3=  ?

Answer 2

0= 1
1=  i
2= -1
3=   -i

Question 3

whatt is the degree of a polynomial with multiple variables

Answer 3

the term with the greatest sum of its exponents

Question 4

6 rules in determining significant numbers :)

Answer 4

1. non zeroes= S
2. zeroes betwe non zeroes = S
3. Trailing zeroes w/i decimal = S
4. Leading Zeroes = InS
5. Trailing Zeroes w/o decimal = InS
6. Mulipliers does not matter such as. X10^n

Question 5

5 available coins in the US & 6 available coinds in the PH

Answer 5

PH:
.01/.05/.25/1/5/10PHP

US:

half: .5$
quarter: .25$
dime: .10$
nickel: .05$
penny: .01$

Question 6

how many decimal places should you follow when adding/subtracting

Answer 6

follow the least no. of decimal places

Question 7

how many decimal places should you follow when multiplying/dividing

Answer 7

follow the least number Significant numbers.

Question 8

in a clock problem, if X is the distance of the minute hand then the distance of the hour hand is?

Answer 8

X/12

Question 9

when the minute hand moves by a min, the degree of elevation/depression equates to ?

Answer 9

6°

Question 10

is a progression formed by taking the reciprocals of an arithmetic progression.

Answer 10

harmonic PROGRESSION

Question 11

how do you geat the mean of each algebraic progressions?

Answer 11

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

Question 12

how does the mean of the 3 algebraic progression relate to each other?

Answer 12

H.M = G.M^2/A.M

Question 13

shortcut to get LCM ON CALCU

Answer 13

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

Question 14

shortcut for GCM, gre8est common factor.

Answer 14

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

Question 15

formula to get the Rth term of a BINOMIAL EXPANSION

Answer 15

given (a+b)^n

rth term = nC(r-1) a^(n-r+1) b^(r-1)

r= rth term duh!?!

Question 16

formula to get the sum of coefficient in trinomial/binomial expansion

Answer 16

given (ax +by + C)^n

Sum= (a+b)^n - C^n

Question 17

formula to get the sum of exponents in a polynomial

Answer 17

SoE = SoE(inside) [(n+r-1)Cr]

where r= number of terms inside

Question 18

Formula to solve the number of terms inside a polynomial

Answer 18

of terms = (n+r-1)C(r-1)

r= number of terms insides
n= exponent

Question 19

HOw to solve the nth term in an ARITHMETIC PROGRESSION

Answer 19

NTH term
nth term= a1 + (n-1)d

where d = an -(an-1)

Question 20

HOw to solve the sum of n terms in an ARITHMETIC progression

Answer 20

Sn= n/2(a1+an)

Question 21

for Geometric progression, what is the equivalent of difference from arithmetic progression, or what is the pattern

Answer 21

we have the COMMON RATION where

r= an / an-1

Question 22

how to solve for the nth term in geometric progression

Answer 22

an= a1 r^(n-1)

n= nth term
a1= 1st term
r= common ratio

Question 23

how to solve for the sum of nth terms for geometric progressions

Answer 23

Sn = [a1(1-r^n)]/ (1-r)

Question 24

what is the difference between an arithmetic progression and a geometric progression in terms of a graph

Answer 24

AP = LINEAR
GP = EXPONENTIAL

Question 25

IN AN INFINITE GEOMETRIC PROGRESSION,

how do you know if it is convergent or divergent, what are they even?

Answer 25

if |r| > 1, it is considered as divergent therefore it increases

if |r| < 1, it is considered as convergent therefore it keeps decreasing infinitely.

Question 26

how do you solve for the S∞ or the approximate sum of all ∞ terms in an convergent series

Answer 26

S∞ = a1 / (1-r)

Question 27

What is the pattern in a harmonic PROGreSsIoN

Answer 27

there is a arithmetic progression within the reciprocal of the terms

Question 28

how to solve for the nth term in a harmonic progression

Answer 28

an= 1/ (a1 + (n-1) d)

Question 29

how to solve for the sum of first n terms in a harmonic progressions

Answer 29

Sn = nΣ(x=1) [1/ (a1 + (x-1)d) ]

Question 30

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

Answer 30

θ = 30h - 11m/2 - hr hand is leading

θ = 11m/2 - 30h - min hand is leading

Question 31

how to solve for the GEOMETRIC MEAN

Answer 31

G.M = n^√(product of n terms)

*nth rooth of the product of n terms

Question 32

how to solve for arithmetic mean

Answer 32

sum of terms/ number of terms

-average lang

Question 33

how to solve for the harmonic MEAN

Answer 33

number of terms / sum of reciprocal of terms

Question 34

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)

Answer 34

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

Question 35

VIETA’S THEOREM, THE SUM OF ROOTS

Answer 35

r1 + r1 +r3 +…. = -b/a

r1r2 + r2r3 + r1r3 + …. = c/a

r1r2r3 + …… = -d/a

.. and so on,,,