Algebra final review

Question 1

Arithmetic sequences Explicit form

Answer 1

an = a1 + d(n-1)

Question 2

Arithmetic sequences Sum form

Answer 2

sn = n(a1+an /2)

Question 3

How to find missing terms in sigma notation, ex: a25

Answer 3

Plug number of term in for “k”
ex: 6-2k —-> 6-2(25) —-> a25=-44

Question 4

Look over questions 93-96 on exam review

Answer 4

I’m serious 😤

Question 5

Geometric explicit form

Answer 5

an= a1*(r) to the n-1

Question 6

Geometric sum form

Answer 6

. /
sn= a(l-r to the n / 1-r)
/

Question 7

Geometric sum infinity form

Answer 7

s of infinity=a/1-r

Question 8

Point-slope form

Answer 8

y-y1=b(x-x1)

Question 9

How to find slope from two points form

Answer 9

y2-y1/x2-x1

Question 10

How to solve absolute value equation

Answer 10

Get absolute value part to one side, then make two equations, one the same, the other one set the non- absolute value side as a negative.

Question 11

How to solve absolute value inequality

Answer 11

Same thing as an equation, but make sure that the absolute value is not less than a negative number because then it would be no solutions.

Question 12

Starting points for a square root graph

Answer 12

(0,0), (1,1), (4,2)

Question 13

Relationship between denominator of exponent and root of radical

Answer 13

Denominator is the root
ex. 7 to the 3/4 —-> 4th root of 7 to the 3rd

Question 14

What to do to exponents when numbers are being divided

Answer 14

Subtract them

Question 15

What to do to exponents when numbers are being multiplied

Answer 15

Add them

Question 16

Exponent of an exponent

Answer 16

Multiply them

Question 17

Negative exponent

ex: x to the -3

Answer 17

Change which part of the fraction it is on (top or bottom), and set exponent to be positive

ex: 1/x to the 3

Question 18

Anything to the 0 power is

Answer 18

1

Question 19

0 to any power is

Answer 19

0

Question 20

How to find possible solutions (explain them as well)

Answer 20

p/q

p- factors of the constant

q-factor of Leading Coefficient

Factors of constant/Factors of Leading Coefficient

Then do synthetic division to simplify into quadratic, then use quadratic formula

Question 21

How to find holes

Answer 21

What ever cancels out, make sure that you set it equal to zero, then plug it into the SIMPLIFIED equation to find the y-value.

Question 22

How to find verticle asymptotes

Answer 22

Whatever did not cancel out in denominator, set it equal to 0

Question 23

How to find horizontal asymptote

Answer 23

Check degree of numerator

Top < Bottom ——-> y=0
Top = Bottom ——->
y= Top LC / Bottom LC
Top > Bottom ——-> None

Question 24

How to find domain (relation to HA, VA, and holes)

Answer 24

Set denomenators to CANNOT equal 0

Question 25

Insurance form.

Answer 25

A=P(1 + r/n) to the nt A= Money accumulated P= Starting value (Principle) r= Annual interest rate (decimal) n= Number of times that the interest is compounded a year t= Time in years

Question 26

How to find domain if "x" is under a radical

Answer 26

Set it GREATER THAN OR EQUAL TO zero

Question 27

How to find domain if "x" is in demoinator

Answer 27

Set it unequal to zero

Question 28

Sum of cubes

Answer 28

a^3 + b^3 = (a+b)(a^2 - ab + b^2)

Question 29

Difference of cubes

Answer 29

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

Question 30

End behavior

Answer 30

Degree Even Odd . + up/up down/up LC . - down/down up/down