Honors Algebra two big test (things i forget)

sum of arithmetic sequences

n((a₁+a_n )/2)

sum of geometric sequences

(a₁ (1 - rⁿ)/ (1-r)

explicit Arithmetic

a_n = a₁ +r(n-1)

recursive Arithmetic

a_n = a_n-1 + r , a₁ = known

Explicit Geometric

a_n = a₁( r^n-1)

Recursive Geometric

a_n = r(a_1-n) , a₁ = known

how find the critical number

aⁿ + a^b + 1a + 3 = na^n-1 + ba^b-1 + 1

n Σ c 1=i

c x n

n
Σ ic

1=i

c x (n(n+1))/ 2

n
Σ i²

1=i

n(n+1)(2n+1)/ 6

n
Σ i³

1=i

(n²(n+1)²)/ 4

sum of infinite geometric series

a/(1-r), if [r] < 1

how to solve for nth

use explicit arithmetic

how to find the fraction for a repeating decimal

write the repeating digits as the numerator over the same number of 9s.

Horizontal Asymptotic rules

(rational functions)

slant asymptote

polynomial long division when the top exponent is greater then the bottom

this to piecewise: y = -1/2[x + 2] -1

the same thing with absolute value in parenthesis when approaching + infinity

opposite of that when approaching - infinity

{-1/2(x+2) -1 → x >= -2 , 1/2(x+2) +1 → x< -2}

transformation rules: y = +- a * F(x + b) + c

+- : - means reflect over x axis

a : y * a

b: x + b

c: y + 1

equation of a circle in standard form

(x - h)² + (y - k)² = r²

exponential formula

y = k(a)^x

power formula

y = k(x)^a

adding/subtracting indexes

if adding to index, minus to the variable

if subtracting the index, add to the variable

inflection point

second derivative which determines when the graph changes from cup to cap or vise versa

number line to absolute value

1) use end points to determine center (in the solute value)

2) determine inequality , unity → >, (-) → <

3) determine distance of center to endpoint, (goes on the other side of the absolute value

line from two points

√(x₁ - x₂)² + (y₁ - y₂)²) Make sure in square root

4^(log_2^8x)

2^(2log28x) → 2^(log28x2) → 8x^2 → 64²

logbbk

k

b^(log_b^k)

k

formula for compounding

P * (1 + r/n ) ^nt r already as a fraction