1 number and algebra Flashcards
integers
whole numbers, positive or negative.
symbol is Z
natural numbers
positive integers.
symbol is N
rational numbers
whole integers and numbers.
any numebr that can be expressed by a/b where a and b are both integers.
symbol is Q
real numbers
every number on a numberline that isnt imaginary.
symbol is R
irrational numbers
any number that isnt rational
examples of irrationals
pi, surds, cube roots, e
exampls of imaginary numbers
square root of -1
a sequence can be
infinite or finite
what is the general or nth term
Un
what is a deductive rule
goes up with an nth term ‘evenly’. e.g. 2n + 1
what does sigma mean
sum of
what is a series
when the terms of a sequence are added together
what is the n on top of a sigma mean
last term in sum
what does the i underneath the sigma mean
first term
what does Un or Ui mean after a sigma
general term
what is an inductive rule (or recursive definition)
where each term is found from the previous one
what does Un mean in an inductive rule
the previous term (if it follows a sigma or is the rule)
arithmetic sequence
goes up by the same amount each time
geometric sequence
gets multiplied by the same amount each time
divergent sequence
if its heading away from a value
convergent sequence
if its leading to a particular value
periodic sequence
if it has a repeating pattern
oscillating????
??
put pictures of
different types of equations on graphs
what is the symbol for the common ratio
r
symbol for common difference
d
symbol for first term
u1
symbol for previous term
Un-1
nth term of the sequence for a geometric sequence =
Un =
n-1
U r
1
sum of the first n terms of a geometric series is
Sn =
U1(1-r^n)
————-
1-r
sum of an arithmetic series
Sn=
n/2 [2U1 + (n-1)d]
simple interest formula
A = P (1 + nr)
compound interest formula
A = P (1 + r) ^n
compound interest formula (no years)
A = P ( 1 + r/n) ^ nt ????
interst formula
a(1+ r/100)^n
(appreciation) FV =
PV x (1 + r/100)^kn
FV =
future value
PV =
present value
n = (compound interst)
number of years
k = (compound itnerest)
number of compounding periods
r = (compound interest)
nominal interst rate
what is the nominal interst rate
does not consider inflation (as opposed to real
real rate =
nominal rate / inflation rate
deduce what must be true about the inflation and the interest rate for the real value of your investment to grow over time
nominal interest rate must be higher than the inflation rate
PMT =
regular payment
P/Y =
number of payments made in a year
C/Y =
number of compounding periods in a year
(deapreciation) FV =
PV x (1 - r/100)^kn
an expression
some letters standing for numbers without an equals sign
an equation
where an expression is equal to another that can be solved
an identity
something that always equals something else no matter the number
a formula
equation used to derive a value where letters stand for real life values. often multiple unknowns
pascals triangle
one for top three
each number is the sum of the two directly above it.
ones down each side.
start counting from 0 to go downwards for correct coefficents
n
C =
r
r! (n-r)!
(x + y)^n =
x^n + ^nC1 x^n-1 y + ^nC2 x^n-2 y^2 ….
