The notes provide summary for five topics studied through the course in IB DP Math Analysis and Approaches (SL): algebra and numbers, functions (linear, quadratics in all forms of it, rational, etc.), trigonometry, statistics and probability, calculus. It also includes a small guide for calculator ...
SIGNIFICANT FIGURES Et 25.30-
Ysig. figures.
0.02 -
I
significantfigure.
700
35g. fig.
-
Harmember
is?
0,083405
en
-
5sig. figures.
1) Zeos to the left are NOT
significant
2)
Make
3)
zeros to the
a non-wo
sight significant.
ARE
sandwich
-----..--,
SCIENTIFIC NOTATION Make
1)
a non-wo sandwich
Decimal after numbe
2) the first
a.10k 12k <
18 3)
Exponentto move as muded.
dicinal
Some
Ex.
pation
Ex
-
35260400000.
-an e 08
002.16 *2 e
↓
10
2.187.14 ause gate
3,52804010
ARITHMETIC NUMBERS
Common difference:a -dU-Un =
Fibonacci sequence:
term:UI
First
1, 1, 2, 3, 5,8
an arithmetic
The nth term of sequence 11 + =
2;12=
3 +
Un u (n =
+ -
1)d
NOTATION
ARITHMETIC SERIES AND SIGMA
Series:sum of
numbers in a
sequence
the sum terms
of an arithmetic
of sequence
Sn (2u 1)d) Sn (u+ un)
Sigma notation:add
up the tune (n
=
+ - =
Ex
timein 3
i1
12 22+
+
1 4
=
+ +
9 14
Ex.
Sn (u (n
first20tums:wo,
Sum of 96,96,94
1)d)
=
= +
=
-
↑
start hur Sc 2(2,100 10 1)) 2)) 1620
=
+ -
-
=
,GEOMETRIC SEQUENCE
Common nation - r
=
Firstterm we -
the nth term of
a
geometric sequence
Un ke(r---)
=
GEOMETRIC SERIES
Geometric series:Sam of in
the turns a
geometric sequent
the a quite
items of
sum
of geometric sequence:
Sn Uelr- 1)
=
& Sn 4 b (1
=
- rn)
r 1 r
-
-
Sigma cx. IHARDER) ESE)*
Do sum
ES5)** 3(5)"13(5)13(5) +3(5)*=
3
=
1
+
+
3(5) 31) +
=
3 1
=
+
5 y
+ +
=
See
as
a
geometric
1
Un 4rn-
=
an
3( w(x) 35) 3 )
3) 3+)-- 2):
-
= =
5
=
=
= -
r
=
3 3
=
-
-
INFINITE GEOMETRIC SEQUENCE
Ex. 1, 2, 4, 8 ... Un =
1, r2,
=
So -- diverges"
=
100
1, 2
Ex. 4,2, 1, 2, 4, 8.
4) as
...
is
. . . . m 4r =
=
=
-
anverges in
U,r-1
Un =
, the an infinite
of
sum geometric sequence
BUT Ime
So =
FINANCE COMPOUND INTEREST
Formula for compound in trust
Ex. 7%
5000D, late
of each
year: FV
DV/1 +
Start:5000$
=
add 1 to the
d percentage
After 1y0:5008.11 0,07) 5350 FV=
future value
3
=
+
k1
yearly
=
After 2ycols:5350. (1.07) 5724.5 grometric PV value
prsent
=
↓
=
After ycou:5724.5(1,07) 6725.22
3 Un 4 rn
=
-
1
a numor of
=
year monthly k12 =
compoundperiods peryear
=
After 7ycou:6125,22.11,07) 6553,98 = k numor
=
of
roo-nominal annual intrust rate
Ex. FV=
1.00. OOP
r7.1
Ta))
=
0
k 12 = 200000
DVA
=
+
n 30=
PV119.586
=
EXPONENTS LOGARITHMS
is
a exponent
latex a =
6 log Nox
>
a
Gabe
Luke
RULES:
↳Ese Logascy=loyax+logay
=ab - c
logacy-logax-logay
ab
(a)
logas* mlogae
=
a=
o
aa =
Ex.
=>
28
-
Eu
mmmebase
rule:
logall=bge
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