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Mathematics AA SL IB Diploma Topic 1 - Numbers and Algebra
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Detailed notes to the first topic of the Mathematics Analysis and Approaches course of the IB Diploma Program. Includes worked examples.
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topics 1 :Numbers and
Algebra
1.1 Exponentials and logarithms
1. 2 Sequences and series
1. 3 Binomial expansion
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Sunday ,B September
remember
⑦ formulas :
1. ( Atb )2 3. -
a
=
C
-
5. ( a- b) 2
a2t2abtb2 b d '
a -
2abtb2
a. D= b. c
2. a-
the 6 .
I
b d 4. ( atbln
antnantbtnabn
'
dtt tbh d
-
a. b. c a.
#
#
bad b. c
⑨ factorization :
1.
Differenceoftwosquares
b ! ( at b) ( a
"
How to discover : 1. Subtraction .
How to factorize : i. Find square root of both .
Example : A -
-
b )
2. Two terms .
2. Open brackets and choose
3. Both have
square root . a positive and a negative
sign .
3. Place the roots .
2.
Perfectsquare
How to discover : 1. Three terms .
How to factorize : 1. Find
square root of first term Example : A2t2abtb2=( at b)2
2. The first and last and last term .
2
2abtb2=( a b)
'
terms have square root 2.
Open only A -
one pair of
-
.
3.The
signs are t
.
-
f. t .
brackets .
4. The middle term has to be 3. When the
first sign is
negative ,
2. times the root of the first the and
answer is
negative
term times the second one .
vice versa .
4. Put the root step
found in one .
5. Put the to the
answer
power of
two .
, Monday 14 September
math review ,
To do
- :
1. Scientific notation and ⑥
significant figures .
2. Laws of exponents .
O
3.
Solving exponential equations O .
Laws of O
4.
logarithms .
5.
Solving logarithmic equations ⑥ .
DV
6.
Change of base .
7. Arithmetic sequence .
D
Scientific Notation
"
2.5 X 10 =
2.500.000.000.000
-
3.41 X 10-8=-0.000000034
"
A X 10
IS a L 10
where :
✓
\ K E 2T
↳ is element of
an
x 108 t 4.1 x 107 → 2.3 x 108 t 0.41 x 108=2.71×1080
£5.52 :X 10-9 t 2.8 x 10-0=35 x 10
-
'
Ot 2.8 x 10-0-137.8×100=3.78×10-90
Ex 3 :
)
"
108)
"
(1.2 x
.
( 1.2 x 10 =
1.44 x yo
Ex 4 :
25644%-3=2.6×510-52 =
26xtsx1O =
2.6 X 2 x 10-6 =
s.2x
, Significant figures rules
1. All non zero -
digits are significant .
Ex : 74818226 =
8s.fi
123.45=54 .
.
2. All zeros between non zero
-
digits are significant .
Ex : 103.05 = 5 Sf .
780002 =
6 Sif .
3. Zeros to the left of an implied decimal point are not significant whereas ,
zeros to the right of an explicit decimal
Ex 23000=25 .f
are significant .
:
.
23000.0 =
Cost .
4. To the follow
right of a decimal point ,
all
leading zeros are not
significant ,
whereas all zeros that non zero -
digits
Ex 0.0043 =
Is .f
are
significant .
: .
0.0043000 =
5. S.f.
Laws Of exponents 3EHeas
pg .
98
Xm
"
Xmtn 4. X m= I
-
1. .
x =
xm
II fxy)m=xmym
n
xm 5.
-
2.
=
"
3. ( Xm)h=Xm 6. XO = 1
To do :3EHeas
-
exercise 313 99-100
f
pg .
exercise 3C
pg .
101-1020
exercise 3D .2
pg .
105-1060
exercise 313 :
1.
Simplify :
pP
"
a. 54×57--5 103-4
-4
,gH÷= ( 3414=316--43046721
"
( 543=5
1,0¥
Ks
pal
i. K
c
g. =p
-
=
e.
-
. .
2. Write as powers of 2
:
22 b. 29.23 d. 2-3 25 g. 21h 26%2-615271.2-7
s '
a. e. f. 2- .
2- i.
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