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This Mathematics Notes is from khanacademy.org/math
where I got Ramanujan in 60 actual days - possibly 3 hours of work everyday
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BODMAS is an acronym and it stands for Bracket, Of, Division, Multiplication, Addition and Subtraction.
In certain regions,
PEDMAS (Parentheses, Exponents, Division, Multiplication, Addition and Subtraction) is the synonym of BODMAS.
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non-statistical - single value like age
statistical question - multiple values - need to gather info about 1+ items/people, etc.
double number lines - show the ratio
dot plot - most often/ frequent, helps finding median, more than x, max and specific - below x
bar graph/histogram - helps finding more than x, less than (some are good, some dont tell)
box & whiskers plot - helps finding median
distribution
left-tailed - decreasing towards left (approximate: skewed to the left: mean is to the left of median and mode)
right-tailed - decreasing towards right (approximate: skewed to the right: mean is to the right of median and mode)
approximately symmetrical - both left-tailed & right-tailed - median will be close to center
for dot plot (only?) we can see below:
outlier = an end element that is far to the right/left - isolated one data point (unusually low or unusually high)
cluster = grouping of data, between two data points, from x to y, saying 100 to 200
peak = most frequent data item
gap = (no values)?
mean (a+b+c+d)/4
median mid element, OR average(2 mid elements)
mode most often
range = max - min
. interquartile range (IQR)
. sort asc
. find median
. IQR = lower half's median - upper half's median
box plot
min Q1 median Q3 max
min lower quartile median upper quartile max
range = max - min
4 = 15 - 11
// 0? ??
min median max
11? 13 15?
|a - b| = |a| - |b|
|a - b| = |b - a|
. Mean absolute deviation (MAD)
. find mean
. average (abs each ele - mean)
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algebra
variables
expressions
equations = a statement that two expressions are equal
value of the variable that makes a true equation is called a solution to the equation
we always have to do the same thing to both sides of an equation to keep it true
Addition and subtraction are inverse operations
inverse operation of addition is subtraction
inverse operation of subtraction is addition
Multiplication and division are inverse operations
inverse operation of division is multiplication
inverse operation of multiplication is division
Inequalities show the relation between two expressions that are not equal.
> open circle and arrow
>= closed circle and arrow
independent variable is a variable that represents a quantity that is being manipulated in an experiment
dependent variable represents a quantity whose value depends on how the independent variable is manipulated
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0 is neither -ve or +ve
0/n=0 where n != 0
n/0=undefined
0/0=undefined
1*n = n
1*0 = 0
1*1 = 1
n^1 = n
n^0 = 1 where n != 0
0^n=0 where n != 0
0^0 = undefined
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25% of 600 is 150
25% . 600 = 150
percent . base = amount
10% = 10/100 = 1/10 = 0.1
~ approximately equal
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shares of stock = how much a person (shareholder) owns in a company
profits (dividends) can be equal or not
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polyhedron
polyhedra
3d shape
flat surfaces
straight edges
Surface area is the amount of space covering the outside of a three-dimensional shape.
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TIPS for khanacademy.org/math
use your calculator instead of given calculator - its a bit cramped
How to work?
instead of doing only arithmetic, OR geometry
i would do 1st class, then 2nd class,
this looks a bit slow but they are better in understanding many things at little bit each
verify
after each answer
i verify in a different way
if 2+4+5 is given
first, i will add 2+4 then add 5 = 11
for verification, i will add 4+5 then add 2 = 11
if both are same, i will Check/ Submit
viewed videos at
X2 speed, possibly after viewing few videos
1st 1 or 2 videos are at 1.5 video speed rate
later videos are at 2 video speed rate
if its text box
that does not give the symbols input
then you can press ENTER to submit answer
if from desktop
you can view all videos at once, continuously
From 6th grade the volume of video seems very slow
GOOD PLUGIN
I used Volume Booster extension of Chrome browser
listen to video/audio sound a bit louder
https://chrome.google.com/webstore/detail/volume-booster/ejkiikneibegknkgimmihdpcbcedgmpo/related
BAD PLUGIN
I installed another chrome extension
https://chrome.google.com/webstore/detail/youtube-playback-speed-co/hdannnflhlmdablckfkjpleikpphncik/reviews?hl=en
and went at 2.25 speed
remembers speed 2.00 Options > Settings tab > 'Remember Playback Speed For All Videos'
but 2.25 failed
This failed as the points were not coming as usual
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