LINEAR EQUATION
summary :
gradient form y = mx + c
general form Ax + By + C = 0
intercept form x/a + y/b = 1

QUADRATIC EQUATION
summary :
general form y = ax2 + bx + c
perfect square form y = a(x+p)2 + q

BASIC POLYNOMIALS
( a + b ) = a2 + 2ab + b2
( a - b ) = a2 - 2ab + b2
( a2 - b2 ) = ( a + b )( a - b )

BASIC TRIGONOMETRY
a = adjacent
o = opposite
h = hypotenuse
Pythagoras Theorem :      h2 = o2 + a2
remember Mr Soh Cah Toa      (    Sin θ = o / h      Cos θ = a / h      Tan θ = o / a    )
0o 30o 45o 60o 90o
sin 0 ≈ 0.707 ≈ 0.866 1
cos 1 ≈ 0.866 ≈ 0.707 0
tan 0 ≈ 0.577 1 ≈ 1.732
remember All Sinful people Telan Crocodile
Sin is + All are +
Tan is + Cos is +

EXPONENTS
am × an = am+n
am an = am-n
am × bm = (a×b)m
am bm = (ab)m
(am)n = am×n

LOGARITHM
log (xa) = a log (x)
log (xy) = log (x) + log (y)
log (x/y) = log (x) - log (y)
logST = logaT / logaS

BASIC STATISTICS
measures of central tendency :
ungroupd data grouped data
mean x = ( ∑ xi ) N x = ( ∑ fixi ) ( ∑ fi )
mode observation that occurs the most frequency distribution table ------> modal class
histogram ---------------------------> mode
median modd = [(N+1)/2]th observation
meven = [ (N/2)th observation + (N/2 + 1)th observation ] 2
cumulative frequency table & m = L + [ (N/2 - F) fm ] C
ogive & (N/2)th observation
measures of dispersion :
ungroupd data grouped data
range largest observation - smallest observation midpoint of highest class - midpoint of lowest class
interquartile range SMILE ! Q1 = L1 + [ N - F1) fQ1 ] C
Q3 = L3 + [ N - F3) fQ3 ] C
variance σ2 = [ ∑(xi-x)2 ] N = [ ( ∑xi2 ) N ] - x2 σ2 = [ ∑fi(xi-x)2 ] ∑ fi = [ ( ∑fixi2 ) ∑ fi ] - x2
standard deviation σ σ
effects of data being changed uniformly :
measures of central tendency measures of dispersion
each data is added by k new mean = original mean + k
new mode = original mode + k
new median = original median + k
range DOES NOT CHANGE
interquartile range DOES NOT CHANGE
variance DOES NOT CHANGE
standard deviation DOES NOT CHANGE
each data is multipied by k new mean = original mean × k
new mode = original mode × k
new median = original median × k
new range = original range × k
new interquartile range = original interquartile range × k
new variance = original variance × k2
new standard deviation = original standard deviation × k


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