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Sec	
  4	
  Formulas	
  

»	
  Standard	
  Deviation	
                                                          Where	
   x =	
  mean	
  
Standard	
  Deviation	
  of	
  an	
  Ungrouped	
  Data	
  Set	
                                  N =	
  no.	
  of	
  terms	
  
                                         ∑x     2
                                                         2
                                                                                             	
  
Standard	
  Deviation	
  =	
                        − x 	
  
                                            N
Standard	
  Deviation	
  of	
  an	
  Grouped	
  Data	
  Set	
  

Standard	
  Deviation	
  =	
  
                                         ∑ fx −     2
                                                             2
                                                                 	
  	
  
                                         ∑f x
	
  

»	
  Multiplication	
  of	
  Matrices	
  
        ! a b $! e f $
e.g	
   #      &#             & 	
  
        " c d %# g h &
                "             %
      ! ae + bg af + bh $
=	
   #                      & 	
  
      # ce + dg cf + dh &
      "                      %
	
  

»	
  Simple	
  &	
  Compound	
  Interest	
                                   Where	
  P	
  =	
  principal	
  
Simple	
  Interest	
                                                                  i %	
  =	
  interest	
  rate	
  per	
  annum	
  
I	
  =	
  P × i % × n	
                                                             n	
  =	
  no.	
  of	
  years	
  
A	
  =	
  P + I	
                                                                   I	
  =	
  interest	
  
Compound	
  Interest	
                                                              A	
  =	
  accumulated	
  amount	
  
                    i n                                                      	
  
An	
  =	
  P(1 +       ) 	
  
                   100
	
  


»	
  Hire	
  Purchase	
  &	
  Utilities	
  Bills	
  
Total	
  Interest	
  =	
  Loan × Flat	
  Rate × Loan	
  Period	
  (In	
  Years)	
  
Repayment	
  Amount	
  =	
  Loan	
  +	
  Total	
  Interest	
  
                                                     Repayment Amount
Monthly	
  Repayment	
  (Installment)	
  =                                                	
  
                                                   Loan Period (In Months)



»	
  Money	
  Exchange	
  &	
  Taxation	
  
Chargeable	
  Income	
  =	
  Assessable	
  Income − Personal	
  Relief	
  
Assessable	
  Income	
  =	
  Annual	
  Income − Donation	
  
	
  
	
  

	
  
	
  
Sec	
  3	
  Formulas	
  
»	
  Functions	
  &	
  Graphs	
  

Graphs	
  of	
   y = ax 	
  (where	
  n=1)	
  
	
  

For	
  a>0,	
                                                    For	
  a<0	
  




	
                                                 	
                                	
  
	
  

Graphs	
  of	
   y = ax 3 	
  (where	
  n=3)	
  
	
  

For	
  a>0,	
                                                       For	
  a<0	
  




                                                          	
                                	
  
	
  

	
  
	
  
	
  

	
  
a
Graphs	
  of	
   y =     	
  (where	
  n=-­‐1)	
  
                       x
	
  

For	
  a>0,	
                                                   For	
  a<0	
  




                                                      	
                         	
  
	
  

                       a
Graphs	
  of	
   y =      	
  (where	
  n=-­‐2)	
  
                       x2
	
  

For	
  a>0,	
                                                   For	
  a<0	
  




                                                         	
  
                                                                                        	
  
	
  
	
  

	
  
	
  
	
  
Graphs	
  of	
   y = a x 	
  (where	
  a	
  is	
  a	
  positive	
  number)	
  
	
  

   y = a x 	
                                                             y = a x 	
  




                                                                   	
  
	
  

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Elementary Mathematics List of Formulas

  • 1. Sec  4  Formulas   »  Standard  Deviation   Where   x =  mean   Standard  Deviation  of  an  Ungrouped  Data  Set   N =  no.  of  terms   ∑x 2 2   Standard  Deviation  =   − x   N Standard  Deviation  of  an  Grouped  Data  Set   Standard  Deviation  =   ∑ fx − 2 2     ∑f x   »  Multiplication  of  Matrices   ! a b $! e f $ e.g   # &# &   " c d %# g h & " % ! ae + bg af + bh $ =   # &   # ce + dg cf + dh & " %   »  Simple  &  Compound  Interest   Where  P  =  principal   Simple  Interest   i %  =  interest  rate  per  annum   I  =  P × i % × n   n  =  no.  of  years   A  =  P + I   I  =  interest   Compound  Interest   A  =  accumulated  amount   i n   An  =  P(1 + )   100   »  Hire  Purchase  &  Utilities  Bills   Total  Interest  =  Loan × Flat  Rate × Loan  Period  (In  Years)   Repayment  Amount  =  Loan  +  Total  Interest   Repayment Amount Monthly  Repayment  (Installment)  =   Loan Period (In Months) »  Money  Exchange  &  Taxation   Chargeable  Income  =  Assessable  Income − Personal  Relief   Assessable  Income  =  Annual  Income − Donation          
  • 2. Sec  3  Formulas   »  Functions  &  Graphs   Graphs  of   y = ax  (where  n=1)     For  a>0,   For  a<0           Graphs  of   y = ax 3  (where  n=3)     For  a>0,   For  a<0                
  • 3. a Graphs  of   y =  (where  n=-­‐1)   x   For  a>0,   For  a<0         a Graphs  of   y =  (where  n=-­‐2)   x2   For  a>0,   For  a<0                
  • 4. Graphs  of   y = a x  (where  a  is  a  positive  number)     y = a x   y = a x