core 2

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  • Created by: courteny
  • Created on: 27-04-16 12:02

core two

core two

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rules of logarithms

(http://www.blc.edu/fac/rbuelow/cal/nt4-3.1.gif)

LOGaN=X is the same as a^x=n

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geometric proof

sn= a + ar + ar^2...........ar^n-2 + ar^n-1

rsn=     ar + ar^2...........ar^n-1 + ar^n-1 + ar^n

sn-rsn =  a-ar^n

sn(1-r)= a(1-r^n)                        5% increase  equals 1.05 

sn = a(1-r^n)                               5% decrease equals 95 

        --------

        1-r 

sum to infinity = a/1-r                a=1st number        r=common ratio 

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radian proves

area of sector  =  angle at center         length of arc  = angle of center 

total area             total angle             circumference    total angle of       

area of sector   =             0                                           center 

pie x r^2                      2x pie                      L         0      

area of sector =              0r^2                  2xpiexr    2x pie 

                                          2                   length of arc = r0

                                                                         

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algebra and functions

if f(a)is a polynomial and f(a)=0 then (x-a) is a factor 

if f(a) is a polynomial and f(b/a)=0 the (ax-b) is a factor 

if a polynomial is divided by (ax-b)then the remainder is is f(b/a)

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the sine and cosine rule

    a       =       b    

  sinA         sin B

A^2=B^2+C^2-2BCCOSA

cosA = b^2+c^2-a^2

               2bc 

area = 1/2absinC 

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coordinate geometry in the (x,y)plane

midpoint = (x1+x2  ,  y1+y2)

                      2            2

distance between two points 

d^2=(x2-x1)^2+(y2-y1)^2

equation of a circle is (x-a)^2+(y-b)^2=r^2

angle inside a semicircle is a right angle 

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the binomial expansion

(http://output.to/sideway/images/knowledge/mathematics/algebra/001/algebra_apgp_019a.png)

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graphs of trigonometric identities

(http://a.files.bbci.co.uk/bam/live/content/z7kgkqt/large)

cos graph                                          sin graph 

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differentiation

increasing function f'(x) > 0 

decreasing function f'(x)<0

coordinates of a stationary point find f'(x) find value of x then find y 

f''(x)<0 maximum point 

f''(x0>0 minimum point 

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trigonometrical identies and simple equations

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integration

(http://mathsathawthorn.pbworks.com/f/1236540672/2009-03-08_1930.png)

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