Core 2 Maths Revision Notes

Just the notes that I made to revise from, maybe someone else will find them useful!

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Core 2 Maths
1. Indices
am x an = am+n
am / an = am-n
(am)n = amn
a-n = 1/an
a0 = 1
a1/n = n a
am/n = n am
2. Further differentiation
If y=xn then dy/dx = nxn-1
If y=cxn then dy/dx = cnxn-1
If y=f(x)+g then dy/dx = f'(x)+g'(x)
Tangent to (x1,y1) is given at y-y1 = m(x-x1) when m=gradient at the point
Normal to a point has gradient of 1/m where m = gradient of tangent
Stationary point second derivative: negative = maximum , positive = minumun
3. Further integration & the trapezium rule
If dy/dx=xn then y=(1/n+1)xn+1 +c
In definite integral no limits need a +c
Definite integral has limits then do F(b)-F(a)
b
Trapezium rule: f (x)dx0.5h{(y0 + yn) + 2(y1 + y2 + yn-1)} where h=(b - a)/n
a
4. Basic trigonometry
y=sin crosses at 0, 180, 360
y=cos crosses at 90, 270
y=tan crosses at 0, 180, 360 heading up
a = b = c = 2R when R is the radius of the circumference of triangle ABC
sin A sin B sin C
a2 = b2 + c2 - 2bccos A
Area = ½ ab sinC
5. Simple transformations of graphs
A translation of transforms the graph of y=f(x) to y=f(x)+b
A translation of transforms the graph of y=f(x) to y=f(x-a)
A translation of transforms the graph of y=f(x) to y=f(x-a)+b
A reflection in y=0 transforms the graph of y=f(x) to y=-f(x)
A reflection in x=0 transforms the graph of y=f(x) to y=f(-x)
A stretch of scale factor d in the y direction transforms the graph of y=f(x) to y=df(x)
A stretch of scale factor c in the x direction transforms the graph of y=f(x) to y=f(x/c)

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Solving trigonometrical equations
To solve sin bx=k substitute u for bx to simplify, find interval of u, solve sin u=k, substitute back in
cos2 + sin2 =1
tan =sin /cos
7. Factorials and binomial expansions
n!= n x (n-1) x (n-2) ...…read more

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S =a/(1-r)…read more

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