# Core 2 Maths Revision Notes

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

- Created by: Charlotte!
- Created on: 27-05-12 19:04

First 349 words of the document:

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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