# Core One - complete set of revision notes.

Set of notes i typed up for my core one maths exam, which helped incredibly on OCR

Sorry the notes are seperated, we had two different teachers so everything is a little all over the place, but everything is pretty much there, hope it can help anyone, took me long enough to do!

Good Luck!

- Created by: Alice_Hone
- Created on: 26-01-13 13:14

First 293 words of the document:

Core 1

Laws of indices

For indices with the same base:

When multiplying the bases , add together the powers e.g. a2X a3 = a5

When dividing the bases, subtract the powers e.g. a2÷ a3 = a-1

When there is power to a power, multiply the powers e.g. (an)m = anm

Other Laws:

When any number is to the power of 0 it is always equal to 1 e.g. x0 = 1

A negative power becomes a fraction e.g. a-n = a1n

mn m

A fractional power turns into a root e.g. a n = ( a)

Solving indices

To solve an indices the base of the two need to be the same, once this is correct an equation can be

made of just the indices and then solved e.g.

5x-1 = 125 x-1 = 3

5x-1 = 53 x=4

Surds

Simplifying surds

To simplify a surd, 2 factors must be taken out of the original one of which is a square number e.g.

50 = 25 X 2 = 52

Rationalising surds (Rationalising the denominator)

When there is a surd on the bottom of a fraction the surd needs to be removed through multiplying

the whole fraction by another fraction that results in a cancelling out of the surd denominator e.g.

3 = 3 X 7 = 37

7 7 7 7

Geometry

Midpoint

To calculate the midpoint you must add the two co-ordinates together and divide by two

(x1+ x2) (y1+ y2 )

Generally: Midpoint = 2 , 2

For example : (0+8 2+4

2 , 2 ) = (4, 3)

Distance between two points (Length of a line segment)

Create a triangle and use Pythagoras' theorem

a2 + b2 = c2

Use these numbers to calculate the length of the hypotenuse : 42 + 32 = 16 + 9

25 = c2

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