# maths

standard form info

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• Created by: Sam
• Created on: 15-06-10 17:40

## Standard form

got to lie between 1 and 10

when it doesnt lie between 1 and 10...move decimal so it does...add 1 to power number if if moved 1 place to left and take 1 off the power number if moved to the right.

example of standard form...17000000 = 1.7 x 10 to the power of 7

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## expanding brackets

times everything outside of brackets by everything inside brackets...eg: 3(y+2) = 3y+6

Expand and simplify

eg: 3 (4+m) +2 (5+2m)

12+3m + 10+4m

= 22+7m

smiley face method!!! (x-4)(x+5)

first do ***= xsquared...then do X x 5 = 5x...then do 4 x X= 4x...finally do -4 x 5 = 20

so...xsquared+5x-4x-20

finally simplify the +5x-4x which = x...so the answer is...xsquared + x - 20

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## Factorising

Factorising is the opposite to expanding.

EG... start with xsquared + 7x + 12...we need to get it into brackets!!!!!

find two numbers that times together to make the 12 and add together to make 7

so (x+4) (x+3) is the answer

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## Direct Proportion

EG...

T is proportional to M

If T=20 when M=4 find the following.......a) T when M=3 b)M when T=10

T is proportional to M

T = K x M.......20=Kx4....so k=5....then T=5xM

a) T=5xM.....T=5x3.....T=15

b) T=5xM.....10=5xM.....M=2

If it is squared then jsut add the square number in.

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## Decimals and fractions

changing decimals to fractions

0.7 = 7/10.........0.64= 64/100 = 32/50 = 16/25.........2.34 = 2 and 34/100

changing fractions to decimals

2/11 = 0.18 reccuring (because 2 divided by 11 = 0.18 reccuring)

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## Surds

surds are numbers which are roots of numbers likw

2....5.....15

general equation for surds: Ta x Tb = Tab

EG

T2 x T2 = T4 = 2.........T2 x T3 = T6

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## Limits of accuracy

EG 1....What would be the longest a stick could be if it were measures as 32 cm to the nearest cm?

the highest possible would be 32.5.... and the lowest would be 31.5

EG 2.... If 53.7 is accurate to 1.d.p. what are the limits of accuracy?

lowest = 53.65 and the highest would be 220.5

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## Powers

• When you multiply you ADD the powers together
• When you divide you take away the powers
• When there is a bracket times the powers

EG......

4 to the power 3 times 4 to the power of 2 = 4 to the power of 4

4 to the power of 4 divided by 4 to the power of 2 = 4 to the power 2

(4 to the power 2) to the power 3 = 4 to the power 6

• to the power of 1/2 means the aquare root of.
• means the cubed root.
• 1/4 means the fourth root (two square roots)
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