# Mathmatics revision guide Gcses to additional maths^^ i am yr 11 ad maths grp plz ask me questions take it in mind im nt a genius tho =o

## Mathmatics revision guide Gcses to additional maths^^ i am yr 11 ad maths grp plz ask me questions take it in mind im nt a genius tho =o

Algebra (yr6-7)

Algebra is one of the easiest topics to come about, it varies through questions such as

find x:

2x=2

x means a number which is multiplied by 2 = 2 therefore we divide the 2x by 2 which equals...

1!

wasn't that easy =)

lets try HARDER one

2x-5 = 10

theres a minus 5 this time =o what do we do?

you simply carry -5 against the equal sign which makes it a plus.

2x = 15

now its much clearer^^

x = 15

2

x = 7.5

that is pretty much all you need for algebra at this stage... if you feel this is waay too easy check out some higher level stuff^^

Algebra is one of the easiest topics to come about, it varies through questions such as

find x:

2x=2

x means a number which is multiplied by 2 = 2 therefore we divide the 2x by 2 which equals...

1!

wasn't that easy =)

lets try HARDER one

2x-5 = 10

theres a minus 5 this time =o what do we do?

you simply carry -5 against the equal sign which makes it a plus.

2x = 15

now its much clearer^^

x = 15

2

x = 7.5

that is pretty much all you need for algebra at this stage... if you feel this is waay too easy check out some higher level stuff^^

Last edited by 016016 on Wed Jan 18, 2012 4:56 am; edited 1 time in total

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## mathmatic revision algebra yr 8-10

at yr 8-10, it starts to get more difficult..

first thing you do rearrange this to get the subject to x.

3x+29 = 6x - 1

all we do is cross the -1 to the + 29...

remember when there is an equal sign, you do the opposite of the sign.

so u get

3x + 30 = 6x.... take 3x over to 6x...

30 = 3x

3x = 30 change it around to get 3x at left hand side

x=10 done!

Rearranging subject seems harder than it truly is^^

change the subject to x

t = abc

x

here, you simply carry the x to the t... remember that x is dividing the abc so it becomes a times by t.

tx = abc

now simply just take t over abc this time because t is timesing the x, when carried over becomes divide.

x = abc

t

easy peazy^^

now for some harder work...

tx = go-x

r

we move the r to tx like the previous question.

rtx = go-x

now move the x to the other side

rtx + x = go

this is the clever part.

factorise the rtx + x so that only x is on its own

x(rt+1) = go

now we can just get the brackets to the =go!

x = go

rt+1

and that is all there is to it^^

first thing you do rearrange this to get the subject to x.

3x+29 = 6x - 1

all we do is cross the -1 to the + 29...

remember when there is an equal sign, you do the opposite of the sign.

so u get

3x + 30 = 6x.... take 3x over to 6x...

30 = 3x

3x = 30 change it around to get 3x at left hand side

x=10 done!

Rearranging subject seems harder than it truly is^^

change the subject to x

t = abc

x

here, you simply carry the x to the t... remember that x is dividing the abc so it becomes a times by t.

tx = abc

now simply just take t over abc this time because t is timesing the x, when carried over becomes divide.

x = abc

t

easy peazy^^

now for some harder work...

tx = go-x

r

we move the r to tx like the previous question.

rtx = go-x

now move the x to the other side

rtx + x = go

this is the clever part.

factorise the rtx + x so that only x is on its own

x(rt+1) = go

now we can just get the brackets to the =go!

x = go

rt+1

and that is all there is to it^^

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## easy version of solving fractions... division

I always found it hard to work out divisions in a fraction and my teacher was like wtf.. its so ez... she showed me how to do it^^ and ill do the same to show how easy it can be~

lets look t this example.

2 / 4

3 5

now the trick is...

... swap the 2nd numbers around, the ned and the donkey... (numerator and the denominator)

the add a cross...

2 X 5 ( remember if you are multiplying fractions, just multiply top nb and bottom number

3 4 as it is)

so you get

10/12

which is the answer =)

clever isnt it? xD

2/3 = 0.66.

4/5 = 0.8

= 10/12 =)

easy~!

lets look t this example.

2 / 4

3 5

now the trick is...

... swap the 2nd numbers around, the ned and the donkey... (numerator and the denominator)

the add a cross...

2 X 5 ( remember if you are multiplying fractions, just multiply top nb and bottom number

3 4 as it is)

so you get

10/12

which is the answer =)

clever isnt it? xD

2/3 = 0.66.

4/5 = 0.8

= 10/12 =)

easy~!

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## Additional maths~ differentiation

differentiation is just about additional maths gcse... it appears frequently on Alevel maths.

you first of all get a question like

y = 12x(1) + 3x(2) -2x(3) () means squared or cubed.

first of all bring down the squared sign to the front number like so by taking down a sqr each time...

dy = 12 + 6x - 6x(2)

dx

now swap it round so it becomes

dy= 6x(2) - 6x -12

dx

from this... do what wecan do, cancel out the ugly numbers to smaller ones =)

dy = (x(2) - x - 2)

dx

which can be factorised to

x =2 x = -1

this work is usually to do with graphs... there are 4 more parts to this... + integration which is the opposite~ keep tuned^^

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## easy indicies

this topic is very easy but it comes and goes through the year.

basics in which you need to know is when ur dividing an indicies, you take away and when ur multiplying u add =)

6(20) / 6(15) = 6(5)

6(30) x 6(10) = 6(40)

there not so hard =')

basics in which you need to know is when ur dividing an indicies, you take away and when ur multiplying u add =)

6(20) / 6(15) = 6(5)

6(30) x 6(10) = 6(40)

there not so hard =')

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## rules of trigonometry

there are 3 parts to a triangle a b c or adjacent opposite and hypotenuse.

basic trig question is adjacent and opposite sides are 3 and 4, find the hypotenuse x.

this is easy and you need to remember it to get easy marks.

when youre asked to find hypotenuse of this question u must remember its 3 4 5 =)

this is the most simple form you will probably find.

but how do you work it out?

well hypotenuse means the longest side and there is a mathematical formula to find this out.

adjacent squared + opposite squared will always equal to the hypotenuse squared.

so in this case 3(2) + 4(2) = 5(2).

9 + 16 = 25.

now why is 3 4 5 simple?

well 3 4 5 is simple because its multipliers works the same way.

for example, 6 8 10 works

36 + 64 = 100

and im sure 9 12 15 works as well.

look for these shortcuts to extend the time to look at other hard questions.

basic trig question is adjacent and opposite sides are 3 and 4, find the hypotenuse x.

this is easy and you need to remember it to get easy marks.

when youre asked to find hypotenuse of this question u must remember its 3 4 5 =)

this is the most simple form you will probably find.

but how do you work it out?

well hypotenuse means the longest side and there is a mathematical formula to find this out.

adjacent squared + opposite squared will always equal to the hypotenuse squared.

so in this case 3(2) + 4(2) = 5(2).

9 + 16 = 25.

now why is 3 4 5 simple?

well 3 4 5 is simple because its multipliers works the same way.

for example, 6 8 10 works

36 + 64 = 100

and im sure 9 12 15 works as well.

look for these shortcuts to extend the time to look at other hard questions.

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## Solving inequalities this is acutally A level.. lol! its a topic cant miss a mark on folks!

this is in algebraic questions sometimes... its actually as easy as normal expansion and factorization...just watch =)

20-x < 2(6x+5)

20 - x < 12x+10

10 < 13x

10 < x

13

but sometimes the examiner wants you to swap the croc clips around...

x > 10

13

arrow means V

bigger number > smaller number

smaller number < bigger number

bigger than 0 > 0 > smaller than 0

arrows with a dash underneathe just means greater or smaller than or equal to.

just remember it like crocodile eats bigger prey... thats all i can say on that topic.

20-x < 2(6x+5)

20 - x < 12x+10

10 < 13x

10 < x

13

but sometimes the examiner wants you to swap the croc clips around...

x > 10

13

arrow means V

bigger number > smaller number

smaller number < bigger number

bigger than 0 > 0 > smaller than 0

arrows with a dash underneathe just means greater or smaller than or equal to.

just remember it like crocodile eats bigger prey... thats all i can say on that topic.

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## Completing the square all the way up to A level.

here we have a quadratic expression.

x2+20x

we want them in brackets =3

but how? we can't factorize it...

or can we?

what we do here is split the 2nd number... the +20 in to 2 and put it in brackets.

so

(x+10) (x+10) now this gives us x2 + 20x + 100

now all we have to do is make it the same as the first number... so

x2+20x = x2 + 20 + 100 - 100

so... (x+10)2 -100 is the answer =)

the 2 after anything means squared by the way people!

there are harder ones but i cant be bothered to do it.. its the same thing just involves other signs such as sqaure roots and waste of time =)

x2+20x

we want them in brackets =3

but how? we can't factorize it...

or can we?

what we do here is split the 2nd number... the +20 in to 2 and put it in brackets.

so

(x+10) (x+10) now this gives us x2 + 20x + 100

now all we have to do is make it the same as the first number... so

x2+20x = x2 + 20 + 100 - 100

so... (x+10)2 -100 is the answer =)

the 2 after anything means squared by the way people!

there are harder ones but i cant be bothered to do it.. its the same thing just involves other signs such as sqaure roots and waste of time =)

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## standard deviation

the trick to standard deviation is quite simple... but some people get it wrong.

it is just the number or the mean divided by the class width...

class width being 1>10 then 9 because difference between 1 to 10 is 9.

it is really that simple... but there maybe a question before that which may say work out the mean from a table, find the standard deviation then plot the graph.

dont think that the normal bar graph will do, work out the standard deviation first then plot the graph, you will get very different answers from the mark scheme.

it is just the number or the mean divided by the class width...

class width being 1>10 then 9 because difference between 1 to 10 is 9.

it is really that simple... but there maybe a question before that which may say work out the mean from a table, find the standard deviation then plot the graph.

dont think that the normal bar graph will do, work out the standard deviation first then plot the graph, you will get very different answers from the mark scheme.

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## there are nothing simpler than....

Differentiation finding the tangent xD

right the trick here folks.. is to think what can i do? =D now theres a question.

you will be given a evil equation like...

3x(4) + 2x(3) + 2x + 4

we just take the square sign and multiply the number... like the last differentiation question.

12x(3) + 6x (2) + 2

now tangent means change in y over the change in dx...

say it was at 6,3 on a graph

we get

12 (6) cubed + 36 squared +2

i can't be bothered to work that out but in GCSE this is called the Mt or M1.

when ever there is a tangent don't fret and think of dy/dx... d being the delta sign of course.

so if this is y =...

it will become 3 = 72 (6) 36 (2) + 2

then to work out a normal... well it is easier to plot it on a graph... visit my maths website for better explanation. this is easier explained in mymaths website with graphs..

right the trick here folks.. is to think what can i do? =D now theres a question.

you will be given a evil equation like...

3x(4) + 2x(3) + 2x + 4

we just take the square sign and multiply the number... like the last differentiation question.

12x(3) + 6x (2) + 2

now tangent means change in y over the change in dx...

say it was at 6,3 on a graph

we get

12 (6) cubed + 36 squared +2

i can't be bothered to work that out but in GCSE this is called the Mt or M1.

when ever there is a tangent don't fret and think of dy/dx... d being the delta sign of course.

so if this is y =...

it will become 3 = 72 (6) 36 (2) + 2

then to work out a normal... well it is easier to plot it on a graph... visit my maths website for better explanation. this is easier explained in mymaths website with graphs..

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## how to find a tangent full

y=x(3) - x(2) - 2x -3

and find the tangent at (3,9)

first of all... differentiate so

dy = 3x(2) - 2x -2

dx

at (3,9) ; 9(2) - 18 - 2 substitute the x number from the coordinates to get this.

so m1 = 19 now we can find the C

y = 19x + C

19x3 + C = 9 or the y we substitute the x from before here to get 57

C = -48 9-57 = 48

therefore y = 19x - 48 and this is done!

and find the tangent at (3,9)

first of all... differentiate so

dy = 3x(2) - 2x -2

dx

at (3,9) ; 9(2) - 18 - 2 substitute the x number from the coordinates to get this.

so m1 = 19 now we can find the C

y = 19x + C

19x3 + C = 9 or the y we substitute the x from before here to get 57

C = -48 9-57 = 48

therefore y = 19x - 48 and this is done!

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## Re: Mathmatics revision guide Gcses to additional maths^^ i am yr 11 ad maths grp plz ask me questions take it in mind im nt a genius tho =o

This is cool... An does work my brain hard aswell.. lol.. maths was never a strong point with me...

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## abc... not as easy as that to work out triangle's areas Alevel

let pq = 8cm rq = 9cm rp =7cm

(please draw this if you are stuck!)

find i) the largest triangle ii) the area

oh nooo what do we do? x)

well it is quite simple actually... all you need to remember is that... largest angle is always the opposite of the largest side... they make things sound so hard doesn't they? =)

to work this out...

tad bit tricky from here.

the formula for working out is

a(2) = b(2) + c(2) - 2bc cosA

so basically we know P is largest angle... b and c is the sides which is next to the angle we are trying to work out so... a is just the hypotenuse, the longest side, now we know this we can start^^

so here we go!

9(2) = 8(2) + 7(2) - 2 x 8 x 7 cosA

-32 = -112 cos A

-112

cosA = 0.285714

A = 73.4 degrees

now part ii, working out the area, we will need to know another formula.

Area = 1/2 ab sinC

now ab here means b and c in the part i and capital C means the angle, meaning the 73.4

so..

1/2 x 8 x 7 x sin 73.4

=26.8

another tricky question done in a nut shell.

(please draw this if you are stuck!)

find i) the largest triangle ii) the area

oh nooo what do we do? x)

well it is quite simple actually... all you need to remember is that... largest angle is always the opposite of the largest side... they make things sound so hard doesn't they? =)

to work this out...

tad bit tricky from here.

the formula for working out is

a(2) = b(2) + c(2) - 2bc cosA

so basically we know P is largest angle... b and c is the sides which is next to the angle we are trying to work out so... a is just the hypotenuse, the longest side, now we know this we can start^^

so here we go!

9(2) = 8(2) + 7(2) - 2 x 8 x 7 cosA

-32 = -112 cos A

__-32__= cos A-112

cosA = 0.285714

A = 73.4 degrees

now part ii, working out the area, we will need to know another formula.

Area = 1/2 ab sinC

now ab here means b and c in the part i and capital C means the angle, meaning the 73.4

so..

1/2 x 8 x 7 x sin 73.4

=26.8

another tricky question done in a nut shell.

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## Suvat Expressions

Suvat ... what is it? =o

Suvat is actually letters that mechanics use.. abbreviations if you like

S = distance

U = initial velocity

V = final velocity

A = acceleration, also G is the same thing = Gravitational pull

T = time

The expression you use is:

V = u + at

S = u+v /2 x t

S = ut + 1/2at(2)

v(2) = u(2) + 2as

Suvat is actually letters that mechanics use.. abbreviations if you like

S = distance

U = initial velocity

V = final velocity

A = acceleration, also G is the same thing = Gravitational pull

T = time

The expression you use is:

V = u + at

S = u+v /2 x t

S = ut + 1/2at(2)

v(2) = u(2) + 2as

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## Re: Mathmatics revision guide Gcses to additional maths^^ i am yr 11 ad maths grp plz ask me questions take it in mind im nt a genius tho =o

Used this to help do my maths hmwk ty

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## aww thats cool~

xD glad it helped.Beflop wrote:Used this to help do my maths hmwk ty

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## what does suvat questions look like? ;)

1) in each following cases

(a) find expressions for the velocity and acceleration at time t

(i) s = 5t(2) - t - 3

to find V and A, we differentiate please scroll up to find what differentiation is.

to find V:

5t(2) - t - 3

10t - 1

to find A:

10t - 1

10.

(a) find expressions for the velocity and acceleration at time t

(i) s = 5t(2) - t - 3

to find V and A, we differentiate please scroll up to find what differentiation is.

to find V:

5t(2) - t - 3

10t - 1

to find A:

10t - 1

10.

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## Re: Mathmatics revision guide Gcses to additional maths^^ i am yr 11 ad maths grp plz ask me questions take it in mind im nt a genius tho =o

cool...

Do we have budding mathemtitions here..

Do we have budding mathemtitions here..

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## lol this is 2nd page~?

ahh.. it spilled over to 2nd page... hope this is helping though.

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