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7/25/2019 formlasheet

1/8

Formula Sheet

Number and algebra

Equation of a line:y = mx + c, where m = gradient; c=yintercept

Space and measurement

opposite adjacent opposite

hypotenuse hypotenuse adjacentIn a right triangle: sin cos tan = = =

2 2 2

Pythagoras Theore :

In a right triangle , where , are the short sides and is the hypotenuseABC a b c

c a b= +

2

!ircle : 2 , where is the circuference, is the radius and is the diaeter

, where is the area

C r D C r D

A r A

= =

=

"

2Triangle: , where is the #ase and is the perpendicular heightA b h b h=

Parallelogra: A b h=

"

2Trape$iu : % & , where and are the lengths of the parallel sides

and is the perpendicular height

= +A a b h a b

h

Pris: where is the 'olue, is the area of the #ase and

is the perpendicular height

V Ah, V A

h

=

"Pyraid: ()

V h=

2

2

!ylinder : 2 2 , where is the total surface areaS r h r S

V r h

= +

=

2

2"

)

!one : , where is the slant height= +

=

S r s r s

V r h

2

)*

)

+phere : *S r

V r

=

=

2 "" " 2 2

2 "

radient of line, , through the points % , & and % , & is gi'en #yy y

x xm x y x y m

=

2 2" " 2 2 2 " 2 "-istance, , #etween the points % , & and % , & is gi'en #y % & % &d x y x y d y y x x= +


2/8

Formula Sheet

Number and algebra

Inde. laws:/or any nuerical 'alue 0 and integers and ,

m n m n

a m n

a a a +

=m n m n

a a a

=

+iple interest : I , where is the principal, is the rate per year and is the tie in yearsP r t P r t=


opposite adjacent opposite

hypotenuse hypotenuse adjacentIn a right triangle: sin cos tan = = =

2 2 2

Pythagoras Theore:

In right triangle , where , are the short sides and is the hypotenuseABC a b c

c a b= +

2 2 22 2 2

sin sin sin

2

"

2

In any triangle :

2 cos cos

sin , where is the area

a b c

A B C

b c a

b c

ABC

a b c b c A A

A a b C A

+

= =

= + =

=

2


, where is the area

C r D C r D

A r A

= =

=

"



"



= +A a b h a b

h



V Ah, V A

h

=

"Pyraid: (

) V h=

2

2


V r h

= +

=


3/8

2

2"

)


=

S r s r s

V r h

2

)*)

+phere : *S r

V r

=

=


2 "" " 2 2

2 "

radient of line, , through the points % , & and % , & is gi'en #yy y

x xm x y x y m

=

2 2" " 2 2 2 " 2 "-istance , #etween the points % , & and % , & is gi'en #y % & % &d x y x y d y y x x= +

" 21ines are perpendicular if "m m =

Chance and Data

% & % & "P A P A+ =


4/8

Number and algebra

Inde. laws: /or , 0a b> and m ,nreal,

( )

0

% & % &

""

for an integer and a positi'e integer

+

= = =

= = =

= =

m m m m n m n m n mn

mm m n

m n

mmn nmn

a b ab a a a a a

aa a a

a a

a a a m n

+iple interest : I , where is the principal, is the rate per year and is the tie in yearsP r t P r t=

( )

!opound interest :

" copounded annually

%" & copounded ties a year

t

ntr

n

A P r

A P n

= +

= +

" "

-ifferentiation: If % & , then % &

Powers: If % & , then % & or If , thenn n n n

dydx

dy

dx

f x y f x

f x x f x n x y x n x

= =

= = = =

then % & % & % & % &

Product rule: If % & % & or If

thendu dv

y f x g x f x g x v udx dx

y f x g x y uv

dy

dx = + = +

= =

"

"Integration : , "

n

n xn

x dx c n+

+= +

"

(ntideri'ati'e: i'en then y = , ""

nndy xx c n

dx n

+

= + +


2 2 22 2 2

sin sin sin

2

"

2

In any triangle :

2 cos cos

sin , where is the area

a b c

A B C

b c a

bc

ABC

a b c b c A A

A a b C A

+

= =

= + =

=


5/8


2


, where is the area

C r D C r D

A r A

= =

=

"



"



= +A a b h a b

h



V Ah, V A

h

=

"Pyraid: (

) V h=

2

2


V r h

= +

=2

2"

)


=

S r s r s

V r h

2

)*

)

+phere : *S r

V r

=

=

Chance and data

% & % & "P A P A+ =

In a noral distri#ution appro.iately:

34 of 'alues lie within one %"& standard de'iation of the ean

564 of 'alues lie within two %2& standard de'iations of the ean55784 of 'alues lie within three %)& standard de'iations of the ean7

Note Any add!t!ona" formu"as !dent!f!ed by the exam!nat!on #ane" as necessary $!"" be

!nc"uded !n the body of the #art!cu"ar %uest!on&


6/8

Mathematics: Units 3C and 3DFormula sheet

Number and algebra

"

If % & then % & If % & then % &

If % & then % &

n n

x x

dy

f x y f x f x x f x n xdx

f x e f x e

= = = =

= =

then % & % & % & % &

Product rule:

If % & % & or If

thendu dv

y f x g x f x g x v udx dx

y f x g x y uv

dy

dx = + = +

= =

2 2

% &

% &

% & % & % & % &

% % &&

9uotient rule:

If or If

then then

f x

g x

du dv

f x g x f x g x dx dx

g x

uy y

v

v udy

ydx v

= =

= =

( )

!hain rule:

If % % && or If % & and =g

then % % && % & thendy du

du dx

y f g x y f u u x

dyy f g x g x

dx

= =

= =

"

Powers , " E.ponentials

"

: : xn

n xx

x dx c n e dx e c

n

+

= + = ++

( ) ( ) ( ) ( ) ( )

/undaental Theore of !alculus :

and

x b

a a

d

f t dt f x f x dx f b f adx= =

Increental forula :dy

dxy x

E.ponential growth and decay :

If , then 'tdy

dt'y y Ae= =


7/8


2


, where is the area

C r D C r D

A r A

= =

=

"

2

Triangle: , where is the #ase and is the perpendicular heightA b h b h=


"



= +A a b h a b

h



V Ah, V A

h

=

"Pyraid: ()

V h=

2

2


V r h

= +

=2

2"

)


=

S r s r s

V r h

2

)*

)

+phere : *S r

V r

=

=

2

2

olue of solids of re'olution :

rotated a#out the . a.is

, rotated a#out the y a.is

y dx

x dy

=

=

Chance and data

Pro#a#ility laws:

% & % & "P A P A+ =

% & % & % & % &P A B P A P B P A B = +

% & % & % & % & % &P A B P A P B A P B P A B = =


8/8

( confidence inter'al for the ean of a population is :

where is the population ean, is the population standard de'iation and

where is the saple ean, is the saple si$e and$ is the

n nx ( x (

x n

+

cut off 'alue on the standard noral distri#ution corresponding to the confidence le'el7

Note Any add!t!ona" formu"as !dent!f!ed by the exam!nat!on #ane" $!"" be !nc"uded !n the body

of the #art!cu"ar %uest!on&

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