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Additional MathematicsFormula that are within the syllabus and which need to be learnt.

The remainder theorem

Given the polynomial f(x), then remainder when f(x) is divided by (x a) is f(a).

The factor theorem

If the remainder whenf(x) is divided by (x a) is 0, then (x a) is a factor of f(x) andx= ais a root

of the equation f(x) = 0

Solution of quadratic equations

By formula and completin the square

!

!

"or the quadratic equation 0

#

!

ax bx c

b b acx

a

+ + =

=

Binomial expansion

This is on the formula sheet available in the examination in the form shown in the box:

When n is a positive integer

-1 -2 -2( ) ... ...

1 2

n n n r n n r nn n na b a a b a b a b b

r+ = + + + + + +

where

( )

n

r

n n!

r r! n r !

C

= =

$lso be aware that

n n

r n r

n nC C

r n r

= = =

Coordinate Geometry

Straiht line

%now the forms of the straiht line, includin

& &

& &

! & ! &

( )

y mx c

y y m x x

y y x x

y y x x

= +

=

=

& !

& !

'ondition for parallel lines

'ondition for perpendicular lines &

m m

m m

= =

( ) ( )! !

& & ! ! & ! & !

& ! & !& & ! !

istance between two points ( , ), ( , )

*idpoint of two points ( , ), ( , ) ,! !

x y x y x x y y

x x y yx y x y

= +

+ + =

+ae &

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The Circle

( ) ( )! ! ! has centre ( , ) and radius .x a y b r a b r + =

Trionometry

In a rihtanled trianle

opposite ad-acent oppositesin , cos , tan

hypotenuse hypotenuse ad-acent = = =

! !

Identities

sintan =

cos

sin cos &

+ =

! ! !

in rule

in in in

'os rule

cos!

a b c

A B C

b c aA

bc

= =

+ =

Note that! ! ! ! cosa b c bc A= + is on the formula sheet available in the examination.

Calculus

&d

d

dtationary points occur when 0

d

$rea under curve between and is d

n n

b

a

yy ax nax

x

y

x

x a x b y x

= =

=

= =

!inematics

'onstant acceleration formulae

( )

!

! !

&

!

!

!

s ut at

u vs t

v u at

v u as

= +

+=

= +

= +

+ae !