Additional Mathematics
Formula 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 when f(x) is divided by (x – a) is 0, then (x – a) is a factor of f(x) and x = a is a root
of the equation f(x) = 0
Solution of quadratic equations
By formula and completing the square
For the quadratic equation ax 2 + bx + c =
0
x=
−b ± b 2 − 4ac
2a
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
 n  n -1
 n  n -2
 n  n -r
(a + b )n = a n +   a b +   a b 2 + ... +   a b r + ... + b n
 1
2
r 
where
n
=

r 
Cr
=
n!
n
r!( n − r )!
 n
Also be aware that n=
Cr =

r
n
 n 
C=


n−r
n−r
Coordinate Geometry
Straight line
Know the forms of the straight line, including
=
y mx + c
y − y1 = m( x − x1 )
y − y1
x − x1
=
y2 − y1 x2 − x1
Condition for parallel lines: m1 = m2
Condition for perpendicular lines: m1 × m2 =
−1
Distance between two points ( x1 , y1 ), ( x2 , y2 ) =
( x1 − x2 ) + ( y1 − y2 )
2
2
 x + x y + y2 
Midpoint of two points ( x1 , y1 ), ( x2 , y2 ) =  1 2 , 1

2 
 2
© MEI
Additional Mathematics Formulae Updated Feb 2009
Page 1
The Circle
( x − a) + ( y − b)
2
2
=
r 2 has centre (a, b) and radius r.
Trigonometry
In a right-angled triangle:
opposite
adjacent
opposite
sin θ
, cos θ =
, tan θ
=
hypotenuse
hypotenuse
adjacent
Identities:
sinθ
cosθ
2
sin θ + cos 2 θ =
1
tanθ =
Sin rule:
a
b
c
= =
SinA SinB SinC
Cos rule:
b2 + c2 − a 2
2bc
2
Note that a = b 2 + c 2 − 2bc cos A is on the formula sheet available in the examination.
cos A =
Calculus
y = ax n ⇒
dy
= nax n −1
dx
Stationary points occur when
dy
=0
dx
b
Area under curve between
and x b is ∫ y dx
x a=
=
a
Kinematics
Constant acceleration formulae
1
=
s ut + at 2
2
(u + v ) t
s=
2
v= u + at
2
v=
u 2 + 2as
© MEI
Additional Mathematics Formulae Updated Feb 2009
Page 2