 ```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
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  an    a b    a b 2  ...    a b r  ...  b n
 1
 2
r 
where
n!
n n
 r   Cr  r!(n  r )!
 
 n
 n 
Also be aware that nCr     nCn r  

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 y 
Midpoint of two points ( x1 , y1 ), ( x2 , y2 )   1 2 , 1 2 
2 
 2
&copy; 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
opposite
, cos 
, tan  
hypotenuse
hypotenuse
Identities:
sin
tan =
cos
2
sin   cos 2   1
sin  
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 x  a and x  b is  y dx
a
Kinematics
Constant acceleration formulae
1
s  ut  at 2
2
u  v  t
s
2
v  u  at
v 2  u 2  2as
&copy; MEI
Additional Mathematics Formulae Updated Feb 2009
Page 2
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