423525 list of formulae and statistical tables

List MF9
CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education Advanced Level
General Certificate of Education Advanced Subsidiary Level
Advanced International Certificate of Education

MATHEMATICS (8709, 9709)
HIGHER MATHEMATICS (8719)
STATISTICS (0390)

LIST OF FORMULAE
AND
TABLES OF THE NORMAL DISTRIBUTION

PURE MATHEMATICS
Algebra
For the quadratic equation ax2 + bx + c = 0 :
x=

− b ± √ (b2 − 4ac)
2a

For an arithmetic series:
Sn = 12 n(a + l ) = 12 n{2a + (n − 1)d }

un = a + (n − 1)d ,

For a geometric series:
un = ar n −1 ,

Sn =

a(1 − r n )
(r ≠ 1) ,
1− r

S∞ =

a
1− r

( r < 1)

Binomial expansion:
n
n
n
(a + b)n = a n +   a n −1b +   a n −2b2 +   a n −3b3 +
1
2
 3

 + b , where n is a positive integer
n

n!
n
and   =
 r  r!(n − r)!
(1 + x)n = 1 + nx +

n(n − 1) 2 n(n − 1)(n − 2) 3
x +
x +
2!
3!

 , where n is rational and

Trigonometry
Arc length of circle = rθ

( θ in radians)

Area of sector of circle = 12 r 2θ
tan θ ≡
cos2 θ + sin2 θ ≡ 1 ,

( θ in radians)

sin θ

cosθ

1 + tan2 θ ≡ sec2 θ ,

cot2 θ + 1 ≡ cosec2 θ

sin( A ± B) ≡ sin A cos B ± cos A sin B

#

cos( A ± B) ≡ cos A cos B sin A sin B
tan( A ± B) ≡

tan A ± tan B
1 tan A tan B

#

sin 2 A ≡ 2 sin A cos A

cos 2 A ≡ cos2 A − sin2 A ≡ 2 cos2 A − 1 ≡ 1 − 2 sin2 A
tan 2 A ≡

2 tan A
1 − tan2 A

Principal values:
− 12 π ≤ sin −1 x ≤ 12 π

0 ≤ cos−1 x ≤ π
− 12 π < tan −1 x < 12 π

2

x