LIST OF MATHEMATICAL FORMULAE FOR USE IN
STAGE 2 SPECIALIST MATHEMATICS
Properties of Derivatives
Circular Functions
2
d
\ f x
g x
^ f a x
g x
f x
g a x
dx
2
sin A cos A 1
tan 2 A 1 sec2 A
d «®® f x º®® f a x g x f x
g a x
»
¬
2
dx ®®­ g x ®®¼
g x
1 cot 2 A cosec 2 A
sin A
B sin A cos B
cos A sin B
cos A
B cosA cos B
sin A sin B
tan A
B
d
f g x f a g x g a x dx
tan A tan B
1 tan A tan B
Quadratic Equations
sin 2 A 2 sin A cos A
2
2
If ax + bx + c = 0 then x 2
cos 2 A cos A sin A
b 2 4ac
.
2a
b
2 cos 2 A 1
Distance from a Point to a Plane
1 2 sin 2 A
tan 2 A The distance from x1 , y1 , z1 to
2 tan A
1 tan 2 A
Ax By C z D 0 is given by
Ax1 By1 C z1 D
2 sin A cos B sin A B sin A B 2 cos A cos B cos A B cos A B .
A2 B 2 C 2
2 sin A sin B cos A B cos A B sin A
1
sin B 2 sin 2 A
1
B cos 2 A
1
B
1
cos A cos B 2 cos 2 A B cos 2 A B 1
1
cos A cos B 2 sin 2 A B sin 2 A B Mensuration
1 2
Area of sector 2 r R
Arc length rR
(where R is in radians)
In any triangle ABC
A
⎡a b⎤
⎥ then det A = A = ad − bc and
⎢⎣ c d ⎥⎦
1 ⎡⎢ d − b ⎤⎥
.
A−1 =
a ⎥⎦
A ⎢⎣ −c
If A = ⎢
Derivatives
f a x
xn
ex
nx n1
ex
1
x
cos x
sin x
sec 2 x
ln x log e x
sin x
cos x
tan x
a
B
1
Area of triangle 2 ab sin C
a
b
c
sin A sin B sin C
a 2 b 2 c 2 2bc cos A
f x
y
b
c
Matrices and Determinants
dy
dx
C