1. The document provides formulas for algebra, calculus, geometry, trigonometry, and statistics. 2. Formulas include those for solving equations, differentiation, integration, distance, area of shapes, probabilities, and trigonometric functions. 3. Fourteen trigonometric formulas are listed relating trig functions, angles, and sides of triangles.

1. By Perfectmaths.com Page 1
SPM Additional Mathematical Formulae
Algebra
1.
2
4
2
b b ac
x
a
− ± −
=
2. m n m n
a a a +
× =
3. m n m n
a a a −
÷ =
4. ( )m n mn
a a=
5. log log loga a amn m n= +
6. log log loga a a
m
m n
n
= −
7. log logn
a am n m=
8.
log
log
log
c
a
c
b
b
a
=
9. ( 1)nT a n d= + −
10. [ ]2 ( 1)
2
n
n
S a n d= + −
11. 1n
nT ar −
=
12.
( 1) (1 )
, 1
1 1
n n
n
a r a r
S r
r r
− −
= = ≠
− −
13. , 1
1
a
S r
r
∞ = <
−
Calculus
1. ,
dy dv du
y uv u v
dx dx dx
= = +
2. 2
,
du dv
v u
u dy dx dxy
v dx v
−
= =
3.
dy dy du
dx du dx
= ×
4. Area under a curve = or
b b
a a
y dx x dy∫ ∫
5. Volume generated = 2 2
or
b b
a a
y dx x dyπ π∫ ∫
Geometry
1. Distance = ( ) ( )
2 2
2 1 2 1x x y y− + −
2. Midpoint 1 2 1 2
( , ) ,
2 2
x x y y
x y
+ + 
=  
 
3. A point dividing a segment of a line
1 2 1 2
( , ) ,
nx mx ny my
x y
m n m n
+ + 
=  
+ + 
4. Area of a triangle =
1 2 2 3 3 1 2 1 3 2 1 3
1
( ) ( )
2
x y x y x y x y x y x y+ + − + +
5. 2 2
r x y= +
6.
2 2
ˆ
xi yj
r
x y
+
=
+

2. By Perfectmaths.com Page 2
Statistics
1.
x
x
N
=
∑
2.
fx
x
f
=
∑
∑
3.
2 2
2( )x x x
x
N N
σ
−
= = −
∑ ∑
4.
2 2
2( )f x x fx
x
f f
σ
−
= = −
∑ ∑
∑ ∑
5.
1
2
m
N F
m L C
f
 
− 
= + 
 
 
6. 1
0
100
Q
I
Q
= × 7. i i
i
W I
I
W
=
∑
∑
8.
!
P
( )!
n
r
n
n r
=
−
9.
!
( )! !
n
r
n
C
n r r
=
−
10. ( ) ( )( ) ( )P A B P A P B P A B∪ = + − ∩
11. ( ) , where 1n r n r
rP X r C p q p q−
= = + =
12. Mean/Min, npµ =
13. npqσ =
14.
X
Z
µ
σ
−
=
Trigonometry
1. Length of an arc, s rθ=
2. Area of a sector, 21
2
A r θ=
3. 2 2
sin cos 1A A+ =
4. 2 2
sec 1 tanA A= +
5. 2 2
cosec 1 cotA A= +
6. sin 2 2sin cosA A A=
7.
2 2
2
2
cos2 cos sin
2cos 1
1 2sin
A A A
A
A
= −
= −
= −
8. ( )sin sin cos cos sinA B A B A B± = ±
9. ( )cos cos cos sin sinA B A B A B± =
10. ( )
tan tan
tan
1 tan tan
A B
A B
A B
±
± =
11. 2
2 tan
tan 2
1 tan
A
A
A
=
−
12.
sin sin sin
a b c
A B C
= =
13. 2 2 2
2 cosa b c bc A= + −
14. Area of a triangle =
1
sin
2
ab C