SPM AddMath Formula List Given

Additional Mathematics (3472)

Thefollowingformulaemaybehelpfulinansweringtheq Thefollowingformulaemaybehelp fulinansweringthequestions.Thesymb uestions.Thesymbols ols givenaretheonescommonlyused.

1 x = 2 a

m

3 a

m

−b±

b

2

− 4ac

8 log a b

2a ×a

n

÷a

n

m n

4 ( a )

=

=

=

a

a

m+ n

a

m −n

9 T n

mn

5 log a mn = log a m + log a n 6 log a

m n

7 log a m

1  y

2  y

3

n

= uv ,

=

dy dx

=

log a m − log a n

=

dy

=

dx

u dy , v dx =

n log a m

dy du

×

u

v =

dv dx du dx

+v

−u

du dx

v2

du

log c b log c a

a + ( n − 1)d 

10 S n

=

11 T n

=

n 2

[ 2a + ( n − 1)d ] n −1

ar 

a( r n

12 S n

=

13 S ∞

≈

− 1)

=

a(1 − r n )

r  − 1 a 1 − r 

, r 

1 − r 

, r  ≠ 1

<1

4Areaunderacurve b

 =

∫  y dx or a

dv dx

=

=

b

 =

∫ x dy a

5Volumegenerated

dx

b

 =

∫ π  y

2

dx or

2

dy

a b

 =

∫ π  x a

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1 x

=

2 x

=

∑ x

7 I  =

 N 

∑ f  x  x ∑  f 

n

∑( x −  x ) 2

3 σ  =

∑ x 2

=

 N 

 N 

∑  f  ( x −  x ) 2 ∑  f 

4 σ  =

∑ W i I i ∑ W i

−  x

2

2 ∑  fx 2 −  x ∑  f 

=

8 Pr 

=

n

=

9 C r 

n! (n - r)! n! (n - r)!r !

10 P( A ∪  B ) = P( A) + P( B ) − P( A ∩ B ) n

⎛   N  − F  ⎞ ⎟⎟C   f  ⎝  m  ⎠

5 m =  L + ⎜⎜

6 I  =

Q1

12Mean, μ  = np 13 σ  =

× 100

Qo

r  n − r 

11 P( X  = r )= C r  p q

1 2

14 Z  =

npq

X  − μ 

σ 

1Distance

( x 2

 =

−  x1 )

2Midpoint  x  ( x,  y ) = ( 1

2

+ ( y 2 −

+  x 2

2

,

 y1

y1 )

+

y2

2

2

)

3Apointdividingasegmentofaline  ( x,  y ) = (

nx1

+ mx 2

m+n

,

ny1

+ my 2

m+n

)

4Areaoftriangle =

1 2

( x1 y 2

5 r 

^

6 r  = ~

=

+  x 2 y3 +  x3 y1 ) − ( y1 x 2 +  y 2 x3 +  y 3 x1 )

 x 2

 x i

+  y

~

+  y  j ~

 x 2

+  y

2

2

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1Arclength, s

=

r θ 

2Areaofsector, A = 2

1 2

2

r  θ 

2

3 sin  A + cos A = 1 2

2

4 sec  A = 1 + tan A 2

2

5 cos ec  A = 1 + cot A 6 sin 2 A = 2 sin  A cos A 2

2

7 cos 2 A = cos  A − sin A 2

 = 2 cos A − 1 2

 = 1 − 2 sin A 8 sin( A ±  B ) = sin  A cos B ± cos  A sin B 9 cos( A ±  B ) = cos  A cos B m sin  A sin B 10 tan( A ±  B) =

11 tan 2 A =

12

a

=

sin  A

13 a

2

=

b

tan  A ± tan B 1 m tan  A tan B

2 tan  A 2

1 − tan  A b

sin B 2

+c

2

c

=

sin C 

− 2bc cos

14Areaoftriangle =

1 2

A

ab sin C 

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