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IGCSE Additional Mathematics 国际高中课程数学公式


Chapter 3
? ? ? ? ? ? ? ? ? 0 = 1 ? =
1

? ?

1 + 2 = 2 1 + 2 = 2

1

Chapter 12
? ?


= =

2

1 2 1 2

(in triangle)

= √ = ( √)


( )(Arc)

= change of base law




? ?

= 2 ( ) =

=

1

= + = ? =


product law quotient law

Chapter 13
? ?


= (?)! = ! →


!

(r ∈ ) power law

=



Chapter 4
? =
?±√2 ?4 , 2

!

= (?)!!

!

Chapter 14
≠0 ? (1 + ) = 1 + 1 1 + ? + + ? + ? In the expansion of (1 + ) , +1 = ? ( + ) = + 1 ?1 + 2 ?2 2 + ? + 2 ?2 + ?1 ?1 + ?2 ? In the expansion of ( + ) ,+1 = ?1

Chapter 6
? ? ?
1 ? = ( ) , ?1 = ? ( ) ? ? determinant + + ( )( )=( ) + +

Chapter 15
? ?


= ?1

Chapter 7
? = √(2 ? 1 )2 + (2 ? 1 )2 length between ? midpoint ? ? ? ?

( )

= ?1

(

+ ) = ?1 + ?1


two points ? (
1 +2 1 +2 , 2 ) 2

=



chain rule +


()

=




product rule

Chapter 10
? ? ? ? ? ? (90° ? ) = (90° ? ) = (90° ? ) = (?) = (?) = ? (?) = ?
1



( )=




? 2

quotient rule

( ) (√)

= ?1 =
1 2√



?



Chapter 16
? ? ≈ (+) ≈ () +
2 2

Chapter 11
? ? =


( ≠ 0) ?

2 + 2 = 1

> 0,

?

2 2

< 0,

For definite integral ? ∫ () = 0 ? ∫ () = ? ∫ () ? ∫ () + ∫ () = ∫ () ? ∫ = + ? ∫ = ? + ? ∫ 2 = + ? ∫ ( + ) = ( + ) + ? ∫ ( + ) = ? ( + ) + ? ∫ 2 ( + ) = ( + ) + ? ∫ = + ? ∫ ? = ? ? + ? ∫ + = + +
1 1 1 1

Chapter 18
? ? ? ? ? ? ? ? ?
( ) ( ) ( ) [( [( [( ( ) ( ) ( )

= = ? = 2 + )] = ( + ) + )] = ? ( + ) + )] = 2 ( + ) = ?1 ? = ? ?1 ? = ?1 ? 2

Chapter 21
? ∫ () ? ∫ () = ∫ [() ? ()]


Chapter 19
? ? ? ? ? ?
( ) ( )

= =


Chapter 22
differentiate ? Displacement intergrate ?
+

differentiate acceleration

( + ) ( ) ( ) [(

= +
1

velocity

=

intergrate

=

1

When the particle is at instantaneously at rest, v=0.

+ )] =

Chapter 23
? ? ????? ????? ????? + = in triangle PQR = + , | + | = √ 2 + 2 1 2 1 + = ( ) + ( ) = (
1 2 1

Chapter 20
?

∫ =

+1 +1

+
+1 +1

?

2 2 )

? ∫( + ) = +1 + +1 +

Chapter 24
? ? ? ? = / + or / = + (? ) / = ?/


? ∫( + ) =
?


(+)+1 (+1)

+

[ ] = () → ∫ () = () + ()


=



=



For indefinite integral ? [() ] = () → ∫ () = () ? ()


2 = 2 + 2 ? 2 ?


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