rumus matematik tambahan
DESCRIPTION
rumus matematik tambahan SPMTRANSCRIPT
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Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan. The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.
ALGEBRA
1. x = a
acbb2
42
2. am an = am + n
3. am an = am n
4. (am)n = am n
5. loga mn = loga m + loga n
6. loga n
m = loga m loga n
7. loga mn = n loga m
8. balog = a
bc
c
loglog
9. nT = a + (n 1)d
10. nS = { }dnan )1(22 +
11. nT = 1n
ar
12. nS = 1)1(
r
ra n =
r
ran
1)1(
, 1r
13.
S = r
a
1, | r | < 1
KALKULUS (CALCULUS)
1. y = uv
dxdy
= u dxdv
+ v dxdu
2. y = v
u,
dxdy
= 2v
dxdv
udxdu
v
3. dxdy
=
dudy
dxdu
4. Luas di bawah lengkung (Area under a curve)
= b
a
dxy atau (or)
= b
a
dyx
5. Isipadu janaan (Volume of revolution)
= b
a
dxy 2pi atau (or)
= b
a
dyx2pi
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STATISTIK (STATISTICS)
1. x = N
x
2. x =
ffx
3. = N
xx 2)(
=
22
xNx
4. =
fxxf 2)(
=
22
xffx
5. m = CLmf
FN
+
21
6. I = 0
1
QQ
100
7. I =
i
ii
WIW
8. rn P =
!)(!rn
n
9. rnC =
!!)(!
rrn
n
10. P(A B) = P(A) + P(B) P(A B)
11. )( rXp = = rnrrn qpC , p + q = 1
12. Min (Mean) = np
13. = npq
14. Z =
X
GEOMETRI (GEOMETRY)
1. Jarak (Distance)
=2
212
21 )()( yyxx +
2. Titik tengah (Midpoint)
(x, y) =
++
2,
22121 yyxx
3. Titik yang membahagi suatu tembereng garis
(A point dividing a segment of a line)
(x, y) = 1 2 1 2,nx mx ny mym n m n
+ + + +
4. Luas segi tiga (Area of triangle) =
)()( 31231213322121
yxyxyxyxyxyx ++++
5. r = 22 yx +
6. r = 22 yx
yx
+
+ ji
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TRIGONOMETRI (TRIGONOMETRY) 1. Panjang lengkok, s = j Arc length, s = r
2. Luas sektor, L = 2
1
2j
Area of sector = 2
1
2r
3. AA 22 kossin + = 1
AA 22 cossin + = 1
4. A2sek = A2tan1 +
A2sec = A2tan1 +
5. A2kosek = A2kot1 +
A2cosec = A2cot1 +
6 sin 2A = 2 sinA kosA sin 2A = 2 sinA cosA
7. kos 2A = kos2 A sin2 A
= 2 kos2 A 1
= 1 2 sin2 A
cos 2A = cos2 A sin2 A
= 2 cos2 A 1
= 1 2 sin2 A
8. )(sin BA = sinA kosB kosA sinB )(sin BA = sinA cosB cosA sinB
9. )(kos BA = kosA kosB m sinA sinB )(cos BA = cosA cosB m sinA sinB
10. )(tan BA = BABA
tantan1tantan
m
11. tan 2A = A
A2tan1
tan2
12. A
a
sin =
Bb
sin =
Cc
sin
13. a2 = b2 + c2 2bc kosA
a2 = b2 + c2 2bc cosA
14. Luas segi tiga (Area of triangle)
=
2
1 ab sin C
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