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Matematik Tambahan SPM
Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan.
ALGEBRA − b ± b 2 − 4ac 2a
1
x=
2
am × an = am+n
3
am ÷ an = am−n m n
mn
4
(a ) = a
5
log a mn = log a m + log a n
6
log a
7
log a m n = n log a m
m = log a m − log a n n
log c b log c a
8
log a b =
9
Tn = a + (n − 1)d
10
Sn =
11
Tn = ar n −1
12
Sn =
a r n −1 a 1− r n = , (r ≠ 1) r −1 1− r
13
S∞ =
a , r <1 1− r
n [ 2a + (n − 1)d 2
(
)
]
(
)
KALKULUS 1
y = uv,
u , v
dy dv du =u +v dx dx dx du dv v −u dy = dx 2 dx dx v
2
y=
3
dy dy du = × dx du dx
Learning To Score 2005 Unit Kurikulum Jabatan Pelajaran Perak
4
5
Luas di bawah lengkung =
∫
=
∫
Isipadu janaan
b a b a
y dx or x dy
b
= ∫ π y 2 dx or a
b
= ∫ π x 2 dy a
Halaman
1
Matematik Tambahan SPM
STATISTIK 1 2
x=
x=
∑x
7
N
∑W I ∑W
i i i
∑ fx ∑f
8
σ=
∑ (x − x )
4
σ=
∑ (
5
N−F C m = L + fm
6
I=
∑x
2
3
I=
=
N f x−x
∑
)
N
∑ ∑f
2
f
fx
=
9
2
−x
2
−x
2
2
1 2
Q1 × 100 Q0
n! (n − r )! n! n Cr = (n − r )! r ! n
Pr =
10
P(A∪B) = P(A) + P(B) − P(A∩B)
11
P (X = r) = nCr p r q n − r, p + q =1
12
Min = np
13
σ = npq
14
Z=
x−µ
σ
GEOMETRI
(x1 − x 2 )2 + ( y1 − y 2 )2
1 Jarak =
4
1 (x1 y 2 + x2 y3 + x3 y1 ) − (x2 y1 + x3 y 2 + x1 y3 ) 2
2 Titik tengah
(x, y ) = x1 + x 2 ,
2
y1 + y 2 2
Luas segitiga =
r = x2 + y2
5
3 Titik yang membahagi suatu
6
tembereng garis
^
r=
xi + yj x2 + y2
(x, y ) = nx1 + mx2 , ny1 + my 2
m+n
Learning To Score 2005 Unit Kurikulum Jabatan Pelajaran Perak
m+n
Halaman
2
Matematik Tambahan SPM
TRIGONOMETRI 1 Panjang lengkok, s = jθ 2 Luas sektor, A = 2
1 2 jθ 2
2
3 sin A + kos A = 1 4 sek2 A = 1 + tan2 A 5 kosek2 A = 1 + kot2 A 6 sin 2A = 2 sin A kos A 7 kos 2A = kos2 A − sin2 A = 2 kos2 A − 1 = 1 − 2 sin2 A
Learning To Score 2005 Unit Kurikulum Jabatan Pelajaran Perak
8
sin (A ± B) = sin A kos B ± kos A sin B
9
kos (A ± B) = kos A kos B m sin A sin B
10
tan (A ± B) =
11
tan 2A =
12
tan A ± tan B 1 m tan A tan B
2 tan A 1 − tan 2 A a b c = = sin A sin B sin C
13
a2 = b2 + c2 − 2bc kos A
14
Luas segitiga =
1 ab sin C 2
Halaman
3
Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan.
ALGEBRA − b ± b 2 − 4ac 2a
1
x=
2
am × an = am+n
3
am ÷ an = am−n m n
mn
4
(a ) = a
5
log a mn = log a m + log a n
6
log a
7
log a m n = n log a m
m = log a m − log a n n
log c b log c a
8
log a b =
9
Tn = a + (n − 1)d
10
Sn =
11
Tn = ar n −1
12
Sn =
a r n −1 a 1− r n = , (r ≠ 1) r −1 1− r
13
S∞ =
a , r <1 1− r
n [ 2a + (n − 1)d 2
(
)
]
(
)
KALKULUS 1
y = uv,
u , v
dy dv du =u +v dx dx dx du dv v −u dy = dx 2 dx dx v
2
y=
3
dy dy du = × dx du dx
Learning To Score 2005 Unit Kurikulum Jabatan Pelajaran Perak
4
5
Luas di bawah lengkung =
∫
=
∫
Isipadu janaan
b a b a
y dx or x dy
b
= ∫ π y 2 dx or a
b
= ∫ π x 2 dy a
Halaman
1
Matematik Tambahan SPM
STATISTIK 1 2
x=
x=
∑x
7
N
∑W I ∑W
i i i
∑ fx ∑f
8
σ=
∑ (x − x )
4
σ=
∑ (
5
N−F C m = L + fm
6
I=
∑x
2
3
I=
=
N f x−x
∑
)
N
∑ ∑f
2
f
fx
=
9
2
−x
2
−x
2
2
1 2
Q1 × 100 Q0
n! (n − r )! n! n Cr = (n − r )! r ! n
Pr =
10
P(A∪B) = P(A) + P(B) − P(A∩B)
11
P (X = r) = nCr p r q n − r, p + q =1
12
Min = np
13
σ = npq
14
Z=
x−µ
σ
GEOMETRI
(x1 − x 2 )2 + ( y1 − y 2 )2
1 Jarak =
4
1 (x1 y 2 + x2 y3 + x3 y1 ) − (x2 y1 + x3 y 2 + x1 y3 ) 2
2 Titik tengah
(x, y ) = x1 + x 2 ,
2
y1 + y 2 2
Luas segitiga =
r = x2 + y2
5
3 Titik yang membahagi suatu
6
tembereng garis
^
r=
xi + yj x2 + y2
(x, y ) = nx1 + mx2 , ny1 + my 2
m+n
Learning To Score 2005 Unit Kurikulum Jabatan Pelajaran Perak
m+n
Halaman
2
Matematik Tambahan SPM
TRIGONOMETRI 1 Panjang lengkok, s = jθ 2 Luas sektor, A = 2
1 2 jθ 2
2
3 sin A + kos A = 1 4 sek2 A = 1 + tan2 A 5 kosek2 A = 1 + kot2 A 6 sin 2A = 2 sin A kos A 7 kos 2A = kos2 A − sin2 A = 2 kos2 A − 1 = 1 − 2 sin2 A
Learning To Score 2005 Unit Kurikulum Jabatan Pelajaran Perak
8
sin (A ± B) = sin A kos B ± kos A sin B
9
kos (A ± B) = kos A kos B m sin A sin B
10
tan (A ± B) =
11
tan 2A =
12
tan A ± tan B 1 m tan A tan B
2 tan A 1 − tan 2 A a b c = = sin A sin B sin C
13
a2 = b2 + c2 − 2bc kos A
14
Luas segitiga =
1 ab sin C 2
Halaman
3
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