rumus matematik tambahan

3472/2 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 − b ± b 2 − 4ac 2a

1.

x =

2.

am × an = am + n m

n

m−n

log c b log c a

8.

log a b =

9.

Tn = a + (n − 1)d

10.

Sn =

11.

Tn = ar n − 1

n {2a + (n − 1)d } 2

3.

a ÷a = a

4.

(am)n = am n

5.

loga mn = loga m + loga n

12.

Sn =

a ( r n − 1) a (1 − r n ) = , r ≠1 r −1 1− r

6.

loga

m = loga m − loga n n

13.

S∞ =

a , |r|<1 1− r

7.

loga mn = n loga m

KALKULUS (CALCULUS) 1.

y = uv

4.

dv dy du +v =u dx dx dx

2.

Luas di bawah lengkung (Area under a curve) b

=

∫ y dx atau (or) a

du dv v −u u dy = dx 2 dx y= , v dx v

b

=

∫ x dy a

3.

5.

dy du dy = × dx dx du

Isipadu janaan (Volume of revolution) b

=

2 ∫ π y dx atau (or)

a b

=

2 ∫ π x dy

a

2

3472/2 STATISTIK (STATISTICS)

∑ Wi I i ∑ Wi

1.

x

=

∑x N

7.

I =

2.

x

=

∑ fx ∑f

8.

n

Pr =

n! (n − r ) !

3.

σ

=

∑ ( x − x) N

9.

n

Cr =

n! (n − r ) ! r !

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

σ

=

2 ∑ f ( x − x) ∑f

10.

4.

11.

p ( X = r) =

12.

Min (Mean) = np

13.

σ =

14.

Z =

2

2

2 ∑x −x N

=

2

=

5.

6.

2 ∑ fx −x ∑f

 N−F C m = L+  fm    1 2

I =

n

Cr p r q n − r , p + q = 1

npq X −µ

σ

Q1 × 100 Q0

GEOMETRI (GEOMETRY) 1.

Jarak (Distance)

4. 1

= ( x1 − x 2 ) 2 + ( y1 − y 2 ) 2

2

2.

3.

Luas segi tiga (Area of triangle) = ( x1 y 2 + x 2 y 3 + x 3 y1 ) − ( x 2 y1 + x 3 y 2 + x1 y 3 )

Titik tengah (Midpoint) y + y2   x + x2 (x, y) =  1 , 1  2   2

5.

r

Titik yang membahagi suatu tembereng garis (A point dividing a segment of a line)

6.

rˆ =

ny1 + my2   nx + mx2 (x, y) =  1 ,  m+n   m+n

3

=

x2 + y2

xi + y j x2 + y2

3472/2 TRIGONOMETRI (TRIGONOMETRY) 1.

8.

Panjang lengkok, s = jθ Arc length, s = rθ

2.

Luas sektor, L =

sin ( A ± B ) = sinA cosB ± cosA sinB

1

9.

j2 θ

2

Area of sector =

1

cos ( A ± B ) = cosA cosB m sinA sinB r θ

5.

tan ( A ± B) =

11.

tan 2A =

12.

a b c = = sin A sin B sin C

13.

a2 = b2 + c2 − 2bc kosA

sek 2 A = 1 + tan 2 A

sec 2 A = 1 + tan 2 A kosek 2 A = 1 + kot 2 A 2

tan A ± tan B 1 m tan A tan B

10.

sin 2 A + kos 2 A = 1 sin 2 A + cos 2 A = 1

4.

kos ( A ± B) = kosA kosB m sinA sinB

2

2

3.

sin ( A ± B ) = sinA kosB ± kosA sinB

2 tan A 1 − tan 2 A

a2 = b2 + c2 − 2bc cosA

2

cosec A = 1 + cot A

14. 6

sin 2A = 2 sinA kosA =

sin 2A = 2 sinA cosA 7.

Luas segi tiga (Area of triangle)

kos 2A

2

= kos2 A − sin2 A = 2 kos2 A − 1 = 1 − 2 sin2 A

cos 2A

1

= cos2 A − sin2 A = 2 cos2 A − 1 = 1 − 2 sin2 A

4

ab sin C

3472/2

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