Page 47 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Formulae

CHAPTER 8 Vectors Form 5

CHAPTER 1
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u r u = √x + y 2 Circular Measure
2
~
r
^ r ~ Arc length,
~ =
u r u s = rq
~
Area of sector,
1
L = r q
2
2
CHAPTER 9 Area of triangle
Solution of Triangles
1
2
= r sin q
2
a = b = c
sin A sin B sin C CHAPTER
a = b + c – 2bc cos A 2 Differentiation
2
2
2
b = a + c – 2ac cos B
2
2
2
2
2
c = a + b – 2ab cos C y = uv, dy = u dv + v du
2
Area of a triangle dx dx du dx dv
1 1 1 v – u
= ab sin C = bc sin A = ac sin B u dy dx dx
2 2 2 y = , = v 2
v dx
Heron’s formula dy dy du
= √s(s – a)(s – b)(s – c), dx = du × dx
a + b + c
s =
2
CHAPTER 3 Integration
CHAPTER 10 Area under a curve
Index Numbers
b
= y dx or
Q a
I = 1 × 100 b
Q
0 = x dy
a
– ∑I w
I = i i Generated volume
∑w i
= b πy dx or
2
a
b
= πx dy
2
a
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0b Rumus Ranger Mate Tambahan SPM.indd 7 25/02/2022 9:06 AM