Page 6 - Spotlight A+ SPM Additional Mathematics Form 4 & 5

Formulae

Area of a quadrilateral: Chapter 3
FORM 4
• 1 [(x y + x y + x y + x y ) Area under the curve:
2
2 3
1 2
3 4
4 1
– (x y + x y + x y + x y )
∫
∫
b
b
Chapter 2 2 1 3 2 4 3 1 4 • y dx or x dy
a
a
2
–b ± ! b – 4ac Chapter 8
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• x = Generated volume:
2a • |r| = ! x + y 2 b b
2
~
∫
∫
2
2
r
^
Chapter 4 • r = ~ • πy dx or πx dy
a
a
~
~
• a × a = a m + n |r|
m
n
Chapter 9 Chapter 4
• a ÷ a = a m – n a b c
m
n
• (a ) = a m × n • sin A = sin B = sin C • P = n!
m n
n
r (n – r)!
2
2
• ! a × ! b = ! ab • a = b + c – 2bc cos A n n!
2
2
2
2
r
!
• ! a ÷ ! b = a b • b = a + c – 2ac cos B • C = (n – r)!r!
• c = a + b – 2ab cos C
2
2
2
• log mn = log m + log n Area of a triangle: Identical object:
a a a • P = n!
m
• log = log m – log n 1 1 a!b!c!…
a n a a • ab sin C = ac sin B
2
2
n
• log m = n log m
a a 1
= bc sin A Chapter 5
log b 2
• log b = c
n
r n – r
a log a Heron’s formula: • P(X = r) = C p q , p + q = 1
c r
• ! s(s – a)(s – b)(s – c) • Mean, m = np
Chapter 5 a + b + c
s =
Arithmetic progression: 2 • s = ! npq
• T = a + (n – 1)d Chapter 10
n X – m
n
• S = [2a + (n – 1)d] Q • Z =
n 2 • I = 1 × 100 s
n
• S = [a + l] Q 0
n 2 ∑I w
• I = i i Chapter 6
Geometric progression: ∑w i
2
2
• T = ar n – 1 • sin A + cos A = 1
n n • 1 + tan A = sec A
2
2
• S = a(1 – r ) , r ≠ 1, (|r| , 1) FORM 5
n 1 – r • 1 + kot A = cosec A
2
2
a(r – 1)
n
• S = , r ≠ 1, (|r| . 1) Chapter 1 • sin (A  B) = sin A cos B 
n r – 1 cos A sin B
• S = a • Arc length, s = rq
∞ 1 – r 1 • cos (A  B) = cos A cos B 
• Area of sector, A = r q sin A sin B
2
2
Chapter 7 tan A  tan B
Chapter 2 • tan (A  B) =
Divisor of a line segment: dy 1  tan A tan B
nx + mx ny + my • y = uv, = u dv + v du • sin 2A = 2 sin A cos A
• 1 2 , 1 2 ) dx dx dx
m + n m + n du dv • cos 2A = cos A – sin A
2
2
2
Area of a triangle: • y = , dy = v dx – u dx = 2 cos A – 1
u
2
= 1 – 2 sin A
1
• [(x y + x y + x y ) v dx v 2 2 tan A
2
2 3
1 2
3 1
– (x y + x y + x y ) dy dy du • tan 2A =
2
2 1 3 2 1 3 • = × 1 – tan A
dx du dx
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Prelims Spotlight Add Math Tg4&5.indd 8 23/04/2021 2:10 PM