Page 3 - 1202 Question Bank Additional Mathematics Form 5

MUST

KNOW Important Facts

Relationships between Angle in Degrees, Angle in Limits and Its Relation to Differentiation
Radians, Arc Length and Area of Sector
If y = f (x), then

dy
δy
f (x + δx) – f (x)
A lim ——————— = lim —– = —– = f ʹ(x)
©PAN ASIA PUBLICATIONS
δx → 0 δx δx → 0 δx dx
r
s
θ
O where δx is a small change in x.
B

θ ° θ rad Arc length, s Area of sector
—— = –—— = –——————–––— = –————–—–—–
360° 2π 2πr (Circumference) πr (Area of circle)
2

Important Facts (Chapter 1) 1 @ Pan Asia Publications Sdn. Bhd. Important Facts (Chapter 2) 7 @ Pan Asia Publications Sdn. Bhd.

Arc Length AB, Length of Chord AB, Area of Sector Stationary Point
AOB and Area of the Shaded Segment
dy
A point P(x, y) is a stationary point if —– = 0.
• Arc length AB, s = rθ A dx
• Length of chord AB: r The stationary point P(x, y) is
2
2
2
2
✤ AB = r + r – 2r cos θ ° (Cosine rule) O θ s d y
2
r
AB
✤ ——— = ———–———— • a maximum point if —–– , 0.
dx
2
180° – θ°
sin θ° sin ————– 2 B d y
1
2
2
dx
2
(Sine rule) • a minimum point if —–– . 0.
1 d y
2
2
• Area of sector AOB = —r θ • a point of inflection if —–– = 0.
2 dx 2
• Area of the shaded segment
= Area of sector AOB – Area of triangle AOB
1 1
2
2
= — r θ – — r sin θ
2 2
Important Facts (Chapter 1) 3 @ Pan Asia Publications Sdn. Bhd. Important Facts (Chapter 2) 9 @ Pan Asia Publications Sdn. Bhd.
Techniques of Differentiation Small Changes and Approximation of
Certain Quantities
dy
• If y = ax , then —– = anx n – 1
n
dx dy • If y = f (x) and δx is a small change in x, then
• If y = a, where a is a constant, then —– = 0
dx
dy
dy δy = —– × δx
• If y = f (x) + g(x), then —– = f ʹ(x) + gʹ(x) dx
dx
dy
dy
du
• If y = g(u), where u = h(x), then —– = —– × —–
dx du dx • If y = f (x) and x = g(t), thus the rate of change of y is:
• If y = uv, where u = f (x) and v = g(x), then
dy
dy
dx
dy dv du —– = —– × —–
—– = u—– + v—– dt dx dt
dx dx dx
u
• If y = —, where u = f (x) and v = g(x), then
v
du dv • If x changes from x to x + δx, then:
v—– – u—– δx
dy dx dx ✤ The percentage change in x = —– × 100%
x
—– = —————–
dx v 2 δy
✤ The percentage change in y = —– × 100%
y
Important Facts (Chapter 2) 5 @ Pan Asia Publications Sdn. Bhd. Important Facts (Chapter 2) 11 @ Pan Asia Publications Sdn. Bhd.
00B_1202 QB AMath F5.indd 3 02/12/2021 8:24 PM