Maths Pure 2 Flashcards
30, 40, 60
P/6 , p/4, p/3
Sin p/6, p/4, p/3
1/2 , 1/root 2, root 3/2
Cos p/6, p/4, p/3
Root 3/2, 1/ root 2, 1/2
Tan p/6, p/4, p/3
1/root 3, 1, root 3
Arc
Radius x angle
Sector
0.5 x radius^2 x angle
Segment
0.5 x radius^2(angle-sin angle)
Small angle approximations
Sin angle to angle
Cos angle to 1-0.5angle^2
Tan angle to angle
Identities for reciprocal angle
Tan^2x + 1 = sec^2x
Cot^2x + 1 = cosec^2x
Arithmetic Sequences
Un = 1st term + (n-1) d
Sn = n/2 (2a + (n-1)d)
Geometric Sequence
Un = ar^(n-1)
Sn = a(1-r^n)/1-r
Double Angle Formulae
Sin 2ø to 2sinøcosø
Cos2ø to :
cos^2ø - sin^2ø
2cos^2ø - 1
1 - 2sin^2ø
Tan2ø to (2tanø)/(1-tan^2ø)
Diff: sinx
Cos x
Diff: cos x
-sinx
Diff: e^kx
ke^kx
Diff: a^kx
a^x k lna
Diff: lnx
1/x
Chain rule
Dy/dx = dy/du x du/dx
Product rule
y = uv
Dy/dx = u dv/dx + v du/dx
Quotient rule
y= uv
Dy/dx = (v du/dx - u dv/dx) / v^2
Diff: tankx
K sec^2 kx
Diff: coseckx
-k coseckx cotkx
Diff: seckx
K secks tankx
Diff: cotkx
-k cosec^2kx
Diff: arcsinx
1/root(1-x^2)
Diff: arc cosx
-1/root(1-x^2)
Diff: arctanx
1/(1+x^2)
Implicit Differentiation
D(f(y))/dx = f’(y) dy/dx
Second Derivative
F’’(x) <= 0
Concave/max
= 0
Concave, point of inflection, convex
> = 0
Convex/min
Newton Raphson Method
X n+1 = X n - (f(x n)/f’(x n))
Order of transformation
Inside bracket then outside bracket
Inside: translation, then stretch
Outside: stretch, then translation
