[quote
Cosec = 1/cos
Sec = 1/sin
Sec and Cosec are the wrong way around. I think the double angle and compound angle formulas are useful (although I don;t know how often they pop up in methods) and possibly the altered versions of the Pythagorean identity (Although I think these are more so used in spesh)
*Edit: I can't quote for shit
They are the wrong way around; cos=1/sec, sin=1/cosec
You'll just have to use sec as the (square root of the) derivative of tan x I think
There wasn't that much trig in Methods last year from memory.
Can someone explain the highlighted justification for why the approximation of 
is less than the true value? The gradient isn't decreasing for [8, inf)?
So, you're using linear approximation on x^1/3. Differentiating once yields 1/3*x^(-2/3). Differentiating again yields -2/9*x^(-5/3)
As you can see, for positive x, the gradient is decreasing for x>0 (as the gradient of the gradient, if you want, is decreasing). Linear approximation works by drawing a tangent line and extrapolating from that. As the gradient is decreasing, the tangent line becomes an overestimate.
Draw out your transition matrix. I don't know how to use latex to do that so bear with me.
From my rather limited knowledge of transition matrices, it would look like this:
Superior | p p-0.2 |
Regular | 1-p 1.2-p |
So what you'd do is that given you know the first statue is superior, your initial state vector looks like
|1|
|0| from the way I've defined the matrix. If the transition state is T, the probabilities of the third state are given by T^2*initial state.
Read off the top row for the probability that the statue is superior. Set this equal to 0.7
ETC.
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