Relevant content from GCSE/KS3 is
Students who have only done GCSE are likely to struggle with indices, notation and formal manipulation.
All AS maths students will do C1 and C2 and one of S1, M1 and D1
For potential biology students, the strong recommendation is to choose the S1 option.
For potential physics or engineering students, the strong recommendation is to choose M1.
You could expect an AS student with statistics to have encountered
Note: they will not have met e, any other differentiation
For a full Alevel in maths students will have done C1C4 and two of S1, D1, M1, S2, D2, M2
Where there is a choice, potential biologists would be strongly recommended to choose S1 and S2. Physicists and engineers should choose M1 and M2.
Alevel maths candiates will know the graphs of e, ln, trig identities, trig differentiation, product, quotient and chain rule.
If they have taken S2 then they will also know some other distributions, know what a random variable is and know about hypothesis testing in simple contexts.
Specifically, the key module content (full Alevel in grey) is
Calculus 

C2 
Diff / Int $Ax^n$ 
C3 
$\frac{d}{dx}\left(\ln(Ax)\right)$ 
C3 
Diff / int $Ae^{nx}$ 
C3 
Diff / int $\sin(ax)$ 
C3 
Diff / int $\cos(ax)$ 
C3 
Diff / int $\tan(ax)$ 
C3 
$\int \frac{1}{ax+b}$ 
C3 
Product rule 
C3 
Quotient rule 
C3 
Function of a function rule': $\frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx}$ 
Logarithms 

C2 
If $y = n^x $then $\log_n(y) = x$ 
C2 
$\ln(a)+\ln(b) = \ln(ab)\quad \ln(a) \ln(b) = \ln\left(\frac{a}{b}\right)$ 
C2 
$\ln(x^p) = p \ln (x)$ 
C3 
$e^{\ln(a)} = a$ 
C3 
$\ln(y) = ln(a) x log_a(y)$ 
Integral change of variable 

C2 
Area enclosed by function, average value 
C2 
$\tan(x) = \frac{\sin(x)}{\cos(x)}$ 
C2  $\sin^2(x)+\cos^2(x) =1$ 
C3 
$\int y(x)dx = \int y(x(u))\frac{dx}{du} du$ 
C4 
$\sec(x) = \frac{1}{\cos(x)}$ 
C4 
$\mbox{cosec}(x) = \frac{1}{\sin(x)}$ 
C4 
$\cot(x) = \frac{1}{\tan(x)}$ 