Make sure you have your algebra skills down (factoring, simplifying, square roots, etc).
Know your log/exponent properties
Know the unit circle and as many trig identities you can fit in your head
Get ready for some seemingly weird concepts and don't settle for hand-wavey, take-it-as-it-is
answers
Don't brute force the memorization of the formulas.
Instead be able to recall the formulas due to the numerous amounts of time you've had to use them
to solve problem sets.
Understand why they work and when they apply. This will make it so much easier in the long run.
how to differentiate (and understand the meaning of) the following:
polynomials (bring power down and multiply, reduce power by one)
sinx and cosx (sinx -> cosx -> -sinx -> -cosx -> repeats)
ex (still ex )
ln x (1/x)
Also, the product rule and chain rule. There's also the quotient rule but you don't need it, you can
always use a combination of product and chain instead.
integration by parts (it's just product rule rearranged)
changing variables for integration
the fact that integration is the opposite of differentiation.
how to manipulate exponents and logs. what negative and fractional powers are and how to deal
with them.
the major trig identities, and how to use algebra to manipulate stuff involving trig functions. the
MOST important are:
sin2 x + cos2 x = 1
the two other identies you get by dividing the above by sin2 x and cos2 x .
and
tanx = sinx/ cosx
but you've also got the double angle/ angle addition formulae, as well.
I don't know if it's relevant to calculus itself, but graphs you should know include:
polynomials vaguely (if the highest power is n, it has n-1 bends, if the highest power is negative it's
'upside down'. factorising it gives you the roots, highest power is n means it has upto n roots) as well
as quadratics in detail (how to solve them using quadratic formula, completing the square and
factorising).
you should know the shape of sinx, cosx tanx and where the important parts are (minima, maxima,
crossing x axis, asymptotes).
what 1/x looks like
what ex and ln x look like
how to draw linear graphs (y = mx + c) and find m and c given a linear graph.
Also you should know how changing a function changes the graph (things like if y = f(x) is the
original, then y = f(x - a) is a translation in x direction by a, y-a = f(x) or y = f(x) + a is a translation in
y direction by a, and the ones for reflections and stretches. rotations are harder and you might not
need to know them).
you should be comfortable in general with manipulating algebraic expressions.
basic stuff to make sure you know include:
how to multiply and add negative numbers
inverse operations/ functions (+ and - are opposites, as are * and /, squaring and square rooting, sinx
and sin-1x, lnx and ex etc.)
expanding brackets and factorising
BODMAS/ BIDMAS/ PEMDAS (all names for the same thing).
adding and multiplying fractions (whether with numbers or symbols).