Speedy Review of Critical Precalculus Skills Overview of Limits and Continuity Concept of a Derivative and Derivative Rules Applications of Derivatives Concept of the Integral Application of the Integral

Calculus is the study of change, it has two main branches Differential Calculus – The study of change Integral Calculus- The study of area/accumulation But they both start with a foundation in: Precalculus (Algebra, Geometry and Trig) Limits

Algebra Functions Exponents and Logs Trigonometry

 The next slides contain mathematical concepts that you must commit to memory to be successful in the AP Calculus exam.  When you think you know the answer,  Or if you give up  Go to the next slide to see the answer

Define an Even Function

Note: It is NOT enough to know the graph is symmetric with respect to the y-axis. Geometrically speaking, the graph face of an even function is symmetric with respect to the y-axis, meaning that its graph remains unchanged after reflection about the y-axis. Examples: x 2, x 4, cos (x)

Define an Odd Function

Again, please note that it is NOT enough to know that the graph has origin symmetry. Geometrically, the graph of an odd function has rotational symmetry with respect to the origin, meaning that its graph remains unchanged after rotation of 180 degrees about origin. Examples: x, x 3, sin (x)

Can you identify the function that probably goes with each of these simple graphs?

How about these?

f(x) = sin (x)

What about this one?

How about these?

AND FINALLY…

The graph of x = a is… A VERTICAL LINE

The graph of y = a is… … a horizontal line.

OK…that ’ s enough about graphs! Let ’ s move on…

Think “ flower ” & “ root ”

OK…enough of the logs already!

The formula for the slope of a line is m = ?

Point slope equation of a line ?

Midpoint Formula = ?

Distance Formula=?

Define:

{ |x| x for x 0 -x for x<0

Here comes your favorite thing! Yeah! Trigonometry!

because:

(or undefined)

or

What are the Principle domains of the 6 trigonometric functions? That is, what quadrants are the angles in which can be used to answer inverse trig function problems?

for cosine for sine for tangent (Different texts assign different principle domains to the other three trig functions, so we won ’ t bother with them.)

sine and cosine have to be equal!

Answer:

OK…now let ’ s see if you know your identities!

I hope you knew that one!!!

OK, that ’ s really the same one!

What ’ s the one with the ½ ’ s in it?

That one is harder, but you will need it in calculus!

Do you know both of them?

You rock!!!

Did ya get the ol ’ “ stamp of approval ” on that one?

They ’ re laughing because this is really the same one again!

Ho Ho Ho!!

I don ’ t know why Santa thought this was funny!

This one is very important!!

Now for a little algebra and you ’ ll be done!!

Notice there is NO “ 2 ”

Still no 2!!!

(almost finished!!!)

There ’ s that two you wanted before!!

Last one!!!!

Don ’ t be foiled! Use the binomial Theorem.

If you know all this material, then you are prepared to begin calculus… All you need now is a sharp mind, a sharp pencil and a really big eraser!