Precalc review for calc p pt
135
Developed by Susan Cantey and student Elizabeth Albert at Walnut Hills H.S. 2006 Welcome to the Pre-Calculus Power Point Flash Drill!
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Transcript of Precalc review for calc p pt
Developed by Susan Canteyand student Elizabeth Albert
at Walnut Hills H.S.2006
Welcome to the
Pre-Calculus Power Point Flash Drill!
I’m going to ask you a lot of questions about math. These are facts that you should know extremely
well. You also need to be able to recall them quickly if you want to succeed in Calculus.
When you think you know the answer,
(or if you give up ) click to get to the next slide to see if you were correct.
Ready?
Define an
Even Function
)()( xfxf
Note: It is NOT enough to know the graph is
symmetric with respect to the y-axis.
Define an
Odd Function
)()( xfxf Again, please note that it is NOT enough to know that the graph has origin
symmetry.
See if you can identify the function that probably goes with each of these simple
graphs….
lyrespective
xxf
and
xxf
)(
)( 2
How about these?
lyrespective
xxf
and
xxf
3
3
)(
)(
What about this one?
2
2
xxf 1tan)(
Did you know it?
You are a tiger!
How about these?
xxf
1)(
and222 ryx
respectively
and finally:
lyrespective
xxf
and
exf x
ln)(
)(
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…
?1 x
x
1
?2/1 x
x
?2 x
2
1
x
?n mx
nm
xThink “flower” & “root”
?ln nx
xn ln
?ln xy
yx lnln
?ln y
x
yx lnln
?
?log xb
b
x
ln
ln
?1
ln
x
xln
?1ln
0
?ln xe
x
?ln xe
x
OK…enough of the logs already!
The formula for the slope of a
line is
m = ?
12
12
xx
yy
x
y
Point slope equation of a
line ?
)( 11 xxmyy
Midpoint Formula = ?
2,
22121 yyxx
Distance Formula=?
212
212 )()( xxyy
xDefine:
{|x|x for x 0-x for x<0
?98.2
2(Greatest integer < 2.98)
?17.2
3You always round
down the number line!
Here comes your favorite thing!
Yeah! Trigonometry!
?0sin
0
?0cos
1
?6
sin
2
1
?4
sin
2
2
2
1or
?3
sin
2
3
?2
sin
1
?2
cos
0
?3
cos
2
1
?4
cos
2
2
2
1or
?6
cos
2
3
?cos
1
?0tan
0
?4
tan
14
sin4
cos
because:
?2
tan
(or undefined)
?3
tan
3
?6
tan
3
1or
3
3
What are the Principle domains of the 6 trig
functions?
That is, what quadrants are the angles in which can be used to
answer inverse trig function problems?
2,2
2,2
,0
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.)
?2
1sin 1
6
?2
1cos 1
4
3
?2
3sin 1
3
?1tan 1
sine and cosine have to be equal!
4
?3tan 1
3131
0
31
13
Answer:3
OK…now let’s see if you know your identities!
?cossin 22 xx
1I hope you knew that one!!!
?sin 2 x
x2cos1OK, that’s really the same one!
?sin 2 xWhat’s the one with the ½’s in it?
x2cos21
21
That one is harder, but you will need it in calculus!
?cos2 xDo you know both of them?
x
and
x
2cos
sin1
21
21
2
You rock!!!
?tan1 2 x
x2secDid ya get the ol’
“stamp of approval” on that one?
?1sec2 x
x2tanThey’re laughing because this is really the same
one again!
?sincos 22 xx
Ho Ho Ho!!
x2cosI don’t know why Santa thought
this was funny!
?2sin x
xx cossin2This one is very important!!
Now for a little algebra and you’ll be done!!
?22 ba
baba
?33 ba
22 bababa
Notice there is NO “2”
?33 ba
22 bababa Still no 2!!!
?)( 2 ba
(almost finished!!!)
22 2 baba There’s that two you wanted before!!
Last one!!!!
3ba
3223 33 babbaa 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!
GOODBYE!!!!
ADIOS!
AUFWIEDESEHEN!
CHOW!
