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Welcome to the Pre-Calculus Power Point Flash Drill!
Developed by Susan Canteyand student Elizabeth Albert
at Walnut Hills H.S.2006
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 anEven FunctionEven Function
)()( xfxf =−
Note: It is NOT enough to 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 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….
xxf
and
xxf
=
=
)(
)( 2
lyrespective
xxf =)(
How about these?
and
xxf
3
3)(
=
=
lyrespective
xxf 3)( =
What about this one?
2
π2
2
π−
xxf 1tan)( −=
Did you know it?
You are a tiger!
How about these?
xxf
1)( =
andand222 ryx =+
respectively
and finally:
xxf
and
exf x
ln)(
)(
=
=
lyrespective
xxf ln)( =
The graph of x = a of x = a
is…
… a vertical line.
The graph of y = a of y = a
is…
… a horizontal line.
OK…that’s enough about graphs!
Let’s move on…
?1 =−x
1
x
?2/1 =x ?=x
xx
2 =−x 2 =−x
2
1
x2x
?=n mx ?=x
nmn
Think “flower” & “root”
?ln =nx ?ln =x
xn ln xn ln
?ln =xy ?ln =xy
yx lnln +
?ln =y
x
y
yx lnln −
?
?log =xb ?b
xln
bln
?1
ln =
x?ln =
x
xln−
ln xln x
?ln =xe ?ln =e
OK…enough of the logs already!
The formula for the slope of a
line is line is
m = ?
12
12
xx
yy
x
y
−−=
∆∆
12
Point slope equation of a equation of a
line ?
)( 11 xxmyy −=−
Midpoint Formula = ?
++2
,2
2121 yyxx
22
Distance Formula=?
212
212 )()( xxyy −+−
xDefine:
|x|x for x 0≥-x for x<0-x for x<0
[ ][ ] ?98.2 =
(Greatest integer < 2.98)
?17.2 =− ?17.2 =−
You always round
down the number line!
Here comes your favorite thing!
Yeah! Trigonometry!
?sin =π?
6sin =
?sin =π?
4sin =
2
2
2
1or
22
?sin =π?
3sin =
3
2
?2
sin =π2
=
?2
cos =π?
2cos =
?3
cos =π?
3cos =
?4
cos =π?
4cos =
2
2
2
1or
22
?cos =π?
6cos =
3
2
?cos =π ?cos =π
==
?4
tan =π?
4tan =
4sin
4cos
ππ =because:
?tan =π?
2tan =
(or undefined)
?3
tan =π?
3tan =
33
?tan =π?
6tan =
3
1or
3
33
or3
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
,0
ππ
πππ for cosine
for sine
−2
,2
ππfor tangent
(Different texts assign different principle domains to the other three trig functions,
so we won’t bother with them.)
?1
sin 1 =− ?2
sin =
6
π6
?1
cos 1 = −− ?
2cos =
4
3π4
?3
sin 1 =− ?2
3sin 1 =−
3
π3
?1tan 1 =− ?1tan =
sine and cosine have to be equal!
π4
π
?3tan 1 =−− ?3tan =−
31
31
0
31−
∞
31−
3−
Answer:3
π−∞−
OK…now let’s see if you know your identities!
?cossin 22 =+ xx
I hope you knew that one!!!
?sin 2 =x ?sin =x
x2cos1−OK, that’s really the same one!
?sin 2 =x
What’s the one with the ½’s in it?
?sin =x
x2cos21
21 −
That one is harder, but you will That one is harder, but you will need it in calculus!
?cos2 =x ?cos =xDo you know both of them?
and
xsin1 2−
x
and
2cos21
21 +
You rock!!!
?tan1 2 =+ x ?tan1 =+ x
x2secDid ya get the ol’
“stamp of approval” on that one?
?1sec2 =−x ?1sec =−x
x2tanThey’re laughing because this is really the same
one again!
?sincos 22 =− xx
Ho Ho Ho!!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 ?=− ba
( )( )baba −+
?33 =− ba ?=− ba
( )( )22 bababa ++−Notice there is NO “2”
?33 =+ ba ?=+ ba
( )( )22 bababa +−+Still no 2!!!
?)( 2 =+ ba
(almost finished!!!)
22 2 baba ++There’s that two you wanted before!!There’s that two you wanted before!!
Last one!!!!
( )3ba +( )3ba +
3223 33 babbaa +++Don’t be foiled!
Use the 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!a really big eraser!
GOODBYE!!!!
ADIOS!
AUFWIEDESEHEN! AUFWIEDESEHEN!
CHOW!
