Pre cal drill
sunfloursk
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135 slides
Jul 11, 2014
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About This Presentation
No description available for this slideshow.
Slide Content
Developed by Susan Cantey
and student Elizabeth Albert
at Walnut Hills H.S.
2006
Welcome to the
Pre-Calculus
Power Point
Flash Drill!
and 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?
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
Even Function
)()( xfxf =-
Note: It is NOT enough to
know the graph is
symmetric with respect to
the y-axis.
Note: It is NOT enough to
know the graph is
symmetric with respect to
the y-axis.
Define an
Odd Function
Odd Function
)()( xfxf -=-
Again, please note that it
is NOT enough to know
that the graph has origin
symmetry.
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….
function that probably goes
with each of these simple
graphs….
lyrespective
xxf
and
xxf
=
=
)(
)(
2
xxf
and
xxf
=
=
)(
)(
2
How about these?
lyrespective
xxf
and
xxf
3
3
)(
)(
=
=
xxf
and
xxf
3
3
)(
)(
=
=
What about this one?
2
p
2
p-
2
p
2
p-
xxf
1
tan)(
-
=
Did you know it?
You are a tiger!
1
tan)(
-
=
Did you know it?
You are a tiger!
How about these?
x
xf
1
)(=
and
222
ryx =+
respectively
xf
1
)(=
and
222
ryx =+
respectively
and finally:
lyrespective
xxf
and
exf
x
ln)(
)(
=
=
xxf
and
exf
x
ln)(
)(
=
=
The graph
of x = a
is…
of x = a
is…
… a vertical line.
The graph
of y = a
is…
of y = a
is…
… a horizontal line.
OK…that’s enough about
graphs!
Let’s move on…
graphs!
Let’s move on…
?
1
=
-
x
1
=
-
x
x
1
1
?
2/1
=x
2/1
=x
x
?
2
=
-
x
2
=
-
x
2
1
x
1
x
?=
nm
x
nm
x
n
m
x
Think “flower” & “root”
m
x
Think “flower” & “root”
?ln=
n
x
n
x
xnln
?ln=xy
yxlnln+
?ln=
y
x
y
x
yxlnln-
?
?
log=x
b
?
log=x
b
b
x
ln
ln
x
ln
ln
?
1
ln=÷
ø
ö
ç
è
æ
x
1
ln=÷
ø
ö
ç
è
æ
x
xln-
?1ln=
?
ln
=
x
e
ln
=
x
e
x
?ln=
x
e
x
e
x
OK…enough of the logs
already!
already!
The formula for
the slope of a
line is
m = ?
the slope of a
line is
m = ?
12
12
xx
yy
x
y
-
-
=
D
D
12
xx
yy
x
y
-
-
=
D
D
Point slope
equation of a
line ?
equation of a
line ?
)(
11
xxmyy -=-
11
xxmyy -=-
Midpoint Formula = ?
÷
ø
ö
ç
è
æ ++
2
,
2
2121 yyxx
ø
ö
ç
è
æ ++
2
,
2
2121 yyxx
Distance Formula=?
2
12
2
12 )()( xxyy -+-
12
2
12 )()( xxyy -+-
xDefine:
{
|x|
x for x 0³
-x for x<0
|x|
x for x 0³
-x for x<0
[ ][ ]?98.2 =
2
(Greatest integer < 2.98)
(Greatest integer < 2.98)
[ ][ ]?17.2 =-
3-
You always round
down the number line!
You always round
down the number line!
Here comes your favorite
thing!
Yeah! Trigonometry!
thing!
Yeah! Trigonometry!
?0sin=
?0cos=
1
?
6
sin=
p
6
sin=
p
2
1
1
?
4
sin=
p
4
sin=
p
2
2
2
1
or
2
2
1
or
?
3
sin=
p
3
sin=
p
2
3
3
?
2
sin=
p
2
sin=
p
1
?
2
cos=
p
2
cos=
p
?
3
cos=
p
3
cos=
p
2
1
1
?
4
cos=
p
4
cos=
p
2
2
2
1
or
2
2
1
or
?
6
cos=
p
6
cos=
p
2
3
3
?cos=p
1-
?0tan=
?
4
tan=
p
4
tan=
p
1
4
sin
4
cos
pp
=because:
4
sin
4
cos
pp
=because:
?
2
tan=
p
2
tan=
p
¥
(or undefined)
(or undefined)
?
3
tan=
p
3
tan=
p
3
?
6
tan=
p
6
tan=
p
3
1
or
3
3
1
or
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?
domains of the 6 trig
functions?
That is, what quadrants are the
angles in which can be used to
answer inverse trig function
problems?
[ ]
÷
ø
ö
ç
è
æ
-
ú
û
ù
ê
ë
é
-
2
,
2
2
,
2
,0
pp
pp
pfor cosine
for sine
for tangent
(Different texts assign different principle
domains to the other three trig
functions, so we won’t bother with
them.)
÷
ø
ö
ç
è
æ
-
ú
û
ù
ê
ë
é
-
2
,
2
2
,
2
,0
pp
pp
pfor 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
1
sin
1
=
-
2
1
sin
1
=
-
6
p
p
?
2
1
cos
1
=÷
ø
ö
ç
è
æ-
-
2
1
cos
1
=÷
ø
ö
ç
è
æ-
-
4
3p
3p
?
2
3
sin
1
=
-
2
3
sin
1
=
-
3
p
p
?1tan
1
=
-
1
=
-
sine and cosine
have to be equal!
4
p
have to be equal!
4
p
( )?3tan
1
=-
-
1
=-
-
3
1
3
1
0
3
1-
1-
3-
Answer:
3
p-
¥
¥-
1
3
1
0
3
1-
1-
3-
Answer:
3
p-
¥
¥-
OK…now let’s see if you know your
identities!
identities!
?cossin
22
=+ xx
22
=+ xx
1
I hope you knew that one!!!
I hope you knew that one!!!
?sin
2
=x
2
=x
x
2
cos1-
OK, that’s really the same one!
2
cos1-
OK, that’s really the same one!
?sin
2
=x
What’s the one with the ½’s in it?
2
=x
What’s the one with the ½’s in it?
x2cos
2
1
2
1
-
That one is harder, but you will
need it in calculus!
2
1
2
1
-
That one is harder, but you will
need it in calculus!
?cos
2
=x
Do you know both of them?
2
=x
Do you know both of them?
x
and
x
2cos
sin1
2
1
2
1
2
+
-
You rock!!!
and
x
2cos
sin1
2
1
2
1
2
+
-
You rock!!!
?tan1
2
=+ x
2
=+ x
x
2
sec
Did ya get the ol’
“stamp of approval”
on that one?
2
sec
Did ya get the ol’
“stamp of approval”
on that one?
?1sec
2
=-x
2
=-x
x
2
tan
They’re laughing
because this is
really the same
one again!
2
tan
They’re laughing
because this is
really the same
one again!
?sincos
22
=- xx
Ho Ho Ho!!
22
=- xx
Ho Ho Ho!!
x2cos
I don’t know why Santa thought
this was funny!
I don’t know why Santa thought
this was funny!
?2sin=x
xxcossin2
This one is very important!!
This one is very important!!
Now for a little algebra and you’ll be done!!
?
22
=-ba
22
=-ba
( )( )baba -+
?
33
=-ba
33
=-ba
( )( )
22
bababa ++-
Notice there is NO “2”
22
bababa ++-
Notice there is NO “2”
?
33
=+ba
33
=+ba
( )( )
22
bababa +-+
Still no 2!!!
22
bababa +-+
Still no 2!!!
?)(
2
=+ba
(almost finished!!!)
2
=+ba
(almost finished!!!)
22
2baba ++
There’s that two you wanted before!!
2baba ++
There’s that two you wanted before!!
Last one!!!!
( )
3
ba+
( )
3
ba+
3223
33 babbaa +++
Don’t be
foiled!
Use the
binomial
Theorem.
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!
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!
ADIOS!
AUFWIEDESEHEN!
CHOW!
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