welcome to the pre-calculus power point flash drill! · welcome to the pre-calculus power point...

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!