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Developed by Susan Cantey

and student Elizabeth Albert

at Walnut Hills H.S.

2006

Welcome to the

Pre-CalculusPower Point

Flash Drill!

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Im 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 themquickly 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?

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Define an

Even Function

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)()( xfxf

Note: It is NOT enough to

know the graph is

symmetric with respect tothe y-axis.

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Define an

Odd Function

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)()( xfxf

Again, please note that it

is NOT enough to know

that the graph has origin

symmetry.

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See if you can identify the

function that probably goeswith each of these simple

graphs.

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lyrespective

xxf

and

xxf

)(

)( 2

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How about these?

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lyrespective

xxf

andxxf

3

3

)(

)(

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What about this one?

2

2

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xxf 1tan)(

Did you know it?

You are a tiger!

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How about these?

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xxf

1

)(

and222 ryx

respectively

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and finally:

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lyrespective

xxf

andexf

x

ln)(

)(

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The graph

of x = a

is

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a vertical line.

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The graph

of y = ais

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a horizontal line.

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OKthats enough about

graphs!

Lets move on

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?1

x

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x

1

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?2/1

x

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x

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?2 x

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2

1

x

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?n mx

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n

m

xThink flower & root

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?ln nx

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xn ln

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?ln xy

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yx lnln

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?ln yx

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yx lnln

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?

?log xb

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b

x

ln

ln

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?

1

ln

x

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xln

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?1ln

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0

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?ln xe

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x

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?ln xe

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x

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OKenough of the logs

already!

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The formula forthe slope of a

line is

m = ?

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12

12

xx

yy

x

y

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Point slope

equation of aline ?

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)( 11 xxmyy

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Midpoint Formula = ?

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2

,

2

2121 yyxx

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Distance Formula=?

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2

12

2

12 )()( xxyy

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xDefine:

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|x|

x for x 0-x for x

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?98.2

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2(Greatest integer < 2.98)

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?17.2

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3You always round

down the number line!

Here comes o r fa orite

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Here comes your favorite

thing!Yeah! Trigonometry!

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?0sin

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0

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?0cos

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1

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?6

sin

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2

1

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?4

sin

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2

2

2

1 or

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?

3

sin

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2

3

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?2sin

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1

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?2

cos

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0

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?3

cos

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2

1

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?4cos

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2

2

2

1 or

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?6

cos

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2

3

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?cos

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1

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?0tan

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0

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?4

tan

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14

sin4

cos

because:

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?2

tan

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(or undefined)

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?3

tan

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3

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?6

tan

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3

1

or 3

3

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What are the Principle

domains of the 6 trig

functions?

That is, what quadrants are the

angles in which can be used toanswer inverse trig function

problems?

0 for cosine

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2,

2

2,

2

,0

for cosine

for sine

for tangent

(Different texts assign different principledomains to the other three trig functions,

so we wont bother with them.)

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?2

1sin

1

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6

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?2

1cos

1

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4

3

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?23sin 1

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3

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?1tan 1

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sine and cosine

have to be equal!

4

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?3tan 1

3

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3

1

3

1

0

3

1

13

Answer:3

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OKnow lets see if you know your

identities!

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?cossin 22 xx

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1I hope you knew that one!!!

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?sin2 x

2

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x

2

cos1OK, thats really the same one!

Whats the one with the s in it?

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?sin2 x

What s the one with the s in it?

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x2cos2121 That one is harder, but you will

need it in calculus!

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?cos2 xDo you know both of them?

2

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x

and

x

2cos

sin1

21

21

2

You rock!!!

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?tan1

2 x

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x2secDid ya get the ol

stamp of approvalon that one?

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?1sec

2 x

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x2tanTheyre laughing

because this is

really the sameone again!

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?sincos 22

xxHo Ho Ho!!

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x2cosI dont know why Santa thought

this was funny!

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?2sin x

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xxcossin2This one is very important!!

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Now for a little algebra and youll be done!!

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?22 ba

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baba

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?33 ba

22 bbb

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22 bababa

Notice there is NO 2

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?33 ba

22 bbb

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22 bababa

Still no 2!!!

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?)( 2 ba

(almost finished!!!)

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22

2 baba Theres that two you wanted before!!

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Last one!!!!

3ba

3223 33 babbaa

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33 babbaa

Dont be foiled!

Use thebinomial

Theorem.

If you know all this material,

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then you are prepared to begin

calculus All you need now is a

sharp mind, a sharp pencil and

a really big eraser!

GOODBYE!!!!

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ADIOS!

AUFWIEDESEHEN!

CHOW!