Math Placement Test Review

Front 1

What is bigger 10^x or x^10?

Back 1

10^x, initially x^10 is bigger, but as they increase 10^x will overtake x^10

Front 2

Define exponential decay.

Back 2

when get the graph is getting smaller and smaller (opposite of exponential growth)

Front 3

What indicates that a exponential expression's graph will be a exponential decay?

Back 3

If the exponent is negative, or base is between 0 and 1

Front 4

Give two examples of exponential expressions that would result in a decay.

Back 4

3^(-x) and/or 0.15^x

Front 5

Give an example of a exponential expression that would result in a exponential growth.

Back 5

5^x

Front 6

Draw an example of a exponential decay and growth graph.

Back 6

http://www.google.com/imgres?imgurl=http://fym.la.asu.edu/~tturner/MAT_117_online/Exponential_Functions/decay_e%255E-x.gif&imgrefurl=http://fym.la.asu.edu/~tturner/MAT_117_online/Exponential_Functions/Exponentials.htm&usg=__LzyfOOLqw0_z-mJEQVpOOqWFiaw=&h=486&w=486&sz=12&hl=en&start=11&sig2=58ZQrrjPaLwfJS6oPG8FMA&zoom=1&tbnid=yTYwgck0D-0-bM:&tbnh=150&tbnw=150&ei=rigITp3iD4uDtgfsvbGwDQ&prev=/search%3Fq%3Dexponential%2Bdecay%26um%3D1%26hl%3Den%26client%3Dfirefox-a%26sa%3DN%26rls%3Dorg.mozilla:en-US:official%26biw%3D1252%26bih%3D496%26tbm%3Disch&um=1&itbs=1&iact=hc&vpx=140&vpy=172&dur=590&hovh=150&hovw=150&tx=154&ty=121&page=2&ndsp=10&ved=1t:429,r:5,s:11&biw=1252&bih=496 (decay)

http://www.google.com/imgres?imgurl=http://www.adambreckler.com/wp-content/uploads/2009/08/exponential_growth_520.jpg&imgrefurl=http://www.adambreckler.com/the-impact-of-exponential-growth&usg=__uo4zfOm1JRlU3aGwLIuE55j-9M0=&h=520&w=629&sz=89&hl=en&start=3&sig2=SZWLPfhsoYDG1ABQhLyDDw&zoom=1&tbnid=7sMTi8lEQ2V2aM:&tbnh=113&tbnw=137&ei=-CgITrCODNKXtwfcppjFDQ&prev=/search%3Fq%3Dexponential%2Bgrowth%26um%3D1%26hl%3Den%26client%3Dfirefox-a%26sa%3DN%26rls%3Dorg.mozilla:en-US:official%26biw%3D1252%26bih%3D496%26tbm%3Disch&um=1&itbs=1 (growth)

Front 7

What type of graphs do logarithmic functions resemble?

Back 7

square root graphs

Front 8

True or False:
Logs are the inverse of exponents.

Back 8

TRUE

Front 9

True of False:
The graphs of 2^x and log2(x) are inverses.

Back 9

TRUE

Front 10

What does a composite function look like? Or how can you identify that a function is a composite function.

Back 10

g o f (x) and/or f o g (x)

Front 11

Translate f o g(x) into a parenthetical form.

Back 11

f(g(x))

Front 12

How can you determine that a function is an inverse of its parent function?

Back 12

The x and y coordinates of the inverse will be switched in comparison to the parent function.

ex. parent function (6,3)
inverse function (3, 6)

Front 13

Find the inverse of y=3x+6, writing out the steps as you go.

Back 13

1) write out original equation
2) solve original function for the un-isolated variable (in this example it is x)
ex. y-6/3=x
3) now switch the x and y of the equation created in step 2
ex. x-6/3=y
4) you have now found the inverse

Front 14

What test can be used to determine that a graph cannot have an inverse?

Back 14

Horizontal Line Test

Front 15

What type of functions don't have inverses?

Back 15

quadratic functions
ex. f(x)= x^2+4x-3

Front 16

How can you algebraically find if a function has an inverse or not?

Back 16

If you cannot isolate x, which is what happens in quadratic equations

Front 17

What is the trig identity for csc(x)?

Back 17

1/sin(x)

WTR:
Corey Skillfully Creates SINES

Front 18

What is the trig identity for tan(x)?

Back 18

sin(x)/cos(x) or 1/cot(x)

WTR:
Tommy Stole Cookies

Front 19

True or False:
tan(x) and cot(x) are inverses or eachother

Back 19

True

Front 20

Due to the fact that csc(x) and sin(x) are inverses, what is sin(x)'s trig identity?

Back 20

1/csc(x)

Front 21

What is the inverse of cos(x)?

Back 21

sec(x)

Front 22

True or False:
cos(x) and sec(x) are inverses

Back 22

True

Front 23

What is the trig identity of cos(x)?

Back 23

1/sec(x)

Front 24

True or False:
cos(-x)= 3cos(x)

Back 24

False, this cos(-x)= -cos(x). This rule also applies for sin(x) and tan(x).

Front 25

What is pi equal to in degrees?

Back 25

180 degrees

Front 26

Describe the movement of a sine graph (for one period).

Back 26

axis to maximum to axis to minimum

Front 27

3sin(x-2)+6=f(x)
Tell the amplitude, period, phase shift, and vertical shift of this function.

Back 27

amplitude=3
period=360 (coefficient of x is 1)
vertical shift=6
phase shift=2 units to the right

Front 28

Describe the graph of a regular cosine graph.

Back 28

maximum to axis to minimum to axis to maximum

Front 29

What does a negative amplitude suggest about a sine or cosine graph?

Back 29

The graph is inverted.

Front 30

Describe the shape of a tan(x) graph.

Back 30

Three graphs, first is a upright half parobola (right) starting at 0 degress, second is an s-shape at 180 degrees, and the final is a inverted half parabola (left) at 360 degrees

Front 31

For triangle problems, what is important to remember?

Back 31

SOHCAHTOA

Front 32

When you see "arc" in from of tan(x), sin(x), cos(x), csc(x), sec(x), and cot(x) what does it mean?

Back 32

it is the inverse of that particular trig function

Front 33

Change arccos N= θ into non-inverse form, include the steps.

Back 33

1) isolate the N, by moving the arccos next to the θ
ex. N= arccos θ
2) remove the "arc" from the arccos
ex. N=cos θ
3)you are finished

Front 34

How do you remember the unit circle?

Back 34

1) learn your quadrants and the signs that go with it.
2) the coordinates of the point closest to the x-axis will always be:
(±√3/2 , ±1/2)
3)the coordinates closest to the y-axis will always be:
(±1/2 , ± √3/2)
4)the coordinates in the middle will be:
(± √2/2 , ± √2/2)
5) the radians that go with (± √2/2 , ± √2/2) go in intervals of 1/4 (make sure to include ╥ in the numerator)
6) the radians of the y and x axis go by 1/2 (make sure to include ╥ in the numerator)
7)

Front 35

Rewrite this problem:
Evaluate arcsin √2/2.

Back 35

√2/2 is the sine of what angle?

Front 36

True or false: the ranges of arcsin(x) and arctan(x) are the same.

Back 36

True

Front 37

True or False:
Sine applies to x-axis

Back 37

False, y-axis

Front 38

What axis does cosine apply to?

Back 38

x-axis

Front 39

What is the quadratic equation?

Back 39

-b ± √b²-4ac/2a

Front 40

True or False: A function can have more than one output (y-value) for each input (x-value).

Back 40

FALSE

Front 41

For functions, what is the x-value called and what are the y-values called?

Back 41

x-value=domain
y-value=range

Front 42

When given the graph of a function, how can you determine whether or not it is a function?

Back 42

Vertical Line Test

Front 43

What is another name for a rational expression?

Back 43

polynomial fraction

Front 44

√x= -3
True or False?

Back 44

False

Front 45

(x²)^4= x^8

Back 45

True

Front 46

True or False:
(x^3)(x^5) = x^15

Back 46

False, it is x^8

Front 47

True or False:
(x/y)²=x²/y²

Back 47

True

Front 48

Solve: (x²y^3)^0=?

Back 48

1, anything to an exponent of 0 will equal 1

Front 49

What is √4 in exponent form?

Back 49

4^½

Front 50

What is the circumference formula?

Back 50

2πr

Front 51

What is the formula to determine the area of a circle?

Back 51

A=πr²

Front 52

When is a quadratic graph "skinny"?

Back 52

when a>1
ex. when a=9, the quadratic will be skinny

WTR:
higher the number the skinnier it is

Front 53

When is a quadratic graph "fat"?

Back 53

when a<1
ex. when a=½ the quadratic will be fat
WTR:
the smaller the number the fatter the graph

Front 54

What point is the vertex?

Back 54

(h,k)

Front 55

Write out vertex form of a quadratic equation?

Back 55

a(x-h)²+k

Front 56

What is the formula for velocity?

Back 56

v=d/t

Front 57

sin²(x) + cos²(x)=?

Back 57

1