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Math > Exam prep > Flashcards

Exam prep Flashcards

1
Q

A relation is a function if:

A

It pass the two test:
VLT or for every x- coordinate their is only one y-coordinate

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2
Q

What is domain?

A

Values of all the x- coordinate

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3
Q

What is range?

A

Values of all the y- coordinate

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4
Q

How can you tell apart a linear, quadratic, and exponential?

A

linear: first difference are the same
quadratic: second difference are the same
exponential: difference aren’t the same ex. 2 with a little x.

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5
Q

What is function notation?

A

It’s substituting f of x, and then solving

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6
Q

In y = a ( x-h)2 +k
what is “a”

A

If a is positive: open up
if a is negative it open down, and reflects into the x- axis
if a is a whole number it has a vertical stretch (narrower)
if it a faction or decimal it a compression ( wider)

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7
Q

In y= a (x-h)2 + k
what is h

A

if h is positive: shifts right
if h is negative: shifts left

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8
Q

In y= a (x-h)2 + k
what is k

A

if k is positive it shifts up
if k is negative it shifts down

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9
Q

what is the mother of all parabolas?

A

y=x2

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10
Q

How do you foil?

A

first, outside, inside, last
( x + 4) (2x-9)

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11
Q

how do you common factor?

A

Find the GCF
dived all number by
the GCF goes outside the bracket, and the dived number go inside.

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12
Q

how do you do simple trinomials

A

find the GCF
then do the chart method find the two numbers that multiply by a and c, but add to b
then put those number in the bracket

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13
Q

How do you know if it’s simple or complex trinomials?

A

simple their GCF is the first number “a”
complex find another GCF or do the chart method

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14
Q

in y= a (x-r) (x-s)
what is a

A

if a is positive the graph open up if it’s negative it open down
if a is > 1 it stretches’
if 0< a> a it compressed

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15
Q

in y= a( x-r) (x-s)
what is r and s?

A

r and s are the zeros

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16
Q

how do you find the zeros in an equation from standard from?

A

fully factor
then replace y for 0
and you switch the sign of the number

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17
Q

how do you find the difference of the square?

A

common factor if need be
you square root each factor
then plug it in
(x-6) (x+6)

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18
Q

how do you find the perfect square?

A

keep the sign
square root the a and c term
and plug it in with a exponent
(x-4)2 check it by multiply 2(4) (x) = the b term

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19
Q

what is the optimal value

A

is the value of the y- co-ordinate of the vertex

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20
Q

what is the axis of symmetry

A

divides the the parabola into two equal halfs

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21
Q

what the discriminant

A

b2 - 4 a c

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22
Q

how many roots are their if the discriminant is positive, negative or equal

A

positive= 2
negative= 0
equal= 1

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23
Q

how do you use the discriminant to find the roots?

A

plug into your equation

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24
Q

when do you use the whole discriminant formula?

A

when your looking for zeros, and the number are tricky like decimal

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25
Q

In application of quadratics how do you find the height?

A

you plug in 0 as you x in your equation
and then you solve

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26
Q

In application of quadratics how do you find when something is going to hit the ground?

A

your looking for the zeros
so factor if needed then plug in zeros and change the signs.

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27
Q

In application of quadratics how do you find the max/ min height?

A

add your zeros and dived by 2
this get you your x value
the plug that number into your equation

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28
Q

how do you solve by graphing?

A

this is used for standard form
Use the formula x= -b/ 2(a)
this find you the x of your vertex
then plug that x into your equation to get y of your vertex
then make a t chart, and plug in the x to find your y
graph
find your solution

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29
Q

when creating an equation from graphs
for factor form what do you need?

A

y= a (x-s) (x-r)
x= inter
y= inter
plug in to solve for “a”

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30
Q

when creating an equation from graphs for vertex form what do you need?

A

y= a (x-h) 2 +k
vertex
y= inter
plug in to solve for “a”

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31
Q

how do you complete the square?

A

stander to vertex
remove a from the first two terms
then find b/2 exponent 2
plug in that number as positive and negative
find the square root of a and the positive
now plug those number (x+3) 2 -9
multiply the negative by the outside number
then add by the out out side number to
get you equation.

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32
Q

what can you find with Vertex form?
y= a ( x-h) 2 +k

A

Vertex: can be found (h,k)
y= inter: plug in 0 to solve
axis: is h
optimal value: k
x- inter: hard to find you have to factor first

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33
Q

what can you find with factored form?
a(x-s) (x-r)

A

x- inter: switch the sign of s and r
vertex: add the x’s and then dived by 2: (x,?)
then sub to solve for for y of the vertex
y= inter: plug in 0 to slove
axis: x
optimal: y

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34
Q

what can you find with standard form?
ax2 + bx+ c

A

y= inter: plug in 0 to solve
vertex: must compete the square
x- inter: factor first
axis symmetry/ optimal value: factoring, x= -b/ 2(a)
or complete the square

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35
Q

how do you get from standard to vertex, and the opposite?

A

standard to vertex: factoring
vertex to standard: foil

36
Q

how do you get from standard to factoring, and the opposite?

A

standard to factoring: completing the square
factoring to standard: foil

37
Q

how do you get from factoring to vertex, and the opposite?

A

factoring to vertex: graphing
vertex to factoring: solve for “a”

38
Q

where does the hyp, opp, and adj go on right triangle?

A

hyp: is the longest side
adj: has the right angle, and the angle
opp: is opposite from the angle

39
Q

when solving for the unknowns
tan 30= X/ 10 what do you do?

A

you add 10 to both sides
then solve 10 tan 30

40
Q

when solving for the unknowns
cos 52= 20/ x what do you do?

A

add y to both side
y cos 52= 30
dived the one side by the cos 52
y= 30/ cos 52
dived to solve

41
Q

when solving for the unknowns
sin x = 5/12 what do you do?

A

do the sign inverse
-1 sin (5/12)
plug it in to solve

42
Q

what the angle of elevation?

A

the angle looking up

43
Q

what the angle of depression?

A

the angle looking down

44
Q

what the one thing to remeber with the angle of depression and elevation

A

it makes the z pattern

45
Q

in sine law how do you solve
sin 93/ x+= sin 55/ 17

A

you change the dominator
dived the both sides by number with x
to get x

46
Q

in sine law how do you solve for an angle?

A

you change the dominator
dived both sides by that number
to sine inverse to get an angle

47
Q

in cosine law how do you find SAS?

A

use the formula
cos < = c2-a2-b2/ -2 a b
Then you should get a fraction to do the invers

48
Q

in cosine law how do you find the SSS?

A

use the formula
c2= a2+b2-2 ab cos <
solve get a positive number and the square root

49
Q

what is peak?

A

the highest point on the graph

50
Q

what is trough?

A

the lowest point on the graph

51
Q

how do you know if it’s periodic?

A

there a repeating pattern

52
Q

what is period?

A

the horizontal length of one cycle on the graph

53
Q

what the amp?, and how do you find it?

A

half the distance between the max and min
max - min/ 2

54
Q

what is period of a sine function?

A

period is 360

55
Q

what is equation of axis and how do you find it?

A

half the distance horizontally
add the max and min and divide by 2

56
Q

what is the sin function formula?

A

a sin ( x +<) + d

57
Q

how do you graph
-2 sin ( x + 180 degrees) -1

A
  1. sin x
  2. strech by -2
    so multiply each y by -2
  3. reflection in x-axis
  4. shift left by 180 degrees so move the point over left 180
  5. shift down by 1
58
Q

what is the sin x

A
  • 360, 0
    -270, 1
    -180, 0
    -90, -1
    0, 0
    90, 1
    180, 0
    270, -1
    360, 0
59
Q

what the multiplication rule?

A

add the exponent if the base is the same

60
Q

what the division rule?

A

subtract the exponent if the base is the same

61
Q

what the power of power?

A

multiply the 2 exponent
6 3) 5 3x5+= 15
6 15

62
Q

what the zero exponent rule?

A

a0= 1

63
Q

how do you do fraction exponents?

A

the exponent goes on both the numerator and the dominator

64
Q

how do you do the negative exponents?

A

if there a negative exponent you have to flip the number so it’s a positive , and then solve

65
Q

how do you do the rational exponents?

A

if their a one as the numerator you put into the calculator as the denomator square root the number
if there a another number on top you put the bottom number and the square root to the exponent of the top number

66
Q

In y= a. b x what does it mean

A

a= y= inter
b= ratio

67
Q

what does an exponential graph have?

A
  1. they never touch the asymptote
  2. they have y-inter
  3. if the b
    is greater than 1 it increasing
    if between 0- 1 it’s decreasing
    =1 : horizonatl line
  4. if there a constant ratio
68
Q

what happen when the b value is greater

A

the graphs becomes greater

69
Q

what the ratio?

A

it the number the y are multiply by

70
Q

what is the doubling time?

A

it’s the time it takes for a population to double in size
P= Po (2) t/d

71
Q

what is the population of growth or decay?

A

The population for growth means it’s increasing
P= P0 ( 1+r) n
The population for decay means it’s decreasing
P= P0 ( 1-r)n

72
Q

what is the half-life?

A

the half life is the time it takes for a quantity to decay to half it’s original amount.

73
Q

What is simple interest?

A

I= prt
FV= p+ I
It’s simple so their no compounding periods or monthly payment

74
Q

what is Fv compound interest?

A

Fv= p ( 1 + r) t
I= fv-p
it has compounding periods, but no monthly payments. it in the future so later

75
Q

What is FV annuity?

A

Fv= R x (1 + i) n- 1/ i
it has compounding periods, monthly payments, and is in the future so later

76
Q

what PV annuity?

A

PV= R x( 1-( 1+i)-n/ i
it has compounding periods, monthly payments, and is present so right now

77
Q

what the annually compounding period?

A

1

78
Q

what the semi- annually compounding period?

A

2

79
Q

what the quarterly compounding period?

A

4

80
Q

what the monthly compounding period?

A

12

81
Q

what the daily compounding period?

A

356

82
Q

what an amortization schedule?

A

a record of payment showing the interest paid, the principal, the current balance on a loan or investment

83
Q

what the PV in compound interest?

A

Pv = fv/ ( 1+ r) n
it has compounding periods, but no monthly payment. it the present so right now

84
Q

In y= a sin ( x- <) + d
what is a

A

if a is multiply by a number between 0 and 1 it compress
if it multiply by a number greater than 1 will compress
if there a negative it reflection into x- axis

85
Q

In y= a sin ( x- <) + d
what is <

A

that the degrees
by adding it shift left
by subtracting it shift right

86
Q

In y= a sin ( x- <) + d
what is d

A

by adding it shift up
by subtracting it shift down

Math (7 decks)

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