math final Flashcards

1
Q

completing the square formula

A

(b/2) squared

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2
Q

exponential formula

A

y= a(b) to the power of x

a represents y intercept, b represents growth/decay

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3
Q

how to find zeros of function on calc

called the zero product property

A

plug function into calc, go to split screen table, and find x’s that have y as zero. Ex: (9,0) (4,0). 9 and 4 would be the zeros

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4
Q

remember to always first try and find the _____ when factoring

A

gcf

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5
Q

what does open circle represent

A

less than or greater than/not included

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6
Q

what kind of line is a less than greater than

A

dotted

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7
Q

what does closed circle represent

A

less than or equal to, greater than or equal to/included

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8
Q

when putting inequalities on a number line such as x is greater than 7, or 15 is less than 7, the number line’s line will point in the ______ direction of the less than/greater than symbol. If its less than/greater than, the circle is _____

A

opposite

open

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9
Q

when 2 sides of an inequality equal each other, such as 10a -8 is greater than 10a -8, there are ______

A

infinite solutions

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10
Q

when you multiply or divide a neg number in a inequality, you _____

A

flip the sign

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11
Q

what is an empty set

A

a set that contains no elements- the empty set is a subset of every set

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12
Q

what is the universal set

A

the largest set you are using

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13
Q

what is the complement of a set

A

the set of all the elements in the universal set that are NOT in the set

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14
Q

ex: what are the subsets of {3,4,5}

A

{3,4} {3}{4}{4,5}{3,5}….

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15
Q

rate of change aka

A

slope

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16
Q

function rules:

A

x values cannot repeat
one output per input
y values can repeat

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17
Q

linear function equation

A

y=mx+b

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18
Q

what is a nonlinear function

A

a function whose graph is not a line or part of a line

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19
Q

what is a continuous graph

A

a graph that is unbroken

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20
Q

what is a discrete graph

A

a graph composed of distinct, isolated points

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21
Q

relation uses:

A

domain and range

relations may or may not be a function

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22
Q

point slope form equation

A

y-y =m(x-x )
1 1
y sub 1 is y coordinate, m is slope, x sub 1 is x coordinate

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23
Q

h or v? y=5

A

horizontal

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24
Q

h or v? x=6

A

vertical

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25
Q

standard form equation

A

ax + by =c

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26
Q

the x intercept is

A

where the line crosses the x axis

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27
Q

the y intercept is

A

where the line crosses the y axis

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28
Q

to find x intercept

A

plug in zero for y and solve

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29
Q

to find y intercept

A

plug in zero for x and solve

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30
Q

positive line is

A

low to high

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31
Q

negative line is

A

high to low

32
Q

y = IxI + 2 means

A

up 2

33
Q

y = IxI -2 means

A

down 2

34
Q

y = Ix+2I means

A

left 2

35
Q

y = Ix-2I means

A

down 2

36
Q

perpendicular line means

A

negative reciprocal of other line’s slope

37
Q

parallel line means

A

same slope different y intercept

38
Q

domain

A

x values,

39
Q

range

A

y values

40
Q

horizontal line is

A

zero

41
Q

vertical line is

A

undefined

42
Q

how to solve line of best fit

A

write for the equation, by finding slope using point slope form, then converting that into slope intercept form

43
Q

linear equations: one solution

A

two lines that intersect at one point

44
Q

linear equations: infinitely many solutions

A

two equations have same line

45
Q

linear equations: no solution

A

parallel lines

46
Q

exponential growth

A

b is GREATER THAN 1 (1 + %)

47
Q

exponential decay

A

b is LESS THAN 1 (1 - %)

48
Q

compound interest formula

A
A = P(1+ r/n) to the nt power
a= balance/what we are looking for
p=inital amount
r= annual rate (expressed as decimal)
n= number of times interest is compounded per year
t= time in years
49
Q

monomial

A

1 term

50
Q

binomial

A

2 terms

51
Q

trinomial

A

3 terms

52
Q

polynomial

A

4 and up terms

53
Q

constant

A

degree of zero

54
Q

linear

A

degree of one. ex: 4x + 2. number of highest exponent)

55
Q

quadratic

A

2

degree of 2. ex: 4x. +2 (number of highest exponent)

56
Q

cubic

A

3

degree of 3. ex: 4x. +2 (number of highest exponent)

57
Q

fourth degree

A

4

degree of 4. ex: 4x. +2. (number of highest exponent)

58
Q

roots mean

A

zeros

59
Q

linear functions

A

common difference between y values
ex: 2, 5, 8
+3 +3

straight line

60
Q

exponential functions

A

common ratio: multiplying by the same value overtime for each y value
ex: 0.25, 0.5, 1,
x2 x2

slight curve

61
Q

quadratic functions

A

second set has common difference
ex: 1, -1, 1, 7, 17
-2 +2 +6 +10 first differences
+4 +4 +4

parabola

62
Q

axis of symmetry

A

-b/2a

63
Q

minmum

A

a is less than zero. shaped like upside down u

64
Q

maximum

A

a is greater than zero. shaped like: U

65
Q

If the quadratic is written in the form y = a(x – h)2 + k, then the vertex is the point ______

A

(h,k)

66
Q

the closer a is to zero, ______

A

the wider the graph

67
Q

mode

A

value that appears the most

68
Q

mean

A

average

69
Q

uniform

A

all the bars on histogram are about the same height

70
Q

symmetric

A

peak is at center of histogram

71
Q

skewed

A

peak is to the side of histogram

72
Q

communative property

A

changing the order doesn’t change the sum. ex: a + b = b + a

73
Q

associative property

A

part of a group, order doesn’t matter ex: (a + b) + c = a + (b + c)

74
Q

identity property

A

the sum of any real number 0 is original number.

the product of any real number and 1 is the original number

75
Q

percent change

A
    original amount
76
Q

percent increase

A

new amount- original amount
—————————————
original amount

77
Q

percent decrease

A
  original amount