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math basics Flashcards

(83 cards)

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1
Q

(a+b)^2

A

a^2+2ab+b^2

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2
Q

(a-b)^2

A

a^2-2ab+b^2

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3
Q

a^2-b^2

A

(a+b)(a-b)

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4
Q

can you add terms b^2+b?

A

no lol

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5
Q

(a) / (b/c)

A

(ac) / (b)

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6
Q

(a/b) / (c)

A

(a) / (bc)

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7
Q

is it possible to split up the numerator or denominators of fractions?

A

numerators

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8
Q

exponential growth equation

A

y=ab^t

y= final quantity
a= initial quantity
b= growth factor
t= time

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9
Q

exponential growth graph

A

gradual and then rapidly increasing curve (left to right)

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10
Q

exponential decay graph

A

rapidly decreasing curve that slows down near the end (left to right should I kmrs google

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11
Q

exponential decay equation

A

y=ab^t

*same as the exponential growth equation but b= less than one

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12
Q

exponential growth/decay equation with periods of growth

A

y=ab^t/k

where K is the amount of time required for y to increase by one factor of b. K and b must be the same unit (e.g years)

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13
Q

linear growth

A

linear line with a positive slope

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14
Q

linear decay

A

linear line with a negative slope

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15
Q

negative association

A

as one thing increases, the other decreases

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16
Q

positive association

A

as one thing increases, the other also increases

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17
Q

x^1

A

x

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18
Q

x^0

A

1

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19
Q

x^-m

A

1/x^m

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20
Q

how do you simplify √2x

A

(√2x)^2

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21
Q

if g(x)=ax+24
what does g(4)=8 mean?

A

when x is 4, the entire expression equals 8

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22
Q

slope

A

change in y/change in x

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23
Q

mean

A

sum of values/number of values

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24
Q

median

A

middle value when the data set is ordered least to greatest

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25
mode
most common value
26
range
max value-minimum value
27
standard deviation
measures the typical spread from the mean. larger standard deviation=more spread out from the mean smaller standard deviation=less spread out from the mean
28
what is the effect of outliers on range/standard deviation?
larger range or standard deviation
29
what is the effect of outliers on mean?
very large outlier=greater mean very small outlier=smaller mean
30
what is the effect of outliers on median?
a very large outlier will increase the median or have no effect, a very small outlier will decrease the median or have no effect
31
polynomial long division formula
quotient+remainder/divisor
32
quadratic formula
x=(-b±√(b²-4ac))/(2a)
33
what part of the quadratic formula is the discriminant?
b²-4ac
34
if the discriminant is greater than 0, how many solutions?
two
35
if the discriminant = 0, how many solutions?
one
36
if the discriminant is less than zero, how many solutions?
no real solutions
37
circle equation
(x-h)^2+(y-k)^2=r^2 (h, k) is the center r is the radius
38
complete the square
(b/2)^2
39
midpoint formula
(x1-x2/2) , (y1-y2/2)
40
ultimate circle proportion (degrees)
central angle/360=arc length/circumference=sector area/circle area
41
ultimate circle proportion (radians)
central angle/2𝝅=arc length/circumference=sector area/circle area
42
what does an angle's point of intersection with the unit circle tell you?
cos(θ)= x coordinate of intersection sin(θ)= y coordinate of intersection
43
how do you find tangent with cos and sin?
tan(θ)=sin(θ)/cos(θ)
44
when do you flip an inequality sign?
when you divide by a negative
45
if a linear equation comes down to x=a
one solution
46
if a linear equation comes down to a=b
no solution
47
if a of a parabola is larger...
the parabola is longer and more narrow
48
if a of a parabola is smaller...
the parabola is shallow and wide
49
complete the square
(b/2)^2
50
vertex form
A parabola with the equation y=a(x-h)^2+k has its vertex located at (h,k) .
51
if y=x^2 becomes y=(x-a)^2...
there was a transformation of a units to the right
52
if y=x^2 becomes y=(x+a)^2...
there was a transformation of a units to the left
53
if y=x^2 becomes y=x^2-a
there was a transformation of a units down
54
if y=x^2 becomes y=x^2+a
there was a transformation of a units up
55
basic exponential growth/decay equation
f(x)=b^x
56
shifting the horizontal asymptote in an exponential equation
introducing a constant to the exponential equation changes the horizontal asymptote. If f(x)=b^x+d, the horizontal asymptote approaches d
57
shifting the y-intercept in an exponential equation
if f(x)=a ⋅ b^x+d, the y-intercept is a+b if f(x)=a ⋅ b^x, the y intercept is a ⋅ 1 If f(x)=b^x+d, the y intercept is d+1
58
circumference
C=2πr
59
most common Pythagorean triple
3-4-5 and all multiples ...less common are 5-12-13 and 7-24-25
60
the sin(θ) is equal to...
the cos(90-θ), or the cos of θ's complementary angle
61
height of an equilateral triangle
h = (√3/2)a, where a is the side of the equilateral triangle.
62
triangle similaritty
AA, SSS, SAS
63
work rate where two individuals work at different rates
w=rt w is the amount of work done r is the overall rate t is the time spent
64
product of roots in a quadratic
c/a
65
percent change
final-initial/initial x 100
66
cos(0)
1
67
sin(0)
0
68
tan(0)
0
69
cos(90)
0
70
sin(90)
1
71
tan(90)
undefined
72
what is 90 degress in radians?
π/2
73
arc length with a degree angle measure
θ/360 x 2πr
74
arc length with a radian angle measure
θr
75
area of a sector with a degree angle measure
θ/360 x πr^2
76
area of a sector with radians
(0.5)(r^2)(θ)
77
how does the measure of a central angle relate to the arc measure?
central angle=arc measure
78
how does the measure of an inscribed angle relate to the arc measure?
inscribed angles are half of their arc measure
79
angles inscribed in a semicircle are always...
90 degrees
80
radius and tangent line of a circle
a line tangent to a circle is perpendicular to any radius drawn to it
81
ASTC (all students take calculus)
A- all trig functions are positive in the first quadrant S- sin is positive in the second quadrant T- tan is positive in the third quadrant C- cos is positive in the fourth quadrant
82
estimating using sample proportion
estimate= sample proportion x population
83
two ways to decrease margin of error
1. have a large sample size 2. have less variability in your data

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