math basics Flashcards
(a+b)^2
a^2+2ab+b^2
(a-b)^2
a^2-2ab+b^2
a^2-b^2
(a+b)(a-b)
can you add terms b^2+b?
no lol
(a) / (b/c)
(ac) / (b)
(a/b) / (c)
(a) / (bc)
is it possible to split up the numerator or denominators of fractions?
numerators
exponential growth equation
y=ab^t
y= final quantity
a= initial quantity
b= growth factor
t= time
exponential growth graph
gradual and then rapidly increasing curve (left to right)
exponential decay graph
rapidly decreasing curve that slows down near the end (left to right should I kmrs google
exponential decay equation
y=ab^t
*same as the exponential growth equation but b= less than one
exponential growth/decay equation with periods of growth
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)
linear growth
linear line with a positive slope
linear decay
linear line with a negative slope
negative association
as one thing increases, the other decreases
positive association
as one thing increases, the other also increases
x^1
x
x^0
1
x^-m
1/x^m
how do you simplify √2x
(√2x)^2
if g(x)=ax+24
what does g(4)=8 mean?
when x is 4, the entire expression equals 8
slope
change in y/change in x
mean
sum of values/number of values
median
middle value when the data set is ordered least to greatest
mode
most common value
range
max value-minimum value
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
what is the effect of outliers on range/standard deviation?
larger range or standard deviation
what is the effect of outliers on mean?
very large outlier=greater mean
very small outlier=smaller mean
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
polynomial long division formula
quotient+remainder/divisor
quadratic formula
x=(-b±√(b²-4ac))/(2a)
what part of the quadratic formula is the discriminant?
b²-4ac
if the discriminant is greater than 0, how many solutions?
two
if the discriminant = 0, how many solutions?
one
if the discriminant is less than zero, how many solutions?
no real solutions
circle equation
(x-h)^2+(y-k)^2=r^2
(h, k) is the center
r is the radius
complete the square
(b/2)^2
midpoint formula
(x1-x2/2) , (y1-y2/2)
ultimate circle proportion (degrees)
central angle/360=arc length/circumference=sector area/circle area
ultimate circle proportion (radians)
central angle/2𝝅=arc length/circumference=sector area/circle area
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
how do you find tangent with cos and sin?
tan(θ)=sin(θ)/cos(θ)
when do you flip an inequality sign?
when you divide by a negative
if a linear equation comes down to x=a
one solution
if a linear equation comes down to a=b
no solution
if a of a parabola is larger…
the parabola is longer and more narrow
if a of a parabola is smaller…
the parabola is shallow and wide
complete the square
(b/2)^2
vertex form
A parabola with the equation y=a(x-h)^2+k
has its vertex located at (h,k)
.
if y=x^2 becomes y=(x-a)^2…
there was a transformation of a units to the right
if y=x^2 becomes y=(x+a)^2…
there was a transformation of a units to the left
if y=x^2 becomes y=x^2-a
there was a transformation of a units down
if y=x^2 becomes y=x^2+a
there was a transformation of a units up
basic exponential growth/decay equation
f(x)=b^x
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
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
circumference
C=2πr
most common Pythagorean triple
3-4-5 and all multiples
…less common are 5-12-13 and 7-24-25
the sin(θ) is equal to…
the cos(90-θ), or the cos of θ’s complementary angle
height of an equilateral triangle
h = (√3/2)a, where a is the side of the equilateral triangle.
triangle similaritty
AA, SSS, SAS
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
product of roots in a quadratic
c/a
percent change
final-initial/initial x 100
cos(0)
1
sin(0)
0
tan(0)
0
cos(90)
0
sin(90)
1
tan(90)
undefined
what is 90 degress in radians?
π/2
arc length with a degree angle measure
θ/360 x 2πr
arc length with a radian angle measure
θr
area of a sector with a degree angle measure
θ/360 x πr^2
area of a sector with radians
(0.5)(r^2)(θ)
how does the measure of a central angle relate to the arc measure?
central angle=arc measure
how does the measure of an inscribed angle relate to the arc measure?
inscribed angles are half of their arc measure
angles inscribed in a semicircle are always…
90 degrees
radius and tangent line of a circle
a line tangent to a circle is perpendicular to any radius drawn to it
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
estimating using sample proportion
estimate= sample proportion x population
two ways to decrease margin of error
- have a large sample size
- have less variability in your data
