NCVPS math 3 honors final exam
vertex
"middle" highest/lowest point in a parbola
volume of a pyramid
(1/3) b h
volume of a cone
(1/3) pi r^2 h
volume of a sphere
(4/3) pi r^3
what point is the vertexy=a(x-h)^2+k
(h,k)
pythagoras theorem
(the equation of the unit circle) x^2 + y^2 = 1^2 and/or (cos(θ))2 + (sin(θ))2 = 1
quadrant 1
++
quadrant 4
+-
quadrant 2
-+
quadrant 3
--
solve: g(x) = -2x^3 if g(2)
-16
quadratic formula
-b +- sqrt. b^2-4ac / 2a
adjacent value
1
function
1. relations in which the x values of its points (ordered pairs) do not repeat 2. if a graph passes the vertical line test, then it is the graph of a function
exponent rule
1/a^b = a^-b
opposite value
2
circumference of a circle
2 pi r
360=
2pi radians
write 6x^7+3^4-2x^2+5x^4 in standard form and classify it
6x^7+8x^4-2x^2 it is a trinomial has a degree of 7 (seventh degree) = seventh degree trinomial
point of discontinuity
= no solution // zero
If an apple orchard grows medium sized, red apples, then we can expect the sample to consist of medium sized, red apples.
A sample is likely to be a good representation of the population.
When graphing, you will encounter three possibilities. what are they?
Consistent Systems (one solution) Inconsistent Systems (no solutions) Dependent Systems (Infinite number of solutions)
identify the domain and range for (-4, 3), (-1, 2), (0, -4), (2, 3), (3, -3)
D: -4, -1, 0, 2, 3 R: -4, -3, -2, 3
parabola. what is true about the domain and range?
D: all reals R: y> or y<
If the equation is a line (y = mx + b or y = #) what is true?
DOMAIN AND RANGE ARE ALL REAL NUMBERS
find the inverse of a function
STEP 1: Stick a "y" in for the "f(x)" guy: STEP 2: Switch the x and y. ( because every (x, y) has a (y, x) partner! ): STEP 3: Solve for y: STEP 4: Stick in the inverse notation, continue. 1 2 3.
Consistent Systems
The lines will intersect. The point where the lines intersect is your solution.
Non-sampling errors are very important to avoid. It is imperative that the sample be representative of the whole population. This happens when every individual has a chance of being chosen for the sample.
The way the sample is taken matters.
Samples will NEVER be a perfect representation of the population. All samples will never be the same. Through simulation and probability theory, we can get a good idea of what the population will likely be like based on the information the sample has given us.
There is an element of uncertainly as to how well the sample represents the population.
Dependent Systems
These lines are the same! Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS!
Inconsistent Systems
These lines never intersect as the lines are parallel! Since the lines never cross, there is NO SOLUTION!
adjacent = a or b
a
cos = a or b
a
unit circle
a circle with a radius of 1
mapping
a diagram used to see if a relation is a function
y=a(x-h)^2+k what is true about "a"
a is positve: opens up a is negative: opens down
rational
a number that can be expressed as the ratio of two integers
parameter
a number that describes a population
statistic
a number that describes a sample
relation
a set of ordered pairs
completing the square // finding the vertex formula
a(x - h)^2 + k
cluster sample
all members of a randomly-chosen group are surveyed
radical
an expression with a square root, cube root, etc.
opposite = a or b
b
sin = a or b
b
what is the discriminant
b^2 - 4ac
two terms
binomial
convenience sample
chooses individuals easiest to reach
which direction for the negative angle on the unit circle?
clockwise
degree 0
constant
what happens when the angle, θ, is 0°?
cos 0° = 1, sin 0° = 0 and tan 0° = 0
what happens when θ is 90°?
cos 90° = 0, sin 90° = 1 and tan 90° is undefined
which direction for the positive angle on the unit circle?
counterclockwise
degree 3
cubic
if the higher power is on the bottom there is ______ horizontal asymptote
definitely (y=0)
< x < (<=underlined)
domain
negative opens:
down
function rule
evaluate the function at a given domain value to find the corresponding range value (vice versa)
degree 4
fourth degree
confidence interval
gives a range of values (mean-ME to mean+ME)
how can you know if something is a function by looking at the x column?
if each number in the x column appears only once in that column, it is a function
how can you know if there are holes in your graph
if the top and bottom of the fraction have common factors (factor and set equal to zero) ex. (x+6)(x+2)/(x+2) then x=-2
experiment
imposes a treatment on individual to collect data on their response to the treatment
randomized comparative treatment
individuals are assigned to control and treatment groups randomly
voluntary response sample
individuals respond to a general request
how can you find the radian measure?
intercepted arc/perimeter * x/2pi
if the powers are the same you make the horizontal asymptote...
into a fraction with the numbers
volume of a cube
l * w * h
population
large group of individuals
degree 1
linear
hypotenuse
longest side of the right triangle
stratified sample
members are chosen at random from groups created from a population
systematic sample
members are chosen using a pattern, like every third person
convienence sample
members are chosen who are easily accessible
simple random sample
members chosen using a method that gives everyone an equally likely chance of being selected
self-selected sample
members volunteer to participate
midpoint
middle point of a line segment
one term
monomial
if the higher power is on the top there is ______ horizontal asymptote
no
is this a function? x= -2,-3,5,5
no
bias
not representative of an entire population
observational study
observes individuals and measures variables without controlling the individuals or their environment in any way
denominator
on the bottom of the fraction
numerator
on top of the fraction
discriminant // 0
one real number
y=ax^2+bx+c
parabola
sample
part of the population
individual
person, animal, or object described by data
volume of a cylinder
pi r^2 h
degree 2
quadratic
< y < (<=underlined)
range
subtended
s = r theta ex. 6 = radius 4pi/3 = angle s = 6 (4pi/3)
what can you easily measure because the radius is 1
sin, cos and tan
sin/cos/tan for 30°
sin= 1/2 cos=sqrt3/2 tan= 1/sqrt3 = sqrt3/3
sin/cos/tan for 45°
sin= sqrt2/2 cos=sqrt2/2 tan=1
sin/cos/tan for 60°
sin= sqrt3/2 cos= 1/2 tan= sqrt3
what is the a/b for sin, cos and tan?
soh cah toa
axis of symmetry
splits parabola in half
hypotenuse value
sqrt3
census
survey of an entire population
the margin of error
tells us how far off our estimate is likely to be off and how much confidence we can have in our estimate
circumcenter
the center of a triangle's circumcircle
incenter
the center of the incircle of a triangle or other figure
index
the exponent at the beginning of a radical sign indicating the root to be taken or extracted
centroid
the intersection of the three medians of the triangle (each median connecting a vertex with the midpoint of the opposite side)
coefficient
the number in front of a variable or term
radicand
the number under the inclusion bar of the radical sign
solution to the system
the point that satisfies ALL of the equations. This point will be an ordered pair.
the axis of symmetry in y=a(x-h)^2+k
the vertical line x=h
three terms
trinomial
discriminant // -
two complex/imaginary numbers
discriminant // +
two real numbers
positive opens:
up
random digit table
used to randomly select individuals for a sample
vertical line test
using a vertical straight edge to see if the relation is a function (x1: pass x2: fail)
supplementary
when angle add up to 180 degrees
system of equations
when you have two or more equations using the same variables
change 5^x = 25 into a log function
x = log b5 25
domain
x-values in relation (input)
f(2)
x=2
f(x), g(x), h(x) all mean:
y
range
y-values in a relation (output)
f(x)=2
y=2
is this a function? x= -2,-3,12,5
yes
is this graph a function?
yes because the vertical line only passes at one point
