NCVPS math 3 honors final exam

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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


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