ALEKS EXAM
The cosine and sine of a coordinate are what
(X,Y)
what is the vertex with a parabola that has a + something?
(h,k)
when graphing a parabola, what should the coordinates of the vertex equal to?
0,0
one full angle revolution of a circle is equal to how many radians?
2pi radians
What does an exponential graph look like when the b is greater than 1? Less than 1 but greater than o?
Greater than 1= upward sloping (Vice versa) is
if you get a negative absolute value, why is it said to not have a solution?
because distance can't be negative
why is it that you can have a both negative and positive solution for absolute value?
because if your main solution is positive, if u plug that back into the absolute value bars, you'll still get a positive number. absolute value always has to be positive, so if you get a negative number its not the absolute value. remember this numbers that u get are the result, not the ones u plug in
why is the rolled rectangle 2pir?
because when you unroll it, the length will be the circumference of both of the small circles and then the height of the entire cylinder
when you're graphing a log graph, whats the first thing you should do in order to get your coordinates?
change it to e form
you have the graph y=f(x) and youre trying to get y=2f(x), what do you have to do in this case?
multiply y values by 2
does a horizontal shift affect the asymtope?
no
what is the distance formula?
square root of (x2-x1)^2 + (y2-y1)^2
how do u find the inverse that is expressed through an equation?
step 1:replace f(x) with y step 2: switch y and x step 3: solve for y step 4: replace with with the inverse function notation
what is the change of base formula for logarithms?
when you want to make the base the standard 10 so u put B/A
when should u switch the sign on an inequality?
when you're dividing or multiplying by a negative number
what is the difference between writing the logarithm as a single logarithm and then changing its form?
when youre writing it as a single log, the log of a power is different, when youre just changing its form its logamp=plogam, but when youre using it in an expression to write a single log, you use mlogna=lognam
what is the formula for a circle?
(x-h)^2 + (y-k)^2= r^2
what is formula for area of a triangle
1/2bh
name 4 perfect cubes
2 (8) ,3( 27),4(64),5(125)
when graphing absolute value equation on the coordinate plane, what does it look like?
2 rays
name 3 perfect 4th powers
2=16 3=81 4=256
name 2 perfect 5th powers
2=32 3=
What is the formula for surface area of a rectangular prism?
A=2(lw + wh + lh)
what is the formula for circumference of a circle?
C= pi x d
When going from radians to angle (having to move an angle from standard position), if the radians is negative which direction do you move it in?
Clockwise
What do u do when you get a solution that takes the square root of a negative?
It's no solution
How to convert from degrees to radians?
Multiply pi/180
What trig functions should be used to find an angle measure?
The functions to the negative power
what is the formula for volume of a cylinder?
V=pi r squared h
When you're graphing an exponential function and and you don't have a + something, what should you assume is ur asymtope?
Y=0
true or false, it is impossible for the square of a real number to be negative
`true
what is a rational number?
a ratio of two integers, also fractions and squares that equal integers
What is the formula you should use for an exponential growth problem?
a(1 + r) ^t
what is formula for area of a semicircle
a=1/2r^2
What sides does COT equal to?
adjacent/opposite
when you get 0=0 as the solution to an expression, what does this mean?
all real numbers are solutions, because a real number equals a real number
what are integers?
all whole negative and positive numbers
when solving a compound inequality(having 2 inequalities seperated by and/or), whats the difference between finding solutions for "and" and "or?"
and=finding solution to satisfy both equations or=finding solution that will satisy at least one equation
when youre doing the law of cosines to find and angle and then apply law of sines, what angle should you work on finding first?
angle opposite the longest side
when you split up an absolute value inequality, what's something you need to do that you wouldn't do for an absolute value equation?
change not only the sign of the solution, but also the sign of the inequality to correspond
how do u find the other 2 points on each side of the parabola?
choose 2 values on each side of x=0
what units is volume always in?
cubed
what is absolute value?
distance from zero on a number line
what is the distance formula word problem formula?
distance= time x rate
what is the formula for solving a distance, rate, and time word problem?
distance= time x rate
you have the graph y=f(x) and youre trying to get y=f(2x), what do you have to do in this case?
divide x values by 2
what happens if you dont get the two identical binomials by grouping?
either try grouping them differently or it cant be factored by grouping
what are the steps from taking a quadratic equation to parabola form?
first 2 terms of the quadratic, factor them, half and square to get the coefficient, subtract the product of the coefficient and the factorer to the constant of the original quadratic equation, do the diamond thing to get ur binomials and put into parabola form
what's the first step to solving a quadratic equation needing simplification?
foil and get everything on one side, then make it equal 0
how do you convert from a radical form to an exponent form?
from radical to exponent you go counterclockwise, from exponent to radical, numerator goes on the inside. also, this rule only works if the number on the outside of the radical is odd, or if the outside is even but the inside is greater than 0
what do u do to find the roots?
get the expression into quadratic form, get solutions and set equal to 0
whats one thing to remember when graphing an absolute value equation?
have to take the absolute value of whats inside the parathenses
What sides does SEC equal to?
hypotenuse/adjacent
What sides does CSC equal to?
hypotenuse/opposite
how do you know how many solutions to the quadratic you could have based on the discriminant?
if its greater than 0, there are 2 solutions, if its less than 0 theres no solutions, if its equal to 0, one real solution
what is a rule of the square root property?
if the number that youre squaring is positive, the solution will be one positive one negative, if the number that youre squaring is negative there are no solutions
what is a rule to remember when youre applying that perfect square property?
if the perfect square simplifies to another perfect square, dont simplify it further
the slope of a perpendicular line will be what?
if the product if their slopes is equal to -1
what should u remember when solving an absolute value equation that is different from an absolute value inequality?
if the solution to the equation is bigger than 0, then you split them up and consider both solutions, if the solution is already less than 0, it has no solutions because its already negative
whats one thing u should add in when doing grouping?
if you have to factor by 1 to get the identical binomial, then you have to add a +1
what is the difference between finding the perfect square of an integer and finding perfect square of a variable exponent?
integer youre finding 2 like terms that will MULTIPLY to get this number, exponent youre finding 2 like terms that will ADD to get this number
when using elimination, what is the first step you have to do?
isolate one of the variables,you can do this by multiplying both equations by different variables because they're not equal to each other, so you can do that and once its all in order just add down
what do you do when it asks you to find all real zero's?
it means that there needs to be a solution equal to 0, for the equation to equal 0, at least one of the products has to be equal to 0, so set them equal to 0 and find out
what is an LCM?
its exactly like the least common denominator but without the fraction
what is a discriminant and what does its value mean?
its the area under the radical of the quadratic formula, it gives u a hint as to how many solutions the quadratic expression is going to give you,
if you have a negative exponent as a denominator and one as the numerator, what rule can you follow to make the numerator positive?
move the negative exponent to the numerator and make it positive
How to convert from radians to degrees?
multiply by 180/pi
what will your equation look like if something is inversely related?
one will be in the numerator and one on the other side in the denominator, like a proportion
when youre simplifying the ratio of polynomials, what does the -1 rule apply to?
only if its x-1, 1-x
what is the first step in simplifying a radical expression with an exponent?
perfect square factors that could come from it, then use the product property to split them up, and then simplify
what is the formula for surface area of a cylinder?
pi*r^2 x pi*r^2 x 2pirh
when solving a radical equation that simplifies to a quadratic, whats something you have to do at the end that you CANT FORGET?
plug back into the original equation to see if its a solution
how do u make a negative log on a log graph?
reflect across the x axis
should u shift then reflect or reflect then shift?
reflect then shift
when graphing a radical term, whats something you should make sure that under the radical equals to make a real number?
set it equal to 0 to make sure its a real number
the difference between finding a union of a set and the intersection of a set?
set of all elements that are in set a or set b for union, set of all elements that are in set a and set b for intersection
how do u find the excluded values of the domain of a rational function?
set the denominator equal to 0 and solve
difference between finding square factors when simplifying a radical with variable exponents and finding square factors when simplifying negative exponents in fraction form?
simplifying a radical, you split up pieces of a term that include a perfect square term, when doing the fraction you dont do this
how do u find the perfect square term?
take half of the coefficient term, then square it
what to do when vertical shifting a graph?
take what's in the parentheses and put it equal to 0, then translate left or right that exact amount
what happens to a set of coordinates when youre trying to find the inverse of them?
the coordinates switch around
the slope of parallel lines will be what?
the same slope as the other line
what does the word OR mean when youre grpahing the solutions for compound inequalities?
the values of both graphs that will make at least one of them true
when youre reflecting a graph, when it says negative x what axis should you reflect it across?
the y axis
when you get 0=-3 as the solution, what does this mean?
there's no solution
anything to the 0 power is equal to 1 unless?
theres a negative in front of it
a pair of coordinates represent a function if what?
they don't have the same x-coordinates
when youre solving for x in an log, what is the most important step to get your solution?
to plug in your answer to the original equation, this will let you know if the answer is undefined or not
for the equation of a circle, what will give you the radius? and how do u find the center?
what its equal to, take the square root of it; the same way you find a vertex of the parabola, its just h and k
what is the equation for a parabola with (h,k)?
y=a(x-h)^2+k
what is the formula for a parabola>
y=a(x-h)^2+k
does a vertical shift affect a vertical asymtope?
yes
with absolute value inequalities, do you still have to split them up if the value is greater than 0?
yes
whats something to remember when simplify radical expressions with variables?
you can have a square term out of the radical sign when youre simplifying if you need to continue to simplify out of the radical
whats something to remember when you're plugging your solution back into the log?
you have to continue to apply the rules when youre plugging it back in
how do you use the union symbol for the "or" inequality?
you have to denote both of the areas seperatley that need to come together and seperate them by the union sign
what's something to keep in mind when you're determining the LCD for one fraction on one side of the equation and one on the other?
you have to multiply both sides of the LCD even if one side already has it, because they're equal to each other
when finding the vertex when graphing an absolute value equation, how do u find the vertex?
you make the x+ whatever =0, then to find the y value u plug in the x value to get the y value
when youre finding the vertex and x intercepts of a parabola, what do you do?
you use the midpoint formula if theres 2 solutions (x1 +x2/2) and then plug that answer into the quadratic to get your y for the vertex
when youre solving a quadratic equation, whats something you cant forget when youre squaring both sides?
you're always going to get one negative and one positive solution