ALEKS EXAM WITH COMPLETE SOLUTIONS
100% 2023/2024
what is absolute value?
distance from zero on a number line
if you get a negative absolute value, why is it said to not have a solution?
because distance can't be negative
what are integers?
all whole negative and positive numbers
when should u switch the sign on an inequality?
when you're dividing or multiplying by a negative number
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
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
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
when you get 0=-3 as the solution, what does this mean?
there's no solution
a pair of coordinates represent a function if what?
they don't have the same x-coordinates
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
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 is the formula for volume of a cylinder?
V=pi r squared h
what units is volume always in?
cubed
, how do u find the perfect square term?
take half of the coefficient term, then square it
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
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
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
what is a rational number?
a ratio of two integers, also fractions and squares that equal integers
what is formula for area of a semicircle
a=1/2r^2
what is formula for area of a triangle
1/2bh
what do u do to find the roots?
get the expression into quadratic form, get solutions and set equal to 0
what happens if you dont get the two identical binomials by grouping?
either try grouping them differently or it cant be factored by grouping
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 formula for circumference of a circle?
C= pi x d
what is an LCM?
its exactly like the least common denominator but without the fraction
what's the first step to solving a quadratic equation needing simplification?
foil and get everything on one side, then make it equal 0
100% 2023/2024
what is absolute value?
distance from zero on a number line
if you get a negative absolute value, why is it said to not have a solution?
because distance can't be negative
what are integers?
all whole negative and positive numbers
when should u switch the sign on an inequality?
when you're dividing or multiplying by a negative number
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
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
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
when you get 0=-3 as the solution, what does this mean?
there's no solution
a pair of coordinates represent a function if what?
they don't have the same x-coordinates
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
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 is the formula for volume of a cylinder?
V=pi r squared h
what units is volume always in?
cubed
, how do u find the perfect square term?
take half of the coefficient term, then square it
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
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
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
what is a rational number?
a ratio of two integers, also fractions and squares that equal integers
what is formula for area of a semicircle
a=1/2r^2
what is formula for area of a triangle
1/2bh
what do u do to find the roots?
get the expression into quadratic form, get solutions and set equal to 0
what happens if you dont get the two identical binomials by grouping?
either try grouping them differently or it cant be factored by grouping
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 formula for circumference of a circle?
C= pi x d
what is an LCM?
its exactly like the least common denominator but without the fraction
what's the first step to solving a quadratic equation needing simplification?
foil and get everything on one side, then make it equal 0
