ALEKS MATH PLACEMENT WITH COMPLETE
SOLUTIONS 100% 2023/2024
graph ≥, ≤
solid line
graph >, <
DOTTED line
every, each, per (writing equations)
rate/ set y value equal to (multiply this value by the x variable)
When writing an equation or working ANY inequality problem what does it help to do first?
write out what's happening
What should you double check for EVERY time
writing problem down wrong (NEGATIVE SIGNS), uncarried negative signs, unflipped inequality signs,
undotted lines, incorrect multiplication, fully simplified
distance =
rate x time
When solving a system of equations can you add the equations together if one of the variables will
cancel out?
YES
What should you always write out when doing your work?
Fraction conversions, simplification steps, line graphs (interval notation)
What standard does an equation/ graph have to meet to be considered a function?
Each input can only have one output
How do you translate a graph up or down?
The value outside of the parentheses (DONT change sign)
How do you translate a graph side to side?
The value inside the parentheses (CHANGE SIGN)
Translate -(x + 3)^3 - 2 from -x^3
left 3, down 2
When translating do you need to solve the equation?
No, just look at the numbers inside (side to side change sign) and outside (up and down DONT change
sign) the parentheses
, What is the domain?
The x limits
What is the range?
The y limits
U represents
Numbers in EITHER set (Union)
⋂ represents
Numbers in BOTH sets (Intersection)
What is the quadratic formula?
-b±√b^2-4ac/2a
When asked for the rate, should you give the rate or the rate times the time?
THE RATE
(x-6)(x+4) < 0
Where is the product of (x-6) and (x+4) less than 0?
Should you graph two separate equations on the same number line when doing your work?
No
When you take the square root of a variable, how many answers are there?
2 answers (negative and positive)
x^a/x^b
x^a-b
x^a times x^b =
x^a+b
(x^a)^b
x^ab
What should you always physically mark on inequality graphs that are getting compared before
attempting to solve the problem?
Where the graphs intersect
BETC
divide the top leading coefficient by the bottom leading coefficient (Bottom Equals Top Coefficient
HORIZONTAL ASYMPTOTE)
SOLUTIONS 100% 2023/2024
graph ≥, ≤
solid line
graph >, <
DOTTED line
every, each, per (writing equations)
rate/ set y value equal to (multiply this value by the x variable)
When writing an equation or working ANY inequality problem what does it help to do first?
write out what's happening
What should you double check for EVERY time
writing problem down wrong (NEGATIVE SIGNS), uncarried negative signs, unflipped inequality signs,
undotted lines, incorrect multiplication, fully simplified
distance =
rate x time
When solving a system of equations can you add the equations together if one of the variables will
cancel out?
YES
What should you always write out when doing your work?
Fraction conversions, simplification steps, line graphs (interval notation)
What standard does an equation/ graph have to meet to be considered a function?
Each input can only have one output
How do you translate a graph up or down?
The value outside of the parentheses (DONT change sign)
How do you translate a graph side to side?
The value inside the parentheses (CHANGE SIGN)
Translate -(x + 3)^3 - 2 from -x^3
left 3, down 2
When translating do you need to solve the equation?
No, just look at the numbers inside (side to side change sign) and outside (up and down DONT change
sign) the parentheses
, What is the domain?
The x limits
What is the range?
The y limits
U represents
Numbers in EITHER set (Union)
⋂ represents
Numbers in BOTH sets (Intersection)
What is the quadratic formula?
-b±√b^2-4ac/2a
When asked for the rate, should you give the rate or the rate times the time?
THE RATE
(x-6)(x+4) < 0
Where is the product of (x-6) and (x+4) less than 0?
Should you graph two separate equations on the same number line when doing your work?
No
When you take the square root of a variable, how many answers are there?
2 answers (negative and positive)
x^a/x^b
x^a-b
x^a times x^b =
x^a+b
(x^a)^b
x^ab
What should you always physically mark on inequality graphs that are getting compared before
attempting to solve the problem?
Where the graphs intersect
BETC
divide the top leading coefficient by the bottom leading coefficient (Bottom Equals Top Coefficient
HORIZONTAL ASYMPTOTE)
