ALEKS Math Placement Exam Questions
with Revised Answers
When you're trying to find the width do you disregard negative answers? - Answer-yes
When the number under the radical is large should you trust that it's simplified fully? -
Answer-No (it's probably not fam)
sqrt(a/b) = - Answer-sqrt(a)/sqrt(b)
What should you do any time you solve by squaring? - Answer-Plug the answers back
in (to double check)
Hw do you find the domain of an equation with a radical? - Answer-Set the value under
the radical equal to 0. IGNORE values outside the radical. (The domain ONLY includes
values that make the numbers under the radical greater than or equal to 0)
What helps when you're trying to simplify a radical with a power higher than 2? -
Answer-Writing out a table with perfect roots of the power
What is the range of an inverse function? - Answer-The domain of the original function
When finding the domain of composition functions should you find the domain of the
simplified function or the unsimplified function? - Answer-The unsimplified function
(ESPECIALLY if there radicals)
Should you leave negatives in the denominator? - Answer-no (multiply by everything
negative 1)
log_a c = b if - Answer-a^(b) = c
log_6 36 = 2 - Answer-6^2 = 36
log - Answer-log_10
What do you do for exponential growth or decay problems? - Answer-initial x
percent^time
log_a (xy) - Answer-log_a x + log_a y
log_a(x/y) - Answer-log_a x - log_a y
, log_a x^r - Answer-rlog_a x
Should you round down when a problem asks for the smallest whole number? - Answer-
no (round up to the next whole number regardless of the decimal size- it can be less
than .5 and you'd still round up)
log_e - Answer-ln
If two logs with the same base are on different sides of an equation can you cancel the
logs? - Answer-yes (queen:3)
Can you take the log of a negative number? - Answer-NO
What do you do when solving complex log/exponential equations? - Answer-distribute
and factor
What is -log when graphing? - Answer-a reflection about the x axis (multiply y
coordinates by negative 1)
What do you need to change when graphing log transformations that involve a change
in x coordinate? - Answer-The domain and vertical asymptote
What is the vertical asymptote of a normal log equation? - Answer-the y axis
How do you complete the square? - Answer-Divide the middle coordinate by 2, square it
(This is the third coefficient) , ADD THIS TO THE OTHER SIDE OF THE EQUATION
AS WELL
What is the equation of a circle - Answer-(x-h)^2 + (y-k)^2 = r^2
What is the center of the circle (x-h)^2 + (y-k)^2 = r^2 - Answer-(h,k) (h -> -h)
What is the radius of the circle (x-h)^2 + (y-k)^2 = r^2 - Answer-r
You graph negative angles in standard form - Answer-clockwise
You graph positive angles in standard form - Answer-counterclockwise
How do you find the value of an angle? - Answer-Find its coordinate on the unit circle
What are the Pythagorean identities? - Answer-sin^2 + cos^2 = 1
tan^2 + 1 = sec^2
cot^2 + 1 = csc^2
graph ≥, ≤ - Answer-solid line
with Revised Answers
When you're trying to find the width do you disregard negative answers? - Answer-yes
When the number under the radical is large should you trust that it's simplified fully? -
Answer-No (it's probably not fam)
sqrt(a/b) = - Answer-sqrt(a)/sqrt(b)
What should you do any time you solve by squaring? - Answer-Plug the answers back
in (to double check)
Hw do you find the domain of an equation with a radical? - Answer-Set the value under
the radical equal to 0. IGNORE values outside the radical. (The domain ONLY includes
values that make the numbers under the radical greater than or equal to 0)
What helps when you're trying to simplify a radical with a power higher than 2? -
Answer-Writing out a table with perfect roots of the power
What is the range of an inverse function? - Answer-The domain of the original function
When finding the domain of composition functions should you find the domain of the
simplified function or the unsimplified function? - Answer-The unsimplified function
(ESPECIALLY if there radicals)
Should you leave negatives in the denominator? - Answer-no (multiply by everything
negative 1)
log_a c = b if - Answer-a^(b) = c
log_6 36 = 2 - Answer-6^2 = 36
log - Answer-log_10
What do you do for exponential growth or decay problems? - Answer-initial x
percent^time
log_a (xy) - Answer-log_a x + log_a y
log_a(x/y) - Answer-log_a x - log_a y
, log_a x^r - Answer-rlog_a x
Should you round down when a problem asks for the smallest whole number? - Answer-
no (round up to the next whole number regardless of the decimal size- it can be less
than .5 and you'd still round up)
log_e - Answer-ln
If two logs with the same base are on different sides of an equation can you cancel the
logs? - Answer-yes (queen:3)
Can you take the log of a negative number? - Answer-NO
What do you do when solving complex log/exponential equations? - Answer-distribute
and factor
What is -log when graphing? - Answer-a reflection about the x axis (multiply y
coordinates by negative 1)
What do you need to change when graphing log transformations that involve a change
in x coordinate? - Answer-The domain and vertical asymptote
What is the vertical asymptote of a normal log equation? - Answer-the y axis
How do you complete the square? - Answer-Divide the middle coordinate by 2, square it
(This is the third coefficient) , ADD THIS TO THE OTHER SIDE OF THE EQUATION
AS WELL
What is the equation of a circle - Answer-(x-h)^2 + (y-k)^2 = r^2
What is the center of the circle (x-h)^2 + (y-k)^2 = r^2 - Answer-(h,k) (h -> -h)
What is the radius of the circle (x-h)^2 + (y-k)^2 = r^2 - Answer-r
You graph negative angles in standard form - Answer-clockwise
You graph positive angles in standard form - Answer-counterclockwise
How do you find the value of an angle? - Answer-Find its coordinate on the unit circle
What are the Pythagorean identities? - Answer-sin^2 + cos^2 = 1
tan^2 + 1 = sec^2
cot^2 + 1 = csc^2
graph ≥, ≤ - Answer-solid line
