Math 2 Exam II Practice
These are a collection of problems you can use to practice for the exam. To see the answers go to this page.
P-level
Take
to be an invertible function with a domain of and a range of . Determine the domain and range of .The point
is in an invertible function . Determine a point onCalculate
Take
DetermineDetermine the fraction of a circle of the angle that is
radians.Take
to be an angle on the unit circle with coordinates . Calculate , andTake
to be the function given by Determine the vertex of and the maximum and minimum value ofTake
to be the function given by Determine the zeros of and the orders of each zero.Take
to be the function given by Determine the zeros and poles of and the orders of each zero and pole.Take
to be the function given by Determine the asymptotic behavior of .Take
to be a function with fundamental period and to be the function . Determine the fundamental period of the function .Take
to be an odd function. Suppose that and are points on . Determine and .Take
to be an even function. Suppose that and . Determine and .Determine the fundamental period of each trigonometric function.
Determine the horizontal and vertical asymptotes of each function.
Take
to be a polynomial and to be the line that is tangent to at The line is given by the equation Determine and .Take
to be a polynomial and to be the line that is tangent to at The line is given by the equation DetermineTake
to be an invertible function and to be the line that is tangent to at . The line is given by Determine the line that is tangent to at .Take
to be a function and to be the line that is tangent to at . The line is given by Determine the line that is tangent to at where is given by
C-level
Take
to be the function given by . Find the inverse of and its domain and range.Identify a point
on the unit circle so thatRotate the point
about the point by the angleTake
to be an angle on the unit circle with coordinates and in quadrant IV. Determine , , , , and .Sketch the function
given bySketch the function
given byTake
to be an odd function whose graph is shown below on the restriction . Sketch on the restriction In other words, “complete” the graph.
Take
and to be two angles in quadrant I with and . Calculate the following.Sketch the function
by using transformations on the given function . Indicate what the transformations are and the order of the transformations. Include also the domain and range and any asymptotes. , , , , , ,
Take
, and to be positive real numbers so that and Calculate the following.A quantity
changes according to an exponential model for change and Identify a formula forTake
and to be given by- Identify a quadratic equation that determines
so that is tangent to at . - Use part a to determine the equation of the line tangent to
at You must use part a in order to receive credit.
- Identify a quadratic equation that determines
Determine the equation of the line that is tangent to the circle
at the point , where is the circle given byTake
to be a function and to be the line that is tangent to at . The line is given by Determine the line that is tangent to at where is given by
B-Level
- Take
to be the rational function that is given by- Sketch
. - Use the sketch of
to determine all solutions to the inequality - Use the sketch of
to determine all solutions to the inequality - Use the sketch of
to determine all solutions to the inequality - Use the sketch of
to determine all solutions to the inequality
- Sketch
- A mass of bacteria experiences exponential growth. At time
an experimenter has grams of bacteria. At time , the mass has grown to a mass of .- Determine the doubling time of the bacteria.
- Determine the growth rate of the bacteria.
- Take
to be a particle that moves on the line segment with endpoints and . It is at at time and it moves along the line segment at unit speed. Take to be a particle that rotates around in a counter-clockwise direction as travels. It is a distance of to the right of at time and has a speed of .- Write down equations that model the motion for
and . - Determine how long it takes for
to reach . - Determine how many full orbits
has made by the time reached .
- Write down equations that model the motion for
A-level
Take
to be a function given by defined on- Sketch
and . - Write a formula for
.
- Sketch
Determine the equation of the line that is tangent to the ellipse
at the point , where is the ellipse given byTake
to be the function whose graph is given below. Use -axis inversion to graph the function that is given by
- Take
to be a circle and to be a point on . A graph of and is given below. Use the graph to determine the equation of the line that is tangent to at .