Robert is collecting books to donate to the
library. The number of books he collects, n, is
defined by n = 14d + 21 where d is the
number of days he spends collecting books.
Part A: What does 14 represent in the context
of Robert’s book collecting?
Part B: What does 21 represent in the context
of Robert’s book collecting?
The graph of the function h(x) is obtained
from the graph of f(x) by shrinking the graph
of f(x) vertically by a factor of 5 and reflecting
the result over the y-axis. Which of the
following equations gives h(x) in terms of
f(x)?
1
a. h( x)  5 f ( x)
b. h( x)  5 f ( x)

c. h( x)  5 f ( x)
1
d. h( x)   5 f ( x)
3
1

h( x)    x  1
3
9
0  x  10
10  x  28
28  x  50
A person standing at the wall at the shallow end of an
empty swimming pool begins walking toward the
wall at the deep end of the pool. The height from
the bottom to the top of the swimming pool varies
depending on the number of feet, x, the person has
walked away from the wall at the shallow end. The
function h(x) above gives the height, in feet, from
the bottom to the top of the pool, where x is
measured in feet.
Part A: Graph the function h(x) on a coordinate plane.
Part B: Describe the change in the height of the pool
as the person walks 50 feet from the wall at the
shallow end toward the wall at the deep end.

The cost for a phone call on a cruise ship is 65
cents per minute (or part of a minute). Create a
graph that shows the total cost, in dollars, for
calls between 0 and 10 minutes in length.
The graph of the function g is
shown in the coordinate plane.
2
f
(
x
)

x
If
, and g ( x)  kf ( x)  c ,
what are the values of k and c ?
a. k = 1/3, c = 2
b. k = 1/3, c = -2
c. k = 3, c = 2
d. k = 3, c = -2
The area of a rectangular garden is expressed by the
function A(x) = x(8 – x), where the length of the
garden is x feet and the width of the garden is (8 –
x) feet.
Part A: What values of x make sense in the context of
the problem?
Part B: Graph the function A(x) in the coordinate plane
below for the x-values you identified in Part A.
Part C: What are the dimensions of the garden that
will result in the maximum possible area?
The height above ground, h, of an arrow t seconds
after being shot straight up into the air can be
2
modeled by the formula h(t )  1.5  40t  4.9t , where
t is in seconds and h is in meters. What is the
average rate of change of the height, in meters per
second, of the arrow over the first three seconds
after being shot? Show your work.

A grain silo is in the shape of a right circular cylinder
with a hemisphere on top. The volume, V, of the silo is
2 3
2
given by V  r  r h , where r is the radius of the
3
silo and h is the height of its cylindrical portion. Which
of the following is an equivalent form of the volume
function that can be used to find a silo’s height when
its volume and radius are known?
V
2
h
 r
2
a.
3
r
 r2
2
c. h 
 r
V
3
b.
h
d. h 
V
2
3


r
 r2 3
 r2
2
  r3
V
3
The graph of the quadratic
function g(x) is shown in the
coordinate plane, and
.3
f ( x)  x
Answer each of the following
questions about f(x) and g(x).



Part A: Compute the average rates of change of the
two functions on the interval [0, 1]. Compare the two
average rates of change.
Part B: Compute the average rates of change of the two
functions on the interval [1, 2]. Compare the two
average rates of change.
Part C: Compare the end behavior of the two functions.

A box in the shape of a rectangular prism has a
width that is 5 inches greater than the height and
a length that is 2 inches greater than the width.
Write a polynomial expression in standard form
for the volume of the box. Explain the meaning
of any variables used.

A stained-glass window design is in
the shape of a square with semicircles
along each side of the square, as
shown above. The length of a side of
the square is d. Write a function that
gives the area of the window design,
A, as a function of d.
An ice cream cone is created by
packing ice cream into a wafer in the
shape of a right circular cone with
height 3r and base radius r, as shown.
The ice cream forms a hemisphere with
radius r that sits on top of the wafer
cone. Which of the following functions
gives the volume, V, of ice cream both
inside and outside the cone as a
function of r ?
a. V  r   53  r 3 b. V  r   73  r 3
c. V  r   53  2r 6 d. V  r   73  2r 6


x 4  x 3  3x 2  10x  2
x 2  3x  3
Write the expression
Rx
Q
x

as   x 2  3x  3 , where Q  x  is the quotient
with degree 2 and R  x  is the remainder.
Show your work.

Given that the factored form of a polynomial
function is f(x) = (x + a)(x – b)(x + c)(c – d),
where a, b, c, and d are positive numbers,
describe the graph of the function in the
coordinate plane including intercepts and end
behavior.
Describe each of the following key features of the graph
of f ( x)  x  3x  22 x  13 .
Part A: Where does the graph intersect the x-axis?
Part B: Where does the graph intersect the y-axis?
Part C: Is the value of f positive or negative for 2 < x < 3?
Part D: Is the graph increasing or decreasing when x > 5?

The graph of the fourth-degree polynomial
function f(x) is shown in the coordinate plane.
Based on the graph, list all linear factors of f(x).

A polynomial function has the following
characteristics: the function has exactly 3 real
zeros at -3, 1, and 3; the leading coefficient of
the polynomial is positive. Sketch a function that
meets the characteristics.

At a diving competition, Holly jumps from a springboard
that is 3 meters above the surface of the water at time t = 0
seconds. She reaches a maximum height of 4.5 meters
above the surface of the water after 0.5 seconds and enters
the water 1.5 seconds after jumping. She then sinks to a
minimum height of 1.5 meters below the surface of the
water 1 second after entering the water and rises back to
the surface of the water 2.5 seconds later. Sketch a possible
graph of Holly’s height above the water, h, from the time
she jumps until she rises to the surface of the water.
Provide labels and scales for the axes.

When the nth root of a positive number a is
written as , what is the value of x ? Fill in the
blanks in the partial solution below to explain
your answer.
n
a  ax
 
_____  a
x
n
a1  _____

1  _____
_____  x

Rewrite the expression 95 27 as a power of 3.

12 34
Which of the following is equivalent to a b ?
a. ab3
b.
a 2b3
c.
4
ab 3
2 3
a
b
d.
4
For each of the following statements, put a check mark in the
circle to indicate whether the statement is never true,
sometimes true, or always true for the operation.
Never
When solving equations for real solutions,
extraneous solutions occur when
a. Squaring both sides of an equation.
b. Multiplying both sides of an equation by an
expression containing one or more variables.
c. Multiplying both sides of an equation by a constant
d. Raising both sides of an equation to the power,
where m and n are integers.
e. Dividing both sides of an equation that has the
variable x by x.
f. Taking the square root of both sides of an equation.
Sometimes Always



A certain bacterial culture grows at a rate that
triples the number of bacteria every 2 hours. When
the first measurement is made (at time t = 0
hours), there are 1,000 bacteria.
Part A: Create a graph to show the number of
bacteria present for the 4 hours after the
measurement.
Part B: Interpret the intercepts (if any), in context.
As t increases, what happens to the number of
bacteria?

Rounded to three decimal places, log 2 5 is
approximately equal to 2.322. Use this approximation
x
to solve for x in the equation 40  4 . Show your work,
and round the answer to three decimal places.