Name ________________________
Period ______
Date ____________
Algebra II Unit 1 Model Curriculum Assessment
1.
Which of the following is equivalent to i 49 ?
a.
b.
c.
d.
i
1
i
1
2.
What is the sum 2  3i     4  2i  ?
3.
What is the difference 5  8i     6  11i  ?
4.
What is the product 1  6i   5  8i  ?
5.
The function f is defined by f  x   x2  6x  21. What are the
solutions of f  x   0 ? Show your work.
6.
Which of the following are the solutions for the equation
0  x2  x  1 ?
a.
x 
1  i 3
1  i 3
and x 
2
2
b.
x 
1  i 5
1  i 5
and x 
2
2
c.
x 
1 i 5
1i 5
and x 
2
2
d.
x 
1 i 3
1i 3
and x 
2
2
7.
What are the solutions to the equation x2  9  0 ?
8.
SP
x
P
100
In the equation above, S represents the sale price of a coat after the
original price P is discounted by x percent. Which of the following
expressions represents the amount of the discount?
a.
x
P
100
b.
Px
c.
x
100
d.
P
x
P
100
9.
The expression 2,000 1.03 gives the number of dollars in an
t
investment account t years after the initial amount is invested. The
account earns a simple annual interest.
a. What does 2,000 represent in the context of the problem?
b. What does 1.03 represent in the context of the problem?
10.
A 40-ounce solution that is 45 percent acid has x ounces of pure acid
added to it. The researcher uses the expression
0.45  40  x
to
40  x
answer some questions about the situation.
a. What does the expression 40  x represent in the situation?
b. What does 0.45  40  x represent in the situation?
5x
as one rational expression that is
x 3
equivalent to the expression for all x values, where x  3.
11.
Rewrite the expression 2x 
12.
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.
13.
What is the difference  4x5  3x 3  2x 2  7   x 4  2x 3  4x  3 ?
a. 5x 9  x 6  2x 3  10
b. 3x 5  5x 3  2 x 2  4
c. 4x 5  x 4  x 3  2x  4x  10
d. 4x 5  x 4  5x 3  2x 2  4x  4
14.
Factor 2x 4  5x 3  6 x 2  15x completely over the set of integers.
15.
For each polynomial expression in the table below, classify the
expression as a difference of squares, difference of cubes, sum of
cubes, or none of these by placing a check mark in all appropriate
boxes. Then factor each polynomial completely in the space provided
below the table.
Expression
a. x12  y 6
b. 8x 3  24y
c. x 3  1
a. x12  y 6
b. 8x 3  24y
c. x 3  1
Difference
of Squares
Difference
of Cubes
Sum of
Cubes
None of
these
16.
Given that the factored form of a polynomial function is
f  x    x  a  x  b  x  c   x  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.
17.
The graph of the fourth-degee polynomial function f  x  is shown in
the coordinate plane below. Based on the graph, list all linear factors
of f  x  .
18.
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 above.