Download NJ DOE Unit 2_Algebra 2

Name ________________________
Period ______
Date ____________
Algebra II Unit 2 Model Curriculum Assessment
 
1
x
1.
If 7 4
 7, what is the value of x ? Explain your reasoning.
2.
When the nth root of a positive number a is written as ax , what is the
value of x ? Fill in the blanks in the partial solution below to explain
your answer.
n
a  ax
 
_____  ax
n
a1  _____

1  _____
_____  x
3.
Rewrite the expression 9 5 27 as a power of 3.
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Unit 2_Algebra 2
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3
x 2 in exponential form.
4.
Rewrite the expression
5.
Which of the following is equivalent to a2 b 4 ?
1
a.
ab3
b.
a2b3
c.
4
ab3
d.
4
a2b3
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Unit 2_Algebra 2
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6.
Which expression is equivalent to
a.
b.
c.
d.
7.
3x 2  2 x  1
, where x  1 ?
x 1
6
3x  2x  1
6
3x  5 
x 1
3x  1
6
3x  5 
x 1
3x  5 
2
3x 2  13x  4 4x  16
in simplest form, where

x2  4
x 2
x  2, x  2, and x   4 ? Show your work.
What is the quotient
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Unit 2_Algebra 2
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8.
Which expression is equivalent to
x  4 ?
9.
a.
1
x4
b.
 x  2 x  2
 x  4 x  4
c.
x 2  8x  4
 x  4 x  4
d.
x 2  8x  4
 x  4 x  4
2x
x2  4
 2
, where x  4 and
x  4 x  16
Rx
x 4  x 3  3x 2  10x  2
,
as Q  x   2
2
x  3x  3
x  3x  3
where Q  x  is the quotient with degree 2 and R  x  is the remainder.
Write the expression
Show your work.
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Unit 2_Algebra 2
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10.
Solve the equation below. Explain your reasoning for each step.
3
11.
2x  22  18
Solve the equation below. Show your work.
7x  15  x  1
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12.
x  5
x 0
x 5
All Real Numbers Except
All Real Numbers
x  5
or x  0
x  5
No Solution
There are 4 equation cards labeled a–d below and 7 potential solution
set cards above. Match each equation card to its corresponding
solution set. Write the solution set in the box beside its corresponding
equation. A solution set card can be used more than once.
a.
x
x
2x


2 x  5 2x  10
x
2x

x  5 2x  10
b.
x
x

x 5 x 5
c.
1
5

x  5 x  x  5
d.
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13.
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
True
Sometimes
True
Always
True
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
m
to the
power, where m and n
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
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Unit 2_Algebra 2
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14.
Solve the system of equations below by graphing on the coordinate
plane provided.
1
x 3
2
1
1
y 
x
6
3
y 
Solution: _______________________
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15.
Solve the system of equations below algebraically.
2 x  3y  8
4 x  2y  10
Solution: _______________________
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y  2x  5
16.
y  x 2  4x  10
Part A Solve the system of equations above algebraically.
Show your work.
Solution set: _______________________
Part B Graph both equations and indicate the solution on the graph.
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17.
The function f  x   82x 3 is equivalent to the function f  x   2a bx ,
where a and b are integers. What are the values of a and b ?
a  _____ and b  _____
18.
 0.1  in the form g  x   n  b
Rewrite the function g  x   104 23 x
x
where n and b are constants.
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x
,
19.
Which of the following functions is equivalent to f  x   3x  23x 2 ?
a.
f  x   2 24
b.
f  x   2 6
c.
f  x   4 24
d.
f  x   4 6 
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x
3 x2
x
3 x2
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Unit 2_Algebra 2
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20.
Darah has 200 milliliters of a salt and water solution that is 12% salt.
She begins to add a salt and water solution that is 5% salt to the 12%
solution. The percent of salt in Darah’s combined solution when
x milliliters of the 5% solution have been added can be modeled by
2, 400  5x
C x 
.
200  x
Two different tables of values for C  x  are given below. Use the tables
to answer the questions that follow.
x
C x
50
100
150
200
250
300
350
400
450
500
10.6
9.67
9.0
8.5
8.11
7.8
7.55
7.33
7.15
7.0
x
C x
500
1,000
5,000
10,000
50,000
100,000
1,000,000
7.0
6.17
5.27
5.14
5.03
5.01
5.001
Part A Is the function increasing or decreasing? What does this mean
in the context of the problem?
Part B What is the horizontal asymptote of the functions? Interpret
the meaning of the asymptote in the context of the problem.
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21.
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.
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22.
The figure above shows the graph of the profit function for a
company. In the graph, y represents the profit, in thousands of
dollars, that the company earns for selling x thousand items.
Interpret the meaning of the two intercepts shown in the context
of the problem.
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