Algebra II 1st Semester Exam Review Sheet 2014-2015
Name _______________________
Date ___________ Period _______
1. Simplify
 n  2  n  3  2n 2
2. The function f  x   3 x 2  6, 000 represents BurgerLand’s income on Potato Stix, where x is the price of the
Potato Stix in dollars. What is the maximum income BurgerLand’s company could make selling the Potato Stix?
3. Which table could not be values from a linear function? Why?
a.
b.
x
1
2
3
4
f(x)
1
-1
-3
-5
c.
x
1
2
3
4
f(x)
-4
-7
-10
-13
d.
x
-6
-5
-4
-3
f(x)
11
16
21
25
x
1
2
3
4
f(x)
1
4
7
11
4. A homeowner is planning a garden. One side of the garden is against a house, but the other sides need a fence.
Which graph can you use to determine the largest area the homeowner can have for the garden using 100 feet of
fencing?
a.
b.
c.
d.
1
Algebra II 1st Semester Exam Review Sheet 2014-2015
5. Expand  2 x  3 y  .
4
6. Analyze the table of values for the functions f  x   x 2  1 and g  x   3x  1
x
f(x)
g(x)
p(x)
3
8
10
18
2
3
7
10
1
0
4
4
0
1
1
0
1
0
2
2
2
3
5
2
3
8
8
0
Identify the relationship between f(x) and g(x) that produces p(x).
7. The diagram shows the first four of a series of designs that an artist draws as artwork.
The artist wants to use a design with a maximum of 19 shaded circles. What number of design should the artist
use?
2
Algebra II 1st Semester Exam Review Sheet 2014-2015
8. Determine the quotient.
13. The function c(x) models the number of cookies
sold each day by a bakery during a 10-day period.
2 x  1 6 x 4  x3  2 x 2  4 x  1
9. What are the possible rational roots of
4 x3  x 2  5 x  7 ?
Between which days did the number of cookies
sold by the bakery decrease? Justify your answer.
10. Factor completely. 100 x6  36 x4
14. Graph.
f  x    x  3 x  1
11. Which is a factor of x4  4 x3  6 x2  7 x  10 ?
a.
b.
c.
d.
12. Factor completely. 10 x2  23x  5
15. Calculate the value of i 85
16. Simplify the expression.
 3  5i  9  2i 
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Algebra II 1st Semester Exam Review Sheet 2014-2015
17. Simplify the expression.
22. Write the equation of a function g(x) which could
model the following graph.
 3  5i    9  2i 
18. A soccer player kicks a soccer ball across the
soccer field. The ball leaves the player’s foot at a
height of 4 feet. It follows a path in the shape of a
parabola. At its highest point, the ball is a
horizontal distance of 75 feet from the player and
40 feet above the ground. Pick either a + or – sign
in each situation until the function represents this
scenario.

  
h  d   0.0064  d 75  40

  
23. Solve the equation for all real or imaginary roots.
3x2  5x  3  0
19. Write a function p(x) which is a reflection of the
function k  x   5  x  4   8 across the y-axis.
2
20. What is the axis of symmetry of the function?
f  x   x2  5x  7
24. Determine the product, h(x), of the given linear and
quadratic factors.
f  x   3x  1 and g  x   2 x 2  4 x  7
21. What is the vertex of the graph of
f  x   2 x 2  12 x  7 ?
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Algebra II 1st Semester Exam Review Sheet 2014-2015
25. Reflect the function f  x   x 5 about the x-axis
and translate it 6 units to the right to produce g(x).
Write a function for g(x).
27. Which could be the graph of
f  x    x3  3x 2  3  x  1 ?
a.
26. Factor.
f  x   4 x3  x 2  4 x  1 .
b.
c.
28. A company makes different sizes of boxes. The
widest box has a width w of 32 inches, a depth d of
8 inches, and a height h of 5 inches. Other boxes
the company makes decrease in width by
increments of 4 inches. For each decrease of 4
inches in width, however, both d and h increase by
2 inches.
d.
Write a function that represents the volume of each
box the company makes?
5
Algebra II 1st Semester Exam Review Sheet 2014-2015
29. Sketch a graph of a polynomial with each given
degree.
30. The graph shown represents the function
.
a. 3rd degree polynomial
Which functions could be p(x), q(x), and r(x)?
b. 4th degree polynomial
a.
b.
c.
d.
p  x  x  2
p  x  x  2
p  x  x  2
p  x  x  2
q  x  x 1
q  x  x 1
q  x  x  1
q  x  x  1
r  x  x  4
r  x  x  4
r  x  x  4
r  x  x  4
31. Analyze the sequence.
c. 5th degree polynomial
1 1 1
, , , 1, 3...
27 9 3
What is the 10th term in the sequence?
d. 6th degree polynomial
32. Analyze the sequence.
27,  21,  15,  9, ...
What is the next term in the sequence?
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Algebra II 1st Semester Exam Review Sheet 2014-2015
33. The parking lot at a science museum is arranged so
that 1 car parks in the first row, 3 cars park in the
second row, 5 cars park in the third row, and so on.
35. What is the inverse of the function f  x   7 x  3 ?
5
36. Compute the series: 4
3
k
k 2
How many cars can park in the lot if there are 16
rows arranged this way?
37. Identify the domain of the following graph.
34. Divide 3  4i by  5  7i . Write the verbal
statement as an expression. Then simplify
completely.
38. Identify the range of the following graph.
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Algebra II 1st Semester Exam Review Sheet 2014-2015
39. The table shows HeMan’s salary for the first five years of his job. The company he works for promises to continue
the same rate of increase in his salary for as long as he works at the company.
Time
(years)
HeMan’s
Salary ($)
1
60,000
2
61,200
3
62,424
4
63,672
5
64,946
8

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