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Algebra II 2010–2011 Semester 1 Exam — Released
1. To which sets of numbers does –5 belong?
4. What is the value of x when
(A) real numbers, whole numbers

(B) real numbers, rational numbers,
integers, whole numbers
16
3 7
x  ?
5
2 10
(C) real numbers, rational numbers,
integers
(A) 
5
16
(D) real numbers, irrational numbers
(B) 
1
4
2. Evaluate 5  2a  3b  when a 
b  2 .
1
and
2
(C)
1
4
(D) 4
(A) 35
5. Solve the formula for r, where V, r,
and h are positive real numbers.
(B) 1
(C) 25
V   r 2h
(D) 29
(A) r 
3. Which is a simplified form of the
expression 2  x  5  3  x  4 ?
V
h
(B) r  V  h
(A)  x  2
(C) r 
(B) x 1
(C)  x  17
V
h
(D) r  V   h
(D) x  22
6. Solve for y:
2 x  y  5x  3 y  4  x 1
7
(A) y   x  2
2
1
1
(B) y   x 
2
2
1
(C) y   x  2
2
(D) y 
2010–2011
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x2
2
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Algebra II 2010–2011 Semester 1 Exam — Released
7. What is the solution set of 2 x  12  8 ?
(A)
2, 10
(B)
2
(C)
2
(D)
2, 2
10. Which graph is NOT a function?
(A)
8. Which expresses all of the solutions for the
compound inequality?
7  3x  2  13
(B)
(A) x  3 or x  5
(B) 3  x  5
(C) x  3 and x  5
(D) no solution
9. A television repairman charges a $55
service charge for each visit and $40 per
hour for labor. Let C represent the total
cost of the repairman’s visit and h
represent the number of hours in the visit.
(C)
Which is a model for the total cost of the
repairman’s visit?
(A) C  55h  40
(B) C  55h  40
(C) C  40h  55
(D)
(D) C  40h  55
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Algebra II 2010–2011 Semester 1 Exam — Released
11. What is the domain of the relation?
14. Use the graph.
 5, 3 ,  2, 1 , 6, 4
(A)
5, 2, 6
(B)
6,  2, 5
(C)
4, 3, 1
(D)
1, 3, 4
12. Which is the equation of a line that passes
through the points 1, 1 and  3,  5 ?
(A) y  2 x  1
What is the slope of the line?
(B) y  2 x  1
(C) y  2 x  3
1
1
(D) y   x 
2
2
13. Which equation represents the relation?
x −3
y −14
−1
−8
1
−2
3
4
5
10
(A) y  3x  2
(B) y 
1
7
x
3
3
(C) y 
7
x 3
3
(A) 
5
3
(B) 
3
5
(C)
3
5
(D)
5
3
15. At 1:00 p.m. an airplane is at an altitude of
30,000 ft. At 3:00 p.m. the airplane is at
an altitude of 18,000 ft. What is the
average rate of change of the altitude of the
airplane?
(A) 24, 000 ft per hour
(D) y  3 x  5
(B) 6, 000 ft per hour
(C) 4, 000 ft per hour
(D) 6,000 ft per hour
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Algebra II 2010–2011 Semester 1 Exam — Released
16. Classify the relationship between the lines
1
y  x  5 and 4 x  y  3 .
4
17. Which graph represents the equation
y   x  2  3?
(A) The lines are parallel.
(A)
(B) The lines are perpendicular.
(C) The lines coincide.
(D) None of these
(B)
(C)
(D)
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Algebra II 2010–2011 Semester 1 Exam — Released
18. The cost c of placing an advertisement in
the newspaper varies directly with the
number of lines n. The cost of an
advertisement with 12 lines was $84. How
many lines would an advertisement have
that costs $56?
19. Which graph represents the piecewise
function?
3x  1, x  1
f  x  
 x  2, x  1
(A)
(A) 7
(B) 8
(C) 9
(D) 10
(B)
(C)
(D)
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Algebra II 2010–2011 Semester 1 Exam — Released
20. The equations of two lines are given.
23. Which graph shows the solution to the
system of inequalities?
1

y  x  4
3

 y  2 x  5
y  x2
4 x  3 y  13
What is the x-coordinate of the point of
intersection of the two lines?
(A)
(A) x = −5
(B) x = −7
(C) x = −11
(D) x = −15
21. What is the y-coordinate of the solution of
the system of equations?
(B)
 x  y  8

2 x  5 y  31
(A) y = −5
(B) y = −3
(C) y = 3
(D) y = 5
(C)
22. What is the z-coordinate of the solution of
the system of equations?
 x  2 y  5 z  1

2 x  y  z  2
3x  4 y  4 z  14

(A) z = –2
(B) z = –1
(D)
(C) z = 1
(D) z = 2
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Algebra II 2010–2011 Semester 1 Exam — Released
24. An artist opens a business of selling handpainted greeting cards. Her start-up cost is
$40 for paint and brushes. She buys plain
cards for $3 per box, and will sell the
painted cards for $5 per box. How many
boxes must the artist sell for her income to
equal her expenses?
25. A carpenter produces c chairs and t tables
under the following constraints:
2c  3t  30 c  0
c  t  12 t  0
The constraints are illustrated in the graph.
(A) 5 boxes
(B) 8 boxes
(C) 10 boxes
(D) 20 boxes
The objective function maximizing the
carpenter’s profit is P  40c  30t . How
many tables and chairs should the
carpenter make to maximize profit?
(A) 12 chairs, 0 tables
(B) 0 chairs, 10 tables
(C) 4 chairs, 10 tables
(D) 6 chairs, 6 tables
2010–2011
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Algebra II 2010–2011 Semester 1 Exam — Released
26. The tables show the deposit amounts d and
withdrawal amounts w of a bank
customer’s checking and savings accounts.
Checking Account
Week
d
w
1
450 200
2
350 350
3
475 325
4
500 475
27. Determine the values of x and y that make
the equation true.
 11 4  6 7   x 3


3 y
8  6 9  12 17 

Savings Account
Week
d
w
1
1000 500
2
1200 1100
3
1500 1200
4
1000 1000
(A) x = 11, y = –4
(B) x = –5, y = 2
(C) x = 5, y = –6
Which could be used to find the total
weekly deposits and withdrawals for the
two accounts?
 450
350
(A) 
 475

500
1000   200 500 
1200  350 1100 

1500   325 1200 
 

1000   475 1000 
 450
350
(B) 
 475

500
200  1000 500 
350  1200 1100 

325  1500 1200 
 

475 1000 1000 
(D) x = 17, y = –2
28. What is the product AB?
 1 0
 1 3
A
, B


 2 4
 2 1
 1 3 
(A) 

 6 2 
 7 12 
(B) 

 4 4 
 0 3
(C) 

 4 5 
1450   700 
1550  1450 


(C) 
1975 1525

 

1500  1475
 1 0
(D) 

 4 4
650  1500 
700   2300 


(D) 
800   2700 

 

975   2000 
 3 4 
29. What is the determinant of 
?
 2 5 
(A) −23
(B) −22
(C) −7
(D) −4
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Algebra II 2010–2011 Semester 1 Exam — Released
30. A linear system is written as a matrix
equation:
31. What graph represents
2
f  x     x  2  1 ?
 4 11  x   6
 1 3  y    1

   
(A)
Solve the matrix equation for x.
(A) x  9
(B) x  2
(C) x  7
(D) x  35
(B)
(C)
(D)
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Algebra II 2010–2011 Semester 1 Exam — Released
32. What are the solutions of the quadratic
equation x 2  10 x  24 ?
35. What is the solution set of the equation
2 x 2  7  25 ?
(A) x  4, x  6
(A)
4, 4
(B) x  6, x  4
(B)
3, 3
(C)
3
(D)
4
(C) x  2, x  12
(D) x  12, x  2
33. What is the solution set of the quadratic
equation x 2  6 x  4  0 ?
(A)
(B)
(C)
(D)
6 
3 
6 
3 
36. Using the discriminant, how many real and
imaginary solutions are there for the
equation 2 x 2  3x  7  0 ?

5, 3  5
13, 6  13
13, 3  13
5,  6  5
(A) 2 real solutions, no imaginary
solutions
(B) no real solutions, 2 imaginary
solutions
(C) 1 real solution, 1 imaginary solution
(D) no real solutions, 1 imaginary
solution
34. What value of c makes the left side of the
equation a perfect square trinomial?
37. What is the solution set of
x 2  4 x  20  0 ?
x2  6x  c  0
(A)
4  8i, 4  8i
(C) −3
(B)
4  4i, 4  4i
(D) −9
(C)
2  4i, 2  4i
(D)
2  4i, 2  4i
(A) 36
(B) 9
38. What is the product 1  3i  2  3i  ?
(A) 7  3i
(B) 11  3i
(C) 3
(D) 11
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Algebra II 2010–2011 Semester 1 Exam — Released
39. What graph represents the quadratic
inequality?
40. Use the formula below, where h is the
height (in feet) of a falling object after t
seconds and h0 is the object’s initial height
(in feet).
y  x2  2 x  3
h  16t 2  h0
(A)
A rock falls from the edge of a cliff 256
feet above the ground. How much time
does it take for the rock to reach the
ground? (Note: h  0 when the rock
reaches the ground.)
(A)
1
second
4
(B) 3 seconds
(B)
(C) 4 seconds
(D) 5 seconds
(C)
(D)
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Algebra II 2010–2011 Semester 1 Exam — Released
42. What graph represents the polynomial
function y   x 4  3x3  3x  2 ?
41. What graph represents the polynomial
function f  x    x  3 x  1 x  4 ?
(A)
(A)
(B)
(B)
(C)
(C)
(D)
(D)
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Algebra II 2010–2011 Semester 1 Exam — Released
43. Which polynomial represents the product
 x3  3 x2  4  ?
46. What is the set of all real zeros of the
polynomial function
f  x   x3  2 x 2  4 x  8 ?
(A) x5  4 x3  3x 2  12
(B) x 5  12
(A)
4, 2
(C) x 6  4 x 4  3x3  12
(B)
2, 2
(D) x 6  7
(C)
2
(D)
2, 4, 8
44. What is the solution set of the equation
x 4  3x 2  4  0 ?
(A)
2, 2
(B)
2i, 2i
(C)
i, i, 2, 2
(D)
2, 1, 1, 2
47. According to the Fundamental Theorem of
Algebra, how many zeros does the
function have?
f  x   3x4  2x3  x  5
(A) 2
(B) 3
(C) 4
45. What are the zeros of the polynomial
function represented by this graph?
(D) 5
48. What is  x3  x 2  4 x  4  divided by
 x  2 ?
(A) x 2  x  1
(B) x 2  x  8
(C) x 2  3 x  2
(D) x 2  x  2
(A)
3, 1, 2, 6
(B)
3, 1, 2
(C)
2, 1, 3, 6
(D)
2, 1, 3
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Algebra II 2010–2011 Semester 1 Exam — Released
49. Which describes the end behavior of the
graph of f  x    x4  3x2  15 as
x   ?
(A) f  x   
(B) f  x   
(C) f  x   15
(D) f  x   1
50. What function represents the graph?
(A) f  x    x3  2x2  3x  4
(B) f  x    x4  5x3  2 x2  5x  4
(C) f  x   x3  5x2  3x  4
(D) f  x   x4  5x3  4x2  5x  4
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Algebra II 2010–2011 Semester 1 Exam — Released
Free Response
1. This question obsolete as of 2011–2012. See new test specifications and practice questions.
2. This question obsolete as of 2011–2012. See new test specifications and practice questions.
3. This question obsolete as of 2011–2012. See new test specifications and practice questions.
2010–2011
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Revised 08/02/2011
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