spring 2013 algebra 2 ccps sol review...
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Spring 2013 Algebra 2 CCPS SOL Review Items
AII.1 The student, given rational, radical, or polynomial expressions, will
a) add, subtract, multiply, divide, and simplify rational algebraic expressions;
b) add, subtract, multiply, divide, and simplify radical expressions containing
rational numbers and variables, and expressions containing rational
exponents;
c) write radical expressions as expressions containing rational exponents and
vice versa; and
d) factor polynomials completely.
AII. 1a
1. Simplify the expression:
2 2
2 2
5 20 10 24
4 12 6 8
x x x
x x x x
2. Simplify the expression:
3.
Spring 2013 Algebra 2 CCPS SOL Review Items
AII.1b 4. Which of the following is the simplified form for 8 28 4 63 ?
A 4 35 B 12 91 C 4 7 D 32 35
5. Simplify the algebraic expression completely.
4 6 3 9 4 63 3 354 24 128x y x y x y
A 2 3 2 3 46 8 2 4 6x y x y xy xy
B 2 33 37 2 2 3xy x xy
C 2 4 33 37 2 2 3x y x xy
D 5 33 158x y
6. Simplify 2
52 3 2x y .
A 5 212 8 3 4x x xy y
B 5 4 212 16 3 4x x xy y
C 4 24 3 4 6 4x x x xy y
D 512 4x y
AII. 1c 7. Which expression is equivalent to x y
3 3 5
2 2 22 ?
A x y3 53 2 C x y3 53 4
B xy xy22 2 D x y xy2 42 2
Spring 2013 Algebra 2 CCPS SOL Review Items
8.
AII.1d 9. Which of the following is a factor of 210x 14x 12 ?
A (5x + 3) B (x + 2) C (x – 2) D 2x
10. Which of the following is a factor of 3 327x 343y ?
A 2 29x 21xy 49y B (3x – 7y) C 2 23x 21xy 7y D 2 29x 21xy 49y
11. Factor the following expression completely. 6 480x 45y
AII.2 The student will investigate and apply the properties of arithmetic and geometric sequences
and series to solve real-world problems, including writing the first n terms, finding the nth
term, and evaluating summation formulas. Notation will include and an.
AII.2 12. If n 1
nA 3 2
, which of the following is A5?
A 16 B 24 C 48 D 96
Spring 2013 Algebra 2 CCPS SOL Review Items
AII.2 13. Evaluate
n7
n 3
12
2
.
A 7
32 B
15
64 C
31
64 D
61
64
14. Find the sum of the infinite geometric series 3 3 3
3 ...4 16 64
, if it exists.
A 5 B 4 C 3.98 D does not exist
15.
AII. 3 The student will perform operations on complex numbers, express the results in simplest
form using patterns of the powers of i, and identify field properties that are valid for the
complex numbers.
AII.3 16. Which of the following are equivalent to 63i ?
A II only B I and IV only C III and V only D II, IV and V only
I i II i III 12i
IV 15i V 4
i
{
The following sequence is given in recursive form.
What is the 3rd
term of this sequence?
Spring 2013 Algebra 2 CCPS SOL Review Items
17. Perform the indicated operation and simplify 7 6 3 2i i .
A 33 4i
B 33 32i
C 9 4i
D 9 32i
18.
AII.4 The student will solve, algebraically and graphically,
a) absolute value equations and inequalities;
b) quadratic equations over the set of complex numbers;
c) equations containing rational algebraic expressions; and
d) equations containing radical expressions.
Graphing calculators will be used for solving and for confirming the algebraic solutions.
AII.4a 19. What is the solution set for 3 2x 7 9 15 ?
A B 15
2
C 1
2
D 15 1
,2 2
Directions: Write the selected property to the correct box.
Spring 2013 Algebra 2 CCPS SOL Review Items
20.
Select all solutions to |
|
21. Which of the following is the solution of x3
3 8 54
?
A B C D
AII.4b 22. Which of the following are the roots for 3x2 – 2x + 7 = x
2 + 2 ?
A 1
3i2 B
1 3i
2
C 1 8i D
3 5,
2 2
23. Determine the nature of the solutions of 211x 9x 2 0 .
A Two real solutions
B Two imaginary solutions
C 1 real solution
D 1 real and 1 imaginary solution
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
Spring 2013 Algebra 2 CCPS SOL Review Items
x
y
24. Solve x x x x2 2 25 2(3 2 ) 7 2 .
A
4 6
5
i C
2 6
5
i
B 4 6
5
D 2 6
5
AII.4c
25. Solve 1 2x 1
2x 6x
.
A 2 B 3
2
C 5
14
D 1
2
AII.4d
26. Solve the equation: 1
47 2 7 12 v
27. What is the solution set for the equation? 3 2x 4 6 3
A 5
2
B 1
2
C 1
2
D
AII.5 The student will solve nonlinear systems of equations, including linear-quadratic and
quadratic-quadratic, algebraically and graphically. Graphing calculators will be used as a
tool to visualize graphs and predict the number of solutions.
AII.5
28. The graphs of functions f(x) and g(x) are shown in the graph to the right. How
many solutions does the system have?
A None
B One
C Two
D Four
Spring 2013 Algebra 2 CCPS SOL Review Items
29.
y x2 7 x 6
y 5( x 2)2 8
AII.6 The student will recognize the general shape of function (absolute value, square root, cube
root, rational, polynomial, exponential, and logarithmic) families and will convert between
graphic and symbolic forms of functions. A transformational approach to graphing will be
employed. Graphing calculators will be used as a tool to investigate the shapes and
behaviors of these functions.
AII.6
30.
A 8
f (x)x 3
B 8
f (x)x 3
C x 1
f (x)x 3
D
x 1f (x)
x 3
Directions: You must select all of the correct solutions.
Identify the x-coordinate of each point that is in the solution set of the system of equations.
72
6
Spring 2013 Algebra 2 CCPS SOL Review Items
31.
32.
AII.7 The student will investigate and analyze functions algebraically and graphically. Key
concepts include
a) domain and range, including limited and discontinuous domains and ranges;
b) zeros;
c) x- and y-intercepts;
d) intervals in which a function is increasing or decreasing;
e) asymptotes;
f) end behavior;
g) inverse of a function; and
h) composition of multiple functions.
Graphing calculators will be used as a tool to assist in investigation of functions.
Directions: You must select all of the correct functions.
Spring 2013 Algebra 2 CCPS SOL Review Items
AII.7a
33.
34.
35.
Directions: You must select all correct functions.
What appears to be the range of this function?
A.
B.
C.
D.
The graph of a function is shown on the grid.
Spring 2013 Algebra 2 CCPS SOL Review Items
AII.7b
36.
What is the zero of ( )
AII.7c
37.
AII.7d
38. Throughout which interval is 3 2f (x) 2x 3x 12x increasing?
A 2 x 0 B x 1 C 1 x 2 D 20 x
Directions: Circle all of the points that apply.
Spring 2013 Algebra 2 CCPS SOL Review Items
39.
AII.7e
40. The graphs of
x xy y y
x x x
2
2
3 2 3 4, ,
2 2 3 12
all share an asymptote of
A x = 2 B x = 1 C y = 2 D y = 1
41.
Directions: Write the correct equation in the space provided.
Directions: You must select all correct intervals.
Indicate the intervals where the graph of ( ) is only
decreasing throughout the interval.
Identify the equation of the horizontal asymptote and the equation of the vertical
asymptote of ( )
Spring 2013 Algebra 2 CCPS SOL Review Items
AII.7f
42. Which of the following describes the end behavior of 2
x 6h(x)
x
as x approaches
negative infinity?
A y approaches negative infinity
B y approaches -6
C y approaches -1
D y approaches 0
43.
A f(x) approaches
B f(x) approaches 0
C f(x) approaches 5
D f(x) approaches
44.
AII.7g
45. Which of the following is the inverse of 3g x x 8 ?
A 1g x x 2 B 1g x x 2 C 1 3g x x 8 D 1 3g x x 8
Spring 2013 Algebra 2 CCPS SOL Review Items
AII.7h
46.
47. If f(x) = 5x – 4 and g(x) = x2 + 3, find g(f(x)).
AII.8 The student will investigate and describe the relationships among solutions of an equation,
zeros of a function, x-intercepts of a graph, and factors of a polynomial expression.
AII.8
48.
49. How many non-real solutions exist for the polynomial function?
5 3 22 12 8f x x x x x ?
A 3 B 2 C 1 D 0
TAII.9 The student will collect and analyze data, determine the equation of the curve of best fit,
make predictions, and solve real-world problems, using mathematical models.
Mathematical models will include polynomial, exponential, and logarithmic functions.
Directions: Type your answer in the box. Your answer must be in decimal form.
Let ( ) and ( )
. What is ( ( )
The zeros of a cubic function ( ) are -2,
and 4. Select all of the factors of ( )
( )
( ) ( ) ( )
( ) ( )
Spring 2013 Algebra 2 CCPS SOL Review Items
AII.9
50. The table shows the number of new stores in a coffee shop chain that opened
during the years 1986 through
1994.Using x = 1 to represent the
year 1986 and y to represent the
number of new stores, determine
the equation for the curve of best
fit that most closely models the
data. Round all values to the
nearest hundredths.
A y = 71.58x – 160.47
B y = 10.60(1.59)x
C y = 14.98x2 – 78.17x + 114.07
D y = -128.40 + (229.08)lnx
51.
A xy 1,218(1.01) B
xy 997(1.03) C y 400x 11,570 D y 156x 10,000
Year Number of
New Stores
1986 14
1987 27
1988 48
1989 80
1990 110
1991 153
1992 261
1993 403
1994 681
AII.10 The student will identify, create, and solve real-world problems involving inverse
variation, joint variation, and a combination of direct and inverse variations.
Spring 2013 Algebra 2 CCPS SOL Review Items
AII.10
52. The amount of time required to stack boxes varies directly with the number of
boxes and inversely with the number of people who are stacking them. If 2 people can
stack 60 boxes in 10 minutes, how many minutes will be required for 6 people to stack
120 boxes?
53.
AII.11 The student will identify properties of a normal distribution and apply those properties to
determine probabilities associated with areas under the standard normal curve.
AII.11
54.
55.
The mean amount of time that a manager spends in annual performance
review with an employee is 27.2 minutes, with a standard deviation of 4.9
minutes. Approximately what percentage of annual performance reviews
in the department take between 17.4 and 37 minutes?
A 20%
B 50%
C 68%
D 95%
The braking distance of an automobile varies directly as the square of the speed.
If the braking distance of a certain car is 49 feet at 30 miles per hour, find the
approximate braking distance at 65 miles per hour.
Spring 2013 Algebra 2 CCPS SOL Review Items
56.
57.
The running times for a group of 200 runners to complete a one mile run are
normally distributed with a mean of 6.5 minutes and a standard deviation of 1.5
minutes. Approximately how many of the runners have a time greater than 8
minutes?
Runners
AII.12 The student will compute and distinguish between permutations and combinations and use
technology for applications.
AII.12
58.
59.
A 10 person student council will be selected from 18 students at a school. How many
possibilities are there for this student council?
60.
How many different four-digit numbers can be made using the digits 1, 2, 3, 4,
5, 6, if no digit can be used more than once?
A 360
B 90
C 30
D 15
Directions: Write your answer in the box.
Directions: Write your answer in the box.
Spring 2013 Algebra 2 CCPS SOL Review Items
Solutions
1. 5
2. ( )
3. ( )
4. C
5. B
6. A
7. C
8.
and √
9. B
10. D
11. ( )( )
12. C
13. C
14. B
15. 79
16. B
17. A
18. Distributive Property
Commutative Property of Addition
Associative Property of Addition
19. A
20. x = -2 or 6
21. D
22. B
23. B
24. C
25. D
26. v = 89
27. D
28. D
29.
30. B
31. A
32. ( )
( )
( )
33. A
34. ( ) -3 and
( ) √
35. ( )
√ + 1
36.
or 2.5
37. x-int: (1, 0) and y-int: (0, -1)
38. B
39.
40. A
41. and
42. D
43. A
44. C
45. C
46. 22
47. ( ( ))
48. ( )( )( )
49. B
50. B
51. B
52. 6 hours 40 minutes or 400 minutes
53. 230 feet
54. D
55. D
56. Approximately 185
57. Approximately 32
58. A
59. 43,758
60. C
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