Spring 2013 Algebra 2 CCPS SOL Review...

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.


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


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


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?


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.


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


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


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


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.


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.


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.


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 ( )


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


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 ( )

( )

( ) ( ) ( )

( ) ( )


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.


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.


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.


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

Spring 2013 Algebra 2 CCPS SOL Review...

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