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. Simplify the expression:
AII.1b
4. Which of the following is the simplified form for ?
A B C D
5. Simplify the algebraic expression completely.
A B C
D
6. Simplify .
A B C D
AII. 1c
7. Which expression is equivalent to ?
A C
8.
AII.1d
9. Which of the following is a factorof ?
A (5x + 3) B (x + 2) C (x – 2) D 2x
10. Which of the following is a factor of ?
A B (3x – 7y) C D
11. Factor the following expression completely.
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 , which of the following is A5?
AII.2
13. Evaluate .
A B C D
14. Find the sum of the infinite geometric series , 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 i63
?
A II only
The following sequence is given in recursive form.
{
a1=7an=3an−1+4, for n ≥2
What is the 3rd term of this sequence?
B I and IV only C III and V only D II, IV and V only
17.Perform the indicated operation and simplify . A
B C
D
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 ?
-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
A B C D
20.
Select all solutions to
|
121 x−16
|
= 1 321.
Which of the following is the solution of ?
A
B
C
D
AII.4b 22. Which of the following are the roots for 3x2 – 2x + 7 = x2 + 2 ?
A B C D
A Two real solutions B Two imaginary solutions C 1 real solution
D 1 real and 1 imaginary solution
24. Solve .
A C
B D
AII.4c
25. Solve .
A B C D AII.4d
26. Solve the equation:
27. What is the solution set for the equation?
A B C D
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.
Directions: You must select all of the correct solutions.
72 6
Identify the x-coordinate of each point that is in the solution set of the system of equations.
A
B C D
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. AII.7a 33.
34. Directions: You must select all correct functions.
What appears to be the range of this function?
A. {y∨−9≤ y ≤3}
B. {y∨−5≤ y ≤2}
C. {y∨−5≤ y ≤−1∧−1<y<2}
D. {y∨−9≤ y ≤0∧2<y ≤3}
35.
AII.7b 36.
What is the zero of g(x)=16x−1024
AII.7d
38. Throughout which interval is increasing?
A B C D
39.
AII.7e
40. The graphs of all share an asymptote of
Directions: You must select all correct intervals. Directions: Circle all of the points that apply.
A x = 2 B x = 1 C y = 2 D y = 1
41.
AII.7f
42. Which of the following describes the end behavior of 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.
Directions: Write the correct equation in the space provided.
Identify the equation of the horizontal asymptote and the equation of the vertical
asymptote of g(x)=2x−1 x+5
x=−1
5 x=0 y=0 x=1 2 x=−5
AII.7g
45. Which of the following is the inverse of ?
A B C D
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.
Directions: Type your answer in the box. Your answer must be in decimal form.
Let g(x)=3x2−5 and h(x)=4x−7. What is g¿
The zeros of a cubic function f(x) are -2, 3
49. How many non-real solutions exist for the polynomial function?
?
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.
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.
Year Number of
A B C D
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 variesdirectly 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 for6 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.
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
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%
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