Algebra 2(Y) Name: Algebra II End-of-Course Exam Period: Date: Review Score: / 5 Points

The Algebra II End-of-Course Exam contains questions that require the following types of answers: multiple-choice, short answer, and extended response. About 70% of you score will be based on the multiple-choice items, and about 30% will be based on the short-answer and extended response items. The exam is split into to two sessions. Our test dates are Tuesday, May 3, 2011, and Friday, May 6, 2011. In the first session, you may NOT use a calculator. In the second session, you may used calculator; so, be sure to bring your calculator.

OPERATIONS ON NUMBERS AND EXPRESSIONS (15% Priority) 1. Real Numbers a. Benchmark: Convert between and among radical and exponential forms of numerical expressions.

Refer to your notes on Section 7.1

1. Convert

!

53 2 in to radical form.

2. Convert

!

274 in to exponential form.

b. Benchmark: Simplify and perform operations on numerical expressions containing radicals. Refer to Section 7.2

3.

!

8 + 18

4.

!

10243 + 163 + 40965

c. Benchmark: Apply the laws of exponents to numerical expressions with rational and negative exponents to order and rewrite them in alternative forms. Refer to Sections 6.1 and 7.2

5.

!

35 • 32 6.

!

35

32

7.

!

35( )2

8.

!

35 2

9.

!

3"2 10.

!

2"3

7"1

2. Complex Numbers a. Benchmark: Represent complex numbers in the form a +bi, where a and b are real; simplify powers of pure

imaginary numbers. Refer to Section 5.7 11.

!

"8

12.

!

"256

13.

!

i5

b. Benchmark: Perform operations on the set of complex numbers. Refer to Section 5.7

14.

!

5 + 4i( )3 " 2i

3. Algebraic Expressions a. Benchmark: Convert between and among radical and exponential forms of algebraic expressions. Refer to

Sections 6.1, 7.1, and 7.2 15. Convert

!

x 5 4 in to radical form.

16. Convert

!

25a6b4 in to exponential form.

b. Benchmark: Simplify and perform operations on radical algebraic expressions. Refer to Section 5.5 17.

!

x 2 " 6x + 9 c. Benchmark: Apply the laws of exponents to algebraic expressions, including those involving rational and

negative exponents, to order and rewrite them in alternative forms. Refer to Sections 6.1 and 7.2

18.

!

5a4 • 3a3 19.

!

a4

a3

20.

!

a4( )3

21.

!

y "2

22.

!

z2 3 23.

!

r"3

t "2

24.

!

a"4

b3

25.

!

a3b5( )2

d. Benchmark: Perform operations on polynomial expressions. Refer to Sections 6.3 and 6.4 26.

!

x 4 + 5x 2 " 3x + 2( ) " 2x 2 " 8x +1( )

27.

!

3x 3 +17x 2 + 21x "11( ) ÷ x + 3( )

e. Benchmark: Perform operations on rational expressions, including complex fractions. Refer to Sections 9.3

to 9.6

28.

!

a + b( )1a

+1b

"

# $

%

& '

÷ ab

f. Benchmark: Identify or wrote equivalent algebraic expressions in one or more variables.

29. Rewrite

!

x "y 2

x

EQUATIONS AND INEQUALITIES (20% Priority) 1. Linear Equations and Inequalities a. Benchmark: Solve equations and inequalities involving the absolute value of a linear expression. Refer to

Section 4.5

30.

!

x " 6 # 8 b. Benchmark: Express and solve systems of linear equations in three variables with and without the use of

technology. Refer to Section 3.5

31.

!

2x + z =11

!

x + 2y = 7

!

2x " 4y + z = 3

c. Benchmark: Solve systems of linear inequalities in two variables and graph the solution set. Refer to Section 4.3

32.

!

3x " 2y < 7

!

x " 0

!

y " 0

d. Benchmark: Recognize and solve problems that can be represented by single variable linear equations or

inequalities or systems of linear equations or inequalities involving two or more variables. Interpret the solution(s) in terms of the context of the problem.

2. Nonlinear Equations and Inequalities a. Benchmark: Solve single-variable quadratic, exponential, rational, radical, and factorable higher-order

polynomial equations over the set of real numbers, including quadratic equations involving absolute value.

b. Benchmark: Solve single variable quadratic equations and inequalities over the complex numbers’ graph real solution sets on a number line. Refer to Chapter 5

33. Solve the given function using 3 different methods: factoring, completing the square, and the quadratic formula.

!

f (x) = x 2 +16x " 36 c. Benchmark: Use the discriminant, D=b2–4ac, to determine the nature of the solutions of the equation

ax2+bx+c=0. Refer to Section 5.9

d. Benchmark: Graph the solution set of a two-variable quadratic inequality in the coordinate plane.

e. Benchmark: Rewrite nonlinear equations and inequalities to express them in multiple forms in order to facilitate finding a solution set or to extract information about the relationships or graphs.

POLYNOMIAL AND RATIONAL FUNCTIONS (30% Priority) 1. Linear Equations and Inequalities a. Benchmark: Determine key characteristics of quadratic functions and their graphs. Refer to Sections 5.1

and 5.2

34. A quadratic function is given in three versions: standard form, vertex form, and intercept form. Graph the function. Identify the axis of symmetry, vertex, y-intercept, and x-intercepts (a.k.a. roots, zeros, solutions)

!

y = x 2 " 6x + 8

!

y = x " 3( )2 "1

!

y = x " 2( ) x " 4( )

b. Benchmark: Represent quadratic functions using tables, graphs, verbal statements, and equations.

Translate among these representations.

c. Benchmark: Describe and represent the effect that changes in the parameters of a quadratic function have on the shape and position of its graph.

d. Benchmark: Recognize, express, and solve problems that can be modeled using quadratic functions. Interpret their solutions in terms of the context.

2. Higher-Order Polynomial and Rational Functions a. Benchmark: Determine key characteristics of power functions in the form f(x)=axn, where a cannot equal 0,

and n is a positive integer, and their graphs. Refer to Section 5.2

35. What is the parent function of

!

y = 3 x " 2( )3 "1 b. Benchmark: Determine key characteristics of polynomial functions and their graphs.

c. Benchmark: Represent polynomial functions using tables, graphs, verbal statements, and equations. Translate among these representations.

d. Benchmark: Determine key characteristics of simple rational functions and their graphs. Refer to Section 9.2

e. Benchmark: Represent simple rational functions using tables, graphs, verbal statements, and equations Translate among these representations. Refer to Section 9.2

36. Graph

!

f (x) =x

x 2 " x+ 5

f. Benchmark: Recognize, express, and solve problems that can be modeled using polynomial and simple

rational functions. Interpret their solutions in terms of the context. EXPONENTIAL FUNCTIONS (20% Priority) 1. Exponential Functions a. Benchmark: Determine key characteristics of exponential functions and their graphs. Refer to Sections

8.1to 8.3

b. Benchmark: Represent exponential functions using tables, graphs, verbal statements, and equations. Represent exponential equations in multiple forms. Translate among these representations. Refer to Chapter 8 37. Determine which function displays exponential decay.

!

f (x) = 3• 2x

!

f (x) = 3• 2"x 38. Translate to

!

x 5 = 32 from exponential form to logarithmic form. c. Benchmark: Describe and represent the effect that changes in the parameters of an exponential function

have on the shape and position of its graph.

d. Benchmark: Recognize, express, and solve problems that can be modeled using exponential functions, including those where logarithms provide an efficient method of solution. Interpret their solutions in terms of the context.

FUNCTION OPERATIONS AND INVERSES (15% Priority) 1. Function Operations a. Benchmark: Combine functions by addition, subtraction, multiplication, and division. Refer to Sections 6.3,

6.4, and 7.4 39. If

!

f (x) = 3x 4 " 5x 3 + 3, and

!

g(x) = x 4 " 3x 3 + 2x 2 + 5, then

!

f (x) " g(x)= ?

40. If

!

h(x) = x 4 + x 3 + 2x 2 + 6x + 4 , and

!

j(x) = x +1, then

!

h(x) ÷ j(x)= ? b. Benchmark: Determine the composition of two functions, including any necessary restrictions on the

domain. Refer to Section 7.4 41. If

!

f (x) = 3x " 2 , and

!

g(x) = x +1, then find

!

f (g(x)) and

!

g( f (x))

42. If

!

f (x) =35

+25x

, and

!

g(x) =2

5x " 3, determine whether they inverses.

2. Inverse Functions a. Benchmark: Describe the conditions under which an inverse relation is a function. Refer to Section 7.5

b. Benchmark: Determine and graph the inverse relation of a function. 43. Determine the inverse relation for

!

f (x) = 3x 2 + 5

44. Determine

!

g(x) when

!

g"1(x) = 9x " 81

44. Graphically represent

!

f "1(x) when

!

f (x) =2x"7 3. Piecewise-Defined Functions a. Benchmark: Determine key characteristics of absolute value, step, and other piecewise-defined functions.

b. Benchmark: Represent piecewise-defined functions using tables, graphs, verbal statements, and equations. Translate among these representations.

c. Benchmark: Recognize, express, and solve problems that can be modeled using absolute value, step, and other piecewise-defined functions. Interpret their solutions in terms of the context.