a 2 x y 1 y SOL AII.1a

Similar documents
a 2 x y 1 x 1 y SOL AII.1a

Topic: Expressions & Operations AII.1

Learning Goals. College of Charleston Department of Mathematics Math 101: College Algebra Final Exam Review Problems 1

Algebra 1 Skills Needed for Success in Math

Math 030 Review for Final Exam Revised Fall 2010 RH/ DM 1

H.Algebra 2 Summer Review Packet

Algebra 2 Math Curriculum Pacing Guide (Revised 2017) Amherst County Public Schools. Suggested Sequence of Instruction and Pacing

INTRODUCTION GOOD LUCK!

The American School of Marrakesh. Algebra 2 Algebra 2 Summer Preparation Packet

3.1 Graphing Quadratic Functions. Quadratic functions are of the form.

Algebra 2 Curriculum Guide Lunenburg County Public Schools June 2014

A. Simplifying Polynomial Expressions

Glossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards. An equation that contains an absolute value expression

FINAL EXAM REVIEW ITEMS Math 0312: Intermediate Algebra Name

Algebra 2 Honors Summer Packet 2018

Pacing Guide. Algebra II. Robert E. Lee High School Staunton City Schools Staunton, Virginia

Algebra 1 Skills Needed to be Successful in Algebra 2

Math Intermediate Algebra

Algebra II Notes Unit Five: Quadratic Functions. Syllabus Objectives: 5.1 The student will graph quadratic functions with and without technology.

Algebra 2 CPA Summer Assignment 2018

COUNCIL ROCK HIGH SCHOOL MATHEMATICS. A Note Guideline of Algebraic Concepts. Designed to assist students in A Summer Review of Algebra

Applied Algebra II Semester 2 Practice Exam A DRAFT. 6. Let f ( x) = 2x A. 47 B. 92 C. 139 D. 407

Ch 5 Alg 2 L2 Note Sheet Key Do Activity 1 on your Ch 5 Activity Sheet.

MATH 0312 FINAL EXAM REVIEW ITEMS

Unit 2 Notes Packet on Quadratic Functions and Factoring

Polynomial and Rational Functions

STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA II. 2 nd Nine Weeks,

Algebra II Curriculum Guide

Name Period Date. Practice FINAL EXAM Intro to Calculus (50 points) Show all work on separate sheet of paper for full credit!

College Algebra Final, 7/2/10

Summer Math Packet (revised 2017)

MATH 115: Final Exam Review. Can you find the distance between two points and the midpoint of a line segment? (1.1)

Use the slope-intercept form to graph the equation. 8) 6x + y = 0

WESTMORELAND COUNTY PUBLIC SCHOOLS Integrated Instructional Pacing Guide and Checklist Algebra II

Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs

Algebra/Pre-calc Review

ALGEBRA II CURRICULUM GUIDE Overview and Scope & Sequence

Graphing Calculator Computations 2

Northwest High School s Algebra 2/Honors Algebra 2

5. Perform the indicated operation and simplify each of the following expressions:

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

6.4 graphs OF logarithmic FUnCTIOnS

Mathematics Online Instructional Materials Correlation to the 2009 Algebra II Standards of Learning and Curriculum Framework

1.2 Functions and Their Properties PreCalculus

Summer Review For Students Entering Algebra 2

Find the distance between the pair of points. 2) (7, -7) and (3, -5) A) 12 3 units B) 2 5 units C) 6 units D) 12 units B) 8 C) 63 2

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MCPS Algebra II Pacing Guide

Pre-Calculus Summer Packet

(2.5) 1. Solve the following compound inequality and graph the solution set.

Course 15 Numbers and Their Properties

ACCUPLACER MATH 0311 OR MATH 0120

Algebra II Notes Unit Six: Polynomials Syllabus Objectives: 6.2 The student will simplify polynomial expressions.

( ) ( ) ( )( ) Algebra II Semester 2 Practice Exam A DRAFT. = x. Which expression is equivalent to. 1. Find the solution set of. f g x? B.

Are You Ready For Math Analysis?

Diagnostic Tests Study Guide

KEY IDEAS. Chapter 1 Function Transformations. 1.1 Horizontal and Vertical Translations Pre-Calculus 12 Student Workbook MHR 1

Ready To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions

McKinney High School AP Calculus Summer Packet

Algebra II. Math Curriculum Guide

Name Please print your name as it appears on the class roster.

math FALL developmental mathematics sullivan 1e

Are You Ready For Math Analysis?

Solutions to the Math 1051 Sample Final Exam (from Spring 2003) Page 1

ZETA MATHS. Higher Mathematics Revision Checklist

STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS ALGEBRA II. 1 st Nine Weeks,

review math0410 (1-174) and math 0320 ( ) aafinm mg

Summer Review Packet for Students Entering AP Calculus BC. Complex Fractions

PreCalculus. Ocean Township High School Mathematics Department

20 points Completion 20 points - Accuracy

EOC Review. Algebra I

ALGEBRA 2. Background Knowledge/Prior Skills Knows what operation properties hold for operations with matrices

Math RE - Calculus I Functions Page 1 of 10. Topics of Functions used in Calculus

Algebra Review C H A P T E R. To solve an algebraic equation with one variable, find the value of the unknown variable.

Ready To Go On? Skills Intervention 12-1 Inverse Variation

Secondary Mathematics 2 Table of Contents

CHAPTER 2 Polynomial and Rational Functions

Algebra II Vocabulary Word Wall Cards

Algebra 2 End of Term Final REVIEW

Pre AP Algebra. Mathematics Standards of Learning Curriculum Framework 2009: Pre AP Algebra

LESSON #48 - INTEGER EXPONENTS COMMON CORE ALGEBRA II

Algebra II Practice Semester Exam Specification Sheet

First Semester Final Review NON-Graphing Calculator

College Algebra with Corequisite Support: Targeted Review

Secondary Honors Algebra II Objectives

2.1 Evaluate and Graph Polynomial

Algebra II Standards of Learning Curriculum Guide

Algebra Placement Test Review 1

Answer Explanations. The SAT Subject Tests. Mathematics Level 1 & 2 TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE

MATHEMATICS Mathematics Curriculum---Hanover County Public Schools Revised Summer Inequalities

+ = + + = x = + = + = 36x

Answers for the problems can be found at the end of this packet starting on Page 12.

Graph the linear system and estimate the solution. Then check the solution algebraically.

All rights reserved. Reproduction of these materials for instructional purposes in public school classrooms in Virginia is permitted.

review for math TSI 55 practice aafm m


math0320 FALL interactmath sections developmental mathematics sullivan 1e

Advanced Algebra Scope and Sequence First Semester. Second Semester

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Lesson #33 Solving Incomplete Quadratics

Transcription:

SOL AII.a The student, given rational, radical, or polnomial epressions, will a) add, subtract, multipl, divide, and simplif rational algebraic epressions; Hints and Notes Rules for fractions: ) Alwas factor an squared terms completel watch for greatest common factors ) Addition & Subtraction of fractions require a common denominator ) When dividing fractions flip the second fraction and multipl 4) Comple Fractions simplif numeration, simplif the denominator, then divide PRACTICE AII.a. Simplif: a a a a a a a a. Simplif: a a a a G.. Simplif: m m m m m m m m m Henrico Count Public Schools EOC Algebra II Review 0-0

PRACTICE AII.a 4. Multipl: 6 4 5 4 7. Divide: 4 8. Simplif: 7 5 4 8 60 G. 4 4 5 5 4 5 5. Multipl: 4 9 6 4 0 6. Divide: 4 5 4 5 4 7 4 7 5 5 7 0 0 4 4 4 G. G. 9 5 5 7 5 9. Simplif: 64 6 8 6 8 6 5 8 6 9 0 4 6 64 4 8 4 5 Henrico Count Public Schools EOC Algebra II Review 0-0

SOL AII.b The student, given rational, radical, or polnomial epressions, will add, subtract, multipl, divide, and simplif radical epressions containing rational numbers and variables, and epressions containing rational eponents; HINTS AND NOTES PRACTICE AII.b. Simplif: 6. Simplif: 9 7 5 8 4 5 Simplif Radicals ) Take root of coefficient ) Divide eponents of radicand b the inde; answer outside, remainder inside G. 5 4 7 4. Simplif: 4 6 6 6 4 6 6 5 4 6 4. Simplif: G. 6 5 4 5 6 Henrico Count Public Schools EOC Algebra II Review 0-0

HINTS AND NOTES Adding & Subtracting Radical Epressions Onl radical epressions with like radicands (stuff under the radical) can be added or subtracted. PRACTICE AII.b 5. Simplif: 5 49 0 5 5 4 0 5 4 74 6. Simplif: 8 7 4 6 6 4 7 G. 6 7 74 Rationalize Denominator inde or root is radicand is The radicand contains no fractions in the answer. No radicals can be in the denominator of the answer. 6 7 6 6 7. Rationalize the denominator: 4 4 4 4 8. Rationalize the denominator: G. 4 4 Henrico Count Public Schools 4 EOC Algebra II Review 0-0

HINTS AND NOTES Multipling & Dividing Radicals n n n a b ab n n a b n a b PRACTICE AII.b 4 4 9. Multipl: 9 8 9 8 0. Divide: 8 5 6 5 Conjugate pairs: and G. 8 5 8 5 Properties of Rational Eponents 6 5. Simplif: 4 ( 4 )( ). m n m n a a a. ( a ) a m n mn. ( ab) m a m b m 9 8 8 8 6 6 8 6 6 8 4. 5. 6. a a a m m n a b a a m m m n a b m m. Simplif: G. 4 4 6 4 9 4 ( )( 6 ) 4 6 Henrico Count Public Schools 5 EOC Algebra II Review 0-0

HINTS AND NOTES PRACTICE AII.b. Simplif: 7 4 6 9 7 9 4. Simplif: 7 8 7 G. 4 5 6 4 5 6 6 4 4 9 8 5 Henrico Count Public Schools 6 EOC Algebra II Review 0-0

SOL AII.c The student, given rational, radical, or polnomial epressions, will write radical epressions as epressions containing rational eponents and vice versa. PRACTICE AII.c. Rewrite 5 6 using rational eponents. Don t Forget: a a b a b b 6 5 6 5 5 6 5 6. Rewrite 8 7 using rational eponents G. 8 7 7 8 7 8 8 7. Simplif and write in simplest radical form: 5 5 0 7 7 0 4. Simplif and write in simplest radical form: 5 6 G. 6 6 5 5 Henrico Count Public Schools 7 EOC Algebra II Review 0-0

Henrico Count Public Schools 8 EOC Algebra II Review 0-0

SOL AII.d The student, given rational, radical, or polnomial epressions, will factor polnomials completel. PRACTICE AII.d. Which is the factored form of 64? Was to Factor: ) Greatest Common Factor w ( w) (4 )(4 4 ) (4 )(6 ) (4 )(6 4 ) (4 )(6 4 ) ) Difference of Squares. Factor: 00 a b a b a b ( )( ) ( 50)( 50) G. ( 0)( 0) ) Sum of Cubes* a b ( a b)( a ab b ) ( 0)( 0) ( 5)( 4) 4) Difference of Cubes* a b ( a b)( a ab b ) * (a [same sign] b)(a [opposite sign] ab [alwas positive] b ) 5) Trinomials 6) Factor b Grouping (leading coefficient) four terms 7) Completing the square. Factor: 4. Factor: 9 6 9 6 9 ( 7 ) 5 8 ( 7 ) 6 ( 7 ) 6 (9 ) 7 4 ( )( 4) G. ( 4)( ) ( )( 4) ( )( 4) Henrico Count Public Schools 9 EOC Algebra II Review 0-0

PRACTICE AII.d 5. Factor: ( )( ) ( )( ) ( )( ) ( )( ) 6. Factor: 8u u (6u )( u ) 9. Factor: b ( b 4) 64 ( b 4)( b 4)( b 4) ( b 4)( b 4b 6) ( b 4)( b 4b 6) 0. Find the term that must be added to both sides of the equation so that the equation can be solved b the method of completing the square 8. 7. G. (6u )( u ) (6u )( u ) (6u )( u ) 5 represents the area of a rectangle. Which of the following could represent the length of one side of the rectangle? 4 6 G. 64. Find the term that must be added to both sides of the equation so that the equation can be solved b the method of completing the square 6 9. 8 9 6-9 8. 5 represents the area of a rectangle. Which of the following could represent the length of one side of the rectangle? G. Henrico Count Public Schools 0 EOC Algebra II Review 0-0

AII. The student will investigate and appl the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the n th term, and evaluating summation formulas. Notation will include Σ and a n. Term Formulas A: a a ( n ) d G: n a a r n n Sum Formulas A: G: IG: S n a a n ( ) ( n a ) r S r a S r If ou forget the formulas, just list series out and count terms or add terms on calculator. PRACTICE AII.. Insert two arithmetic means between - and., 0, 8, 9 4, 7. Evaluate: 984 G. 000 05 050 5 n (n ). Which is an arithmetic sequence?, 5, 9, 4... 00, 50,.5,.6..., 0, 7, 4... -8, -4, -, -... 4. If an () n which of the following represents a? G. 8 4 7 5. Which of the following represents (n )? 6 69 9 9 8 n 6. Find the net term in the sequence 8, 5,, -. - G. - -4-5 Henrico Count Public Schools EOC Algebra II Review 0-0

SOL AII. The student will perform operations on comple numbers, epress the results in simplest form using. patterns of the powers of i, and identif field properties that are valid for the comple numbers. Calculator (TI-8 or TI-84) Use i button on the calculator, however remember to use the parentheses to separate operations. EX. i i ( i) ( i) Don t Forget: i PRACTICE AII. 4i. Simplif: i i i 5i. Simplif: G. 47 65 65 i 47 65 65 i 5i 7 4i 47 65 65 i 47 65 65 i. Simplif: 7 i 8 i 57 i 65 57 i 65 57 i 65 57 i 65 Henrico Count Public Schools EOC Algebra II Review 0-0

PRACTICE AII. 4. Simplif: ( 46i G. 4i 4i 46i 5. Simplif: ( 7 i )( 9 4 i ) 7 59i 9 59i 9 67i 7 67i 6. Simplif: ( 8 i) (7 6 i) 0 i G. 0 i 69 8i 4 4i 7. Simplif: (6 6 i ) ( i ) 7 8i 7 8i 6 8i 5 4i 8. Simplif: ( 4 i) (5i 6) 4 i G. 9 4i 8 4i 5i Henrico Count Public Schools EOC Algebra II Review 0-0

PRACTICE AII. To simplif powers of i Change to ( i ) to (- ) Eample ( i ) Power then change 9. Simplif: i i 44 i i ( i ) i ( ) ( ) i i i 0. Simplif: G. i i 7 i Don t Forget: i. Write the given epression in terms of i : 8. 8i i i 8 i. Write the given epression in terms of i : 64. 8 G. 8i 8i 8 Henrico Count Public Schools 4 EOC Algebra II Review 0-0

SOL AII.4a The student will solve, algebraicall and graphicall, absolute value equations and inequalities. Graphing calculators will be used for solving and for confirming the algebraic solutions. To Solve Absolute Value Equations Set = to positive value Set = to negative value To Solve Absolute Value Inequalities. Write equation as is. Write equation, switch inequalit smbol, change to negative value PRACTICE AII.4a. Which graph represents the solution of 6 9? - - 0 4 5 6 - - 0 4 5 6 - - 0 4 5 6-6 -5-4 - - - 0. Solve: 4 0 G. 4 0 no solution To Graph Absolute Value Inequalities GreatOR Than Less ThAND OR. (Open Left & Right) (Closed Left & Right) (Open Between) (Closed Between). Solve: 4 5, 5,,, 4. Solve and Graph: 5 9 8 7 6 5 4 0 G. 8 7 6 5 4 0 8 7 6 5 4 0 8 7 6 5 4 0 Henrico Count Public Schools 5 EOC Algebra II Review 0-0

SOL AII.4b The student will solve, algebraicall and graphicall, quadratic equations over the set of comple numbers; Graphing calculators will be used for solving and for confirming the algebraic solutions. Methods for Solving Quadratics. Factor. Complete the Square. Square Root Method 4. Quadratic Formula PRACTICE AII.4b. Solve: 4 4 0,, 4,, b b 4ac a negative number use i Calculator Hints: To Find Roots, Solutions, Zeros. Graph quadratic in =. Press nd Trace. Press # for zeros 4. Left Enter 5. Right Enter 6. (Guess) Enter. Solve:, G. i. i, 4 8 i, i. Solve:,,,. 4. Solve:, G., 0 ( ) 8, No Solution Henrico Count Public Schools 6 EOC Algebra II Review 0-0

PRACTICE AII.4b 5. Solve: 4 0 4 4, 4, 4 4, 4 4 4, 6. Solve: 0 0 5, G.,5 5, 5, 7. Solve: 6 5 i 5 8. Which statement is true for the quadratic 0 4 48? The product of the roots is 4. G. The product of the roots is 4. The sum of the roots is 4. Henrico Count Public Schools 7 EOC Algebra II Review 0-0

The sum of the roots is. PRACTICE AII.4b Describe nature of roots. You can graph the quadratic in the calculator look for the number of times the graph touches the -ais. Touches once One real solution Touches twice Two real solutions Does not touch Two Imaginar solutions. Use the discriminant b 4ac Discriminant > 0 Two real solutions Discriminant < 0 Two imaginar solutions Discriminant = 0 One real solution 9. Find the quadratic equation with roots and 5 7 6 0 5 7 6 0 5 7 6 0 5 7 6 0. 5 0. Find the quadratic equation with roots and 5. G. 5 0 5 0 5 0 5 0. Describe the nature of the roots of the equation 0. One real root Two imaginar roots One real root and one imaginar root Two real roots. Describe the nature of the roots of the equation 4 4 5 0. Two imaginar roots G. Two real roots One real root One real root and one imaginar root Henrico Count Public Schools 8 EOC Algebra II Review 0-0

SOL AII.4c The student will solve, algebraicall and graphicall, equ epressions; Graphing calculators will be used for solving and for con PRACTICE AII.4c Solve a rational equation. Determine the least common denominator.. Eliminate the fraction(s) b multipling ALL terms b the least common denominator.. Simplif the terms. 4. Solve the resulting equation. 5. Check our answers to make sure the solution does not make the fraction undefined.. Solve:. Solve: G.. Solve: Henrico Count Public Schools 9 EOC Algebra II Review 0-0

PRACTICE AII.4c 4. Solve: G. 5. Solve: Henrico Count Public Schools 0 EOC Algebra II Review 0-0

SOL AII.4d The student will solve, algebraicall and graphicall, equations containing radical epressions. Graphing calculators will be used for solving and for confirming the algebraic solutions. PRACTICE AII.4d. Solve: 4 Solve a radical equation Isolate the radical Square or cube both sides 0 5 0 and 5 no solution. Solve: 9 7 G. 7 7 and 7 0 and 7. Solve: 4 7 7 7 7 and Henrico Count Public Schools EOC Algebra II Review 0-0

SOL AII.5 The student will solve nonlinear sstems of equations, including linear-quadratic and quadratic-quadratic, algebraicall and graphicall. Graphing calculators will be used as a tool to visualize graphs and predict the number of solutions. PRACTICE AII.5. How man solutions are there for this sstem? Number of solutions Number of points of intersection on graph 0. Solve: 4 7 (-4, -4) G. (4, 5) (5, 8) (-4, -9). Which is the solution to the sstem below? {(0, 7),(0,7)} {( 7,0),(7,0)} {(0, 5),(0,5)} 4. Solve the sstem graphicall: 49 64 8 {(0, 8),(0,8)} G. {(0, 9),(0,9)} {( 8,0),(8,0)} Henrico Count Public Schools EOC Algebra II Review 0-0

SOL AII.6 The student will recognize the general shape of function (absolute value, square root, cube root, rational, polnomial, eponential, and logarithmic) families and will convert between graphic and smbolic forms of functions. A transformational approach to graphing will be emploed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions. PRACTICE AII.6. Which of the following is the graph of a quadratic?. Which of the following could represent? G. Henrico Count Public Schools EOC Algebra II Review 0-0

For the functions below, use these rules to translate the graph: h>0 shifts right h units h<0 shifts left h units k>0 shifts up k units k<0 shifts down k units PRACTICE AII.6. Which of the following is most likel the equation represented b this graph? 4 a<o reflects across ais change to, reflects across ais 4. Given the graph: 5 4 5 4 4 5 4 5 Write an equation for it using a translation of =. G. Henrico Count Public Schools 4 EOC Algebra II Review 0-0

PRACTICE AII.6 5. Which most likel represents the equation of the graph below? 6. What could be the graph of? G. 4 4 4 4 4 4 4 Henrico Count Public Schools 5 EOC Algebra II Review 0-0

SOL AII.7a The student will investigate and analze functions algebraicall and graphicall. Ke concepts include domain and range, including limited and discontinuous domains and ranges. Graphing calculators will be used as a tool to assist in investigation of functions. PRACTICE AII.7a domain: values range: values Eliminate values in domain and range when:. If the domain of is limited to {-, -,, }, what is the range? {-, -5, -, 5} {-, 5} {-, 5} {, 5, 5, }. State the domain and range of this graph: division b zero radicand (number under radical) is negative Domain:, Range: { } G. Domain: { }, Range: Domain: { > - and < }, Range: Domain:, Range: { }. Find the domain of. all real numbers ecept = and = - all real numbers ecept = and = all real numbers ecept = - and = all real numbers ecept = - and = - 4. Find the domain of. all real numbers ecept = G. all real numbers ecept = and = - all real numbers ecept = - all real numbers. Henrico Count Public Schools 6 EOC Algebra II Review 0-0

SOL AII.7b The student will investigate and analze functions algebraicall and graphicall. Ke concepts include zeros. Graphing calculators will be used as a tool to assist in investigation of functions. PRACTICE AII.7b Zeros when f() = 0 when graph crosses or touches the ais number of comple zeros = n (degree of polnomial) number of real zeros < n (degree of polnomial) factor polnomial to find zeros. What are the zeros of? and and - and and. Which is a zero of the function f() = - - 6? 0 G. 6-6. Find all the real zeros of the function. 0,, 6 0, 0,, 7, 6 7 56 84 4 Henrico Count Public Schools 7 EOC Algebra II Review 0-0

SOL AII.7c The student will investigate and analze functions algebraicall and graphicall. Ke concepts include - and - intercepts. Graphing calculators will be used as a tool to assist in investigation of functions. and intercepts To find the -intercept, plug in zero for. PRACTICE AII.7c. Graph 7 5 5 b determining its - and -intercepts. To find the -intercept, plug in zero for.. Graph 5 5 b determining its - and -intercepts. G. Henrico Count Public Schools 8 EOC Algebra II Review 0-0

SOL AII.7d The student will investigate and analze functions algebraicall and graphicall. Ke concepts include intervals in which a function is increasing or decreasing. Graphing calculators will be used as a tool to assist in investigation of functions. Practice AII.7d. For what values of is this function increasing? Increasing Function - -value increases as the -value increases (left to right) Decreasing Function -value decreases as the -value increases (left to right) 8 6 4 0 8 6 4 0 8 6 4 0 8 6 4 4 6 8 0 4 6 8 0 4 6 8 (-4, ) (, ) (-,-4) and (, ) (-, ). For what intervals is this function decreasing? 4 4 4 4 (0,) and (,) G. (-,0) and ((,) (-,0) and (, ) (,) and (, ) Henrico Count Public Schools 9 EOC Algebra II Review 0-0

SOL AII.7e The student will investigate and analze functions algebraicall and graphicall. Ke concepts include asmptotes. Graphing calculators will be used as a tool to assist in investigation of functions. Vertical Asmptotes Possible to have multiple vertical asmptotes Vertical asmptotes are when the denominator = 0 Factor denominator Practice AII.7e. What are the vertical asmptote(s) for the function? = -, = ½ = - ½, = = = -, = Horizontal Asmptotes One or no horizontal asmptote TEST degree numerator < =0 degree denominator degree num = = degree denom Horiz As. What is the horizontal asmptote for the function? = 0 G. = = none. Which of the following functions will have a horizontal asmptote at =? degree num > degree denom none (ma have slant asmptote) Henrico Count Public Schools 0 EOC Algebra II Review 0-0

SOL AII.7f The student will investigate and analze functions algebraicall and graphicall. Ke concepts include end behavior. Graphing calculators will be used as a tool to assist in investigation of functions. End Behavior Use term with highest eponent + coefficient - coefficient Even degree Odd degree PRACTICE AII.7f. Determine the end behavior of the graph of. Down to the left, Up to the right Up to the left, Down to the right Up to the left, Up to the right Down to the left, Down to the right. Determine the end behavior of the graph of. Down to the left, Up to the right G. Up to the left, Down to the right Up to the left, Up to the right Down to the left, Down to the right. Determine the end behavior of the graph of. Down to the left, Up to the right Up to the left, Down to the right Up to the left, Up to the right Down to the left, Down to the right 4. Determine the end behavior of the graph of Down to the left, Up to the right G. Up to the left, Down to the right Up to the left, Up to the right Down to the left, Down to the right Henrico Count Public Schools EOC Algebra II Review 0-0.

SOL AII.7g The student will investigate and analze functions algebraicall and graphicall. Ke concepts include inverse of a function. Graphing calculators will be used as a tool to assist in investigation of functions. PRACTICE AII.7g To find an inverse ) Switch and ) Solve for. If, find the inverse of f(). A. Graph of inverse function f - () is reflection of f() across the graph =.. Find the inverse given the function f ( ) 5 9. 5 9 G. 9 5 ( 9) 5 5 9. Which graph represents a function and its inverse? 4 4 6 5 4 4 6 5 4 4 4 4 5 5 6 6 4 4 6 5 4 4 4 5 6 6 5 4 4 4 5 6 Henrico Count Public Schools EOC Algebra II Review 0-0

Logarithmic and Eponential Equations Eponential and logarithmic functions are inverses of each other. is the equivalent of Log rules PRACTICE AII.7g 4. Use the graphing calculator to evaluate log 5.98. 5.98 G..648 5.98.76 5. Use the graphing calculator to evaluate log 7..68.77.4 -.68 6. Evaluate. G. 7. Solve. = 0 = =.7 = 0.457 Change of Base Formula 8. Solve. =.6 G. = -. =.86 =.6 9. Solve. 7.5 7.5 6.5.5 0. Solve for : G. Henrico Count Public Schools EOC Algebra II Review 0-0

SOL AII.7h The student will investigate and analze functions algebraicall and graphicall. Ke concepts include composition of multiple functions. Graphing calculators will be used as a tool to assist in investigation of functions. Composite Functions f(g()) is equivalent to Practice AII.7h. If and, which is correct? To find f(g()): Substitute the entire epression for g() into all of the s in the epression for f().. If and, which is the value of? -5 G. 48-00 -50. Find and. = = = = 4. Find. G. = Henrico Count Public Schools 4 EOC Algebra II Review 0-0

SOL AII.8 The student will investigate and describe the relationships among solutions of an equation, zeros of a function, -intercepts of a graph, and factors of a polnomial epression. Equivalent statements: k is a zero of the polnomial function (-k) is a factor of f() k is a solution of the polnomial equation f()=0 k is an -intercept for the graph = f() PRACTICE AII.8. Which could be the graph of? 4 4 4 Possible Rational Roots 4. Name the possible rational roots of. Descartes Rule of Signs gives number and sign of real roots G. number of sign changes in f() is number of positive real roots or is less than the number b multiple of number of sign changes in f(-) is number of negative real roots or is less than the number b multiple of. Determine consecutive values of between which each real zeros is located for There are zeros between = and =, =0 and =-. There are zeros between =0 and =-. There are zeros between =0 and =. There are zeros between = and =, =- and =0, =- and =-. Henrico Count Public Schools 5 EOC Algebra II Review 0-0

Imaginar roots must be conjugate pairs (a + bi) (a bi PRACTICE AII.8 4. Give the possible number of imaginar roots for:. 5 G. 4 5. Find the roots of. 6. Write a polnomial function with zeros at -5, - and. G. 7. Find all of the zeros of..6,, -.6, - -.6, -, -.6, 8. A polnomial equation with rational coefficients has the roots. Find two additional roots. F G. Henrico Count Public Schools 6 EOC Algebra II Review 0-0

SOL AII.9 The student will collect and analze data, determine the equation of the curve of best fit, make predictions, and solve real-world problems, using mathematical models. Mathematical models will include polnomial, eponential, and logarithmic functions. PRACTICE AII.9. Determine the correlation for the scatter plot. Negative slope & correlation Strong positive correlation. Strong negative correlation. No correlation Not enough information given. Positive slope & correlation Line of best fit: Look for slope & -intercept Calculator:. Put data into lists. Look at the given scatter plot. This data best fits what tpe of equation? Linear G. Eponential Logarithmic Quadratic Stat-edit-L -L. Stat-calc-4:Lin Reg-enter. Equation for line of best fit is = a + b and substitute the values given for a and b.. Which of the following equations represents the line of best fit for the following data? X 6 6 4 44 44 45 64 Y 5 5 6 8 9 9 5 4.8 0.5 0.4 0.4.4.4 Henrico Count Public Schools 7 EOC Algebra II Review 0-0

PRACTICE AII.9 4. The table shows the number of students enrolled in the Honors Algebra-Trig program at Menchville High School the first 5 ears since its initiation. What is our prediction for the number of students in the eighth ear? Year (X) Number of Students (Y) 55 7 84 4 97 5 08 9 students G. 4 students 4 students 49 students 5. Which is most likel the equation for the curve of best fit for the scatterplot below? Henrico Count Public Schools 8 EOC Algebra II Review 0-0

SOL AII.0 The student will identif, create, and solve real-world problems involving inverse variation, joint variation, and a combination of direct and inverse variations. PRACTICE AII.0 Inverse Variation varies inversel with k k Direct Variation. The area (A) of a circle varies directl as the square of the radius (r). If k is the constant of proportionalit, which is the formula for this relationship? k A r A kr A kr r ka varies directl with k k Joint Variation z varies jointl with and z = k k =. The frequenc of a radio signal varies inversel as the wave length. A signal of frequenc 00 kilohertz (khz), which might be the frequenc of an AM radio station, has a wave length 50 m. What frequenc has a signal wave length of 400m? 8 khz G. 750 khz 50 khz 90 khz. Suppose that varies jointl with w and and inversel with z. Write the equation that models the relationship. Henrico Count Public Schools 9 EOC Algebra II Review 0-0

SOL AII. The student will identif properties of a normal distribution and appl those properties to determine probabilities associated with areas under the standard curve. PRACTICE AII. Normal Distribution. Grades on an Algebra test follow a normal distribution with a mean of 74 and a standard deviation of. Approimatel what percentage of the students have scores below 50? 4% 4% 0% %. Grades on an Algebra test follow a normal distribution with a mean of 8 and a standard deviation of 8. How man of the 5 students scored above a 90%? Standard Normal Distribution Mean = μ = 0 Standard Deviation = σ = z-score 4 students 9 students students not enough information. Susan scored a 8 on the math portion of the ACT which had a μ=0 and σ =5. She scored a 60 on the math portion of the SAT which had a μ=500 and a σ =80. Which test score has the higher percentile and what was that percentile? ACT, 94.5% SAT, 94.5% ACT, 98.4% SAT, 98.4% z-score reflects how man standard deviations it is above or below the mean Henrico Count Public Schools 40 EOC Algebra II Review 0-0

SOL AII. The student will compute and distinguish between permutations and combinations and use technolog for applications. PRACTICE ALGII. Fundamental Counting Principle. Mama Mia s Pizza offers three crust choices, twelve topping choices, and five cheese choices. If a customer can choose one crust choice, one topping, and one cheese choice, how man different pizzas are available? Event M can occur in m was and event N can occur in n was, then event M followed b event N can occur in m n was. Permutation Number of was to arrange items - order matters. Combination Number of was to arrange items - order does not matter. 0 pizzas 60 pizzas 6 pizzas 80 pizzas. How man different basketball teams of five plaers can be chosen from a team of siteen plaers? 4,68 teams G. 54,60 teams 80 teams 6 teams. The Technolog Club is electing officers. If there are to be four officers elected out of the thirt members, how man different possible election results are there? A 7,405 outcomes 6,80 outcomes 657,70 outcomes 0 outcomes 4 How man different five card hands can be dealt from a standard deck of fift-two cards? Permutation > Combination,598,960 hands,875,00 hands 60 hands 70,75 hands Henrico Count Public Schools 4 EOC Algebra II Review 0-0