1. 4 2y 1 2 = x = x 1 2 x + 1 = x x + 1 = x = 6. w = 2. 5 x

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "1. 4 2y 1 2 = x = x 1 2 x + 1 = x x + 1 = x = 6. w = 2. 5 x"

Transcription

1

2 .... VII x + x + = x x x 8 x x = x + a = a + x x = x + x x Solve the absolute value equations.. z = 8. x + 7 =. x =. x =. y = 7 + y VIII Solve the exponential equations.. 0 x = x+ = 00. x+ = 8. x (9 x ) = X Solve the radical equations.. y = 0. x + + = 8. x x + = 0. x x + = 0.. XI x + + = w + 7 = Solving Inequalities Solve the following inequalities. Express the answer graphically and using interval notation.. x +. (x + ) (x ). (x + ) > (x ) +. x 0. x +. x + + > 9 7. x + 8. x < 9. x x < 0 (. x x ) = 8 IX Solve the logarithmic equations.. log (x + ) = log ( x). log (x + ) = log (x). log (x + ) + log (x ) =. ln x + ln(x + ) = 0. ln x + ln(x + ) = ln. x = x+ 0. x + x.. x + x 0 (x + )(x ) x + 7 0

3 XII Lines and Regions. Given the equation x + y = 0, draw the graph and find the x and y intercepts and the slope.. Given the equation x =, draw the graph and find the x and y intercepts and the slope.. Given the equation y =, draw the graph and find the x and y intercepts and the slope.. Write, in slope-intercept form, the equation of the line that passes through the points (, ) and (, ). XIV Exponents and Radicals. 8x ( )... ( x / y / x / 0x y 9 ( a b 9a b 8 ) ). Write, in slope-intercept form, the equation of the line perpendicular to the line x y = and through the point (, ).. Graph the solution set of x y. 7. Graph the solution set of x + y < a a b x x + XIII Relations, Domain, and Range For each relation, state if it is a function, state the domain and the range, and sketch a graph.. y = x +. y = x. y = x x +. f(x) = x + +. f(x) = x x 9. x = y + 7. y = x + 8x XV Complex Numbers Perform the indicated operations and simplify ( i)( + i). ( i). i 7. i + i 8. y = x 9. y = x 0. h(x) = x x x

4 XVI Exponential Functions and Logarithms. Graph f(x) = x +. Graph g(x) = x. Express 8 = in logarithmic form.. Express log = in exponential form.. Solve log x =. Solve log x 9 = 7. Graph h(x) = log x 8. Use the properties of logarithms to completely expand log y 9. How long will it take $80 to be worth $000 if it is invested at % interest, compounded quarterly? XVII Systems of Equations and Matrices { x + y = 7. Solve the system x y = x + y + z =. Solve the system x + y + z = x + y + z = 0 [ ] [ ]. Simplify + 0. Multiply [ ]. Find the determinant of [ ]. Find the inverse of XVIII Applications. Sam made $0 more than twice what Pete earned in one month. If together they earned $70, how much did each earn that month?. A woman burns three times as many calories running as she does when walking the same distance. If she runs miles and walks miles to burn a total of 770 calories, how many calories does she burn while running mile?. A vertical pole is standing in a small lake. If one-sixth of the length of the pole is in the sand at the bottom of the lake, feet of the pole is in the water, and two-thirds the total length is in the air above the water, what is the length of the pole? XIX Conic Sections Graph the following. Find the center, foci, and, if they exist, asymptotes.. (x ) + y =.. (x + ) + (x + ) (y ) 9 (y ) 9. (x ) + y = = = Identify the conic section and write in standard form.. x x + y = 0. 9x + 8x + y y = 7. 9x + 8x y y = 99. x + y x = 0

5 XX Sequences and Series. Write out the first four terms of the sequence whose general term is a n = n.. Write out the first four terms of the sequence whose general term is a n = n.. Write out the first four terms of the sequence whose general term is a n = n +.. Find the general term for the following sequence:,, 8,,, 7,.... Find the general term for the following sequence:,,,,,.... Find the sum: (k ) k=0 7. Expand the sum: XXI Functions k=0 [( ] )x k y k k Let f(x) = x + 9 and g(x) = x. Find the following.. f( ) + g(). f() g(). f( ) g( ). f() g(). (g f)( ). f (g(x)) XXII Fundamental Counting Rule, Factorials, Permutations, and Combinations 8!. Evaluate!(8 )!. A particular new car model is available with five choices of color, three choices of transmission, four types of interior, and two types of engine. How many difference variations of this model car are possible?. In a horse race, how many different finishes among the first three places are possible for a ten-horse race?. How many ways can a three-person subcommittee be selected from a committee of seven people?. How many ways can a president, vice-president, and secretary be selected from a committee of seven people? XXIII Trigonometry. Graph f(x) = sin(x) through one period.. Graph g(x) = cos(x) through one period.. A man whose eye level is feet above the ground stands 0 feet from a building. The angle of elevation from eye level to the top of the building is 7. How tall is the building?. A man standing at the top of a meter lighthouse observes two boats. The angle of depression to the farther boat is 8. The angle of depression to the closer boat is 0. What is the distance between the two boats? 7. f () 8. f ( f () ) st boat nd boat lighthouse

6 Answers I II Factor the following polynomials.. a b a b 0a b = a b ( ab b ). Start by factoring out the common term 7x y + x y 0x y 0x y = x y [ 7xy + y 0xy 0 ] Factor [ this result using grouping. ] x y 7xy + y 0xy 0 = x }{{}}{{} y [7y(xy + ) 0(xy + )] = x y [(7y 0)(xy + )]. x y x y + 8xy 8 = ( x y + ) ( xy ). x 7xy + y = (x y)(x y). y + y = ( y ) ( y + ). 7x + y = 7 ( x + 8y ) = 7(x + y) ( x xy + y ) 7. 8r s = ( 9r s ) ( 9r + s ) = (r s)(r + s) ( 9r + s ) 8. Consider the polynomial u + u + = (u + ). If we let u = x + y, then (x + y) + (x + y) + = (x + y + ). Expand the following polynomials.. (x + )(x )(x ) = ( x ) (x ) = x x x +. (x + y) = x + xy + 9y. ( x + ) ( x ) = 8x + 8x 8x 8 = x. ( x x + ) = x x + 0x x + 9. (x + ) = x + x + 0x + 0x + x +. (x ) = x x + x 0x + x x + III Simplifying Rational Expressions Simplify the following. Assume all variable are greater than zero = = = + 7 = 8. 8 x = 9 x = = 9

7 IV V VI. x = Solve the linear equations.. x = =. y =. x = Solve the polynomial equations.. y = 8, y =. x = 0, x =, x =. x =, x = ± i. x = 0, x =. t = ± i. x =, x = ± i 7. x =, x = 8. y = ± 0. y = Solve the rational equations.. Working the problem, we get x =. However, x = causes the denominators to be zero in the original equation. Hence, there is no solution.. x =. x =. a =, a =. x =, x = VII Solve the absolute value equations.. z =, z = 7. x = 0, x = 0. No solution. An absolute value can not equal a negative number.. x =, x =. y = VIII IX. x =. x =. x =. x = Solve the exponential equations.. x =, x = Solve the logarithmic equations. Rules of logarithms: log b (x) = y x = b y log b (x y) = log b (x) + log b (y) log b (x y) = log b (x) log b (y) log b (x y ) = y log b (x) The argument and base of a logarithm must be positive.. x =. x =. x = ; Note that x = is not a solution since the argument of a logarithm must be positive.. x =. x = ln. x = ln ln 7

8 X Solve the radical equations.. y = 8. x < or x > or Interval: (, ) (, ). x = XI. x =. No solution. Substituting x = into the original equation fails.. x =. w =, w = Solving Inequalities Solve the following inequalities. Express the answer graphically and using interval notation.. x 0 or Interval: (, 0] 0 7. x 0 or x 0 or Interval: (, 0] [0, ) < x < 0 or Interval: (, 0) 9. (, ) 0. x 7 or Interval: (, 7]. x > or Interval: (, ) 7 0. (, ] [ ),. x or Interval: [, ]. [, ). 7 x [ or Interval: 7, ]. (, 7 ) [, ] 7 7 8

9 XII Lines and Regions. x y. x-intercept: (, 0) y-intercept: (0, ) slope: x + y < x-intercept: (, 0) y-intercept: none slope: none x-intercept: none y-intercept: (0, ) slope: XIII Relations, Domain, and Range For each relation, state if it is a function, state the domain and the range, and sketch a graph.. y = x + Domain: [, ) Range: [0, ) y = x +. y = x + 7 9

10 . y = x Domain: [0, ) Range: [, ) -. f(x) = x x 9 Domain: All real numbers except ± Range: (, ) y = x x + Domain: All real numbers except Range: All real numbers except 0. x = y + Domain: [, ) Range: (, ) f(x) = x + + Domain: (, ) Range: (, ] y = x + 8x Domain: (, ) Range: [, )

11 8. y = x Domain: (, 0] Range: [0, ) y = x Domain: (, ) Range: (0, ) 9 x 0. h(x) = x x Domain: All real numbers except and Range: (, 0] ( ), XIV Exponents and Radicals. 8x = x. 7 8 = 9. ( ) =.. ( ) x / y / = x7 x / 0x y 9 = x x y y ( a b ) = a b 9a b 8 7a a b = ab b = + x = x ( x ) x + x 9

12 XV Complex Numbers Perform the indicated operations and simplify.. 9 = 8i. 9 =. = 9. ( i)( + i) =. ( i) = 7 i. i = i 7. XVI i + i = i Exponential Functions and Logarithms. f(x) = x +. g(x) = x ( ). log 8 = =.. 7. h(x) = log x log log y ( 9. Use A = P + r ) kt ( k 000 = t.7 years. ) t XVII Systems of Equations and Matrices ( ).,, k +. 8 k + for k natural numbers. k [ ]

13 XVIII Applications. Let x = money Pete earns, x + 0 = money Sam earns (x + 0) + x = 70 x = 0 so Pete earns $0 and Sam earns $0.. Let x = calories burned walking, x = calories burned running (x) + x = 770 x = 70 so 0 calories burned running.. Let x = length of the pole. x + + x = x x = 0 feet. XIX Conic Sections Graph the following. Find the center, foci, and asymptotes if possible.. (x ) + y = Circle: center (, 0), radius (x + ) (y ) + = 9 Ellipse: center (, ), foci ( ± 7, ) (x + ) (y ). = 9 Hyperbola: center (, ), foci (, ), (, ), asymptotes y = x, y = x (x ) + y = - Parabola: vertex (, ), focus directrix y = Identify the conic section and write in standard form.. Circle: (x ) + y =. Ellipse: (x + ) + (y ) 9 (, ), = Hyperbola: (x + ) (y ) 9. Parabola: y = (x ) + =

14 XX Sequences and Series.,, 7, 0. 0,, 8, XXIII Trigonometry. Graph f(x) = sin(x) through one period..,, 9, 7. a n = n. a n = ( ) n = n - Π Π Π Π = 7. y + xy + x y + x y + x XXI Functions Let f(x) = x + 9 and g(x) = x. Find the following.. f( ) + g() = + =. Graph g(x) = cos(x) through one period. - Π Π Π. x = + 0 tan 7 9. ft.. Distance between the boats = tan tan 0.9 meters. Π. f() g() = 9 0 = 9. f( ) g( ) = 7 = 8. f() g() = 9 9 = 9 9. (g f)( ) = g (f( )) = g() = 9. f (g(x)) = f ( x ) = ( x ) + 9 = x + 7. f (x) = x 9 ; f () = 9 = 7 8. f ( f () ) = XXII. Fundamental Counting Rule, Factorials, Permutations, and Combinations

Accuplacer College Level Math Study Guide

Accuplacer College Level Math Study Guide Testing Center Student Success Center Accuplacer Study Guide The following sample questions are similar to the format and content of questions on the Accuplacer College Level Math test. Reviewing these

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. B) 6x + 4

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. B) 6x + 4 Math1420 Review Comprehesive Final Assessment Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Add or subtract as indicated. x + 5 1) x2

More information

Mock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28}

Mock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28} Mock Final Exam Name Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) 1) A) {- 30} B) {- 6} C) {30} D) {- 28} First, write the value(s) that make the denominator(s) zero. Then solve the

More information

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14 Final Exam A Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 1 1) x + 3 + 5 x - 3 = 30 (x + 3)(x - 3) 1) A) x -3, 3; B) x -3, 3; {4} C) No restrictions; {3} D)

More information

xvi xxiii xxvi Construction of the Real Line 2 Is Every Real Number Rational? 3 Problems Algebra of the Real Numbers 7

xvi xxiii xxvi Construction of the Real Line 2 Is Every Real Number Rational? 3 Problems Algebra of the Real Numbers 7 About the Author v Preface to the Instructor xvi WileyPLUS xxii Acknowledgments xxiii Preface to the Student xxvi 1 The Real Numbers 1 1.1 The Real Line 2 Construction of the Real Line 2 Is Every Real

More information

Albertson AP Calculus AB AP CALCULUS AB SUMMER PACKET DUE DATE: The beginning of class on the last class day of the first week of school.

Albertson AP Calculus AB AP CALCULUS AB SUMMER PACKET DUE DATE: The beginning of class on the last class day of the first week of school. Albertson AP Calculus AB Name AP CALCULUS AB SUMMER PACKET 2015 DUE DATE: The beginning of class on the last class day of the first week of school. This assignment is to be done at you leisure during the

More information

I) Simplifying fractions: x x. 1) 1 1 y x. 1 1 x 1. 4 x. 13x. x y xy. x 2. Factoring: 10) 13) 12) III) Solving: x 9 Prime (using only) 11)

I) Simplifying fractions: x x. 1) 1 1 y x. 1 1 x 1. 4 x. 13x. x y xy. x 2. Factoring: 10) 13) 12) III) Solving: x 9 Prime (using only) 11) AP Calculus Summer Packet Answer Key Reminders:. This is not an assignment.. This will not be collected.. You WILL be assessed on these skills at various times throughout the course.. You are epected to

More information

2. Determine the domain of the function. Verify your result with a graph. f(x) = 25 x 2

2. Determine the domain of the function. Verify your result with a graph. f(x) = 25 x 2 29 April PreCalculus Final Review 1. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line: y = 3x + 13 2. Determine the domain of the function. Verify your result with

More information

Spiral Review Probability, Enter Your Grade Online Quiz - Probability Pascal's Triangle, Enter Your Grade

Spiral Review Probability, Enter Your Grade Online Quiz - Probability Pascal's Triangle, Enter Your Grade Course Description This course includes an in-depth analysis of algebraic problem solving preparing for College Level Algebra. Topics include: Equations and Inequalities, Linear Relations and Functions,

More information

Algebra II Final Examination Mr. Pleacher Name (A) - 4 (B) 2 (C) 3 (D) What is the product of the polynomials (4c 1) and (3c + 5)?

Algebra II Final Examination Mr. Pleacher Name (A) - 4 (B) 2 (C) 3 (D) What is the product of the polynomials (4c 1) and (3c + 5)? Algebra II Final Examination Mr. Pleacher Name I. Multiple Choice 1. If f( x) = x 1, then f ( 3) = (A) - 4 (B) (C) 3 (D) 4. What is the product of the polynomials (4c 1) and (3c + 5)? A) 7c 4 B) 1c + 17c

More information

INTERNET MAT 117. Solution for the Review Problems. (1) Let us consider the circle with equation. x 2 + 2x + y 2 + 3y = 3 4. (x + 1) 2 + (y + 3 2

INTERNET MAT 117. Solution for the Review Problems. (1) Let us consider the circle with equation. x 2 + 2x + y 2 + 3y = 3 4. (x + 1) 2 + (y + 3 2 INTERNET MAT 117 Solution for the Review Problems (1) Let us consider the circle with equation x 2 + y 2 + 2x + 3y + 3 4 = 0. (a) Find the standard form of the equation of the circle given above. (i) Group

More information

Math 370 Semester Review Name

Math 370 Semester Review Name Math 370 Semester Review Name 1) State the following theorems: (a) Remainder Theorem (b) Factor Theorem (c) Rational Root Theorem (d) Fundamental Theorem of Algebra (a) If a polynomial f(x) is divided

More information

f(x) = 2x + 5 3x 1. f 1 (x) = x + 5 3x 2. f(x) = 102x x

f(x) = 2x + 5 3x 1. f 1 (x) = x + 5 3x 2. f(x) = 102x x 1. Let f(x) = x 3 + 7x 2 x 2. Use the fact that f( 1) = 0 to factor f completely. (2x-1)(3x+2)(x+1). 2. Find x if log 2 x = 5. x = 1/32 3. Find the vertex of the parabola given by f(x) = 2x 2 + 3x 4. (Give

More information

Final Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i

Final Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i Final Exam C Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 7 ) x + + 3 x - = 6 (x + )(x - ) ) A) No restrictions; {} B) x -, ; C) x -; {} D) x -, ; {2} Add

More information

Math 370 Semester Review Name

Math 370 Semester Review Name Math 370 Semester Review Name These problems will give you an idea of what may be included on the final exam. Don't worry! The final exam will not be this long! 1) State the following theorems: (a) Remainder

More information

4x 2-5x+3. 7x-1 HOMEWORK 1-1

4x 2-5x+3. 7x-1 HOMEWORK 1-1 HOMEWORK 1-1 As it is always the case that correct answers without sufficient mathematical justification may not receive full credit, make sure that you show all your work. Please circle, draw a box around,

More information

AP Calculus Summer Homework MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

AP Calculus Summer Homework MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. AP Calculus Summer Homework 2015-2016 Part 2 Name Score MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance d(p1, P2) between the points

More information

MR. YATES. Vocabulary. Quadratic Cubic Monomial Binomial Trinomial Term Leading Term Leading Coefficient

MR. YATES. Vocabulary. Quadratic Cubic Monomial Binomial Trinomial Term Leading Term Leading Coefficient ALGEBRA II WITH TRIGONOMETRY COURSE OUTLINE SPRING 2009. MR. YATES Vocabulary Unit 1: Polynomials Scientific Notation Exponent Base Polynomial Degree (of a polynomial) Constant Linear Quadratic Cubic Monomial

More information

3. Solve the following inequalities and express your answer in interval notation.

3. Solve the following inequalities and express your answer in interval notation. Youngstown State University College Algebra Final Exam Review (Math 50). Find all Real solutions for the following: a) x 2 + 5x = 6 b) 9 x2 x 8 = 0 c) (x 2) 2 = 6 d) 4x = 8 x 2 e) x 2 + 4x = 5 f) 36x 3

More information

Please print the following information in case your scan sheet is misplaced:

Please print the following information in case your scan sheet is misplaced: MATH 1100 Common Final Exam FALL 010 December 10, 010 Please print the following information in case your scan sheet is misplaced: Name: Instructor: Student ID: Section/Time: The exam consists of 40 multiple

More information

Mathematics Syllabus UNIT I ALGEBRA : 1. SETS, RELATIONS AND FUNCTIONS

Mathematics Syllabus UNIT I ALGEBRA : 1. SETS, RELATIONS AND FUNCTIONS Mathematics Syllabus UNIT I ALGEBRA : 1. SETS, RELATIONS AND FUNCTIONS (i) Sets and their Representations: Finite and Infinite sets; Empty set; Equal sets; Subsets; Power set; Universal set; Venn Diagrams;

More information

Algebra 2A Unit 1 Week 1 Day Activity Unit 1 Week 2 Day Activity Unit 1 Week 3 Day Activity Unit 2 Week 1 Day Activity

Algebra 2A Unit 1 Week 1 Day Activity Unit 1 Week 2 Day Activity Unit 1 Week 3 Day Activity Unit 2 Week 1 Day Activity Algebra 2A Unit 1 Week 1 1 Pretest Unit 1 2 Evaluating Rational Expressions 3 Restrictions on Rational Expressions 4 Equivalent Forms of Rational Expressions 5 Simplifying Rational Expressions Unit 1 Week

More information

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

ALGEBRA 2. Background Knowledge/Prior Skills Knows what operation properties hold for operations with matrices ALGEBRA 2 Numbers and Operations Standard: 1 Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers, and number

More information

1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.

1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents. Math120 - Precalculus. Final Review. Fall, 2011 Prepared by Dr. P. Babaali 1 Algebra 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.

More information

Math Academy I Fall Study Guide. CHAPTER ONE: FUNDAMENTALS Due Thursday, December 8

Math Academy I Fall Study Guide. CHAPTER ONE: FUNDAMENTALS Due Thursday, December 8 Name: Math Academy I Fall Study Guide CHAPTER ONE: FUNDAMENTALS Due Thursday, December 8 1-A Terminology natural integer rational real complex irrational imaginary term expression argument monomial degree

More information

1 x. II. CHAPTER 2: (A) Graphing Rational Functions: Show Asymptotes using dotted lines, Intercepts, Holes(Coordinates, if any.)

1 x. II. CHAPTER 2: (A) Graphing Rational Functions: Show Asymptotes using dotted lines, Intercepts, Holes(Coordinates, if any.) FINAL REVIEW-014: Before using this review guide be sure to study your test and quizzes from this year. The final will contain big ideas from the first half of the year (chapters 1-) but it will be focused

More information

Topics from Algebra and Pre-Calculus. (Key contains solved problems)

Topics from Algebra and Pre-Calculus. (Key contains solved problems) Topics from Algebra and Pre-Calculus (Key contains solved problems) Note: The purpose of this packet is to give you a review of basic skills. You are asked not to use the calculator, except on p. (8) and

More information

AP Calculus AB Summer Math Packet

AP Calculus AB Summer Math Packet Name Date Section AP Calculus AB Summer Math Packet This assignment is to be done at you leisure during the summer. It is meant to help you practice mathematical skills necessary to be successful in Calculus

More information

1. Graph each of the given equations, state the domain and range, and specify all intercepts and symmetry. a) y 3x

1. Graph each of the given equations, state the domain and range, and specify all intercepts and symmetry. a) y 3x MATH 94 Final Exam Review. Graph each of the given equations, state the domain and range, and specify all intercepts and symmetry. a) y x b) y x 4 c) y x 4. Determine whether or not each of the following

More information

ALGEBRA II Grades 9-12

ALGEBRA II Grades 9-12 Summer 2015 Units: 10 high school credits UC Requirement Category: c General Description: ALGEBRA II Grades 9-12 Algebra II is a course which further develops the concepts learned in Algebra I. It will

More information

Algebra 2. Chapter 4 Exponential and Logarithmic Functions. Chapter 1 Foundations for Functions. Chapter 3 Polynomial Functions

Algebra 2. Chapter 4 Exponential and Logarithmic Functions. Chapter 1 Foundations for Functions. Chapter 3 Polynomial Functions Algebra 2 Chapter 1 Foundations for Chapter 2 Quadratic Chapter 3 Polynomial Chapter 4 Exponential and Logarithmic Chapter 5 Rational and Radical Chapter 6 Properties and Attributes of Chapter 7 Probability

More information

Centerville High School Curriculum Mapping Algebra II 1 st Nine Weeks

Centerville High School Curriculum Mapping Algebra II 1 st Nine Weeks Centerville High School Curriculum Mapping Algebra II 1 st Nine Weeks Chapter/ Lesson Common Core Standard(s) 1-1 SMP1 1. How do you use a number line to graph and order real numbers? 2. How do you identify

More information

Algebra II. A2.1.1 Recognize and graph various types of functions, including polynomial, rational, and algebraic functions.

Algebra II. A2.1.1 Recognize and graph various types of functions, including polynomial, rational, and algebraic functions. Standard 1: Relations and Functions Students graph relations and functions and find zeros. They use function notation and combine functions by composition. They interpret functions in given situations.

More information

SKILL BUILDER TEN. Graphs of Linear Equations with Two Variables. If x = 2 then y = = = 7 and (2, 7) is a solution.

SKILL BUILDER TEN. Graphs of Linear Equations with Two Variables. If x = 2 then y = = = 7 and (2, 7) is a solution. SKILL BUILDER TEN Graphs of Linear Equations with Two Variables A first degree equation is called a linear equation, since its graph is a straight line. In a linear equation, each term is a constant or

More information

Final Review. Non-calculator problems are indicated. 1. (No calculator) Graph the function: y = x 3 + 2

Final Review. Non-calculator problems are indicated. 1. (No calculator) Graph the function: y = x 3 + 2 Algebra II Final Review Name Non-calculator problems are indicated. 1. (No calculator) Graph the function: y = x 3 + 2 2. (No calculator) Given the function y = -2 x + 3-1 and the value x = -5, find the

More information

MCPS Algebra 2 and Precalculus Standards, Categories, and Indicators*

MCPS Algebra 2 and Precalculus Standards, Categories, and Indicators* Content Standard 1.0 (HS) Patterns, Algebra and Functions Students will algebraically represent, model, analyze, and solve mathematical and real-world problems involving functional patterns and relationships.

More information

Portable Assisted Study Sequence ALGEBRA IIB

Portable Assisted Study Sequence ALGEBRA IIB SCOPE This course is divided into two semesters of study (A & B) comprised of five units each. Each unit teaches concepts and strategies recommended for intermediate algebra students. The second half of

More information

CALCULUS AB/BC SUMMER REVIEW PACKET (Answers)

CALCULUS AB/BC SUMMER REVIEW PACKET (Answers) Name CALCULUS AB/BC SUMMER REVIEW PACKET (Answers) I. Simplify. Identify the zeros, vertical asymptotes, horizontal asymptotes, holes and sketch each rational function. Show the work that leads to your

More information

Summer Review Packet AP Calculus

Summer Review Packet AP Calculus Summer Review Packet AP Calculus ************************************************************************ Directions for this packet: On a separate sheet of paper, show your work for each problem in this

More information

My Math Plan Assessment #3 Study Guide

My Math Plan Assessment #3 Study Guide My Math Plan Assessment # Study Guide 1. Identify the vertex of the parabola with the given equation. f(x) = (x 5) 2 7 2. Find the value of the function. Find f( 6) for f(x) = 2x + 11. Graph the linear

More information

Algebra II. In this technological age, mathematics is more important than ever. When students

Algebra II. In this technological age, mathematics is more important than ever. When students In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,

More information

Homework. Basic properties of real numbers. Adding, subtracting, multiplying and dividing real numbers. Solve one step inequalities with integers.

Homework. Basic properties of real numbers. Adding, subtracting, multiplying and dividing real numbers. Solve one step inequalities with integers. Morgan County School District Re-3 A.P. Calculus August What is the language of algebra? Graphing real numbers. Comparing and ordering real numbers. Finding absolute value. September How do you solve one

More information

Quantile Textbook Report

Quantile Textbook Report Quantile Textbook Report Algebra 2 Author Charles, Randall I., et al StateEdition West Virginia Grade Algebra 2 1 Expressions, Equations, and Inequalities 1.1 Patterns and Expressions 930Q 1.2 Properties

More information

UNIT 1 EQUATIONS, INEQUALITIES, FUNCTIONS

UNIT 1 EQUATIONS, INEQUALITIES, FUNCTIONS UNIT 1 EQUATIONS, INEQUALITIES, FUNCTIONS Act 1 Act 2 A rental car company charges $50.00 per day, plus $0.05 per mile driven. Write a function to model the story. How far did Angie drive if she rented

More information

Logs and Exponential functions e, ln, solving exponential functions, solving log and exponential equations, properties of logs

Logs and Exponential functions e, ln, solving exponential functions, solving log and exponential equations, properties of logs Page 1 AM1 Final Exam Review Packet TOPICS Complex Numbers, Vectors, and Parametric Equations Change back and forth from and to polar and rectangular forms. Raise a term in polar form to a power (DeMoivre).

More information

Southington High School 720 Pleasant Street Southington, CT 06489

Southington High School 720 Pleasant Street Southington, CT 06489 BLUE KNIGHTS Southington High School 720 Pleasant Street Southington, CT 06489 Phone: (860) 628-3229 Fax: (860) 628-3397 Home Page: www.southingtonschools.org Principal Brian Stranieri Assistant Principals

More information

2.6 Logarithmic Functions. Inverse Functions. Question: What is the relationship between f(x) = x 2 and g(x) = x?

2.6 Logarithmic Functions. Inverse Functions. Question: What is the relationship between f(x) = x 2 and g(x) = x? Inverse Functions Question: What is the relationship between f(x) = x 3 and g(x) = 3 x? Question: What is the relationship between f(x) = x 2 and g(x) = x? Definition (One-to-One Function) A function f

More information

Instructional Units Plan Algebra II

Instructional Units Plan Algebra II Instructional Units Plan Algebra II This set of plans presents the topics and selected for ACT s rigorous Algebra II course. The topics and standards are arranged in ten units by suggested instructional

More information

Prentice Hall: Algebra 2 with Trigonometry 2006 Correlated to: California Mathematics Content Standards for Algebra II (Grades 9-12)

Prentice Hall: Algebra 2 with Trigonometry 2006 Correlated to: California Mathematics Content Standards for Algebra II (Grades 9-12) California Mathematics Content Standards for Algebra II (Grades 9-12) This discipline complements and expands the mathematical content and concepts of algebra I and geometry. Students who master algebra

More information

INTERNET MAT 117 Review Problems. (1) Let us consider the circle with equation. (b) Find the center and the radius of the circle given above.

INTERNET MAT 117 Review Problems. (1) Let us consider the circle with equation. (b) Find the center and the radius of the circle given above. INTERNET MAT 117 Review Problems (1) Let us consider the circle with equation x 2 + y 2 + 2x + 3y + 3 4 = 0. (a) Find the standard form of the equation of the circle given above. (b) Find the center and

More information

ALGEBRA 2 X. Final Exam. Review Packet

ALGEBRA 2 X. Final Exam. Review Packet ALGEBRA X Final Exam Review Packet Multiple Choice Match: 1) x + y = r a) equation of a line ) x = 5y 4y+ b) equation of a hyperbola ) 4) x y + = 1 64 9 c) equation of a parabola x y = 1 4 49 d) equation

More information

!"#$%&'(&)*$%&+",#$$-$%&+./#-+ (&)*$%&+%"-$+0!#1%&

!#$%&'(&)*$%&+,#$$-$%&+./#-+ (&)*$%&+%-$+0!#1%& !"#$%&'(&)*$%&",#$$-$%&./#- (&)*$%&%"-$0!#1%&23 44444444444444444444444444444444444444444444444444444444444444444444 &53.67689:5;978?58"@A9;8=B!=89C7DE,6=8FG=CD=CF(76F9C7D!)#!/($"%*$H!I"%"&1/%/.!"JK$&3

More information

RADNOR TOWNSHIP SCHOOL DISTRICT Course Overview Seminar Algebra 2 ( )

RADNOR TOWNSHIP SCHOOL DISTRICT Course Overview Seminar Algebra 2 ( ) RADNOR TOWNSHIP SCHOOL DISTRICT Course Overview Seminar Algebra 2 (05040430) General Information Prerequisite: Seminar Geometry Honors with a grade of C or teacher recommendation. Length: Full Year Format:

More information

This image cannot currently be displayed. Course Catalog. Algebra II Glynlyon, Inc.

This image cannot currently be displayed. Course Catalog. Algebra II Glynlyon, Inc. This image cannot currently be displayed. Course Catalog Algebra II 2016 Glynlyon, Inc. Table of Contents COURSE OVERVIEW... 1 UNIT 1: SET, STRUCTURE, AND FUNCTION... 1 UNIT 2: NUMBERS, SENTENCES, AND

More information

Summer Review for Students Entering AP Calculus AB

Summer Review for Students Entering AP Calculus AB Summer Review for Students Entering AP Calculus AB Class: Date: AP Calculus AB Summer Packet Please show all work in the spaces provided The answers are provided at the end of the packet Algebraic Manipulation

More information

NFC ACADEMY COURSE OVERVIEW

NFC ACADEMY COURSE OVERVIEW NFC ACADEMY COURSE OVERVIEW Algebra II Honors is a full-year, high school math course intended for the student who has successfully completed the prerequisite course Algebra I. This course focuses on algebraic

More information

Curriculum Catalog

Curriculum Catalog 2017-2018 Curriculum Catalog 2017 Glynlyon, Inc. Table of Contents ALGEBRA II FUNDAMENTALS COURSE OVERVIEW... 1 UNIT 1: SET, STRUCTURE, AND FUNCTION... 1 UNIT 2: NUMBERS, SENTENCES, AND PROBLEMS... 1 UNIT

More information

AP Calculus Summer Prep

AP Calculus Summer Prep AP Calculus Summer Prep Topics from Algebra and Pre-Calculus (Solutions are on the Answer Key on the Last Pages) The purpose of this packet is to give you a review of basic skills. You are asked to have

More information

CP Pre-Calculus Summer Packet

CP Pre-Calculus Summer Packet Page CP Pre-Calculus Summer Packet Name: Ø Do all work on a separate sheet of paper. Number your problems and show your work when appropriate. Ø This packet will count as your first homework assignment

More information

College Algebra and College Algebra with Review Final Review

College Algebra and College Algebra with Review Final Review The final exam comprises 30 questions. Each of the 20 multiple choice questions is worth 3 points and each of the 10 open-ended questions is worth 4 points. Instructions for the Actual Final Exam: Work

More information

Math Exam Jam Solutions. Contents. 1 Linear Inequalities and Absolute Value Equations 2

Math Exam Jam Solutions. Contents. 1 Linear Inequalities and Absolute Value Equations 2 Math 11100 Exam Jam Solutions Contents 1 Linear Inequalities and Absolute Value Equations 2 2 Linear Equations, Graphing and Solving Systems of Equations 4 3 Polynomials and Rational Expressions 13 4 Radical

More information

Algebra II Honors Final Exam Review

Algebra II Honors Final Exam Review Class: Date: Algebra II Honors Final Exam Review 2013-2014 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the graph of the complex number 3 2i.

More information

The Research- Driven Solution to Raise the Quality of High School Core Courses. Algebra I I. Instructional Units Plan

The Research- Driven Solution to Raise the Quality of High School Core Courses. Algebra I I. Instructional Units Plan The Research- Driven Solution to Raise the Quality of High School Core Courses Algebra I I Instructional Units Plan Instructional Units Plan Algebra II This set of plans presents the topics and selected

More information

3 Inequalities Absolute Values Inequalities and Intervals... 5

3 Inequalities Absolute Values Inequalities and Intervals... 5 Contents 1 Real Numbers, Exponents, and Radicals 3 1.1 Rationalizing the Denominator................................... 3 1.2 Factoring Polynomials........................................ 3 1.3 Algebraic

More information

North Seattle Community College Computer Based Mathematics Instruction Math 102 Test Reviews

North Seattle Community College Computer Based Mathematics Instruction Math 102 Test Reviews North Seattle Community College Computer Based Mathematics Instruction Math 10 Test Reviews Click on a bookmarked heading on the left to access individual reviews. To print a review, choose print and the

More information

Final Exam Review for DMAT 0310

Final Exam Review for DMAT 0310 Final Exam Review for DMAT 010 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor the polynomial completely. What is one of the factors? 1) x

More information

CALCULUS OPTIONAL SUMMER WORK

CALCULUS OPTIONAL SUMMER WORK NAME JUNE 016 CALCULUS OPTIONAL SUMMER WORK PART I - NO CALCULATOR I. COORDINATE GEOMETRY 1) Identify the indicated quantities for -8x + 15y = 0. x-int y-int slope ) A line has a slope of 5/7 and contains

More information

Math Exam Jam Concise. Contents. 1 Algebra Review 2. 2 Functions and Graphs 2. 3 Exponents and Radicals 3. 4 Quadratic Functions and Equations 4

Math Exam Jam Concise. Contents. 1 Algebra Review 2. 2 Functions and Graphs 2. 3 Exponents and Radicals 3. 4 Quadratic Functions and Equations 4 Contents 1 Algebra Review 2 2 Functions and Graphs 2 3 Exponents and Radicals 3 4 Quadratic Functions and Equations 4 5 Exponential and Logarithmic Functions 5 6 Systems of Linear Equations 6 7 Inequalities

More information

Utah Math Standards for College Prep Mathematics

Utah Math Standards for College Prep Mathematics A Correlation of 8 th Edition 2016 To the A Correlation of, 8 th Edition to the Resource Title:, 8 th Edition Publisher: Pearson Education publishing as Prentice Hall ISBN: SE: 9780133941753/ 9780133969078/

More information

Curriculum Catalog

Curriculum Catalog 2017-2018 Curriculum Catalog 2017 Glynlyon, Inc. Table of Contents ALGEBRA II COURSE OVERVIEW... 1 UNIT 1: SET, STRUCTURE, AND FUNCTION... 1 UNIT 2: NUMBERS, SENTENCES, AND PROBLEMS... 2 UNIT 3: LINEAR

More information

Directions: This is a final exam review which covers all of the topics of the course. Please use this as a guide to assist you in your studies.

Directions: This is a final exam review which covers all of the topics of the course. Please use this as a guide to assist you in your studies. MATH 1113 Precalculus FINAL EXAM REVIEW irections: This is a final exam review which covers all of the topics of the course. Please use this as a guide to assist you in your studies. Question: 1 QI: 758

More information

Algebra 2 & Trigonometry Honors Midterm Review 2016

Algebra 2 & Trigonometry Honors Midterm Review 2016 Algebra & Trigonometry Honors Midterm Review 016 Solving Equations 1) Find all values of x that satisfy the equation, 5x 1 = x + 3 ) Solve the following by completing the square. Express your answer in

More information

MATH-1420 Review Concepts (Haugen)

MATH-1420 Review Concepts (Haugen) MATH-40 Review Concepts (Haugen) Unit : Equations, Inequalities, Functions, and Graphs Rational Expressions Determine the domain of a rational expression Simplify rational expressions -factor and then

More information

Exam Review 2 nd Semester 6-1 Operations on Functions

Exam Review 2 nd Semester 6-1 Operations on Functions NAME DATE PERIOD Exam Review 2 nd Semester 6-1 Operations on Functions Find (f + g)(x), (f g)(x), (f g)(x), and (x) for each f(x) and g(x). 1. f(x) = 8x 3; g(x) = 4x + 5 2. f(x) = + x 6; g(x) = x 2 If

More information

Curriculum Map: Mathematics

Curriculum Map: Mathematics Curriculum Map: Mathematics Course: Honors Algebra II Grade(s): 9/10 Unit 1: Expressions, Equations, and Inequalities In this unit, students review basics concepts and skills of algebra studied in previous

More information

Geometry Placement Exam Review Revised 2017 Maine East High School

Geometry Placement Exam Review Revised 2017 Maine East High School Geometry Placement Exam Review Revised 017 Maine East High School The actual placement exam has 91 questions. The placement exam is free response students must solve questions and write answer in space

More information

How to use this Algebra II - Semester 2 Study Packet

How to use this Algebra II - Semester 2 Study Packet Excellence is not an act, but a habit. Aristotle Dear Algebra II Student, First of all, Congrats! for making it this far in your math career. Passing Algebra II is a huge mile-stone Give yourself a pat

More information

Essential Learning Outcomes for Algebra 2

Essential Learning Outcomes for Algebra 2 ALGEBRA 2 ELOs 1 Essential Learning Outcomes for Algebra 2 The following essential learning outcomes (ELOs) represent the 12 skills that students should be able to demonstrate knowledge of upon completion

More information

Honors Algebra 2 Final Exam 2002

Honors Algebra 2 Final Exam 2002 Honors Algebra 2 Final Exam 2002 Name PART A. MULTIPLE CHOICE. Circle the letter in front of each correct answer. You do not have to show work. There is no partial credit. EACH PROBLEM IN THIS SECTION

More information

Algebra 2 (2006) Correlation of the ALEKS Course Algebra 2 to the California Content Standards for Algebra 2

Algebra 2 (2006) Correlation of the ALEKS Course Algebra 2 to the California Content Standards for Algebra 2 Algebra 2 (2006) Correlation of the ALEKS Course Algebra 2 to the California Content Standards for Algebra 2 Algebra II - This discipline complements and expands the mathematical content and concepts of

More information

CURRICULUM MAP. Course/Subject: Honors Math I Grade: 10 Teacher: Davis. Month: September (19 instructional days)

CURRICULUM MAP. Course/Subject: Honors Math I Grade: 10 Teacher: Davis. Month: September (19 instructional days) Month: September (19 instructional days) Numbers, Number Systems and Number Relationships Standard 2.1.11.A: Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots,

More information

y z ). Write all solutions using only positive

y z ). Write all solutions using only positive 1. a) Graph the equation x y =. b) What is the x-intercept? What is the y-intercept? d) What is the slope of this line?. a) Find the slope of the line joining the points and ( b) Find the equation of this

More information

2. Find the midpoint of the segment that joins the points (5, 1) and (3, 5). 6. Find an equation of the line with slope 7 that passes through (4, 1).

2. Find the midpoint of the segment that joins the points (5, 1) and (3, 5). 6. Find an equation of the line with slope 7 that passes through (4, 1). Math 129: Pre-Calculus Spring 2018 Practice Problems for Final Exam Name (Print): 1. Find the distance between the points (6, 2) and ( 4, 5). 2. Find the midpoint of the segment that joins the points (5,

More information

MATH 1301, Solutions to practice problems

MATH 1301, Solutions to practice problems MATH 1301, Solutions to practice problems 1. (a) (C) and (D); x = 7. In 3 years, Ann is x + 3 years old and years ago, when was x years old. We get the equation x + 3 = (x ) which is (D); (C) is obtained

More information

Step 1: Greatest Common Factor Step 2: Count the number of terms If there are: 2 Terms: Difference of 2 Perfect Squares ( + )( - )

Step 1: Greatest Common Factor Step 2: Count the number of terms If there are: 2 Terms: Difference of 2 Perfect Squares ( + )( - ) Review for Algebra 2 CC Radicals: r x p 1 r x p p r = x p r = x Imaginary Numbers: i = 1 Polynomials (to Solve) Try Factoring: i 2 = 1 Step 1: Greatest Common Factor Step 2: Count the number of terms If

More information

COLLEGE ALGEBRA PRACTICE FINAL (Revised 3/04)

COLLEGE ALGEBRA PRACTICE FINAL (Revised 3/04) Sketch the following graphs:. y x 0 COLLEGE ALGEBRA PRACTICE FINAL (Revised /0) + =. ( ) ( ) f x = x+. ( ) g x = x + 8x 7. y = x. y = x + 6. f ( x) = x + 7. h( x) x + = x + 8. g( x) = x x 9. y = x( x+

More information

Final Exam Review Calculators Not Allowed

Final Exam Review Calculators Not Allowed Math 35 Final Exam Review Calculators Not Allowed From the Chapter 2 and 3 Test: (Refer to the White Ch. 2/3 Test answer key.) Solve this literal equation for the variable requested. 4. y = mx + b (solve

More information

Welcome to AP Calculus!

Welcome to AP Calculus! Welcome to AP Calculus! This packet is meant to help you review some of the mathematics that lead up to calculus. Of course, all mathematics up until this point has simply been a build-up to calculus,

More information

Pre-calculus 12 Curriculum Outcomes Framework (110 hours)

Pre-calculus 12 Curriculum Outcomes Framework (110 hours) Curriculum Outcomes Framework (110 hours) Trigonometry (T) (35 40 hours) General Curriculum Outcome: Students will be expected to develop trigonometric reasoning. T01 Students will be expected to T01.01

More information

SMSU Mathematics Course Content

SMSU Mathematics Course Content Southwest Minnesota State University Department of Mathematics SMSU Mathematics Course Content 2012-2013 Thefollowing is a list of possibletopics and techniques to cover in your SMSU College Now course.

More information

AP Calculus Summer Homework

AP Calculus Summer Homework Class: Date: AP Calculus Summer Homework Show your work. Place a circle around your final answer. 1. Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.

More information

DRAFT. Appendix H. Grade 12 Prototype Examination. Pre-calculus 30. Course Code For more information, see the Table of Specifications.

DRAFT. Appendix H. Grade 12 Prototype Examination. Pre-calculus 30. Course Code For more information, see the Table of Specifications. Grade 1 Prototype Examination Pre-calculus 30 Course Code 846 Barcode Number DRAFT Appendix H For more information, see the Table of Specifications. Month Day Date of Birth November 013 AMPLE Pre-calculus

More information

CURRICULUM PACING GUIDE ALG. II WITH TRIG (GRADES 10-12) 1st Nine Weeks 1

CURRICULUM PACING GUIDE ALG. II WITH TRIG (GRADES 10-12) 1st Nine Weeks 1 b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables,

More information