The Final Exam is comprehensive but identifying the topics covered by it should be simple.

Size: px
Start display at page:

Download "The Final Exam is comprehensive but identifying the topics covered by it should be simple."

Transcription

1 Math 10 Final Eam Study Guide The Final Eam is comprehensive ut identifying the topics covered y it should e simple. Use the previous eams as your primary reviewing tool! This document is to help provide you with more specific eamples related to functions and function notation. These concepts are thoroughly covered y the tetoo ut are not isolated to any particular section or chapter. Every chapter (ecept chapter ) contains prolems related to evaluating functions at particular values and solving equations/inequalities involving function notation. 1. Know the difference etween an equation, an epression and a function. Know which instruction might e associated with each, i.e., simplify, solve and graph.. Be ale to graph any of the following ase functions with left/right and/or up/down shifts. a. Linear. Asolute value c. Cuic d. Radical e. Rational f. Quadratic g. Eponential h. Log. Be ale to recognize the difference etween rational, irrational, and imaginary numers. Refer to Eam Functions and their inverses. The 4 Biggies. Handout with solutions is availale on the wesite.

2 Use the following functions to respond to questions 5 through 1. Rationalize all denominators. Use i notation with imaginary solutions. f( 5 g ( ( ) 1 p ( 1 ( log h( r ( 5 1 q( w ( ) 6 n ( ) ( ) j ( ) log ( 1) 5. Use interval notation to identify the domain and range of any of the functions listed aove (ecept n( and j(. 6. Evaluate and simplify. f () 7. Find all values of for which a) f ( p( ) r ( c) g ( ) 1 d) w( p( e) w ( 0 f) h ( ) n ( ) g) ( h) ( ) j ( ) 8. Find 1 ( 9. Find p( f( )) 10. Rewrite w( in verte form. w( 11. Use long division or synthetic division to perform. p( 1. Evaluate and simplify. w ( ) w()

3 Math 10 Selected Solutions to the Final Eam Study Guide 1. Know the difference etween an equation, an epression and a function. Know which instruction might e associated with each, i.e., simplify, solve and graph.. Be ale to graph any of the following ase functions with left/right and/or up/down shifts. i. Linear e) Rational j. Asolute value f) Quadratic. Cuic g) Eponential l. Radical h) Logarithm. Be ale to recognize the difference etween rational, irrational, and imaginary numers. Refer to Eam 4. Eamples of: Rational numers: Irrational numers: 7 1 6,, 5,0, 11, 8, e,, 5, 5 Imaginary numers:, i 4, Functions and their inverses. The 4 Biggies. Handout with solutions is availale on the wesite.

4 Use the following functions to respond to questions 5 through 1. Rationalize all denominators. Use i notation with imaginary solutions. f( 5 g ( ( ) 1 p ( 1 ( log h( r ( 5 1 q( w ( ) 6 n ( ) ( ) j ( ) log ( 1) 5. Use interval notation to identify the domain and range of any of the function listed aove. g ( ( ) 1 Domain: All reals., Range: Since the verte is at, 1 and the paraola opens up, the 1, range is all y-values greater than or equal to -1. f( 5 Domain: The value in the square root must not e negative , h ( Domain: All reals., Range: The y values are all positives. 0, ( log This is the inverse of h(. Domain and range are switched. Domain: 0, Range:, 6. Evaluate f ()

5 7. Find all values of for which a) f ( p( 5 1 Square oth sides 5 1 Now it is quadratic. 0 4 Zero product property. Chec your solutions. ) r ( 5 Cue oth sides c) g ( ) 1 ( ) 1 1 Add one to oth sides. ( ) 0 Square root rule. (two solutions) d) w( p( 6 1 set = Doesn t factor. Use another method. e) w ( Doesn t factor. Try completing the square. f) h ( ) n ( ) ( Same ases, therefore eponents are equal. Now solve for. g) ( log Translate into an eponent equation. 9 h) ( ) j ( ) log log ( 1) Same ases. Arguments are equal. 1 Now solve for.

6 8. Find 1 ( To find the inverse, switch and y and then solve for y =. You will need to translate from logarithm to eponent to succeed. p f p( f( )) p 5 9. Find ( ( )) p 1 or Rewrite w( in verte form. Change to the form of the function that indicates where the verte is. Solution: w ( ) 1 5 w( 11. Use long division or synthetic division to perform. p( Note: p( is 1 1 Then w p ( ) 1 ( ) 6 Long division: 1 6 Synthetic division: Evaluate and simplify. w ( ) w() w ( ) w() 6 6 =

Math 120 Handouts. Functions Worksheet I (will be provided in class) Point Slope Equation of the Line 5. Functions Worksheet III 17

Math 120 Handouts. Functions Worksheet I (will be provided in class) Point Slope Equation of the Line 5. Functions Worksheet III 17 Math 0 Handouts HW # (will be provided to class) Lines: Concepts from Previous Classes (emailed to the class) Parabola Plots # (will be provided in class) Functions Worksheet I (will be provided in class)

More information

Math 120 Handouts. Functions Worksheet I (will be provided in class) Point Slope Equation of the Line 3. Functions Worksheet III 15

Math 120 Handouts. Functions Worksheet I (will be provided in class) Point Slope Equation of the Line 3. Functions Worksheet III 15 Math 0 Handouts HW # (will be provided to class) Lines: Concepts from Previous Classes (emailed to the class) Parabola Plots # (will be provided in class) Functions Worksheet I (will be provided in class)

More information

QUADRATIC EQUATIONS. + 6 = 0 This is a quadratic equation written in standard form. x x = 0 (standard form with c=0). 2 = 9

QUADRATIC EQUATIONS. + 6 = 0 This is a quadratic equation written in standard form. x x = 0 (standard form with c=0). 2 = 9 QUADRATIC EQUATIONS A quadratic equation is always written in the form of: a + b + c = where a The form a + b + c = is called the standard form of a quadratic equation. Eamples: 5 + 6 = This is a quadratic

More information

Algebra Final Exam Review Packet

Algebra Final Exam Review Packet Algebra 1 00 Final Eam Review Packet UNIT 1 EXPONENTS / RADICALS Eponents Degree of a monomial: Add the degrees of all the in the monomial together. o Eample - Find the degree of 5 7 yz Degree of a polynomial:

More information

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

Math RE - Calculus I Functions Page 1 of 10. Topics of Functions used in Calculus Math 0-03-RE - Calculus I Functions Page of 0 Definition of a function f() : Topics of Functions used in Calculus A function = f() is a relation between variables and such that for ever value onl one value.

More information

Algebra I Notes Unit Nine: Exponential Expressions

Algebra I Notes Unit Nine: Exponential Expressions Algera I Notes Unit Nine: Eponential Epressions Syllaus Ojectives: 7. The student will determine the value of eponential epressions using a variety of methods. 7. The student will simplify algeraic epressions

More information

This problem set is a good representation of some of the key skills you should have when entering this course.

This problem set is a good representation of some of the key skills you should have when entering this course. Math 4 Review of Previous Material: This problem set is a good representation of some of the key skills you should have when entering this course. Based on the course work leading up to Math 4, you should

More information

Function Gallery: Some Basic Functions and Their Properties

Function Gallery: Some Basic Functions and Their Properties Function Gallery: Some Basic Functions and Their Properties Linear Equation y = m+b Linear Equation y = -m + b This Eample: y = 3 + 3 This Eample: y = - + 0 Domain (-, ) Domain (-, ) Range (-, ) Range

More information

Polynomial Degree and Finite Differences

Polynomial Degree and Finite Differences CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson, you Learn the terminology associated with polynomials Use the finite differences method to determine the degree of a polynomial

More information

Analysis. The student was expected to know and use the Pythagorean theorem to find the missing side. a 2 + b 2 = c 2

Analysis. The student was expected to know and use the Pythagorean theorem to find the missing side. a 2 + b 2 = c 2 Analysis. Correct Answer : meters (m) The student was epected to know and use the Pythagorean theorem to find the missing side. a + b c 8 + 7 64 + 89 89 64 SKILL: Use the Pythagorean theorem to find the

More information

Algebra I Notes Concept 00b: Review Properties of Integer Exponents

Algebra I Notes Concept 00b: Review Properties of Integer Exponents Algera I Notes Concept 00: Review Properties of Integer Eponents In Algera I, a review of properties of integer eponents may e required. Students egin their eploration of power under the Common Core in

More information

a b a b ab b b b Math 154B Elementary Algebra Spring 2012

a b a b ab b b b Math 154B Elementary Algebra Spring 2012 Math 154B Elementar Algera Spring 01 Stud Guide for Eam 4 Eam 4 is scheduled for Thursda, Ma rd. You ma use a " 5" note card (oth sides) and a scientific calculator. You are epected to know (or have written

More information

The Product and Quotient Rules

The Product and Quotient Rules The Product and Quotient Rules In this section, you will learn how to find the derivative of a product of functions and the derivative of a quotient of functions. A function that is the product of functions

More information

Unit 11 - Solving Quadratic Functions PART ONE

Unit 11 - Solving Quadratic Functions PART ONE Unit 11 - Solving Quadratic Functions PART ONE PREREQUISITE SKILLS: students should be able to add, subtract and multiply polynomials students should be able to factor polynomials students should be able

More information

Math-2 Lesson 2-4. Radicals

Math-2 Lesson 2-4. Radicals Math- Lesson - Radicals = What number is equivalent to the square root of? Square both sides of the equation ( ) ( ) = = = is an equivalent statement to = 1.7 1.71 1.70 1.701 1.7008... There is no equivalent

More information

ERASMUS UNIVERSITY ROTTERDAM Information concerning the Entrance examination Mathematics level 2 for International Business Administration (IBA)

ERASMUS UNIVERSITY ROTTERDAM Information concerning the Entrance examination Mathematics level 2 for International Business Administration (IBA) ERASMUS UNIVERSITY ROTTERDAM Information concerning the Entrance examination Mathematics level 2 for International Business Administration (IBA) General information Availale time: 2.5 hours (150 minutes).

More information

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

Math 030 Review for Final Exam Revised Fall 2010 RH/ DM 1 Math 00 Review for Final Eam Revised Fall 010 RH/ DM 1 1. Solve the equations: (-1) (7) (-) (-1) () 1 1 1 1 f. 1 g. h. 1 11 i. 9. Solve the following equations for the given variable: 1 Solve for. D ab

More information

Algebra Concepts Equation Solving Flow Chart Page 1 of 6. How Do I Solve This Equation?

Algebra Concepts Equation Solving Flow Chart Page 1 of 6. How Do I Solve This Equation? Algebra Concepts Equation Solving Flow Chart Page of 6 How Do I Solve This Equation? First, simplify both sides of the equation as much as possible by: combining like terms, removing parentheses using

More information

Pre-Calculus Summer Packet

Pre-Calculus Summer Packet Pre-Calculus Summer Packet Name ALLEN PARK HIGH SCHOOL Summer Assessment Pre-Calculus Summer Packet For Students Entering Pre-Calculus Summer 05 This summer packet is intended to be completed by the FIRST

More information

Higher. Polynomials and Quadratics. Polynomials and Quadratics 1

Higher. Polynomials and Quadratics. Polynomials and Quadratics 1 Higher Mathematics Polnomials and Quadratics Contents Polnomials and Quadratics 1 1 Quadratics EF 1 The Discriminant EF Completing the Square EF Sketching Paraolas EF 7 5 Determining the Equation of a

More information

Performing well in calculus is impossible without a solid algebra foundation. Many calculus

Performing well in calculus is impossible without a solid algebra foundation. Many calculus Chapter Algebra Review Performing well in calculus is impossible without a solid algebra foundation. Many calculus problems that you encounter involve a calculus concept but then require many, many steps

More information

Intermediate Algebra Section 9.3 Logarithmic Functions

Intermediate Algebra Section 9.3 Logarithmic Functions Intermediate Algebra Section 9.3 Logarithmic Functions We have studied inverse functions, learning when they eist and how to find them. If we look at the graph of the eponential function, f ( ) = a, where

More information

COUNCIL ROCK HIGH SCHOOL MATHEMATICS. A Summer Review of Algebra. Designed for the Student Entering Accelerated/Honors Analysis

COUNCIL ROCK HIGH SCHOOL MATHEMATICS. A Summer Review of Algebra. Designed for the Student Entering Accelerated/Honors Analysis COUNCIL ROCK HIGH SCHOOL MATHEMATICS A Summer Review of Algebra Designed for the Student Entering Accelerated/Honors Analysis Please print this packet in its entirety to be completed for evaluation on

More information

Student s Name : Class Roll No. ADDRESS: R-1, Opp. Raiway Track, New Corner Glass Building, Zone-2, M.P. NAGAR, Bhopal

Student s Name : Class Roll No. ADDRESS: R-1, Opp. Raiway Track, New Corner Glass Building, Zone-2, M.P. NAGAR, Bhopal fo/u fopkjr Hkh# tu] ugha vkjehks dke] foifr ns[k NksM+s rqjar e/;e eu dj ';kea iq#"k flag ladyi dj] lgrs foifr vusd] ^cuk^ u NksM+s /;s; dks] j?kqcj jk[ks VsdAA jfpr% ekuo /kez izksrk ln~q# Jh jknksm+nklth

More information

Summer Packet Honors PreCalculus

Summer Packet Honors PreCalculus Summer Packet Honors PreCalculus Honors Pre-Calculus is a demanding course that relies heavily upon a student s algebra, geometry, and trigonometry skills. You are epected to know these topics before entering

More information

3 6 x a. 12 b. 63 c. 27 d. 0. 6, find

3 6 x a. 12 b. 63 c. 27 d. 0. 6, find Advanced Algebra Topics COMPASS Review revised Summer 0 You will be allowed to use a calculator on the COMPASS test Acceptable calculators are basic calculators, scientific calculators, and approved models

More information

where is a constant other than ( and ) and

where is a constant other than ( and ) and Section 12.1: EXPONENTIAL FUNCTIONS When you are done with your homework you should be able to Evaluate eponential functions Graph eponential functions Evaluate functions with base e Use compound interest

More information

Algebra 2-2nd Semester Exam Review 11

Algebra 2-2nd Semester Exam Review 11 Algebra 2-2nd Semester Eam Review 11 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine which binomial is a factor of. a. 14 b. + 4 c. 4 d. + 8

More information

8-1 Exploring Exponential Models

8-1 Exploring Exponential Models 8- Eploring Eponential Models Eponential Function A function with the general form, where is a real number, a 0, b > 0 and b. Eample: y = 4() Growth Factor When b >, b is the growth factor Eample: y =

More information

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

Name. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. REVIEW Eam #3 : 3.2-3.6, 4.1-4.5, 5.1 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the Leading Coefficient Test to determine the end behavior

More information

Algebra II Non-Calculator Spring Semester Exam Review

Algebra II Non-Calculator Spring Semester Exam Review Algebra II Non-Calculator Spring Semester Eam Review Name: Date: Block: Simplify the epression. Leave only positive eponents.. ( a ). ( p s ). mn 9cd cd. mn. ( w )( w ). 7. 7 7 Write the answer in scientific

More information

Section 4.3: Quadratic Formula

Section 4.3: Quadratic Formula Objective: Solve quadratic equations using the quadratic formula. In this section we will develop a formula to solve any quadratic equation ab c 0 where a b and c are real numbers and a 0. Solve for this

More information

3.1 Power Functions & Polynomial Functions

3.1 Power Functions & Polynomial Functions 3.1 Power Functions & Polynomial Functions A power function is a function that can be represented in the form f() = p, where the base is a variable and the eponent, p, is a number. The Effect of the Power

More information

7.3 Adding and Subtracting Rational Expressions

7.3 Adding and Subtracting Rational Expressions 7.3 Adding and Subtracting Rational Epressions LEARNING OBJECTIVES. Add and subtract rational epressions with common denominators. 2. Add and subtract rational epressions with unlike denominators. 3. Add

More information

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

Solutions to the Math 1051 Sample Final Exam (from Spring 2003) Page 1 Solutions to the Math 0 Sample Final Eam (from Spring 00) Page Part : Multiple Choice Questions. Here ou work out the problems and then select the answer that matches our answer. No partial credit is given

More information

Math 120. x x 4 x. . In this problem, we are combining fractions. To do this, we must have

Math 120. x x 4 x. . In this problem, we are combining fractions. To do this, we must have Math 10 Final Eam Review 1. 4 5 6 5 4 4 4 7 5 Worked out solutions. In this problem, we are subtracting one polynomial from another. When adding or subtracting polynomials, we combine like terms. Remember

More information

WBHS Algebra 2 - Final Exam

WBHS Algebra 2 - Final Exam Class: _ Date: _ WBHS Algebra 2 - Final Eam Multiple Choice Identify the choice that best completes the statement or answers the question. Describe the pattern in the sequence. Find the net three terms.

More information

What students need to know for PRE-CALCULUS Students expecting to take Pre-Calculus should demonstrate the ability to:

What students need to know for PRE-CALCULUS Students expecting to take Pre-Calculus should demonstrate the ability to: What students need to know for PRE-CALCULUS 2014-2015 Students expecting to take Pre-Calculus should demonstrate the ability to: General: keep an organized notebook take good notes complete homework every

More information

Example 1: What do you know about the graph of the function

Example 1: What do you know about the graph of the function Section 1.5 Analyzing of Functions In this section, we ll look briefly at four types of functions: polynomial functions, rational functions, eponential functions and logarithmic functions. Eample 1: What

More information

Unit 6: 10 3x 2. Semester 2 Final Review Name: Date: Advanced Algebra

Unit 6: 10 3x 2. Semester 2 Final Review Name: Date: Advanced Algebra Semester Final Review Name: Date: Advanced Algebra Unit 6: # : Find the inverse of: 0 ) f ( ) = ) f ( ) Finding Inverses, Graphing Radical Functions, Simplifying Radical Epressions, & Solving Radical Equations

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Final Eam Review MAC 1 Spring 0 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve and check the linear equation. 1) (- + ) - = -( - 7) {-

More information

ALGEBRA 1 CP FINAL EXAM REVIEW

ALGEBRA 1 CP FINAL EXAM REVIEW ALGEBRA CP FINAL EXAM REVIEW Alg CP Sem Eam Review 0 () Page of 8 Chapter 8: Eponents. Write in rational eponent notation. 7. Write in radical notation. Simplif the epression.. 00.. 6 6. 7 7. 6 6 8. 8

More information

EXPONENT REVIEW!!! Concept Byte (Review): Properties of Exponents. Property of Exponents: Product of Powers. x m x n = x m + n

EXPONENT REVIEW!!! Concept Byte (Review): Properties of Exponents. Property of Exponents: Product of Powers. x m x n = x m + n Algebra B: Chapter 6 Notes 1 EXPONENT REVIEW!!! Concept Byte (Review): Properties of Eponents Recall from Algebra 1, the Properties (Rules) of Eponents. Property of Eponents: Product of Powers m n = m

More information

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

COUNCIL ROCK HIGH SCHOOL MATHEMATICS. A Note Guideline of Algebraic Concepts. Designed to assist students in A Summer Review of Algebra COUNCIL ROCK HIGH SCHOOL MATHEMATICS A Note Guideline of Algebraic Concepts Designed to assist students in A Summer Review of Algebra [A teacher prepared compilation of the 7 Algebraic concepts deemed

More information

C. Finding roots of trinomials: 1st Example: x 2 5x = 14 x 2 5x 14 = 0 (x 7)(x + 2) = 0 Answer: x = 7 or x = -2

C. Finding roots of trinomials: 1st Example: x 2 5x = 14 x 2 5x 14 = 0 (x 7)(x + 2) = 0 Answer: x = 7 or x = -2 AP Calculus Students: Welcome to AP Calculus. Class begins in approimately - months. In this packet, you will find numerous topics that were covered in your Algebra and Pre-Calculus courses. These are

More information

First Semester. Second Semester

First Semester. Second Semester Algebra II Scope and Sequence 014-15 (edited May 014) HOLT Algebra Page -4 Unit Linear and Absolute Value Functions Abbreviated Name 5-8 Quadratics QUADS Algebra II - Unit Outline First Semester TEKS Readiness

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Final Eam Review MAC 1 Fall 011 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve and check the linear equation. 1) (- + ) - = -( - 7) A)

More information

Information Knowledge

Information Knowledge ation ledge -How m lio Learner's Name: ALGEBRA II CAPACITY TRANSCRIPT Equations & Inequalities (Chapter 1) [L1.2.1, A1.1.4, A1.2.9, L3.2.1] Linear Equations and (Chapter 2) [L1.2.1, A1.2.9, A2.3.3, A3.1.2,

More information

Answer the following questions using a fraction and a percent (round to the nearest tenth of a percent).

Answer the following questions using a fraction and a percent (round to the nearest tenth of a percent). ALGEBRA 1 Ch 10 Closure Solving Comple Equations Name: Two-Way Tables: A simple random sample of adults in a metropolitan area was selected and a survey was administered to determine the relationship between

More information

Lecture 7: Indeterminate forms; L Hôpitals rule; Relative rates of growth. If we try to simply substitute x = 1 into the expression, we get

Lecture 7: Indeterminate forms; L Hôpitals rule; Relative rates of growth. If we try to simply substitute x = 1 into the expression, we get Lecture 7: Indeterminate forms; L Hôpitals rule; Relative rates of growth 1. Indeterminate Forms. Eample 1: Consider the it 1 1 1. If we try to simply substitute = 1 into the epression, we get. This is

More information

1. Find the domain of the following functions. Write your answer using interval notation. (9 pts.)

1. Find the domain of the following functions. Write your answer using interval notation. (9 pts.) MATH- Sample Eam Spring 7. Find the domain of the following functions. Write your answer using interval notation. (9 pts.) a. 9 f ( ) b. g ( ) 9 8 8. Write the equation of the circle in standard form given

More information

Section 5.5 Complex Numbers

Section 5.5 Complex Numbers Name: Period: Section 5.5 Comple Numbers Objective(s): Perform operations with comple numbers. Essential Question: Tell whether the statement is true or false, and justify your answer. Every comple number

More information

Algebra II Midterm Exam Review Packet

Algebra II Midterm Exam Review Packet Algebra II Midterm Eam Review Packet Name: Hour: CHAPTER 1 Midterm Review Evaluate the power. 1.. 5 5. 6. 7 Find the value of each epression given the value of each variable. 5. 10 when 5 10 6. when 6

More information

Math RE - Calculus I Exponential & Logarithmic Functions Page 1 of 9. y = f(x) = 2 x. y = f(x)

Math RE - Calculus I Exponential & Logarithmic Functions Page 1 of 9. y = f(x) = 2 x. y = f(x) Math 20-0-RE - Calculus I Eponential & Logarithmic Functions Page of 9 Eponential Function The general form of the eponential function equation is = f) = a where a is a real number called the base of the

More information

Topic: Expressions & Operations AII.1

Topic: Expressions & Operations AII.1 Topic: Epressions & Operations AII.1 AII.1 The student will identify field properties, aioms of equality and inequality, and properties of order that are valid for the set of real numbers and its subsets,

More information

Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions Adding and Subtracting Rational Epressions As a review, adding and subtracting fractions requires the fractions to have the same denominator. If they already have the same denominator, combine the numerators

More information

Finding Slope. Find the slopes of the lines passing through the following points. rise run

Finding Slope. Find the slopes of the lines passing through the following points. rise run Finding Slope Find the slopes of the lines passing through the following points. y y1 Formula for slope: m 1 m rise run Find the slopes of the lines passing through the following points. E #1: (7,0) and

More information

R3.6 Solving Linear Inequalities. 3) Solve: 2(x 4) - 3 > 3x ) Solve: 3(x 2) > 7-4x. R8.7 Rational Exponents

R3.6 Solving Linear Inequalities. 3) Solve: 2(x 4) - 3 > 3x ) Solve: 3(x 2) > 7-4x. R8.7 Rational Exponents Level D Review Packet - MMT This packet briefly reviews the topics covered on the Level D Math Skills Assessment. If you need additional study resources and/or assistance with any of the topics below,

More information

Algebra Notes Quadratic Functions and Equations Unit 08

Algebra Notes Quadratic Functions and Equations Unit 08 Note: This Unit contains concepts that are separated for teacher use, but which must be integrated by the completion of the unit so students can make sense of choosing appropriate methods for solving quadratic

More information

( ) ( ) x. The exponential function f(x) with base b is denoted by x

( ) ( ) x. The exponential function f(x) with base b is denoted by x Page of 7 Eponential and Logarithmic Functions Eponential Functions and Their Graphs: Section Objectives: Students will know how to recognize, graph, and evaluate eponential functions. The eponential function

More information

Define a rational expression: a quotient of two polynomials. ..( 3 10) (3 2) Rational expressions have the same properties as rational numbers:

Define a rational expression: a quotient of two polynomials. ..( 3 10) (3 2) Rational expressions have the same properties as rational numbers: 1 UNIT 7 RATIONAL EXPRESSIONS & EQUATIONS Simplifying Rational Epressions Define a rational epression: a quotient of two polynomials. A rational epression always indicates division EX: 10 means..( 10)

More information

Completing the Square

Completing the Square 3.5 Completing the Square Essential Question How can you complete the square for a quadratic epression? Using Algera Tiles to Complete the Square Work with a partner. Use algera tiles to complete the square

More information

M098 Carson Elementary and Intermediate Algebra 3e Section 11.3

M098 Carson Elementary and Intermediate Algebra 3e Section 11.3 Objectives. Solve equations by writing them in quadratic form.. Solve equations that are quadratic in form by using substitution. Vocabulary Prior Knowledge Solve rational equations: Clear the fraction.

More information

Math-3 Lesson 8-7. b) ph problems c) Sound Intensity Problems d) Money Problems e) Radioactive Decay Problems. a) Cooling problems

Math-3 Lesson 8-7. b) ph problems c) Sound Intensity Problems d) Money Problems e) Radioactive Decay Problems. a) Cooling problems Math- Lesson 8-7 Unit 5 (Part-) Notes 1) Solve Radical Equations ) Solve Eponential and Logarithmic Equations ) Check for Etraneous solutions 4) Find equations for graphs of eponential equations 5) Solve

More information

1 Rational Exponents and Radicals

1 Rational Exponents and Radicals Introductory Algebra Page 1 of 11 1 Rational Eponents and Radicals 1.1 Rules of Eponents The rules for eponents are the same as what you saw earlier. Memorize these rules if you haven t already done so.

More information

ERASMUS UNIVERSITY ROTTERDAM

ERASMUS UNIVERSITY ROTTERDAM Information concerning Colloquium doctum Mathematics level 2 for International Business Administration (IBA) and International Bachelor Economics & Business Economics (IBEB) General information ERASMUS

More information

Algebra II Curriculum Guide Dunmore School District Dunmore, PA

Algebra II Curriculum Guide Dunmore School District Dunmore, PA Algebra II Dunmore School District Dunmore, PA Algebra II Prerequisite: Successful completion of Geometry This course continues and reinforces the mathematical material learned in Algebra I. It deals with

More information

MATH 60 Review Problems for Final Exam

MATH 60 Review Problems for Final Exam MATH 60 Review Problems for Final Eam Scientific Calculators Onl - Graphing Calculators Not Allowed NO CLASS NOTES PERMITTED Evaluate the epression for the given values. m 1) m + 3 for m = 3 2) m 2 - n2

More information

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

(2.5) 1. Solve the following compound inequality and graph the solution set. Intermediate Algebra Practice Final Math 0 (7 th ed.) (Ch. -) (.5). Solve the following compound inequalit and graph the solution set. 0 and and > or or (.7). Solve the following absolute value inequalities.

More information

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

Name Period Date. Practice FINAL EXAM Intro to Calculus (50 points) Show all work on separate sheet of paper for full credit! Name Period Date Practice FINAL EXAM Intro to Calculus (0 points) Show all work on separate sheet of paper for full credit! ) Evaluate the algebraic epression for the given value or values of the variable(s).

More information

Conceptual Explanations: Logarithms

Conceptual Explanations: Logarithms Conceptual Eplanations: Logarithms Suppose you are a iologist investigating a population that doules every year. So if you start with 1 specimen, the population can e epressed as an eponential function:

More information

UNIT 5 QUADRATIC FUNCTIONS Lesson 2: Creating and Solving Quadratic Equations in One Variable Instruction

UNIT 5 QUADRATIC FUNCTIONS Lesson 2: Creating and Solving Quadratic Equations in One Variable Instruction Lesson : Creating and Solving Quadratic Equations in One Variale Prerequisite Skills This lesson requires the use of the following skills: understanding real numers and complex numers understanding rational

More information

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

Learning Goals. College of Charleston Department of Mathematics Math 101: College Algebra Final Exam Review Problems 1 College of Charleston Department of Mathematics Math 0: College Algebra Final Eam Review Problems Learning Goals (AL-) Arithmetic of Real and Comple Numbers: I can classif numbers as natural, integer,

More information

LEARNING OBJECTIVES. guided practice Teacher: anticipates, monitors, selects, sequences, and connects student work. - developing essential skills

LEARNING OBJECTIVES. guided practice Teacher: anticipates, monitors, selects, sequences, and connects student work. - developing essential skills H Quadratics, Lesson, Using the Discriminant (r. 018) QUADRATICS Using the Discriminant Common Core Standard A-REI.4 Solve quadratic equations y inspection (e.g., for x =49), taking square roots, completing

More information

Conceptual Explanations: Radicals

Conceptual Explanations: Radicals Conceptual Eplanations: Radicals The concept of a radical (or root) is a familiar one, and was reviewed in the conceptual eplanation of logarithms in the previous chapter. In this chapter, we are going

More information

MATH 111 Departmental Midterm Exam Review Exam date: Tuesday, March 1 st. Exam will cover sections and will be NON-CALCULATOR EXAM.

MATH 111 Departmental Midterm Exam Review Exam date: Tuesday, March 1 st. Exam will cover sections and will be NON-CALCULATOR EXAM. MATH Departmental Midterm Eam Review Eam date: Tuesday, March st Eam will cover sections -9 + - and will be NON-CALCULATOR EXAM Terms to know: quadratic function, ais of symmetry, verte, minimum/maimum

More information

EPPING HIGH SCHOOL ALGEBRA 2 COURSE SYLLABUS

EPPING HIGH SCHOOL ALGEBRA 2 COURSE SYLLABUS Course Title: Algebra 2 Course Description This course is designed to be the third year of high school mathematics. The material covered is roughly equivalent to that covered in the first Algebra course

More information

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

Algebra II Honors Curriculum Guide Dunmore School District Dunmore, PA

Algebra II Honors Curriculum Guide Dunmore School District Dunmore, PA Algebra II Honors Dunmore School District Dunmore, PA Algebra II Honors Prerequisite: Successful completion of Geometry Honors This course continues and reinforces the mathematical material learned in

More information

Calculus 1 (AP, Honors, Academic) Summer Assignment 2018

Calculus 1 (AP, Honors, Academic) Summer Assignment 2018 Calculus (AP, Honors, Academic) Summer Assignment 08 The summer assignments for Calculus will reinforce some necessary Algebra and Precalculus skills. In order to be successful in Calculus, you must have

More information

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

Summer Review Packet for Students Entering AP Calculus BC. Complex Fractions Summer Review Packet for Students Entering AP Calculus BC Comple Fractions When simplifying comple fractions, multiply by a fraction equal to 1 which has a numerator and denominator composed of the common

More information

Students expecting to take Advanced Qualitative Reasoning should demonstrate the ability to:

Students expecting to take Advanced Qualitative Reasoning should demonstrate the ability to: What students need to know for AQR Students expecting to take Advanced Qualitative Reasoning should demonstrate the ability to: General: keep an organized notebook take good notes complete homework every

More information

In #8-11, Simplify the expression. Write your answer using only positive exponents. 11) 4

In #8-11, Simplify the expression. Write your answer using only positive exponents. 11) 4 Semester Final Eam Review Packet Name Chapter 8: Eponents and Eponential Functions In #1-4 simplify the epression. Write your answer using eponents. 1) ( ) ( )( ) 5 ) ( 6 ) 5 4 ) 7 4 11 7 6 6 4) 8 6 1

More information

Summer MA Lesson 11 Section 1.5 (part 1)

Summer MA Lesson 11 Section 1.5 (part 1) Summer MA 500 Lesson Section.5 (part ) The general form of a quadratic equation is a + b + c = 0, where a, b, and c are real numbers and a 0. This is a second degree equation. There are four ways to possibly

More information

Advanced Algebra Scope and Sequence First Semester. Second Semester

Advanced Algebra Scope and Sequence First Semester. Second Semester Last update: April 03 Advanced Algebra Scope and Sequence 03-4 First Semester Unit Name Unit : Review of Basic Concepts and Polynomials Unit : Rational and Radical Epressions Sections in Book 0308 SLOs

More information

Intermediate Algebra 100A Final Exam Review Fall 2007

Intermediate Algebra 100A Final Exam Review Fall 2007 1 Basic Concepts 1. Sets and Other Basic Concepts Words/Concepts to Know: roster form, set builder notation, union, intersection, real numbers, natural numbers, whole numbers, integers, rational numbers,

More information

Success Center Math Tips

Success Center Math Tips . Asolte Vale Eqations mer of asolte vales 3 3= o soltion Isolate the asolte vale Other side negative? Rewrite the eqation with one asolte vale on each side Write two eqations withot asolte vales: In one,

More information

3.3 Limits and Infinity

3.3 Limits and Infinity Calculus Maimus. Limits Infinity Infinity is not a concrete number, but an abstract idea. It s not a destination, but a really long, never-ending journey. It s one of those mind-warping ideas that is difficult

More information

Exponent Laws Unit 4 Exponential Functions - Lesson 18

Exponent Laws Unit 4 Exponential Functions - Lesson 18 (A) Lesson Contet BIG PICTURE of this UNIT: CONTEXT of this LESSON: What are & how & why do we use eponential and logarithic functions? proficiency with algeraic anipulations/calculations pertinent to

More information

Calculus w/applications Prerequisite Packet Paint Branch High School Math Department

Calculus w/applications Prerequisite Packet Paint Branch High School Math Department Updated 6/014 The problems in this packet are designed to help you review topics from previous math courses that are important to your success in Calculus with Applications. It is important that you take

More information

SOLUTIONS. Math 130 Midterm Spring True-False: Circle T if the statement is always true. Otherwise circle F.

SOLUTIONS. Math 130 Midterm Spring True-False: Circle T if the statement is always true. Otherwise circle F. SOLUTIONS Math 13 Midterm Spring 16 Directions: True-False: Circle T if the statement is always true. Otherwise circle F. Partial-Credit: Please show all work and fully justify each step. No credit will

More information

RATIONAL FUNCTIONS. Finding Asymptotes..347 The Domain Finding Intercepts Graphing Rational Functions

RATIONAL FUNCTIONS. Finding Asymptotes..347 The Domain Finding Intercepts Graphing Rational Functions RATIONAL FUNCTIONS Finding Asymptotes..347 The Domain....350 Finding Intercepts.....35 Graphing Rational Functions... 35 345 Objectives The ollowing is a list o objectives or this section o the workbook.

More information

With topics from Algebra and Pre-Calculus to

With topics from Algebra and Pre-Calculus to With topics from Algebra and Pre-Calculus to get you ready to the AP! (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

More information

Topic Outline for Algebra 2 & and Trigonometry One Year Program

Topic Outline for Algebra 2 & and Trigonometry One Year Program Topic Outline for Algebra 2 & and Trigonometry One Year Program Algebra 2 & and Trigonometry - N - Semester 1 1. Rational Expressions 17 Days A. Factoring A2.A.7 B. Rationals A2.N.3 A2.A.17 A2.A.16 A2.A.23

More information

Graphs and polynomials

Graphs and polynomials 1 1A The inomial theorem 1B Polnomials 1C Division of polnomials 1D Linear graphs 1E Quadratic graphs 1F Cuic graphs 1G Quartic graphs Graphs and polnomials AreAS of STud Graphs of polnomial functions

More information

a+bi form abscissa absolute value x x x absolute value equation x x absolute value function absolute value inequality x x accurate adjacent angles

a+bi form abscissa absolute value x x x absolute value equation x x absolute value function absolute value inequality x x accurate adjacent angles Words CR PS Reason Comm Geom ALG Stat Prob NSO a+bi form abscissa absolute value absolute value equation absolute value function absolute value inequality accurate adjacent angles adjacent sides algebraic

More information

math FALL developmental mathematics sullivan 1e

math FALL developmental mathematics sullivan 1e TSIpractice eam review 1 131 180 plus 34 TSI questions for elementar and intermediate algebra m0300004301 aaa Name www.alvarezmathhelp.com math0300004301 FALL 01 100 interactmath developmental mathematics

More information

AP Calculus AB Summer Assignment

AP Calculus AB Summer Assignment AP Calculus AB Summer Assignment Name: When you come back to school, it is my epectation that you will have this packet completed. You will be way behind at the beginning of the year if you haven t attempted

More information

APPLICATIONS OF DIFFERENTIATION

APPLICATIONS OF DIFFERENTIATION 4 APPLICATIONS OF DIFFERENTIATION APPLICATIONS OF DIFFERENTIATION 4.4 Indeterminate Forms and L Hospital s Rule In this section, we will learn: How to evaluate functions whose values cannot be found at

More information

Math 117, Spring 2003, Math for Business and Economics Final Examination

Math 117, Spring 2003, Math for Business and Economics Final Examination Math 117, Spring 2003, Math for Business and Economics Final Eamination Instructions: Try all of the problems and show all of your work. Answers given with little or no indication of how they were obtained

More information