# MTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 17, 2006

Size: px
Start display at page:

Download "MTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 17, 2006"

Transcription

1 MTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions Created January 7, 2006 Math 092, Elementary Algebra, covers the mathematical content listed below. In order to place out of Math 092 or to prepare for the final examination in this course, one should be extremely comfortable with all of these items. NOTE: Calculators are not permitted in this course. The content listed below is covered in chapters through 7 in the second half of Pre and Introductory Algebra, A Combined Text by Aufman, Barker and Lockwood published by Houghton Mifflin Company), the current textbook used in Math 092. Adding, subtracting, multiplying, dividing, and exponentiating numbers integers, fractions and decimals); reducing fractions to lowest terms simplest form); converting between fractions, decimals, and percents. Evaluating and identifying variable terms, constant terms, and numerical coefficients of polynomials; determining what type of polynomial monomial, binomial, trinomial) a given expression is. Simplifying, adding, subtracting, multiplying, dividing, and exponentiating polynomials and rational expressions; rewriting zero and negative integer exponents. Simplifying arithmetic and algebraic expressions by following the order of operations Factoring by taking out the greatest common factor and by grouping; factoring trinomials, perfect square trinomials and differences of two squares. Solving algebraic equations involving integers, arithmetic and algebraic fractions, decimals, percents and/or parentheses; solving quadratic equations by factoring; solving ratios and proportions; solving literal equations for a specified variable in terms of other variables. Translating verbal expressions or sentences into variable expressions or algebraic equations. Solving application problems including, but not limited to, markup and markdown, determine-the-number problems, uniform motion, perimeters and areas, and ratio/rate problems). Graphing points and lines and identifying coordinates of given points on a rectangular Cartesian) coordinate system. Determining the x-intercepts, y-intercepts and slopes of straight lines. Finding equations of lines by using either the slope-intercept or the point-slope formula. This document was prepared by Ron Bannon using L A TEX 2ε and is a slight modification of Susan Gaulden s MTH 092 Content worksheet.

2 Review Problem Set At Essex County College you should be prepared to show all work clearly and in order, ending your work by boxing the answer. Furthermore, justify your answers algebraically whenever possible. These questions are for review only, and placement tests are not limited to these problems alone. Solutions and work are provided for each question. Please feel free to with questions or comments pertaining to this document. 2. Simplify each of the following. a) 3 + 2) + 6 4) 3 + 2) + 6 4) 3 + 2) b) ) 3 2 4) ) 3 2 4) ) c) ) ) 8.39) ) ) d) ) ) These are sample problems and you should not limit your study to just these problems. 2

3 e) f) g) ) ) ) ) Simplify each of the following and reduce to lowest terms simplest form). a) The LCD is x

4 b) Convert 7 8 into an equivalent decimal and percent. You may have to use long division % 4. Convert 5.2% into an equivalent fraction and decimal. 5.2% Evaluate b 2a) 2 + bc, given a 2, b 3, and c 4. b 2a) 2 + bc 3 2 2) ) 3 4) ) ) ) + 3 4) + 2) 4

5 6. Identify the constant terms) and the variable terms) of the expression 2a 2 8ab+b+0. Then identify the numerical coefficient of each variable term. The constant term is 0, the variable terms are 2a 2, 8ab and b. The numerical coefficient is 2a 2 is 2, the numerical coefficient is 8ab is 8, and the numerical coefficient is b is. 7. Simplify each of the following. 0a 3b 7a + 6b 5 a) 0a 3b 7a + 6b 5 0a 3b 7a + 6b 5 0a 7a 3b + 6b 5 7a + 3b 5 b) 2 x 2 3x ) + 3 4x 2 + ) 2 x 2 3x ) + 3 4x 2 + ) 2x 2 6x + 2x x 2 6x + 3 c) 5x 2 x + 8) 5x 2 x + 8) 5x 2x 6 3x 6 8. Simplify. a) 5m 2 2m + 2 ) 3 + 3m 2m 2) 5m 2 2m + 2 ) 3 + 3m 2m 2) 5m 2 2m m + 2m 2 7m 2 5m + 5 b) 2c 2 d 3) 3cd) 5c 3 d 5) 2c 2 d 3) 3cd) 5c 3 d 5) 2) 3) 5) c 2 c c 3) d 3 dd 5) 30c 6 d 9 5

6 c) 2n 2 ) 3 2n 2 ) 3 2n 2) 2n 2) 2n 2) 2) 2) 2) n 2) n 2) n 2) 8n 6 d) t 2 3t + 4 ) t 3) t 2 3t + 4 ) t 3) t 3) t 2 3t + 4 ) t t 2 3t + 4 ) 3 t 2 3t + 4 ) t 3 3t 2 + 4t 3t 2 + 9t 2 t 3 6t 2 + 3t 2 e) 3x ) 2x + 5) 3x ) 2x + 5) 6x 2 + 5x 2x 5 6x 2 + 3x 5 f) y 3) 2 y 3) 2 y 3) y 3) y 2 3y 3y + 9 y 2 6y + 9 g) 22m 2 n mn 33mn 2 mn 22m 2 n mn 33mn 2 mn 22m2 n mn mn mn 33mn2 mn 2m 3n h) x 2 5x + 8 ) x 3) Using the long division algorithm, please review this process if you cannot get this answer. x x 3. 6

7 i) 2y y 3 Again, using the long division algorithm, but you might find it helpful to rewrite 2y as 2y 2 + 0y + 7 first. 2y y Simplify. a) 2x + 9 9x x 5 5x The LCD is 45x. 2x + 9 9x x 5 5x 2x x 5 x 5 5x 9 9 0x x 45 45x 45x 0x x x x x b) x + + x x 6 5x 2 x 2 5x 6 Factor the denominators and the LCD is clearly x + ) x 6). x + + x x 6 5x 2 x 2 5x 6 x + ) + x x 6) 5x 2 x + ) x 6) x 6) x + ) x 6) + x x + ) x 6) x + ) 5x 2 x + ) x 6) x 6) + x x + ) 5x 2) x + ) x 6) x 6 + x2 + x 5x + 2 x + ) x 6) x 2 3x 4 x + ) x 6) x + ) x 4) x + ) x 6) x 4 x 6 7

8 c) x 2 + 3x 0 x 2 + 2x 8 x 2 + 3x 0 x 2 + 2x 8 x + 5) x 2) x + 4) x 2) x + 5 x + 4 d) x 2 7x 30 x 2 6x 40 2x2 + 5x + 2 2x 2 + 7x + 3 x 2 7x 30 x 2 6x 40 2x2 + 5x + 2 2x 2 + 7x + 3 x 0) x + 3) 2x + ) x + 2) x 0) x + 4) 2x + ) x + 3) x + 3) x + 2) x + 4) x + 3) x + 2 x + 4 e) 3x 2 y 9xy a 2 b 3x2 x 3 ab 2 3x 2 y 9xy a 2 b 3x2 x 3 ab 2 3x2 y 9xy a 2 b 3xy 3 x) a 2 b 3xy a 2 b 3by ax ab2 x 2 ab 2 3x 2 x 3 ab 2 x 2 3 x) 0. Simplify, final answer should not have negative expoments. a) 8x 5 y 2x 3 y 4 8x 5 y 2x 3 y 4 3x2 2y 3 8

9 b) 3ab 2 ) 2a b ) 3 3ab 2 ) 2a b ) 3 ) 3a 2b b 2 a ) 3a a ) 3 b 2 2b ) ) 3a a 3 b 2 8b 3 ) 3 3a4 8b 5 c) 2a 3 b 2 3ab 5 2a 3 b 2 3ab 5 2b2 b 5 3a 3 a 2b7 3a 4. Determine whether 9x 2 5 and y 2 + 3y 2 y of these. are monomials, binomials, trinomials, or none 9x 2 5 is a binomial, whereas y 2 + 3y 2 y is none of these.3 2. Factor each of the following polynomials as completely as possible. a) 2a 2 b 5a 2 b 2 + 7ab 2 2a 2 b 5a 2 b 2 + 7ab 2 ab 2a 5ab + 7b) b) 2x 2 5x 6xy + 5y 2x 2 5x 6xy + 5y x 2x 5) 3y 6x 5y) 2x 5) x 3y) 3 It s not a polynomial because there s a variable used as a divisor. 9

10 c) x 2 + 5x 36 x 2 + 5x 36 x + 9) x 4) d) 9x 2 3x 4 Not factorable over the integers. e) 6 9m 2 6 9m 2 4 3m) 4 + 3m) f) 4x 4 38x x 2 4x 4 38x x 2 2x 2 2x 2 9x + 24 ) 2x 2 2x 3) x 8) 3. Solve each of the following equations. a) 3 2x 5 + 4x 3 2x 5 + 4x 3 5 2x + 4x 2 6x 2 x So the solution is x 2. b) x Multiple both sides by the LCD. x x x x 2 So the solution is x /2. 0

11 c) 3 5 x x 2 x x 20 d) So the solution is x 20. x x x x e) So the solution is x x 4 So the solution is x 3/ x 4 6 8x x 3 8x 3 8 x f) 9x 3 2x ) 5 9x 3 2x ) 5 9x 6x x x 5 3 3x 2 x 4 So the solution is x 4.

12 g) x 2 8x x 2 8x x 5) x 3) 0 So the solution is x 5, or x 3. h) x x ) 2 x x ) 2 x 2 x 2 x 2 x 2 0 x 2) x + ) 0 So the solution is x 2, or x. i) x + 3) x + 4) 72 x + 3) x + 4) 72 x 2 + 7x x 2 + 7x 60 0 x + 2) x 5) 0 So the solution is x 2, or x 5. j) 5 x x So the solution is x x + 3 x 5 x ) 3 x + 3) 5x 5 3x + 9 5x 3x x 4 x 7 2

13 k) x 3 x x x x 3 x 3 2 x 3) x 3 2x 6 x 3 2x x 6 3 x 3 x x 3 x x 3 3 x 3 This equation has no solution. This may not be obvious, but the original statement is a contradiction and can never be true. 4. Solve for the indicated variable. a) R C S t for S R C S t Rt C S Rt C S C Rt S So the solution is S C Rt. b) A P + P rt for P So the solution is P A + rt. A P + P rt A P + rt) A + rt P 3

14 5. What is 35% of 80? 35% of What percent of 20 is 6? x x 6 5 x So the answer is 80% is.5% of what? x x 200 x 8. If 4 5x, evaluate x 2 3x +. First solve for x x 5 5x x Now evaluate x 2 3x + when x Is 5, 3) a solution of 3x 2y 9. Be sure to show enough work to justify your answer. No, because 3 5)

15 20. Determine the x and y-intercepts and the slope of the line given by 2x 3y 2. The x-intercept is 6, 0). The y-intercept is 0, 4). Using the formula for slope m y 2 y 4 0 x 2 x Determine the equation of the line that satisfies the given conditions. a) Contains the point 2, 3) and with slope m 2. y + 3 x 2) 2 2y + 6 x x + 2y Acceptable answers are: point-slope form y + 3 x 2) ; standard form x + 2y 4 ; 2 or slope-intercept form y 2 x 2. b) Contains the points 0, 6) and 2, 0). First determine the slope. m Acceptable answers are: point-slope form y 6 3 x 0) or y 0 3 x 2) ; standard form 3x + y 6 ; or slope-intercept form y 3x Translate each of the following phrases into variable expressions and simplify whenever possible. a) the product of t and the sum of t and 6 The translation is t t + 6), and the simplified form is t 2 + 6t. b) r decreased by the quotient of r and 3 The translation is r r 3, and the simplified form is 2r 3. c) nine less than the total of a number and two The translation is n + 2) 9, and the simplified form is n 7. 5

16 d) twice the difference of six times a number and seven The translation is 2 6n 7), and the simplified form is 2n Translate each of the following sentences into algebraic equations and solve to determine the numbers). Algebra must be used. a) The difference between five and twice a number is one. The translation is 5 2n, and the solution is n 2. b) Four less than three times a number is 25 The translation is 3n 4 25, and the solution is n 7. c) The sum of two numbers is eighteen. The total of three times the smaller and twice the larger is forty-four. The translation, where the small number is s and the larger number is 8 s, is 3s s) 44, and the solution is s 8, so the two numbers are 8 and 0. d) Find two consecutive even integers such that four times the first is three times the second. The translation, where the two consecutive even integers are n and n + 2, is 4n 3 n + 2), and the solution is n 6, so the two consecutive even intergers are 6 and 8. e) The sum of two numbers is six. twenty. The sum of the squares of the two numbers is The translation, where the two numbers are n and 6 n, is n n) 2 20, and the solution is n 4 or n 2, so the two consecutive even intergers are 2 and The high temperatures for a 6-day period in Barrow, Alaska, were 23 F, 29 F, 2 F, 28 F, 28 F, and 27 F. Calculate the average daily high temperature. Here the average is 23 F) + 29 F) + 2 F) + 28 F) + 28 F) + 27 F) 6 56 F 6 26 F. 25. The total cost to paint the inside of a house was \$346. This cost included \$25 for materials and \$33 per hour for labor. How many hours of labor were required to paint the inside of the house? Algebra must be used. The translation, where h is the number of hours of labor, is h, and the solution is h 37, so 37 hours of labor were required. 6

17 26. A 2-foot board is cut into two pieces. Twice the length of the shorter piece is 3 feet less than the length of the longer piece. Find the length of each piece. Algebra must be used. The translation, where the short piece is s feet and the long piece is 2 s, is 2s 2 s) 3, and the solution is s 3, so the lengths are 3 feet and 9 feet. 27. The perimeter of a rectangle is 26 meters. The length of the rectangle is meter more than twice the width. Find the length and width of the rectangle. Algebra must be used. The translation, where the width is w meters and the length piece is 2w +, is w + ) + 2w, and the solution is w 4, so the length and width are are 9 meters and 4 meters. 28. The perimeter of a triangle is 0 inches. One side is twice the second side. The third side is 30 inches more than the second side. Find the length of each side. Algebra must be used. The translation, where the length of the second side is x inches and the other sides 2x inches and x + 30 inches, is x + 2x + x + 30) 0, and the solution is x 20, so the lengths are 20 inches, 40 inches, and 50 inches. 29. The width of a rectangle is 5 feet less than the length. The area of the rectangle is 76 square feet. Find the length and width of the rectangle. Algebra must be used. The translation, where the length is l feet and the width is l 5 feet, is l l 5) 76, and the solution is l 6 or l 4, so the length and width are 6 feet and feet. 30. On a map, two cities are inches apart. If 3 8 inch on the map represents 25 miles, determine the number of miles between the two cities. First convert inches to an improper fraction mi in 3/8 in mi 7 25 mi 75 miles A car leaves a town traveling at 40 mph. Two hours later, a second car leaves the same town, on the same road, traveling at 60 mph. In how many hours will the second car pass the first car? Algebra must be used. The translation, where t represents the time, in hours, the second car has traveled when the two meet, is 60t 40 t + 2), and the solution is t 4, so it will take 4 hours. 4 The is an extraneous solution. 7

18 32. Two cars, one traveling 0 mph faster than the other, start at the same time from the same point and travel in opposite directions. In 3 hours they are 300 miles apart. Determine the rate of each car. Algebra must be used. The translation, where the rate of the slower car is r and the rate of the faster car is r + 0, in mies per hour, is 3r + 3 r + 0) 300, and the solution is r 45, rates are 45 mph and 55 mph. 33. The sales tax on a car that sold for \$2,000 is \$780. At this rate, how much higher is the sales tax on a car that sells for \$3,500? The translation, where the length is x represents the additional tax paid, is x 3500, and the solution is x 97.50, so it will take \$ more. 34. Graph the following lines on a Cartesian rectangular) coordinate system. a) y 2 3 x + Two points, such as 0, ) 3, ) should be used to plot the graph Figure : y 2 3 x + 8

19 b) x 2y 4 Two points, such as 0, 2) 4, 0) should be used to plot the graph Figure 2: x 2y 4 c) x 2 Two points, such as 2, 0) 2, ) should be used to plot the graph Figure 3: x 2 9

20 d) y 3 0 Two points, such as 0, 3), 3) should be used to plot the graph Figure 4: y

### MTH 086 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 20, 2006

MTH 06 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 0, 006 Math 06, Introductory Algebra, covers the mathematical content listed below. In order

### MTH 100 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created June 6, 2011

MTH 00 College Algebra Essex County College Division of Mathematics Sample Review Questions Created June 6, 0 Math 00, Introductory College Mathematics, covers the mathematical content listed below. In

### Florida Math 0028. Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper

Florida Math 0028 Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper Exponents & Polynomials MDECU1: Applies the order of operations to evaluate algebraic

### MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

### Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

### Mathematics Placement

Mathematics Placement The ACT COMPASS math test is a self-adaptive test, which potentially tests students within four different levels of math including pre-algebra, algebra, college algebra, and trigonometry.

### Higher Education Math Placement

Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

### MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,

### FACTORING OUT COMMON FACTORS

278 (6 2) Chapter 6 Factoring 6.1 FACTORING OUT COMMON FACTORS In this section Prime Factorization of Integers Greatest Common Factor Finding the Greatest Common Factor for Monomials Factoring Out the

### HIBBING COMMUNITY COLLEGE COURSE OUTLINE

HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE: - Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,

### Factoring Polynomials

UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can

### MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab

MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring non-course based remediation in developmental mathematics. This structure will

### Vocabulary Words and Definitions for Algebra

Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

### MATD 0390 - Intermediate Algebra Review for Pretest

MATD 090 - Intermediate Algebra Review for Pretest. Evaluate: a) - b) - c) (-) d) 0. Evaluate: [ - ( - )]. Evaluate: - -(-7) + (-8). Evaluate: - - + [6 - ( - 9)]. Simplify: [x - (x - )] 6. Solve: -(x +

### COMPETENCY TEST SAMPLE TEST. A scientific, non-graphing calculator is required for this test. C = pd or. A = pr 2. A = 1 2 bh

BASIC MATHEMATICS COMPETENCY TEST SAMPLE TEST 2004 A scientific, non-graphing calculator is required for this test. The following formulas may be used on this test: Circumference of a circle: C = pd or

### Florida Math 0018. Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower

Florida Math 0018 Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower Whole Numbers MDECL1: Perform operations on whole numbers (with applications, including

### 1.1 Practice Worksheet

Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1. Write each English phrase as a mathematical expression. (a) Three less than twice a number (b) Four more than half of a number (c)

### Algebra I Vocabulary Cards

Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression

### Algebra 1. Curriculum Map

Algebra 1 Curriculum Map Table of Contents Unit 1: Expressions and Unit 2: Linear Unit 3: Representing Linear Unit 4: Linear Inequalities Unit 5: Systems of Linear Unit 6: Polynomials Unit 7: Factoring

### MATH 21. College Algebra 1 Lecture Notes

MATH 21 College Algebra 1 Lecture Notes MATH 21 3.6 Factoring Review College Algebra 1 Factoring and Foiling 1. (a + b) 2 = a 2 + 2ab + b 2. 2. (a b) 2 = a 2 2ab + b 2. 3. (a + b)(a b) = a 2 b 2. 4. (a

### Answer Key for California State Standards: Algebra I

Algebra I: Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences.

### Students will be able to simplify and evaluate numerical and variable expressions using appropriate properties and order of operations.

Outcome 1: (Introduction to Algebra) Skills/Content 1. Simplify numerical expressions: a). Use order of operations b). Use exponents Students will be able to simplify and evaluate numerical and variable

### Florida Algebra 1 End-of-Course Assessment Item Bank, Polk County School District

Benchmark: MA.912.A.2.3; Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. Also assesses MA.912.A.2.13; Solve

### Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any.

Algebra 2 - Chapter Prerequisites Vocabulary Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. P1 p. 1 1. counting(natural) numbers - {1,2,3,4,...}

### COWLEY COUNTY COMMUNITY COLLEGE REVIEW GUIDE Compass Algebra Level 2

COWLEY COUNTY COMMUNITY COLLEGE REVIEW GUIDE Compass Algebra Level This study guide is for students trying to test into College Algebra. There are three levels of math study guides. 1. If x and y 1, what

### LAKE ELSINORE UNIFIED SCHOOL DISTRICT

LAKE ELSINORE UNIFIED SCHOOL DISTRICT Title: PLATO Algebra 1-Semester 2 Grade Level: 10-12 Department: Mathematics Credit: 5 Prerequisite: Letter grade of F and/or N/C in Algebra 1, Semester 2 Course Description:

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

Provider York County School Division Course Syllabus URL http://yorkcountyschools.org/virtuallearning/coursecatalog.aspx Course Title Algebra I AB Last Updated 2010 - A.1 The student will represent verbal

### SPECIAL PRODUCTS AND FACTORS

CHAPTER 442 11 CHAPTER TABLE OF CONTENTS 11-1 Factors and Factoring 11-2 Common Monomial Factors 11-3 The Square of a Monomial 11-4 Multiplying the Sum and the Difference of Two Terms 11-5 Factoring the

### PERT Mathematics Test Review

PERT Mathematics Test Review Prof. Miguel A. Montañez ESL/Math Seminar Math Test? NO!!!!!!! I am not good at Math! I cannot graduate because of Math! I hate Math! Helpful Sites Math Dept Web Site Wolfson

### Indiana State Core Curriculum Standards updated 2009 Algebra I

Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and

### Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III

Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III Name Date Adding and Subtracting Polynomials Algebra Standard 10.0 A polynomial is a sum of one ore more monomials. Polynomial

### CENTRAL TEXAS COLLEGE SYLLABUS FOR DSMA 0306 INTRODUCTORY ALGEBRA. Semester Hours Credit: 3

CENTRAL TEXAS COLLEGE SYLLABUS FOR DSMA 0306 INTRODUCTORY ALGEBRA Semester Hours Credit: 3 (This course is equivalent to DSMA 0301. The difference being that this course is offered only on those campuses

### Algebra 1 If you are okay with that placement then you have no further action to take Algebra 1 Portion of the Math Placement Test

Dear Parents, Based on the results of the High School Placement Test (HSPT), your child should forecast to take Algebra 1 this fall. If you are okay with that placement then you have no further action

### Algebra I. 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,

### What are the place values to the left of the decimal point and their associated powers of ten?

The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything

### 5.1 FACTORING OUT COMMON FACTORS

C H A P T E R 5 Factoring he sport of skydiving was born in the 1930s soon after the military began using parachutes as a means of deploying troops. T Today, skydiving is a popular sport around the world.

### Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.

Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear

### Algebra Cheat Sheets

Sheets Algebra Cheat Sheets provide you with a tool for teaching your students note-taking, problem-solving, and organizational skills in the context of algebra lessons. These sheets teach the concepts

### Review of Intermediate Algebra Content

Review of Intermediate Algebra Content Table of Contents Page Factoring GCF and Trinomials of the Form + b + c... Factoring Trinomials of the Form a + b + c... Factoring Perfect Square Trinomials... 6

### 1.3 Algebraic Expressions

1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n 1 x n 1 +... + a 2 x 2 + a 1 x + a 0 The numbers a 1, a 2,..., a n are called coefficients. Each of the separate parts,

### Answers to Basic Algebra Review

Answers to Basic Algebra Review 1. -1.1 Follow the sign rules when adding and subtracting: If the numbers have the same sign, add them together and keep the sign. If the numbers have different signs, subtract

### Factoring and Applications

Factoring and Applications What is a factor? The Greatest Common Factor (GCF) To factor a number means to write it as a product (multiplication). Therefore, in the problem 48 3, 4 and 8 are called the

### FSCJ PERT. Florida State College at Jacksonville. assessment. and Certification Centers

FSCJ Florida State College at Jacksonville Assessment and Certification Centers PERT Postsecondary Education Readiness Test Study Guide for Mathematics Note: Pages through are a basic review. Pages forward

### Quick Reference ebook

This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

### Algebra and Geometry Review (61 topics, no due date)

Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties

### Definitions 1. A factor of integer is an integer that will divide the given integer evenly (with no remainder).

Math 50, Chapter 8 (Page 1 of 20) 8.1 Common Factors Definitions 1. A factor of integer is an integer that will divide the given integer evenly (with no remainder). Find all the factors of a. 44 b. 32

### How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

### The program also provides supplemental modules on topics in geometry and probability and statistics.

Algebra 1 Course Overview Students develop algebraic fluency by learning the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. Students

### Florida Math for College Readiness

Core Florida Math for College Readiness Florida Math for College Readiness provides a fourth-year math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness

### Veterans Upward Bound Algebra I Concepts - Honors

Veterans Upward Bound Algebra I Concepts - Honors Brenda Meery Kaitlyn Spong Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) www.ck12.org Chapter 6. Factoring CHAPTER

### Math 1. Month Essential Questions Concepts/Skills/Standards Content Assessment Areas of Interaction

Binghamton High School Rev.9/21/05 Math 1 September What is the unknown? Model relationships by using Fundamental skills of 2005 variables as a shorthand way Algebra Why do we use variables? What is a

### POLYNOMIAL FUNCTIONS

POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a

### MATH 100 PRACTICE FINAL EXAM

MATH 100 PRACTICE FINAL EXAM Lecture Version Name: ID Number: Instructor: Section: Do not open this booklet until told to do so! On the separate answer sheet, fill in your name and identification number

### Math Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices.

Math Placement Test Study Guide General Characteristics of the Test 1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that

### Exercise Worksheets. Copyright. 2002 Susan D. Phillips

Exercise Worksheets Copyright 00 Susan D. Phillips Contents WHOLE NUMBERS. Adding. Subtracting. Multiplying. Dividing. Order of Operations FRACTIONS. Mixed Numbers. Prime Factorization. Least Common Multiple.

### Chapter 4 -- Decimals

Chapter 4 -- Decimals \$34.99 decimal notation ex. The cost of an object. ex. The balance of your bank account ex The amount owed ex. The tax on a purchase. Just like Whole Numbers Place Value - 1.23456789

### SUNY ECC. ACCUPLACER Preparation Workshop. Algebra Skills

SUNY ECC ACCUPLACER Preparation Workshop Algebra Skills Gail A. Butler Ph.D. Evaluating Algebraic Epressions Substitute the value (#) in place of the letter (variable). Follow order of operations!!! E)

### Mathematics Common Core Sample Questions

New York State Testing Program Mathematics Common Core Sample Questions Grade The materials contained herein are intended for use by New York State teachers. Permission is hereby granted to teachers and

### A Year-long Pathway to Complete MATH 1111: College Algebra

A Year-long Pathway to Complete MATH 1111: College Algebra A year-long path to complete MATH 1111 will consist of 1-2 Learning Support (LS) classes and MATH 1111. The first semester will consist of the

### ALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form

ALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form Goal Graph quadratic functions. VOCABULARY Quadratic function A function that can be written in the standard form y = ax 2 + bx+ c where a 0 Parabola

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

### Greatest Common Factor (GCF) Factoring

Section 4 4: Greatest Common Factor (GCF) Factoring The last chapter introduced the distributive process. The distributive process takes a product of a monomial and a polynomial and changes the multiplication

### Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year.

Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year. Goal The goal of the summer math program is to help students

### How To Solve Factoring Problems

05-W4801-AM1.qxd 8/19/08 8:45 PM Page 241 Factoring, Solving Equations, and Problem Solving 5 5.1 Factoring by Using the Distributive Property 5.2 Factoring the Difference of Two Squares 5.3 Factoring

### MATH 10034 Fundamental Mathematics IV

MATH 0034 Fundamental Mathematics IV http://www.math.kent.edu/ebooks/0034/funmath4.pdf Department of Mathematical Sciences Kent State University January 2, 2009 ii Contents To the Instructor v Polynomials.

### 6.1 Add & Subtract Polynomial Expression & Functions

6.1 Add & Subtract Polynomial Expression & Functions Objectives 1. Know the meaning of the words term, monomial, binomial, trinomial, polynomial, degree, coefficient, like terms, polynomial funciton, quardrtic

### Polynomials. Key Terms. quadratic equation parabola conjugates trinomial. polynomial coefficient degree monomial binomial GCF

Polynomials 5 5.1 Addition and Subtraction of Polynomials and Polynomial Functions 5.2 Multiplication of Polynomials 5.3 Division of Polynomials Problem Recognition Exercises Operations on Polynomials

### POLYNOMIALS and FACTORING

POLYNOMIALS and FACTORING Exponents ( days); 1. Evaluate exponential expressions. Use the product rule for exponents, 1. How do you remember the rules for exponents?. How do you decide which rule to use

### ALGEBRA I (Created 2014) Amherst County Public Schools

ALGEBRA I (Created 2014) Amherst County Public Schools The 2009 Mathematics Standards of Learning Curriculum Framework is a companion document to the 2009 Mathematics Standards of Learning and amplifies

### Number Sense and Operations

Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

### A synonym is a word that has the same or almost the same definition of

Slope-Intercept Form Determining the Rate of Change and y-intercept Learning Goals In this lesson, you will: Graph lines using the slope and y-intercept. Calculate the y-intercept of a line when given

### Algebra 1 Course Title

Algebra 1 Course Title Course- wide 1. What patterns and methods are being used? Course- wide 1. Students will be adept at solving and graphing linear and quadratic equations 2. Students will be adept

### 1.3 Polynomials and Factoring

1.3 Polynomials and Factoring Polynomials Constant: a number, such as 5 or 27 Variable: a letter or symbol that represents a value. Term: a constant, variable, or the product or a constant and variable.

### ( ) FACTORING. x In this polynomial the only variable in common to all is x.

FACTORING Factoring is similar to breaking up a number into its multiples. For example, 10=5*. The multiples are 5 and. In a polynomial it is the same way, however, the procedure is somewhat more complicated

### MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60

MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60 A Summar of Concepts Needed to be Successful in Mathematics The following sheets list the ke concepts which are taught in the specified math course. The sheets

### IOWA End-of-Course Assessment Programs. Released Items ALGEBRA I. Copyright 2010 by The University of Iowa.

IOWA End-of-Course Assessment Programs Released Items Copyright 2010 by The University of Iowa. ALGEBRA I 1 Sally works as a car salesperson and earns a monthly salary of \$2,000. She also earns \$500 for

### Summer Math Exercises. For students who are entering. Pre-Calculus

Summer Math Eercises For students who are entering Pre-Calculus It has been discovered that idle students lose learning over the summer months. To help you succeed net fall and perhaps to help you learn

### Math Review. for the Quantitative Reasoning Measure of the GRE revised General Test

Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important

### MATH 90 CHAPTER 6 Name:.

MATH 90 CHAPTER 6 Name:. 6.1 GCF and Factoring by Groups Need To Know Definitions How to factor by GCF How to factor by groups The Greatest Common Factor Factoring means to write a number as product. a

### MTH124: Honors Algebra I

MTH124: Honors Algebra I This course prepares students for more advanced courses while they develop algebraic fluency, learn the skills needed to solve equations, and perform manipulations with numbers,

### Use order of operations to simplify. Show all steps in the space provided below each problem. INTEGER OPERATIONS

ORDER OF OPERATIONS In the following order: 1) Work inside the grouping smbols such as parenthesis and brackets. ) Evaluate the powers. 3) Do the multiplication and/or division in order from left to right.

### Algebra 2 PreAP. Name Period

Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for completing

### Free Pre-Algebra Lesson 55! page 1

Free Pre-Algebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can

### Prentice Hall Mathematics, Algebra 1 2009

Prentice Hall Mathematics, Algebra 1 2009 Grades 9-12 C O R R E L A T E D T O Grades 9-12 Prentice Hall Mathematics, Algebra 1 Program Organization Prentice Hall Mathematics supports student comprehension

### SOL Warm-Up Graphing Calculator Active

A.2a (a) Using laws of exponents to simplify monomial expressions and ratios of monomial expressions 1. Which expression is equivalent to (5x 2 )(4x 5 )? A 9x 7 B 9x 10 C 20x 7 D 20x 10 2. Which expression

### Title Location Date Start Time End Time Description

Title Location Date Start Time End Time Description Operations w/ Integers SJC Rm 1457B Aug. 29 12:30 PM 2:00 PM Beginning with an introduction to integers, this workshop will review the four basic operations

### SIMPLIFYING ALGEBRAIC FRACTIONS

Tallahassee Community College 5 SIMPLIFYING ALGEBRAIC FRACTIONS In arithmetic, you learned that a fraction is in simplest form if the Greatest Common Factor (GCF) of the numerator and the denominator is

### Chapter 7 - Roots, Radicals, and Complex Numbers

Math 233 - Spring 2009 Chapter 7 - Roots, Radicals, and Complex Numbers 7.1 Roots and Radicals 7.1.1 Notation and Terminology In the expression x the is called the radical sign. The expression under the

### APPLICATIONS AND MODELING WITH QUADRATIC EQUATIONS

APPLICATIONS AND MODELING WITH QUADRATIC EQUATIONS Now that we are starting to feel comfortable with the factoring process, the question becomes what do we use factoring to do? There are a variety of classic

### Chesapeake College. Syllabus. MAT 031 Elementary Algebra (silcox87517) John H. Silcox

Chesapeake College Syllabus MAT 031 Elementary Algebra (silcox87517) John H. Silcox Phone 410-778-4540 (W) Phone 410-348-5370 (H) john.silcox@1972.usna.com Syllabus For MAT 031 I. OFFICE HOURS: One hour

### Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Solve word problems that call for addition of three whole numbers

### Polynomial Operations and Factoring

Algebra 1, Quarter 4, Unit 4.1 Polynomial Operations and Factoring Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Identify terms, coefficients, and degree of polynomials.

### SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS

(Section 0.6: Polynomial, Rational, and Algebraic Expressions) 0.6.1 SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS LEARNING OBJECTIVES Be able to identify polynomial, rational, and algebraic

### FACTORING POLYNOMIALS

296 (5-40) Chapter 5 Exponents and Polynomials where a 2 is the area of the square base, b 2 is the area of the square top, and H is the distance from the base to the top. Find the volume of a truncated

### Five 5. Rational Expressions and Equations C H A P T E R

Five C H A P T E R Rational Epressions and Equations. Rational Epressions and Functions. Multiplication and Division of Rational Epressions. Addition and Subtraction of Rational Epressions.4 Comple Fractions.

### Section 1.1 Linear Equations: Slope and Equations of Lines

Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of