COWLEY COUNTY COMMUNITY COLLEGE REVIEW GUIDE Compass Algebra Level 2


 Kory Underwood
 7 years ago
 Views:
Transcription
1 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 is the value of the expression y + xy? A. 8 B. 4 C. D. 6. Which of the following expressions represents the product of four less than three times x and two more than x? A. x x 8 B. x x + 8 C. x + x + 8 D. x + x 8 x + x 8. A student earned scores of 9, 89, and 79 on three of four exams. What must the student score on the fourth exam to have an average (arithmetic mean) of exactly 8? A. 80 B. 8 C. 84 D What is the equation of the line that contains the points (, ) and (6, )? 7 A. y x 6 7 B. y x + 1 C. y x + 7 D. y x y x 4
2 x x 4. For all x ± 6, x 6 x 7 A. x + 6 B. C. D. x + 6 x 6 x + 7 x + 6 x + 7 x 6 x 7 x 6 6. A board 79 inches long is cut into pieces. The second piece is inches longer than the first. The third piece is twice as long as the second. If x represents the length of the first piece, then which equation can be used to determine the length of the first piece? A x+1 B. 79 x + (x + ) + x C. 79 x + 1 D. 79 x + (x + ) + (x + ) 79 4x The product of ( x 4)( x + 1) is A. x + 4x x 4 B. x + 4x 4 C. 4x 4 D. x 4 x + x 4x 4 8. The statement any integer evenly divisible by two is even is A. always true B. never true C. true for positive integers only D. true for negative integers only true only if the integer is a perfect square
3 9. If x, what is the value of x + 4x? A. B. 6 C. D. 4. Which of the following is the complete factorization of x + x 8? A. (x +)(x 4) B. (x 1)(x+8) C. (x )(x+4) D. (x )(x+4) (x )(x+1) 11. Which of these is the product of (x y) and (x + y)? A. x xy + y B. C. D. x xy y x + xy y x + xy y x y 1. If x and, what is the value of? A. 0 B. 19 C. 60 D y ( x + y) ( x y)
4 y   x 1. Which of the following equations is graphed above? A. y x + 1 B. y x + 1 C. y x + 1 D. y x + 1 y x Solve this equation: ( x 4) ( x + 1) A. x B. x 1 C. x 4 D. x 0 x A car salesman receives a weekly salary of W dollars plus a 6% commission on his total sales S. Which expression best describes his weekly pay? A. W + S B. (W + S) (0.6) C..06W +S D. W +.06S W + 6S
5 16. Which of these expressions is the product of ( y )( y y + y + )? A. 4 y + y y + y B. 4 y 7 y 8y 7 y 1 C. 4 y + y 8y + 1y + 1 D. 4 y 7 y 8y 7 y 1 4 y 7 y + 1y 7 y 1 y A   x B 17. On the graph shown above, what is the distance from point A to point B? A. 14 B. 6 C. 6 D. 14
6 4 6 x y 18. For all x 0 and y 0, simplify : 4 x y 9 x A. y B. 9 x y C. x y D. xy 1 xy 19. For all a, b, and c, simplify: ( ab c 4 ) A. ab 9 c 1 B a b c C a b c D. 4 ab c 9 1 a b c 0. Solve this equation: (x+1) (x ) 4(x + 1) + A. x 1 B. x 1/ C. x 1 D. x / x 0
7 Answers for Test 1: 1. B. D. A 4. B. E 6. D 7. E 8. A 9. D. C 11. B 1. B 1. A 14. C 1. D 16. E 17. C 18. B 19. E 0. C SOLUTIONS TO PRACTICE TEST 1. If x and y 1, what is the value of the expression y + xy? Answer: B y + xy ( 1) + ()( 1) ( 1) + ()(1) + 6(1) + 6 4
8 . Which of the following expressions represents the product of four less than three times x and two more than x? Answer: D Four less than three times x x 4 and two more than x x + You are asked to multiply the two expressions. (x 4)( x + ) x + 6x 4x 8 x + x 8. A student earned scores of 9, 89, and 79 on three of four exams. What must the student score on the fourth exam to have an average (arithmetic mean) of exactly 8? Answer: A ( x) 8 4 ( x) x x 40 x x 80
9 4. What is the equation of the line that contains the points (, ) and (6, )? Answer: B All of the answers are in slope intercept form, y mx + b. You xould find the slope first and then eliminate some answers. 1 y y 7 The slope m 1 x y 6 Use the point (,) and the y mx +b form to find the value of b. 7 y x + b 7 () + b 7 + b 1 b 7 Therefore, the equation of the line is y x + 1. If you do not remember the slope formula and the slope intercept form for a line, you could plug both points into the five equations and eliminate the distractors. x x 4. For all x ± 6, x 6 Answer: E This problem involves simplifying a rational expression and factoring. Factor the numerator as (x 7)(x + 6). Factor the denominator as (x + 6)(x 6). x 7 Divide out the common factor of (x + 6), and the resulting expression is. x 6 x x 4 x 6 ( x 7)( x + 6) ( x + 6)( x 6) x 7 x 6
10 6. A board 79 inches long is cut into pieces. The second piece is inches longer than the first. The third piece is twice as long as the second. If x represents the length of the first piece, then which equation can be used to determine the length of the first piece? Answer: D Let x represent the length of the first piece. Then x + represents the length of the second piece, and (x + ) represents the length of the third. x x+ (x+). 79 x + ( x + ) + ( x + ) Therefore, equation D, shown above, can be used to determine the length of the first piece. 7. The product of ( x 4)( x + 1) is Answer: E This is the product of two binomials, so you can use the FOIL method. ( x 4)( x + 1) x + x 4x 4 8. The statement any integer evenly divisible by two is even is Answer: A The statement represents the definition of an even integer, and therefore it is always true.
11 9. If x, what is the value of x + 4x? Answer: D x + 4x? ( ) + 4( ) (4) + 4( ) Which of the following is the complete factorization of x + x 8? Answer: C If you do not know how to factor this expression, you could FOIL each of the choices 11. Which of these is the product of (x y) and (x + y)? Answer: B FOIL the two binomials: ( x y)(x + y) x + xy xy y.. Then combine the like terms to obtain x xy y. 1. If x and, what is the value of? Answer: B y ( x + y) ( x y) + () ( ) [ ] ( + 1)( ) (1)( 8) 4( 8) 19 Be careful to keep the negative sign on the. Also, remember that multiplication comes before addition on the +() expression, giving 1 not 0.
12 y   x 1. Which of the following equations is graphed above? Answer: A These equations are all written in slopeintercept form, y mx + b. Look at the graph and note the yintercept is at (0, 1), so b 1. therefore E is not the solution. From point (0, 1), you can go to the point (, 4) by moving down units ( ) verticle change and to the right two units (+). Slope is the ration, so the slope is horizontal change, making the equation of this line y x Solve this equation: ( x 4) ( x + 1) Answer: C ( x 4) ( x + 1) x 1 x x 14 x 4 Make certain that you distribute correctly. The most common mistake in this kind of problem occurs when the is distributed incorrectly over (x + 1). ( x + 1) ( x) + ( )(1) x
13 1. A car salesman receives a weekly salary of W dollars plus a 6% commission on his total sales S. Which expression best describes his weekly pay? Answer: D This can be done by the process of elimination. Answer A is not correct because the 6% is not involved. Answer B is not correct because the 6% should me multiplied by the sales only. Answer C is not correct because the 6% is multiplied by the weekly salary instead of by the sales Answer E is not correct because the 6% is not correctly converted to decimal form. 6 %.06. Answer D is correct 16. Which of these expressions is the product of ( y )( y y + y + )? Answer: E Each term in the binomial must be multiplied by each term in the second polynomial. 4 Multiplying by y: y( y y + y + ) y y + y + y Multiplying by : ( y y + y + ) y + y y 1 4 y y + y + y Combining the like terms: y + y y 1 4 y 7y + 1y 7y 1
14 y A   x B 17. On the graph shown above, what is the distance from point A to point B? Answer: C This question can be answered with the Distance Formula or the Pythagorean Theorem. Using the Distance Formula, first determine the coordinates of the two points on the graph and plug those values into the distance formula. Point A is (, ) and Point B is (4, ). d ( x x ) + ( y y ) d d d d (4 ( )) + ( ) (9) + ( ) Using the Phythagorean Theorem, you could note that segment AB is the hypotenuse of a right triangle with vertex at (, ). You can see that the lengths of the legs of this triangle are 9 and units. Plug those values into the Phythagorean Theorem. a + b c c 6 c c 6 c
15 4 6 x y 18. For all x 0 and y 0, simplify : 4 x y Answer: B n 1 1 n Using the definition of negative exponents, a or a, make all exponents n n a a m n m + n positivel Then using the rule for multiplying with exponents, a a a, add the exponents of like bases. 4 x y x y x x 4 6 y y x y For all a, b, and c, simplify: ( ab c 4 ) Answer: E To find the power of a product, raise each factor to the power: m n mn the power of a power, multiply the exponents: ( x ) x ( ab c ) a b c a b c ( n xy ) n x y n, and to find 0. Solve this equation: (x+1) (x ) 4(x + 1) + Answer: C ( x + 1) ( x ) 4(x + 1) + 6x + x + 9 8x x x x + 6 x 1 x Use the distributive property. Combine like terms. Add x to both sides Add 6 to both sides Divide both sides by. This study guide has been created to give students the opportunity to review concepts covered on the assessment test. This has been prepared as a general study guide an in no way represents every question you will have on the assessment.
Zero: If P is a polynomial and if c is a number such that P (c) = 0 then c is a zero of P.
MATH 11011 FINDING REAL ZEROS KSU OF A POLYNOMIAL Definitions: Polynomial: is a function of the form P (x) = a n x n + a n 1 x n 1 + + a x + a 1 x + a 0. The numbers a n, a n 1,..., a 1, a 0 are called
More informationAlgebraic 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
More informationFlorida 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
More informationBrunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 20142015 school year.
Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 20142015 school year. Goal The goal of the summer math program is to help students
More informationMTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 17, 2006
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
More informationAlgebra Cheat Sheets
Sheets Algebra Cheat Sheets provide you with a tool for teaching your students notetaking, problemsolving, and organizational skills in the context of algebra lessons. These sheets teach the concepts
More informationCOMPETENCY TEST SAMPLE TEST. A scientific, nongraphing 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, nongraphing calculator is required for this test. The following formulas may be used on this test: Circumference of a circle: C = pd or
More informationMATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education)
MATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,
More informationAlgebra 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
More informationLyman Memorial High School. PreCalculus Prerequisite Packet. Name:
Lyman Memorial High School PreCalculus Prerequisite Packet Name: Dear PreCalculus Students, Within this packet you will find mathematical concepts and skills covered in Algebra I, II and Geometry. These
More informationSection 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
More informationMath 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
More informationAlum 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
More informationSAT Math Facts & Formulas Review Quiz
Test your knowledge of SAT math facts, formulas, and vocabulary with the following quiz. Some questions are more challenging, just like a few of the questions that you ll encounter on the SAT; these questions
More informationAlgebra 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
More informationMATH 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
More informationWhat 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
More informationPOLYNOMIAL 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
More informationHigher 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
More informationMATD 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 +
More informationMathematics Placement
Mathematics Placement The ACT COMPASS math test is a selfadaptive test, which potentially tests students within four different levels of math including prealgebra, algebra, college algebra, and trigonometry.
More informationMATH 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.
More informationFlorida Math for College Readiness
Core Florida Math for College Readiness Florida Math for College Readiness provides a fourthyear math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness
More informationLinear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (1,3), (3,3), (2,3)}
Linear Equations Domain and Range Domain refers to the set of possible values of the xcomponent of a point in the form (x,y). Range refers to the set of possible values of the ycomponent of a point in
More informationRadicals  Rational Exponents
8. Radicals  Rational Exponents Objective: Convert between radical notation and exponential notation and simplify expressions with rational exponents using the properties of exponents. When we simplify
More informationRadicals  Multiply and Divide Radicals
8. Radicals  Multiply and Divide Radicals Objective: Multiply and divide radicals using the product and quotient rules of radicals. Multiplying radicals is very simple if the index on all the radicals
More informationSolving Quadratic Equations
9.3 Solving Quadratic Equations by Using the Quadratic Formula 9.3 OBJECTIVES 1. Solve a quadratic equation by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation
More information0.8 Rational Expressions and Equations
96 Prerequisites 0.8 Rational Expressions and Equations We now turn our attention to rational expressions  that is, algebraic fractions  and equations which contain them. The reader is encouraged to
More information12) 13) 14) (5x)2/3. 16) x5/8 x3/8. 19) (r1/7 s1/7) 2
DMA 080 WORKSHEET # (8.8.2) Name Find the square root. Assume that all variables represent positive real numbers. ) 6 2) 8 / 2) 9x8 ) 00 ) 8 27 2/ Use a calculator to approximate the square root to decimal
More informationWarm Up. Write an equation given the slope and yintercept. Write an equation of the line shown.
Warm Up Write an equation given the slope and yintercept Write an equation of the line shown. EXAMPLE 1 Write an equation given the slope and yintercept From the graph, you can see that the slope is
More informationBig Bend Community College. Beginning Algebra MPC 095. Lab Notebook
Big Bend Community College Beginning Algebra MPC 095 Lab Notebook Beginning Algebra Lab Notebook by Tyler Wallace is licensed under a Creative Commons Attribution 3.0 Unported License. Permissions beyond
More informationAnswer 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.
More informationAlgebra 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
More informationOperations with Algebraic Expressions: Multiplication of Polynomials
Operations with Algebraic Expressions: Multiplication of Polynomials The product of a monomial x monomial To multiply a monomial times a monomial, multiply the coefficients and add the on powers with the
More informationAlgebra II End of Course Exam Answer Key Segment I. Scientific Calculator Only
Algebra II End of Course Exam Answer Key Segment I Scientific Calculator Only Question 1 Reporting Category: Algebraic Concepts & Procedures Common Core Standard: AAPR.3: Identify zeros of polynomials
More informationSOLVING EQUATIONS WITH RADICALS AND EXPONENTS 9.5. section ( 3 5 3 2 )( 3 25 3 10 3 4 ). The OddRoot Property
498 (9 3) Chapter 9 Radicals and Rational Exponents Replace the question mark by an expression that makes the equation correct. Equations involving variables are to be identities. 75. 6 76. 3?? 1 77. 1
More informationMTH 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
More informationMath 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
More informationChapter 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
More informationRadicals  Rationalize Denominators
8. Radicals  Rationalize Denominators Objective: Rationalize the denominators of radical expressions. It is considered bad practice to have a radical in the denominator of a fraction. When this happens
More informationHIBBING 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,
More informationMATH 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
More informationExtra Credit Assignment Lesson plan. The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam.
Extra Credit Assignment Lesson plan The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam. The extra credit assignment is to create a typed up lesson
More information5.1 Radical Notation and Rational Exponents
Section 5.1 Radical Notation and Rational Exponents 1 5.1 Radical Notation and Rational Exponents We now review how exponents can be used to describe not only powers (such as 5 2 and 2 3 ), but also roots
More information1.3 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.
More informationUnit 1: Integers and Fractions
Unit 1: Integers and Fractions No Calculators!!! Order Pages (All in CC7 Vol. 1) 31 Integers & Absolute Value 191194, 203206, 195198, 207210 32 Add Integers 33 Subtract Integers 215222 34 Multiply
More information6.4 Special Factoring Rules
6.4 Special Factoring Rules OBJECTIVES 1 Factor a difference of squares. 2 Factor a perfect square trinomial. 3 Factor a difference of cubes. 4 Factor a sum of cubes. By reversing the rules for multiplication
More informationAlgebra 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
More information1.3 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,
More informationPRIMARY CONTENT MODULE Algebra I Linear Equations & Inequalities T71. Applications. F = mc + b.
PRIMARY CONTENT MODULE Algebra I Linear Equations & Inequalities T71 Applications The formula y = mx + b sometimes appears with different symbols. For example, instead of x, we could use the letter C.
More informationCAHSEE on Target UC Davis, School and University Partnerships
UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,
More informationUnit 5: Coordinate Geometry Practice Test
Unit 5: Coordinate Geometry Practice Test Math 10 Common Name: Block: Please initial this box to indicate you carefully read over your test and checked your work for simple mistakes. What I can do in this
More informationVocabulary 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
More informationFactoring 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
More informationLesson 9: Radicals and Conjugates
Student Outcomes Students understand that the sum of two square roots (or two cube roots) is not equal to the square root (or cube root) of their sum. Students convert expressions to simplest radical form.
More informationOverview. Observations. Activities. Chapter 3: Linear Functions Linear Functions: SlopeIntercept Form
Name Date Linear Functions: SlopeIntercept Form Student Worksheet Overview The Overview introduces the topics covered in Observations and Activities. Scroll through the Overview using " (! to review,
More informationExpression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds
Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative
More informationMATH 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
More informationFactoring 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
More informationHow 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 prealgebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More informationAlgebra II A Final Exam
Algebra II A Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. Evaluate the expression for the given value of the variable(s). 1. ; x = 4 a. 34 b.
More informationMATH 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 noncourse based remediation in developmental mathematics. This structure will
More informationReview 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
More informationIV. ALGEBRAIC CONCEPTS
IV. ALGEBRAIC CONCEPTS Algebra is the language of mathematics. Much of the observable world can be characterized as having patterned regularity where a change in one quantity results in changes in other
More informationALGEBRA 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
More informationSuccessful completion of Math 7 or Algebra Readiness along with teacher recommendation.
MODESTO CITY SCHOOLS COURSE OUTLINE COURSE TITLE:... Basic Algebra COURSE NUMBER:... RECOMMENDED GRADE LEVEL:... 811 ABILITY LEVEL:... Basic DURATION:... 1 year CREDIT:... 5.0 per semester MEETS GRADUATION
More informationFactoring (pp. 1 of 4)
Factoring (pp. 1 of 4) Algebra Review Try these items from middle school math. A) What numbers are the factors of 4? B) Write down the prime factorization of 7. C) 6 Simplify 48 using the greatest common
More information2.5 Zeros of a Polynomial Functions
.5 Zeros of a Polynomial Functions Section.5 Notes Page 1 The first rule we will talk about is Descartes Rule of Signs, which can be used to determine the possible times a graph crosses the xaxis and
More informationThnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks
Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Welcome to Thinkwell s Homeschool Precalculus! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson
More informationThe 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
More informationCONTENTS. Please note:
CONTENTS Introduction...iv. Number Systems... 2. Algebraic Expressions.... Factorising...24 4. Solving Linear Equations...8. Solving Quadratic Equations...0 6. Simultaneous Equations.... Long Division
More informationFactoring Special Polynomials
6.6 Factoring Special Polynomials 6.6 OBJECTIVES 1. Factor the difference of two squares 2. Factor the sum or difference of two cubes In this section, we will look at several special polynomials. These
More informationSIMPLIFYING SQUARE ROOTS
40 (88) Chapter 8 Powers and Roots 8. SIMPLIFYING SQUARE ROOTS In this section Using the Product Rule Rationalizing the Denominator Simplified Form of a Square Root In Section 8. you learned to simplify
More informationSIMPLIFYING 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
More informationLAKE ELSINORE UNIFIED SCHOOL DISTRICT
LAKE ELSINORE UNIFIED SCHOOL DISTRICT Title: PLATO Algebra 1Semester 2 Grade Level: 1012 Department: Mathematics Credit: 5 Prerequisite: Letter grade of F and/or N/C in Algebra 1, Semester 2 Course Description:
More informationG r a d e 1 0 I n t r o d u c t i o n t o A p p l i e d a n d P r e  C a l c u l u s M a t h e m a t i c s ( 2 0 S ) Final Practice Exam
G r a d e 1 0 I n t r o d u c t i o n t o A p p l i e d a n d P r e  C a l c u l u s M a t h e m a t i c s ( 2 0 S ) Final Practice Exam G r a d e 1 0 I n t r o d u c t i o n t o A p p l i e d a n d
More informationPowerScore Test Preparation (800) 5451750
Question 1 Test 1, Second QR Section (version 2) Two triangles QA: x QB: y Geometry: Triangles Answer: Quantity A is greater 1. The astute student might recognize the 0:60:90 and 45:45:90 triangle right
More informationCongruent Number Problem
University of Waterloo October 28th, 2015 Number Theory Number theory, can be described as the mathematics of discovering and explaining patterns in numbers. There is nothing in the world which pleases
More informationSAT Subject Math Level 2 Facts & Formulas
Numbers, Sequences, Factors Integers:..., 3, 2, 1, 0, 1, 2, 3,... Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π, etc.) Order Of Operations: Arithmetic Sequences: PEMDAS (Parentheses
More informationAlgebra I Credit Recovery
Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,
More informationPrinciples of Mathematics MPM1D
Principles of Mathematics MPM1D Grade 9 Academic Mathematics Version A MPM1D Principles of Mathematics Introduction Grade 9 Mathematics (Academic) Welcome to the Grade 9 Principals of Mathematics, MPM
More informationAnchorage School District/Alaska Sr. High Math Performance Standards Algebra
Anchorage School District/Alaska Sr. High Math Performance Standards Algebra Algebra 1 2008 STANDARDS PERFORMANCE STANDARDS A1:1 Number Sense.1 Classify numbers as Real, Irrational, Rational, Integer,
More informationThe PointSlope Form
7. The PointSlope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope
More informationSimplifying Algebraic Fractions
5. Simplifying Algebraic Fractions 5. OBJECTIVES. Find the GCF for two monomials and simplify a fraction 2. Find the GCF for two polynomials and simplify a fraction Much of our work with algebraic fractions
More informationAlgebra 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,
More informationSummer Math Exercises. For students who are entering. PreCalculus
Summer Math Eercises For students who are entering PreCalculus 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
More informationGraphing  SlopeIntercept Form
2.3 Graphing  SlopeIntercept Form Objective: Give the equation of a line with a known slope and yintercept. When graphing a line we found one method we could use is to make a table of values. However,
More informationWhat does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b.
PRIMARY CONTENT MODULE Algebra  Linear Equations & Inequalities T37/H37 What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of
More informationA.2. Exponents and Radicals. Integer Exponents. What you should learn. Exponential Notation. Why you should learn it. Properties of Exponents
Appendix A. Exponents and Radicals A11 A. Exponents and Radicals What you should learn Use properties of exponents. Use scientific notation to represent real numbers. Use properties of radicals. Simplify
More informationMAT 135 Midterm Review Dugopolski Sections 2.2,2.3,2.5,2.6,3.3,3.5,4.1,4.2,5.7,5.8,6.1,6.2,6.3
Directions: Complete each problem and select the correct answer. NOTE: Not all topics on the midterm are represented in this review. For a complete set of review problems, please do the bookbased midterm
More informationVeterans 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
More information4. How many integers between 2004 and 4002 are perfect squares?
5 is 0% of what number? What is the value of + 3 4 + 99 00? (alternating signs) 3 A frog is at the bottom of a well 0 feet deep It climbs up 3 feet every day, but slides back feet each night If it started
More informationNSM100 Introduction to Algebra Chapter 5 Notes Factoring
Section 5.1 Greatest Common Factor (GCF) and Factoring by Grouping Greatest Common Factor for a polynomial is the largest monomial that divides (is a factor of) each term of the polynomial. GCF is the
More informationof surface, 569571, 576577, 578581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
More informationDefinition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
More informationA Yearlong Pathway to Complete MATH 1111: College Algebra
A Yearlong Pathway to Complete MATH 1111: College Algebra A yearlong path to complete MATH 1111 will consist of 12 Learning Support (LS) classes and MATH 1111. The first semester will consist of the
More information1.1 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)
More informationIndiana 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
More informationAlgebra 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
More informationMATHCOUNTS TOOLBOX Facts, Formulas and Tricks
MATHCOUNTS TOOLBOX Facts, Formulas and Tricks MATHCOUNTS Coaching Kit 40 I. PRIME NUMBERS from 1 through 100 (1 is not prime!) 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 II.
More information