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


 Roy Warner
 5 years ago
 Views:
Transcription
1 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 in the prealgebra memorization guide should be memorized as well.) Number Basics Starting with the counting numbers and ending with the real numbers, what are the different classifications of numbers and their associated descriptions? Counting numbers The numbers used for counting (,,, 4,, 6,...) Whole numbers The counting numbers and zero (0,,,, 4,, 6,...) Integers Negative and positive counting numbers and zero (...,,,, 0,,,,...) 0 Rational numbers Numbers that can be written as a ratio of two integers (i.e.,, ) 7 Irrational numbers Numbers that cannot be written as a ratio of two integers (i.e., π, ) Real numbers All rational and irrational numbers (i.e.,,, 7, π, ) 4 What are the place values to the left of the decimal point and their associated powers of ten? 4 0,... 0 Ones ( ) 0, tens ( 0 ), hundreds ( 0 ), one thousands ( 0 ), ten thousands ( ) What are the place values to the right of the decimal point and their associated powers of ten? 4 0,... Tenths ( ) 0, hundredths ( 0 ), thousandths ( 0 ), ten thousandths ( ) What is the rule for order of operations? PEMDAS. Parenthesis first, exponents next, then multiplication and division left to right, finally addition and subtraction left to right = + 6 = = + 6 = 7 example: ( ) Algebra Basics What is a variable? A variable is a letter or symbol used to represent a number (often unknown). example: x and y are variables in the expression x 4y. How do you tell if something is a solution to an equation? You plug the value in and see if the equation is true. example: Is x = 7 a solution of the equation x + = 8. Yes, since 7 + = 8. What are domain and range? The domain is the permitted inputs (typically x) and the range is the associated outputs (typically y). What are the restrictions on domain? (The restrictions an algebra student should know) You cannot divide by zero. You cannot have a negative expression in a square root ( x ). Algebra (page /0)
2 What is a function? How can a function relationship be represented? A function is a relationship that maps inputs (domain) to outputs (range). Each input has exactly one output. Functions can be represented verbally, numerically (tables, lists of ordered pairs), graphically, and algebraically (using an equation). What is meant by the distributive property? When an item is multiplied by a quantity, the item needs to be multiplied by all the items in the quantity x + y + z = x + xy + xz examples: ( + ) = + = and ( ) What is a term? What are like terms? A term is set of numbers and/or variables that are all multiplied and/or divided by each other. Terms are separated by addition or subtraction. Like terms are terms that have the same variable portion. example: In the expression "x + 4xy + 8 ", the terms are x, 4 xy, 8, and x x example: xy and 0 xy are like terms since the variable portion xy is the same for both terms. How are distances and rates related? Distance equals rate times time. D = RT example: If a driver drove 7 miles at 0mph, how long did the trip take? 7 = 0 x x =. hours What is direct variation and what is its model? Direct variation is a model where outputs get larger when inputs get larger and outputs get smaller when inputs get smaller. The input and outputs are directly related. The model is y = kx. What is inverse variation and what is its model? Inverse variation is a model where outputs get larger when inputs get smaller and outputs get smaller when inputs get larger. The input and outputs are inversely related. The model is y = k x. How do you find xintercepts? Set y = 0 and solve for x. How do you find yintercepts? Set x = 0 and solve for y. Solving equations How does order of operations affect solving equations? Solving equations is undoing steps. Essentially it is PEMDAS backwards. Undo the addition and subtraction, then undo the multiplication and division, etc. How do you solve linear equations? Get all the variables to one side, everything else to the other, factor if necessary, and then divide. examples: x + 8 = x 8 + = x x = x x = 7 π π ( x + ) = x π x + π = x π = x π x π = x ( π ) x = π Algebra (page /0)
3 How do you solve equations with fractions? Multiply every term by the common denominator of all the fractions to eliminate them and then solve the new equation that no longer has fractions. example: x + = 4 x x + = 4 x 0x + 4 = x 4 = x x = 4 How do you solve quadratic equations? Get everything to one side. Set the equation equal to zero. Factor and set the factors equal to zero. If the equation doesn t factor, use the quadratic formula. x = 6x 8 x 6x + 8 = 0 x x 4 = 0 x = or 4 examples: ( )( ) ± ± x + x = x x + 0 = x x + x = x = 4 ( ) ( ) 4 7 Why do we set quadratic equations equal to zero and factor them when we solve them? If two numbers are multiplied and the answer is zero then one of the numbers must be zero. This is the ZeroProduct Property. What is the quadratic formula? When can it be used? Negative b plus or minus the square root of b squared minus four times a times c all over two times a. ± b b 4ac a. This formula can be used on quadratic equations in the form How do you solve equations with square roots? Get the square root all by itself. Square both sides to undo the square root. example: ( ) ax bx c + + = 0. x + 4 = x + = 9 x + = 9 x + = 8 x = 78 How do you solve equations with absolute value? Since the expression inside the absolute value can be either positive or negative, you must solve two equations. Solve it as is and then make the expression inside the absolute value negative and solve it again. Both answers are solutions. example : x + = a) x + = x = 0 x = b) (x + ) = x + = x = x = 6 How does solving inequalities differ from solving equalities? When you multiply or divide by negative numbers, you must flip the inequality symbol. example: x + 8 < x < 6 x > How do you solve inequalities with absolute value? Since the expression inside the absolute value can be either positive or negative, you must solve two equations. Solve it as is and then make the expression inside the absolute value negative and solve it again. If it is < or the keyword is and. If it is > or the keyword is or. example : x + a) x + x 0 x b) (x + ) x + x x 6 so the answer will x 6 and x which can also be written as 6 x Algebra (page /0)
4 Lines What is the slopeintercept form for the equation of a line? y = mx + b where m is the slope and b is the yintercept. What is the pointslope form for the equation of a line? y y = m x x where m is the slope and x, y is the point. ( ) ( ) What two things do you need in order to write an equation of a line? A point and a slope. How do you write an equation of a line? Find a point on the line and the slope of the line. If you are using pointslope, just plug everything in. If you are using slopeintercept, plug in the point and the slope and solve for b. Write out your answer. example: Write the equation of a line in slopeintercept format going through (, ) with a slope of. y = mx + b = + b = 6 + b = b y = x What are the relationships between parallel and perpendicular lines? Parallel lines have the same slope and perpendicular lines have negative reciprocal slopes. examples: The two lines y = x + and y = x 4 are parallel. 4 The two lines y = x and y = x + are perpendicular. 4 Explain the process of solving a system of equations using substitution. You solve one of the equations for one of the variables and substitute it into the other equation. Then this new equation that has only one variable in it is solved. Finally, substitute the value of the solved variable back into the st equation you solved to find the value of the other variable. example: x + y = 8 x + ( 4x ) = 8 x = (, ) 4x y = y = 4x y = 4 y = Explain the process of solving a system of equations using elimination. The original equations are multiplied by numbers to get one of the variables equal and opposite. These new equations are added together to eliminate that variable. This new equation containing only one variable is solved. That answer is plugged back into one of the original equations to find the value of the other variable. x + y = 8 x + y = 8 example: ( ) 4x y = x y = 6 4 y = y =, Exponents and Radicals 4 x = 4 x = A nonzero number raised to the zero power is? One 0 example: = Algebra (page 4/0)
5 Zero raised to a nonzero power is? Zero example: 0 = 0 If you move a base with a negative exponent from the numerator to the denominator or vice versa what happens? The exponent becomes positive. (The opposite is true as well. If you move a base with a positive exponent from the numerator to the denominator or vice versa, the exponent becomes negative.) 4 examples: a) = b) = 4 What happens when identical bases with exponents are multiplied? The exponents are added example: = What happens when identical bases with exponents are divided? The exponents are subtracted. 9 example: = What happens when a base with an exponent is raised to another exponent? The exponents are multiplied. example: ( ) = 4 What happens when more than one item is raised to an exponent? Each item will be raised to the exponent. 4 4 example: ( ) ( ) xy = x y = 8x y How do you simplify a square root of a number? Find the prime factorization of the number. Whenever there are two identical factors, they can be taken outside of the square root as a single item. (Alternatively, you can look for perfect squares. Once found, the square root of the perfect squares are brought outside.) examples: = =, 90 = = 0, and 00 = = 0 alternative method examples: = 4 =, 90 = 9 0 = 0, and 00 = 00 = 0 In order to simplify a square root, what must be true of the numbers inside the square root? All the numbers in the square root must be multiplied or divided by each other. examples: 6 = =, = = + 4, and x + 9 is already fully simplified. How do you simplify expressions where the denominator is the square root of a number? If the denominator is a square root, then the numerator and the denominator are multiplied by that square root. example: = = = Algebra (page /0)
6 How do you multiply two numbers written in scientific notation? Multiply the numbers. Add the exponents. Convert back to scientific notation if necessary = = = 0 7 example: ( )( ) How do you divide two numbers written in scientific notation? Divide the numbers. Subtract the exponents. Convert back to scientific notation if necessary = 0. 0 = 0 0 = 0 example: ( ) ( ) Polynomials What is the degree of a polynomial? The degree of a polynomial is the same as the largest exponent of a polynomial. example: What is the degree of f ( x) = 4x 8x + 0x? f ( x ) is a rd degree polynomial. How do you add or subtract polynomials? The coefficients of the like terms are combined together. (Do not forget to distribute the negative sign for subtraction.) x 4x + 8 x + x + 0 = x 4x + 8 x x 0 = x 9x example: ( ) ( ) What is the process for multiplying binomials? Explain this process. FOIL. The first terms are multiplied, the outer terms are multiplied, the inner terms are multiplied, and the last terms are multiplied. The polynomial is then simplified. example: ( x + )( x ) = 6x 0x + 9x = 6x x Explain the process for multiplying polynomials. Each term of the first polynomial is multiplied by every term of the second polynomial. example : x + x + x 4x + = x x 4x + + x x 4x + + x 4x + ( )( ) ( ) ( ) ( ) How do you multiply ( a + b) and ( a b) ( ) ( ) +? = x 8x 4 x x x 6 x x 4x = x x 7x x a + b = a + ab + b and a b = a ab + b example: ( ) x y = x 0xy + 4 y How do you multiply ( a + b)( a b) a b +? example: ( )( ) x + y x y = 4x 9 y Explain the process of factoring (algebra topics only)? Factor out the greatest common factor first. Then look for the quadratic factoring patterns of a b, x + bx + c, and ax + bx + c. Finally, look for factoring by grouping. Algebra (page 6/0)
7 How do you factor the pattern of a + b a b ( )( ) a b? example: 6y 4 x = ( 4 y + x)( 4 y x) How do you factor the pattern x + bx + c? You look for two numbers that multiply to the constant term c and add to the middle term b. The factors are then written out as x plus those numbers. x x 8 = x + 4 x + = x 4 x + example: ( )( ) ( )( ) How do you factor the pattern ax + bx + c? You look for two numbers that multiply to the leading coefficient a times the constant term c and add to the middle term b. The factors are then written out as ax plus those numbers and with everything also divided by a. Simplify. ( x + )( x + ) example: x + x = = ( x + )( x ) Explain the process of factoring by grouping? Factoring by grouping works when there are an even number of terms. A common factor is taken out of the st set of terms and another common factor is taken out of the nd set of terms. If the expression that is left over is the same, you can factor by grouping. Factor out the expression that was left over. 4x + 8x 9x 8 = 4x x + 9 x + = 4x 9 x + = x + x x + example: ( ) ( ) ( )( ) ( )( )( ) Explain the process for completing the square on a quadratic expression. (algebra level expressions with a coefficient of one on the x squared term that look like x + bx + c ) Half of the coefficient on the x term (middle term) is squared. This quantity ( ) b is both added and subtracted from the expression. The positive term is used to factor the variable portion of the equation into a perfect square. The negative term is combined with the original constant term. example: 8 8 ( ) ( ) ( ) y = x + 8x y = x + 8x + y = x + 8x y = x How do you simplify rational expressions? Factor all of the rational expressions. Cancel any factors in both the numerator and denominator. x + x 4 x + 7x + 6 ( x + 4)( x ) ( x + )( x + 6) ( x + 6) example: = = x + x + 4 x x + ( x + )( x + 4) x ( x ) Statistics and Probability ( ) What is the difference between theoretical and experimental probability? Theoretical probability is the expected ratio of the number of successful outcomes to the number of possible outcomes. Experimental probability is the probability that an outcome occurs based upon repeated trials. Algebra (page 7/0)
8 What is the complement of an event in a probability problem? The complement of an event is the opposite of the event occurring. How do you find the probability for the complement of an event? The probability of an event and its complement both happening is one so the probability of the complement happening is one minus the probability of the event happening. example: If the probability of winning a particular drawing is 00, what is the probability of not winning the drawing? Probability of not winning = Probability of winning = 00 = How do you find the probability of an independent compound event? The probability of an independent compound event is the product of the probabilities of the two events. example: The 6 letters of the alphabet are placed in a bag. What is the probability of picking a vowel and then a consonant if the st letter is returned to the bag before picking the nd letter? 6 6 How do you find the probability of a dependent compound event? The probability of a dependent compound event is the product of the probabilities of the two events taking into account the effects of the st event on the nd event. example: The 6 letters of the alphabet are placed in a bag. What is the probability of picking a vowel and then a consonant if the st letter is not returned to the bag before picking the nd letter? 6 Graphing How do you graph inequalities on a number line? Less than " < " and greater than " > " are open circles. Less than or equal " " and greater than or equal " " are closed circles. Greater " > or " is shaded to the right. Less " < or " is shaded to the left. examples: x 0 x < How do you graph compound inequalities on a number line? The keyword and means that both inequalities must be true so the overlapping region is shaded. The keyword or means that either inequality must be true so both regions are shaded. examples: x 0 and x < x < 0 or x Algebra (page 8/0)
9 In a coordinate plane, describe the origin, xaxis, yaxis, and quadrants. The origin is the point where the xaxis and yaxis meet. The xaxis is the horizontal axis and the yaxis is the vertical axis. The quadrants are numbered I to IV starting in the top right and going counterclockwise. II I origin yaxis III   xaxis IV How is a point (x, y) plotted in a coordinate plane? The x coordinate is plotted left and right. Positive numbers are to the right and negative numbers are to the left. The y coordinate is plotted up and down. Positive numbers are up and negative numbers are down. examples: Plot the points A (, 4) and B (,). How do you know if a graphical relationship is a function? It passes the vertical line test (all vertical lines cross the graph in at most one point). What is the fallback method for graphing? Start graphing points until you understand what the graph is doing. How do you graph a line? Plot two points and connect them with a straight line. If a line is given in slopeintercept format, plot the yintercept and use the slope to find the nd point. If a line is given in pointslope format, plot the point and use the slope to find the nd point. If the line is given in some other format, find two points on the line and then connect them with a straight line. A line in the form of x equals a constant is what type of line? How do you graph this line? It is a vertical line. Draw a vertical line at the given x value. A line in the form of y equals a constant is what type of line? How do you graph this line? It is a horizontal line. Draw a horizontal line at the given y value. B A What does the graph of an absolute value function look like? Absolute value functions are Vshaped graphs. If the leading coefficient is positive, it opens up. If the leading coefficient is negative, it opens down. Absolute Value Function How do you graph inequalities in the coordinate plane? If the inequality is a or a the line is solid. If the inequality is a < or a > the line is dotted. A point is picked to determine which side of the curve makes the inequality true. The true side is shaded. Algebra (page 9/0)
10 What are the important properties of the graph of an exponential function? What does the graph of an exponential function look like? An exponential function has a horizontal asymptote and its slope is always increasing for exponential growth or its slope is always decreasing for exponential decay. Exponential Growth What does the graph of a quadratic function look like? Quadratic functions are parabolas. They are Ushaped graphs. If the leading coefficient is positive, it opens up. If the leading coefficient is negative, it opens down Exponential Decay Quadratic Function How do you graph a quadratic function in standard form?  b The x coordinate of the vertex occurs at negative b over two a. a.  Plug this x coordinate into the original function to find the y coordinate of the vertex. Plot the vertex and two additional points one on each side of the vertex. Draw in a quadratic Ushaped graph. What does the graph of a square root function look like? The graph of a square root function looks like a half parabola that would open left or right instead of up or down. Coordinate Geometry Square Root Function How do you find the slope between two points (, ) and (, ) x y x y? Slope is the difference in the y values over the difference in the x values it is the =. example: What is the slope between (4, ) and (8, )? = = How do you find the distance between two points (, ) and (, ) ( ) + ( ) distance = x x y y x y x y? example: What is the distance between (4, ) and (8, )? ( ) ( ) How do you find the midpoint of two points (, ) and (, ) x y x y? rise run  y x y x = = 0 = x + x y + y The midpoint is the average of the x coordinates and the average of the y coordinates., example: What is the midpoint of (4, ) and (8, )?, = ( 6,4) Algebra (page 0/0)
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
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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationAlgebra 2 YearataGlance Leander ISD 200708. 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks
Algebra 2 YearataGlance Leander ISD 200708 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks Essential Unit of Study 6 weeks 3 weeks 3 weeks 6 weeks 3 weeks 3 weeks
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 informationCRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide
Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are
More informationALGEBRA 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
More informationMath 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
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 informationAlgebra 2 Chapter 1 Vocabulary. identity  A statement that equates two equivalent expressions.
Chapter 1 Vocabulary identity  A statement that equates two equivalent expressions. verbal model A word equation that represents a reallife problem. algebraic expression  An expression with variables.
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 informationCORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical
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 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 informationFlorida Algebra 1 EndofCourse 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
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 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 informationA Quick Algebra Review
1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals
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 informationCopy 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,...}
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 informationEQUATIONS and INEQUALITIES
EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line
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 informationAlgebra 2: Themes for the Big Final Exam
Algebra : Themes for the Big Final Exam Final will cover the whole year, focusing on the big main ideas. Graphing: Overall: x and y intercepts, fct vs relation, fct vs inverse, x, y and origin symmetries,
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 informationAlgebra 1 Course Information
Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through
More informationUnderstanding Basic Calculus
Understanding Basic Calculus S.K. Chung Dedicated to all the people who have helped me in my life. i Preface This book is a revised and expanded version of the lecture notes for Basic Calculus and other
More informationBookTOC.txt. 1. Functions, Graphs, and Models. Algebra Toolbox. Sets. The Real Numbers. Inequalities and Intervals on the Real Number Line
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences, 3rd Edition Ronald J. Harshbarger, University of South Carolina  Beaufort Lisa S. Yocco, Georgia Southern University
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 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 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 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 informationMath 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
More informationFACTORING QUADRATICS 8.1.1 and 8.1.2
FACTORING QUADRATICS 8.1.1 and 8.1.2 Chapter 8 introduces students to quadratic equations. These equations can be written in the form of y = ax 2 + bx + c and, when graphed, produce a curve called a parabola.
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 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 informationGraphing Linear Equations
Graphing Linear Equations I. Graphing Linear Equations a. The graphs of first degree (linear) equations will always be straight lines. b. Graphs of lines can have Positive Slope Negative Slope Zero slope
More informationExample SECTION 131. XAXIS  the horizontal number line. YAXIS  the vertical number line ORIGIN  the point where the xaxis and yaxis cross
CHAPTER 13 SECTION 131 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants XAXIS  the horizontal
More informationa. all of the above b. none of the above c. B, C, D, and F d. C, D, F e. C only f. C and F
FINAL REVIEW WORKSHEET COLLEGE ALGEBRA Chapter 1. 1. Given the following equations, which are functions? (A) y 2 = 1 x 2 (B) y = 9 (C) y = x 3 5x (D) 5x + 2y = 10 (E) y = ± 1 2x (F) y = 3 x + 5 a. all
More informationA synonym is a word that has the same or almost the same definition of
SlopeIntercept Form Determining the Rate of Change and yintercept Learning Goals In this lesson, you will: Graph lines using the slope and yintercept. Calculate the yintercept of a line when given
More informationEquations. #110 Solve for the variable. Inequalities. 1. Solve the inequality: 2 5 7. 2. Solve the inequality: 4 0
College Algebra Review Problems for Final Exam Equations #110 Solve for the variable 1. 2 1 4 = 0 6. 2 8 7 2. 2 5 3 7. = 3. 3 9 4 21 8. 3 6 9 18 4. 6 27 0 9. 1 + log 3 4 5. 10. 19 0 Inequalities 1. Solve
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 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 informationCourse Outlines. 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit)
Course Outlines 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit) This course will cover Algebra I concepts such as algebra as a language,
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 informationAlgebra 2: Q1 & Q2 Review
Name: Class: Date: ID: A Algebra 2: Q1 & Q2 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which is the graph of y = 2(x 2) 2 4? a. c. b. d. Short
More informationMake sure you look at the reminders or examples before each set of problems to jog your memory! Solve
Name Date Make sure you look at the reminders or examples before each set of problems to jog your memory! I. Solving Linear Equations 1. Eliminate parentheses. Combine like terms 3. Eliminate terms by
More informationAlgebra 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
More informationStudents 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
More informationSAT Subject Math Level 1 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: Aritmetic Sequences: PEMDAS (Parenteses
More informationMA107 Precalculus Algebra Exam 2 Review Solutions
MA107 Precalculus Algebra Exam 2 Review Solutions February 24, 2008 1. The following demand equation models the number of units sold, x, of a product as a function of price, p. x = 4p + 200 a. Please write
More informationAnswers 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
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 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 informationHow To Understand And Solve Algebraic Equations
College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGrawHill, 2008, ISBN: 9780072867381 Course Description This course provides
More informationAlgebra Practice Problems for Precalculus and Calculus
Algebra Practice Problems for Precalculus and Calculus Solve the following equations for the unknown x: 1. 5 = 7x 16 2. 2x 3 = 5 x 3. 4. 1 2 (x 3) + x = 17 + 3(4 x) 5 x = 2 x 3 Multiply the indicated polynomials
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 informationIntro to Linear Equations Algebra 6.0
Intro to Linear Equations Algebra 6.0 Linear Equations: y x 7 y x 5 x y Linear Equations generally contain two variables: x and y. In a linear equation, y is called the dependent variable and x is the
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 informationCAMI Education linked to CAPS: Mathematics
 1  TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to
More informationACCUPLACER. Testing & Study Guide. Prepared by the Admissions Office Staff and General Education Faculty Draft: January 2011
ACCUPLACER Testing & Study Guide Prepared by the Admissions Office Staff and General Education Faculty Draft: January 2011 Thank you to Johnston Community College staff for giving permission to revise
More informationMTH124: 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,
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 informationSimplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
MAC 1105 Final Review Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. 1) 8x 249x + 6 x  6 A) 1, x 6 B) 8x  1, x 6 x 
More informationhttp://www.aleks.com Access Code: RVAE4EGKVN Financial Aid Code: 6A9DBDEE3B74F5157304
MATH 1340.04 College Algebra Location: MAGC 2.202 Meeting day(s): TR 7:45a 9:00a, Instructor Information Name: Virgil Pierce Email: piercevu@utpa.edu Phone: 665.3535 Teaching Assistant Name: Indalecio
More information7.1 Graphs of Quadratic Functions in Vertex Form
7.1 Graphs of Quadratic Functions in Vertex Form Quadratic Function in Vertex Form A quadratic function in vertex form is a function that can be written in the form f (x) = a(x! h) 2 + k where a is called
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 informationAlgebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard
Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express
More information1.6 A LIBRARY OF PARENT FUNCTIONS. Copyright Cengage Learning. All rights reserved.
1.6 A LIBRARY OF PARENT FUNCTIONS Copyright Cengage Learning. All rights reserved. What You Should Learn Identify and graph linear and squaring functions. Identify and graph cubic, square root, and reciprocal
More informationSECTION 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
More information1.3 LINEAR EQUATIONS IN TWO VARIABLES. Copyright Cengage Learning. All rights reserved.
1.3 LINEAR EQUATIONS IN TWO VARIABLES Copyright Cengage Learning. All rights reserved. What You Should Learn Use slope to graph linear equations in two variables. Find the slope of a line given two points
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 informationExponents. Exponents tell us how many times to multiply a base number by itself.
Exponents Exponents tell us how many times to multiply a base number by itself. Exponential form: 5 4 exponent base number Expanded form: 5 5 5 5 25 5 5 125 5 625 To use a calculator: put in the base number,
More informationCOLLEGE ALGEBRA. Paul Dawkins
COLLEGE ALGEBRA Paul Dawkins Table of Contents Preface... iii Outline... iv Preliminaries... Introduction... Integer Exponents... Rational Exponents... 9 Real Exponents...5 Radicals...6 Polynomials...5
More informationWeek 1: Functions and Equations
Week 1: Functions and Equations Goals: Review functions Introduce modeling using linear and quadratic functions Solving equations and systems Suggested Textbook Readings: Chapter 2: 2.12.2, and Chapter
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 informationIOWA EndofCourse Assessment Programs. Released Items ALGEBRA I. Copyright 2010 by The University of Iowa.
IOWA EndofCourse 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
More informationALGEBRA 2 CRA 2 REVIEW  Chapters 16 Answer Section
ALGEBRA 2 CRA 2 REVIEW  Chapters 16 Answer Section MULTIPLE CHOICE 1. ANS: C 2. ANS: A 3. ANS: A OBJ: 53.1 Using Vertex Form SHORT ANSWER 4. ANS: (x + 6)(x 2 6x + 36) OBJ: 64.2 Solving Equations by
More informationCommon Core Unit Summary Grades 6 to 8
Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity 8G18G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations
More information1) (3) + (6) = 2) (2) + (5) = 3) (7) + (1) = 4) (3)  (6) = 5) (+2)  (+5) = 6) (7)  (4) = 7) (5)(4) = 8) (3)(6) = 9) (1)(2) =
Extra Practice for Lesson Add or subtract. ) (3) + (6) = 2) (2) + (5) = 3) (7) + () = 4) (3)  (6) = 5) (+2)  (+5) = 6) (7)  (4) = Multiply. 7) (5)(4) = 8) (3)(6) = 9) ()(2) = Division is
More informationPrentice Hall Mathematics, Algebra 1 2009
Prentice Hall Mathematics, Algebra 1 2009 Grades 912 C O R R E L A T E D T O Grades 912 Prentice Hall Mathematics, Algebra 1 Program Organization Prentice Hall Mathematics supports student comprehension
More informationBlue Pelican Alg II First Semester
Blue Pelican Alg II First Semester Teacher Version 1.01 Copyright 2009 by Charles E. Cook; Refugio, Tx (All rights reserved) Alg II Syllabus (First Semester) Unit 1: Solving linear equations and inequalities
More informationPOLYNOMIALS 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
More informationPolynomial 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.
More informationMathematics 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
More informationSECTION 2.5: FINDING ZEROS OF POLYNOMIAL FUNCTIONS
SECTION 2.5: FINDING ZEROS OF POLYNOMIAL FUNCTIONS Assume f ( x) is a nonconstant polynomial with real coefficients written in standard form. PART A: TECHNIQUES WE HAVE ALREADY SEEN Refer to: Notes 1.31
More informationMSLC Workshop Series Math 1148 1150 Workshop: Polynomial & Rational Functions
MSLC Workshop Series Math 1148 1150 Workshop: Polynomial & Rational Functions The goal of this workshop is to familiarize you with similarities and differences in both the graphing and expression of polynomial
More informationPRECALCULUS GRADE 12
PRECALCULUS GRADE 12 [C] Communication Trigonometry General Outcome: Develop trigonometric reasoning. A1. Demonstrate an understanding of angles in standard position, expressed in degrees and radians.
More information