LAKOTA WEST HIGH SCHOOL HONORS ALGEBRA II EXPECTATIONS ( )

Size: px
Start display at page:

Download "LAKOTA WEST HIGH SCHOOL HONORS ALGEBRA II EXPECTATIONS ( )"

Transcription

1 LAKOTA WEST HIGH SCHOOL HONORS ALGEBRA II EXPECTATIONS (07-08) Upon entering Honors Algebra II class at Lakota West HS it will be expected that you to have an excellent understanding of certain topics covered in CP Algebra I and Honors Geometry. We will not spend time in Honors Algebra II relearning these topics; instead, we will use the properties to work on problems that are more complicated. A TI-8 plus or TI-84 is recommended but not required for this assignment, however, it is a requirement for the Honors Algebra II class. Using the graphing calculator on certain problems will allow you to become more familiar with its potential before the first day of school. It would be advisable to complete the packet during the summer and not wait until the very last minute, because there will be homework problems assigned on the first day of class. You will also have a quiz on Friday, August 8 th over this packet. See you next year and enjoy the summer. Mrs. Green and Mrs. DeRossett Number Sense You should be able to identify Properties of Addition and Multiplication and be familiar with the various number systems. Notation: N: Stands for the set of natural (counting) numbers,,,... W: Stands for the set of whole numbers 0,,,,... Z: Stands for the set of integers...,,,0,,,... R: Stands for the set of real numbers (all # s including rational and irrational) : Stands for the element or element of Rational numbers are those which can be written in the form a b, where b 0. Irrational numbers are those which cannot be written in the form a. Decimals that are non-ending and nonb repeating are also irrational. The set of real numbers includes all rational and irrational numbers. Know basic properties: Commutative Properties, Associative Properties, Distributive Property, Additive/Multiplicative Identity and Inverses, Reflexive Property, Symmetric Property and Transitive Property. Page of 9

2 Put a check mark for the number sets that contain each number. W-whole numbers Z-integers Q-rational numbers I-irrational numbers R-real numbers W Z Q I R State the property illustrated.. 7x 9x 8 7x 9x 8.. 7n n 7 n.. x *y **x * y. 4. *4y y n 0 4n 5. Order of Operations PEMDAS P = Parenthesis (grouping symbols may be brackets, braces, etc.) E = Exponents M,D = Multiplication and Division from left to right A,S = Addition and Subtraction from left to right Page of 9

3 6 * Ex b). 4* 6 Ex a). 66 4*4 6 6* Simplify: a + a a 4 a * *8 4 Evaluating and Simplifying Expressions You should be able to evaluate and simplify expressions following order of operations. Evaluate each expression (#-) at the given values. Simplify each expression #4-6 ab ) x 5y when x and y = 8 ) when a and b a b ) 7x 8x when x 9 x 4 x 4) 5) x 6) x 4 0 Page of 9

4 UNDERSTANDING THE MAIN IDEAS Laws of exponents *Same bases x y x y. b b b. If 4 (Add the exponents.) b b 0, b b x xy (Subtract the exponents.) y 4 4. b x y b if and only if x = y If x 7, then x = 7 provided b 0,, or - (Set the exponents equal) *Same exponents. x x x ab a b 5 5 or If. a a b 0, b x a b x x b if and only if a b (provided x 0, a 0, and b 0) x *Power of a power: y xy b b *Zero exponent: If b 0, then x x If 5 5 *Negative exponent: x If x 0 and b 0, then b x b *Rational exponent ( b 0; b ; p, q integers; q 0) b a p a a b or t 7, then t b x p 4 a p 4 a 5 5 b b b 4 6 Page 4 of 9

5 Exponents You should be able to simplify using the exponent laws: Examples: 5 7 a). x x y 6x y b). x y z 7x y z c). x 9xy 8x y 6x d). 4 4 x y xy y xy z x z y 9y x y y x z 4x z Practice Problems. 6. 5a b c. x y 6 x x y z 5 5 x y z abcdef 0 4xy x y x y 4xy Page 5 of 9

6 Operations on Polynomials You should be able to add, subtract, and multiply polynomial expressions. Examples: a. x x 5 5x 6x 7x 9 5x 9x 5x 4 b. 4x 9 x x x x 6 c. x 4x 8x 4x x 6 8x 8x 6 d. x 5 x 5 x 5 4x 0x 5 Please note, letter d is a binomial square whose product is always a trinomial square. Paying close attention that it is NOT 4x 5, the exponent rule does not apply over addition or subtraction. Recognizing these two patterns will be very helpful to you throughout the higher levels of mathematics. Practice Problems:. 5c c 9 c 4c 7c c. 8n. 4P P 5 4. x 5. x 4x 6x 9 6. d 9 d 9 Solving Equations and Absolute Value Problems You should be able to solve any linear equations, including absolute value equations Examples: a). x x 5 5 5x x 6 8x 9 x b). x x x x x x x 0 Page 6 of 9

7 Absolute Value Examples continued: c). 4 6x d). x x 4 6x or 4 6x 6x or 6x 6 x or x Practice Problems - Solve: x 6 0 and x 5 0 x6 and x5 x 5. x 4. y x x 8 4. x x x 7. x 5x x 5x P = L + W, Solve for W 0. Q P Pr t, for P. x 6. x Inequalities You should be able to solve linear inequalities and be able to graph them on a number line. Examples: a. x 7 b. x 5 5x x 4 8x 8 x x Page 7 of 9

8 Practice Problems Solve and graph on a number line. x 5 7. x x 4. x 0 7x Compound Inequalities You should be able to solve and graph compound inequalities and absolute value inequalities Disjunction is or more statements that are joined by the word OR to make a compound statement. Conjunction is or more statements that are joined by the word AND to make a compound statement. Absolute Value: If ax b c, then c ax b c (conjunction) If ax b c, then ax b c or ax b c (disjunction) Examples: Conjunction: Disjunction: Absolute Value: 6 x 8 x 4 or x 5>7 5x 5x a. 4 x 0 b. x< or x > c. 5 5x x 5 x< or x>6 x 5 Practice Problems: Solve and graph the following problems x<8 8 x. 6 x 0 or 8 x 0 4. x 5 or x x 6 6. x 7 4 Page 8 of 9

9 Equations of Lines Vocabulary: Slope Ordered pairs x, y Vertical line x # Horizontal line y # Slope of a line rate of change Slope of a vertical line is undefined. Slope of horizontal line is 0 The slope, m, of the non-vertical line passing through the points y y xy, and x, y is found by m x x Parallel lines have the same slope. m m Perpendicular lines have slopes that are negative reciprocals of each other. mm Slope intercept form of a line: y mx b (m slope, b yintercept) y - y Point-slope formula: y y mx xor m. x - x Standard form: Ax By C where A, B, and C are integers. (no fractions or decimals) Graph linear equations using an x-y chart, x-y intercepts or slope intercept form. You should be able to find the slope of a line given the graph. A line which is increasing from left to right has a positive slope and a line decreasing from left to right has a negative slope. 9 7 Example: Given the points, and 4, 9 Solution: m 4 7 Find the slope of the following lines. ma mb b a c mc Practice Problems:. 5, 4,9. 9, 89,. 4,74, Page 9 of 9

10 Cartesian Coordinate Plane Know the axes, and quadrants (use Roman Numerals) Plot the following ordered pairs and determine which quadrant or axis the point lies on.. A -,4. B 0,8. C -5, D 7,0 Equation of Lines - You should be very familiar with Slope-Intercept Form, Standard Form, Point-Slope Formula and be able to use all interchangeably. Slope intercept form is y mx b. The m is the slope and b is the y intercept written as0,b Example: Find the slope and the y intercept of the line whose equation is y x m, y- intercept 0, Find the slope and y intercept of the following lines.. y 5x 6. y 0. x 4. y 4 6x m= m= m= m= y-int. = y-int. = y-int. = y-int. = Standard form The standard form of a linear equation is Ax + By = C, where A,B,C, are all integers (no fractions or decimals) and A is positive Example: Put the following equation in standard form. 8x 0 5y 8x 5y 0, therefore A 8, B 5 and C = 0 Page 0 of 9

11 Put the following equations in standard form and identify A, B, and C.. 4x 8 y. 6 x y x 8 6y. A = A = A = B = B = B = C = C = C = 4. Use Point Slope Formula to write the equation of a line that passes through the points, 4. Put the equation in Standard Form., and 5. Use Point Slope Formula to write the equation of a line that passes through the points, and parallel to 5xy 9. Put the equation in Slope-Intercept Form. Graphing You should be able to graph an equation of a line using various methods. Graphing using an x-y chart Graphing using x and y intercepts Graphing using the slope intercept form Examples: a. x y 6 some points that satisfy the equation are,,,4, 6,0 5 b. x 5y 5 x intercept is,0 ; y intercept is 0, c. 8x y 6 rewrite in slope intercept form y 4x Slope is -4 and y-intercept is 0, Page of 9

12 Graph using the x-y chart.. x y 8 X Y. y x 5 X Y Graph using x and y intercepts The y-intercept is the point where the graph intersects the y axis. x 0. It is the ordered pair, 0, y The x-intercept is the point where the graph intersects the x axis. y 0. It is the ordered pair, x,0 Example: Find the y intercept and x intercept of the following equation and graph. y x 4 To find the y - intercept, substitute 0 in for x and solve. y x 4 y 0 4 y 4 Therefore, the To find the x intercept, substitute 0 in for y and solve y x 4 0 x 4 4 x Therefore, the x-intercept is,0 x y intercept is 0,4 Page of 9

13 Find the x and y intercepts and graph the equations.. x 4y. x y y intercept x intercept y intercept x intercept Graph using slope intercept form. Example: y x m ; y intercept 0, Practice Problems:. y 7 x. x 9 y m m y intercept y intercept Page of 9

14 Systems of Equations You should be able to solve two linear equations with two unknowns by using substitution method and linear combination method. Example: Substitution Method: x 4y 0 5x y 0 Solve one of the equations for x or y and substitute into the other equation y 5x 0 x 4 5x 0 0 ; x 0x 40 0 ; x 4; ; 4 x 4 y 5 0 ; Example: 5 y The intersection point then is Linear Combination: 4 5, x 4y 5x y 0 Multiply one or both equations by what you need so that when you add the equations together one of the variables cancels. x 4y x 4y x x y 0 0x 4y 40 x then solve for y The intersection point then is Practice Problems: 4 5, Solve the following system of equations by using substitution method.. y x. x y 5 4x y y x Solve the following system of equations by using the linear combination method.. 5x y 7 4. y x 5 x y 4y x 0 5. What different types of solutions can you have to a system of linear equations? Page 4 of 9

15 Graphing and Transformations You should know the basic parent graphs for a linear, quadratic, absolute value, cubic, square root and exponential graph. You should also be able to describe the type of transformation the parent graph goes through and be able to graph it. You should know the concepts of domain and range. Transformation Appearance in Function Transformation of Point f x f x d x, y x, y d Vertical Translation (up/down) Horizontal Translation (left/right) f x f x c x, y x c, y f x a f x x, y x,a y Vertical Stretch/Shrink If a, then the graph is stretched vertically If a, then the graph is shrunk vertically Horizontal Stretch/Shrink If b, then the graph is stretched horizontally If b, then the graph is shrunk horizontally f b x f x x x, y, y b Reflection over x-axis f x f x x, y x, y Reflection over y-axis f x f x x, y x, y General Graphing Form: y a f b x c d Stretches/Shrinks and reflections are done first and then translations Practice Sketch the following parent graphs; State Domain and Range:. f x x. f x x. f x x x 4. f x x 5. f x 6. f x x Page 5 of 9

16 Practice Describe the transformation of each equation below for 6. f x x 7. f x f x x x 8. f x x 7 9. f x x 5 0. f x x. f x x. f x x. f x x 4. Graph f x x 4 vertex: domain: range: 5. Graph f x x 4 vertex: domain: range: Page 6 of 9

17 Factoring You should be able to factor and solve equations by factoring. Vocabulary: Factor Binomial Trinomial Polynomial Degree of a polynomial Difference of Squares Binomial Square Trinomial Square Greatest Common Factor Prime Examples: Factor: 4x 0 x 5 b). x 9x 4 y x x y a). c). x x 4 x 4x d). x 5x 6 x x e). 6x 9x 0 x x 5 f). 9 4x x x g). 6x 40x 5 4x 5 ; this is a Trinomial Square that factors into a Binomial Square h). Solve: x 6x 6 0 x 8 x 0 x 8, x x =, 8 Practice problems - Factor:. t t 7. x 8x 5. 9y 6x x y 5xy x x y 5 8y 7. 8x x z 5z y y y 0. 9y 0y 5. 6x 7xy 8y x 6y Page 7 of 9

18 Solve.. x 4 x 4. 9y x 0x x Solving Quadratic Equations You should be familiar with Factoring, Complete the Square and the Quadratic Formula: Quadratic Formula (QF): b b 4ac x a Complete the Square (CTS): Example: Practice problems - Solve:. Solve by CTS a). x 4x 0 b) x 5x0 0. Solve by QF: x 6x 4 0 Page 8 of 9

19 Radicals You should be able to work with and simplify all types of radicals. Simplify radicals Add and Subtract radicals remember you need like radicals Multiply and divide radicals including rationalizing the denominator Simplify: Rational exponents: a m k k a m Page 9 of 9

Algebra 2 Summer Work Packet Review and Study Guide

Algebra 2 Summer Work Packet Review and Study Guide Algebra Summer Work Packet Review and Study Guide This study guide is designed to accompany the Algebra Summer Work Packet. Its purpose is to offer a review of the nine specific concepts covered in the

More information

Algebra One Dictionary

Algebra One Dictionary Algebra One Dictionary Page 1 of 17 A Absolute Value - the distance between the number and 0 on a number line Algebraic Expression - An expression that contains numbers, operations and at least one variable.

More information

Simplify each numerical expression. Show all work! Only use a calculator to check. 1) x ) 25 ( x 2 3) 3) 4)

Simplify each numerical expression. Show all work! Only use a calculator to check. 1) x ) 25 ( x 2 3) 3) 4) NAME HONORS ALGEBRA II REVIEW PACKET To maintain a high quality program, students entering Honors Algebra II are expected to remember the basics of the mathematics taught in their Algebra I course. In

More information

x y x y ax bx c x Algebra I Course Standards Gap 1 Gap 2 Comments a. Set up and solve problems following the correct order of operations (including proportions, percent, and absolute value) with rational

More information

Algebra 31 Summer Work Packet Review and Study Guide

Algebra 31 Summer Work Packet Review and Study Guide Algebra Summer Work Packet Review and Study Guide This study guide is designed to accompany the Algebra Summer Work Packet. Its purpose is to offer a review of the ten specific concepts covered in the

More information

Math 75 Mini-Mod Due Dates Spring 2016

Math 75 Mini-Mod Due Dates Spring 2016 Mini-Mod 1 Whole Numbers Due: 4/3 1.1 Whole Numbers 1.2 Rounding 1.3 Adding Whole Numbers; Estimation 1.4 Subtracting Whole Numbers 1.5 Basic Problem Solving 1.6 Multiplying Whole Numbers 1.7 Dividing

More information

Evaluate algebraic expressions for given values of the variables.

Evaluate algebraic expressions for given values of the variables. Algebra I Unit Lesson Title Lesson Objectives 1 FOUNDATIONS OF ALGEBRA Variables and Expressions Exponents and Order of Operations Identify a variable expression and its components: variable, coefficient,

More information

Beginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions

Beginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions Beginning Algebra 1.3 Review of Decimal Numbers and Square Roots 1.4 Review of Percents 1.5 Real Number System 1.6 Translations:

More information

Algebra 1 Seamless Curriculum Guide

Algebra 1 Seamless Curriculum Guide QUALITY STANDARD #1: REAL NUMBERS AND THEIR PROPERTIES 1.1 The student will understand the properties of real numbers. o Identify the subsets of real numbers o Addition- commutative, associative, identity,

More information

Algebra I Vocabulary Cards

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 Order of Operations Expression Variable Coefficient

More information

ASSIGNMENT. Please complete only the assignment for the class you will begin in September 2018.

ASSIGNMENT. Please complete only the assignment for the class you will begin in September 2018. ASSIGNMENT Attached is an assignment containing items necessary for you to have mastered to do well in Algebra II. Please complete only the assignment for the class you will begin in September 2018. Practicing

More information

Algebra I Vocabulary Cards

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

More information

Geometry Summer Assignment 2018

Geometry Summer Assignment 2018 Geometry Summer Assignment 2018 The following packet contains topics and definitions that you will be required to know in order to succeed in Geometry this year. You are advised to be familiar with each

More information

Scope and Sequence Mathematics Algebra 2 400

Scope and Sequence Mathematics Algebra 2 400 Scope and Sequence Mathematics Algebra 2 400 Description : Students will study real numbers, complex numbers, functions, exponents, logarithms, graphs, variation, systems of equations and inequalities,

More information

Algebra I Unit Report Summary

Algebra I Unit Report Summary Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit - ( Ascend Default unit) 1. A01_01_01 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02

More information

Module 1: Whole Numbers Module 2: Fractions Module 3: Decimals and Percent Module 4: Real Numbers and Introduction to Algebra

Module 1: Whole Numbers Module 2: Fractions Module 3: Decimals and Percent Module 4: Real Numbers and Introduction to Algebra Course Title: College Preparatory Mathematics I Prerequisite: Placement with a score below 20 on ACT, below 450 on SAT, or assessing into Basic Applied Mathematics or Basic Algebra using Accuplacer, ASSET

More information

Parenthesis and other grouping symbols. Exponential expressions. Multiplication & Division Addition & Subtraction.

Parenthesis and other grouping symbols. Exponential expressions. Multiplication & Division Addition & Subtraction. NAME SADDLE BROOK HIGH SCHOOL HONORS ALGEBRA II SUMMER PACKET To maintain a high quality program, students entering Honors Algebra II are expected to remember the basics of the mathematics taught in their

More information

Part 2 - Beginning Algebra Summary

Part 2 - Beginning Algebra Summary Part - Beginning Algebra Summary Page 1 of 4 1/1/01 1. Numbers... 1.1. Number Lines... 1.. Interval Notation.... Inequalities... 4.1. Linear with 1 Variable... 4. Linear Equations... 5.1. The Cartesian

More information

MA094 Part 2 - Beginning Algebra Summary

MA094 Part 2 - Beginning Algebra Summary MA094 Part - Beginning Algebra Summary Page of 8/8/0 Big Picture Algebra is Solving Equations with Variables* Variable Variables Linear Equations x 0 MA090 Solution: Point 0 Linear Inequalities x < 0 page

More information

Basic ALGEBRA 2 SUMMER PACKET

Basic ALGEBRA 2 SUMMER PACKET Name Basic ALGEBRA SUMMER PACKET This packet contains Algebra I topics that you have learned before and should be familiar with coming into Algebra II. We will use these concepts on a regular basis throughout

More information

Basic Fraction and Integer Operations (No calculators please!)

Basic Fraction and Integer Operations (No calculators please!) P1 Summer Math Review Packet For Students entering Geometry The problems in this packet are designed to help you review topics from previous mathematics courses that are important to your success in Geometry.

More information

Are you ready for Algebra 3? Summer Packet *Required for all Algebra 3/Trigonometry Students*

Are you ready for Algebra 3? Summer Packet *Required for all Algebra 3/Trigonometry Students* Name: Date: Period: Are you ready for Algebra? Summer Packet *Required for all Students* The course prepares students for Pre Calculus and college math courses. In order to accomplish this, the course

More information

Check boxes of Edited Copy of Sp Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and

Check boxes of Edited Copy of Sp Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and Check boxes of Edited Copy of 10021 Sp 11 152 Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and Additional Topics Appendix Course Readiness Multiplication

More information

Coach Stones Expanded Standard Pre-Calculus Algorithm Packet Page 1 Section: P.1 Algebraic Expressions, Mathematical Models and Real Numbers

Coach Stones Expanded Standard Pre-Calculus Algorithm Packet Page 1 Section: P.1 Algebraic Expressions, Mathematical Models and Real Numbers Coach Stones Expanded Standard Pre-Calculus Algorithm Packet Page 1 Section: P.1 Algebraic Expressions, Mathematical Models and Real Numbers CLASSIFICATIONS OF NUMBERS NATURAL NUMBERS = N = {1,2,3,4,...}

More information

Geometry 21 Summer Work Packet Review and Study Guide

Geometry 21 Summer Work Packet Review and Study Guide Geometry Summer Work Packet Review and Study Guide This study guide is designed to accompany the Geometry Summer Work Packet. Its purpose is to offer a review of the ten specific concepts covered in the

More information

Harbor Creek School District. Algebra II Advanced. Concepts Timeframe Skills Assessment Standards Linear Equations Inequalities

Harbor Creek School District. Algebra II Advanced. Concepts Timeframe Skills Assessment Standards Linear Equations Inequalities Algebra II Advanced and Graphing and Solving Linear Linear Absolute Value Relation vs. Standard Forms of Linear Slope Parallel & Perpendicular Lines Scatterplot & Linear Regression Graphing linear Absolute

More information

Academic Algebra 2. Algebra 1 Review

Academic Algebra 2. Algebra 1 Review Academic Algebra On the following pages you will find a review of the Algebra concepts needed to successfully complete Academic Algebra. Concepts such as fractions, solving equations, inequalities, absolute

More information

Algebra II Honors Curriculum Guide Dunmore School District Dunmore, PA

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

More information

Common Core Standards Addressed in this Resource

Common Core Standards Addressed in this Resource Common Core Standards Addressed in this Resource.EE.3 - Apply the properties of operations to generate equivalent expressions. Activity page: 4 7.RP.3 - Use proportional relationships to solve multistep

More information

MATH Spring 2010 Topics per Section

MATH Spring 2010 Topics per Section MATH 101 - Spring 2010 Topics per Section Chapter 1 : These are the topics in ALEKS covered by each Section of the book. Section 1.1 : Section 1.2 : Ordering integers Plotting integers on a number line

More information

evaluate functions, expressed in function notation, given one or more elements in their domains

evaluate functions, expressed in function notation, given one or more elements in their domains Describing Linear Functions A.3 Linear functions, equations, and inequalities. The student writes and represents linear functions in multiple ways, with and without technology. The student demonstrates

More information

Chapter R - Review of Basic Algebraic Concepts (26 topics, no due date)

Chapter R - Review of Basic Algebraic Concepts (26 topics, no due date) Course Name: Math 00023 Course Code: N/A ALEKS Course: Intermediate Algebra Instructor: Master Templates Course Dates: Begin: 08/15/2014 End: 08/15/2015 Course Content: 245 topics Textbook: Miller/O'Neill/Hyde:

More information

Bishop Kelley High School Summer Math Program Course: Algebra 2 A

Bishop Kelley High School Summer Math Program Course: Algebra 2 A 06 07 Bishop Kelley High School Summer Math Program Course: Algebra A NAME: DIRECTIONS: Show all work in packet!!! The first 6 pages of this packet provide eamples as to how to work some of the problems

More information

Algebra II Curriculum Guide Dunmore School District Dunmore, PA

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

More information

Algebra I. CORE TOPICS (Key Concepts & Real World Context) UNIT TITLE

Algebra I. CORE TOPICS (Key Concepts & Real World Context) UNIT TITLE CHAPTER 1 Using variables Exponents and Order of Operations Exploring real numbers Adding real numbers Subtracting real numbers Multiplying and dividing real numbers The Distributive Property Properties

More information

Algebra 1 Summer Assignment 2018

Algebra 1 Summer Assignment 2018 Algebra 1 Summer Assignment 2018 The following packet contains topics and definitions that you will be required to know in order to succeed in Algebra 1 this coming school year. You are advised to be familiar

More information

Unit 3 Vocabulary. An algebraic expression that can contains. variables, numbers and operators (like +, An equation is a math sentence stating

Unit 3 Vocabulary. An algebraic expression that can contains. variables, numbers and operators (like +, An equation is a math sentence stating Hart Interactive Math Algebra 1 MODULE 2 An algebraic expression that can contains 1 Algebraic Expression variables, numbers and operators (like +,, x and ). 1 Equation An equation is a math sentence stating

More information

Topics Covered in Math 115

Topics Covered in Math 115 Topics Covered in Math 115 Basic Concepts Integer Exponents Use bases and exponents. Evaluate exponential expressions. Apply the product, quotient, and power rules. Polynomial Expressions Perform addition

More information

SUMMER MATH PACKET ADVANCED ALGEBRA A COURSE 215

SUMMER MATH PACKET ADVANCED ALGEBRA A COURSE 215 SUMMER MATH PACKET ADVANCED ALGEBRA A COURSE 5 Updated May 0 MATH SUMMER PACKET INSTRUCTIONS Attached you will find a packet of exciting math problems for your enjoyment over the summer. The purpose of

More information

West Windsor-Plainsboro Regional School District Math A&E Grade 7

West Windsor-Plainsboro Regional School District Math A&E Grade 7 West Windsor-Plainsboro Regional School District Math A&E Grade 7 Page 1 of 24 Unit 1: Introduction to Algebra Content Area: Mathematics Course & Grade Level: A&E Mathematics, Grade 7 Summary and Rationale

More information

ALGEBRA I CURRICULUM OUTLINE

ALGEBRA I CURRICULUM OUTLINE ALGEBRA I CURRICULUM OUTLINE 2013-2014 OVERVIEW: 1. Operations with Real Numbers 2. Equation Solving 3. Word Problems 4. Inequalities 5. Graphs of Functions 6. Linear Functions 7. Scatterplots and Lines

More information

Algebra One As of: September 2014 Teacher Contact: Ms.Zinn (CVHS-NGC)

Algebra One As of: September 2014 Teacher Contact: Ms.Zinn (CVHS-NGC) Algebra One As of: September 2014 Teacher Contact: Ms.Zinn (CVHS-NGC) CCSS Unit Theme SKILLS ASSESSMENT & PRODUCTS Translate sentences into equations such as, The length of a rectangle is ten less than

More information

Section 1.1 Real Numbers and Number Operations

Section 1.1 Real Numbers and Number Operations Section. Real Numbers and Number Operations Objective(s): Differentiate among subsets of the real number system. Essential Question: What is the difference between a rational and irrational number? Homework:

More information

Introduction to Algebra

Introduction to Algebra Translate verbal expressions into mathematics expressions. Write an expression containing identical factors as an expression using exponents. Understand and apply the rules for order of operations to evaluate

More information

Give algebraic and numeric examples to support your answer. Which property is demonstrated when one combines like terms in an algebraic expression?

Give algebraic and numeric examples to support your answer. Which property is demonstrated when one combines like terms in an algebraic expression? Big Idea(s): Algebra is distinguished from arithmetic by the systematic use of symbols for values. Writing and evaluating expressions with algebraic notation follows the same rules/properties as in arithmetic.

More information

R1: Sets A set is a collection of objects sets are written using set brackets each object in onset is called an element or member

R1: Sets A set is a collection of objects sets are written using set brackets each object in onset is called an element or member Chapter R Review of basic concepts * R1: Sets A set is a collection of objects sets are written using set brackets each object in onset is called an element or member Ex: Write the set of counting numbers

More information

Course Number 420 Title Algebra I Honors Grade 9 # of Days 60

Course Number 420 Title Algebra I Honors Grade 9 # of Days 60 Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community. Course Number

More information

MATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline

MATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline MATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline 1. Real Numbers (33 topics) 1.3 Fractions (pg. 27: 1-75 odd) A. Simplify fractions. B. Change mixed numbers

More information

Algebra I+ Pacing Guide. Days Units Notes Chapter 1 ( , )

Algebra I+ Pacing Guide. Days Units Notes Chapter 1 ( , ) Algebra I+ Pacing Guide Days Units Notes Chapter 1 (1.1-1.4, 1.6-1.7) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order

More information

Math Analysis/Honors Math Analysis Summer Assignment

Math Analysis/Honors Math Analysis Summer Assignment Math Analysis/Honors Math Analysis Summer Assignment To be successful in Math Analysis or Honors Math Analysis, a full understanding of the topics listed below is required prior to the school year. To

More information

ADVANCED/HONORS ALGEBRA 2 - SUMMER PACKET

ADVANCED/HONORS ALGEBRA 2 - SUMMER PACKET NAME ADVANCED/HONORS ALGEBRA 2 - SUMMER PACKET Part I. Order of Operations (PEMDAS) Parenthesis and other grouping symbols. Exponential expressions. Multiplication & Division. Addition & Subtraction. Tutorial:

More information

Chapter 1A -- Real Numbers. iff. Math Symbols: Sets of Numbers

Chapter 1A -- Real Numbers. iff. Math Symbols: Sets of Numbers Fry Texas A&M University! Fall 2016! Math 150 Notes! Section 1A! Page 1 Chapter 1A -- Real Numbers Math Symbols: iff or Example: Let A = {2, 4, 6, 8, 10, 12, 14, 16,...} and let B = {3, 6, 9, 12, 15, 18,

More information

Students will be able to simplify numerical expressions and evaluate algebraic expressions. (M)

Students will be able to simplify numerical expressions and evaluate algebraic expressions. (M) Morgan County School District Re-3 August What is algebra? This chapter develops some of the basic symbolism and terminology that students may have seen before but still need to master. The concepts of

More information

Algebra II Summer Packet. Summer Name:

Algebra II Summer Packet. Summer Name: Algebra II Summer Packet Summer 2017 Name: NAME ALGEBRA II & TRIGONOMETRY SUMMER REVIEW PACKET To maintain a high quality program, students entering Algebra II are expected to remember the basics of the

More information

8th Grade Math Definitions

8th Grade Math Definitions 8th Grade Math Definitions Absolute Value: 1. A number s distance from zero. 2. For any x, is defined as follows: x = x, if x < 0; x, if x 0. Acute Angle: An angle whose measure is greater than 0 and less

More information

CP Algebra 2. Summer Packet. Name:

CP Algebra 2. Summer Packet. Name: CP Algebra Summer Packet 018 Name: Objectives for CP Algebra Summer Packet 018 I. Number Sense and Numerical Operations (Problems: 1 to 4) Use the Order of Operations to evaluate expressions. (p. 6) Evaluate

More information

Check boxes of Edited Copy of Sp Topics (was 261-pilot)

Check boxes of Edited Copy of Sp Topics (was 261-pilot) Check boxes of Edited Copy of 10023 Sp 11 253 Topics (was 261-pilot) Intermediate Algebra (2011), 3rd Ed. [open all close all] R-Review of Basic Algebraic Concepts Section R.2 Ordering integers Plotting

More information

OBJECTIVES UNIT 1. Lesson 1.0

OBJECTIVES UNIT 1. Lesson 1.0 OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint

More information

Chetek-Weyerhaeuser High School

Chetek-Weyerhaeuser High School Chetek-Weyerhaeuser High School Unit 1 Variables and Expressions Math RtI Units and s Math RtI A s 1. I can use mathematical properties to evaluate expressions. I can use mathematical properties to evaluate

More information

What students need to know for... ALGEBRA II

What students need to know for... ALGEBRA II What students need to know for... ALGEBRA II 2017-2018 NAME This is a MANDATORY assignment that will be GRADED. It is due the first day of the course. Your teacher will determine how it will be counted

More information

Chapter R - Basic Algebra Operations (94 topics, no due date)

Chapter R - Basic Algebra Operations (94 topics, no due date) Course Name: Math 00024 Course Code: N/A ALEKS Course: College Algebra Instructor: Master Templates Course Dates: Begin: 08/15/2014 End: 08/15/2015 Course Content: 207 topics Textbook: Barnett/Ziegler/Byleen/Sobecki:

More information

Pre-AP Algebra II Summer Packet 2014

Pre-AP Algebra II Summer Packet 2014 Pre-AP Algebra II Summer Packet 014 Name: Period: PLEASE READ THE FOLLOWING!!!!!!! Wait until a few weeks before school starts to work through this packet so that the material will be fresh when you begin

More information

PENNSYLVANIA. There are laws for performing mathematical operations to ensure that the values obtained will be consistent. Absolute value.

PENNSYLVANIA. There are laws for performing mathematical operations to ensure that the values obtained will be consistent. Absolute value. Topic: 1. Real Numbers Days: 15 Know: Understand: Do: Absolute value Number Sets Vocabulary: integers rational numbers irrational numbers simplify evaluate There are laws for performing mathematical operations

More information

Herndon High School Geometry Honors Summer Assignment

Herndon High School Geometry Honors Summer Assignment Welcome to Geometry! This summer packet is for all students enrolled in Geometry Honors at Herndon High School for Fall 07. The packet contains prerequisite skills that you will need to be successful in

More information

Chapter P. Prerequisites. Slide P- 1. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Chapter P. Prerequisites. Slide P- 1. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 1 Chapter P Prerequisites 1 P.1 Real Numbers Quick Review 1. List the positive integers between -4 and 4.. List all negative integers greater than -4. 3. Use a calculator to evaluate the expression

More information

Pre-Calculus Summer Packet Instructions

Pre-Calculus Summer Packet Instructions Pre-Calculus Summer Packet Instructions Dear Student, You are receiving this summer packet as a review of previously covered math topics needed to be successful in the upcoming math class you will be taking

More information

Pre-Calculus Summer Packet

Pre-Calculus Summer Packet 2013-2014 Pre-Calculus Summer Packet 1. Complete the attached summer packet, which is due on Friday, September 6, 2013. 2. The material will be reviewed in class on Friday, September 6 and Monday, September

More information

UNIT 4 NOTES: PROPERTIES & EXPRESSIONS

UNIT 4 NOTES: PROPERTIES & EXPRESSIONS UNIT 4 NOTES: PROPERTIES & EXPRESSIONS Vocabulary Mathematics: (from Greek mathema, knowledge, study, learning ) Is the study of quantity, structure, space, and change. Algebra: Is the branch of mathematics

More information

Expressions and Formulas 1.1. Please Excuse My Dear Aunt Sally

Expressions and Formulas 1.1. Please Excuse My Dear Aunt Sally Expressions and Formulas 1.1 Order of Operations (PEMDAS) 1. Parenthesis 2. Exponents 3. Multiply or Divide from left to right 4. Add of Subtract from left to right Please Excuse My Dear Aunt Sally Example

More information

Elementary Algebra

Elementary Algebra Elementary Algebra 978-1-63545-008-8 To learn more about all our offerings Visit Knewton.com/highered Source Author(s) (Text or Video) Title(s) Link (where applicable) Flatworld Text John Redden Elementary

More information

MATH 60 Course Notebook Chapter #1

MATH 60 Course Notebook Chapter #1 MATH 60 Course Notebook Chapter #1 Integers and Real Numbers Before we start the journey into Algebra, we need to understand more about the numbers and number concepts, which form the foundation of Algebra.

More information

Level Unit Chapter Lesson ChapterTitle LessonTitle Introduction Introduction How to take the placement tests How to take the

Level Unit Chapter Lesson ChapterTitle LessonTitle Introduction Introduction How to take the placement tests How to take the Level Unit Chapter Lesson ChapterTitle LessonTitle 0 0 1 1 Introduction Introduction 0 0 2 1 How to take the placement tests How to take the placement tests 0 0 3 0 Placement Test I 0 0 4 0 Placement Test

More information

Bishop Kelley High School Summer Math Program Course: Algebra 2 A

Bishop Kelley High School Summer Math Program Course: Algebra 2 A 015 016 Bishop Kelley High School Summer Math Program Course: Algebra A NAME: DIRECTIONS: Show all work in packet!!! The first 16 pages of this packet provide eamples as to how to work some of the problems

More information

MA.8.1 Students will apply properties of the real number system to simplify algebraic expressions and solve linear equations.

MA.8.1 Students will apply properties of the real number system to simplify algebraic expressions and solve linear equations. Focus Statement: Students will solve multi-step linear, quadratic, and compound equations and inequalities using the algebraic properties of the real number system. They will also graph linear and quadratic

More information

Accessible Topic - Topics accessible to visually impaired students using a screen reader.

Accessible Topic - Topics accessible to visually impaired students using a screen reader. Course Name: Winter 2018 Math 95 - Course Code: ALEKS Course: Developmental Math Instructor: Course Dates: Begin: 01/07/2018 End: 03/23/2018 Course Content: 390 Topics (172 goal + 218 prerequisite) / 334

More information

In July: Complete the Unit 01- Algebraic Essentials Video packet (print template or take notes on loose leaf)

In July: Complete the Unit 01- Algebraic Essentials Video packet (print template or take notes on loose leaf) Hello Advanced Algebra Students In July: Complete the Unit 01- Algebraic Essentials Video packet (print template or take notes on loose leaf) The link to the video is here: https://www.youtube.com/watch?v=yxy4tamxxro

More information

Algebra Summer Review Packet

Algebra Summer Review Packet Name: Algebra Summer Review Packet About Algebra 1: Algebra 1 teaches students to think, reason, and communicate mathematically. Students use variables to determine solutions to real world problems. Skills

More information

Intermediate Algebra with Applications

Intermediate Algebra with Applications Lakeshore Technical College 10-804-118 Intermediate Algebra with Applications Course Outcome Summary Course Information Alternate Title Description Total Credits 4 Total Hours 72 Pre/Corequisites Prerequisite

More information

Algebra I. abscissa the distance along the horizontal axis in a coordinate graph; graphs the domain.

Algebra I. abscissa the distance along the horizontal axis in a coordinate graph; graphs the domain. Algebra I abscissa the distance along the horizontal axis in a coordinate graph; graphs the domain. absolute value the numerical [value] when direction or sign is not considered. (two words) additive inverse

More information

Algebra II Vocabulary Word Wall Cards

Algebra II Vocabulary Word Wall Cards Algebra II Vocabulary Word Wall Cards Mathematics vocabulary word wall cards provide a display of mathematics content words and associated visual cues to assist in vocabulary development. The cards should

More information

Algebra II Vocabulary Alphabetical Listing. Absolute Maximum: The highest point over the entire domain of a function or relation.

Algebra II Vocabulary Alphabetical Listing. Absolute Maximum: The highest point over the entire domain of a function or relation. Algebra II Vocabulary Alphabetical Listing Absolute Maximum: The highest point over the entire domain of a function or relation. Absolute Minimum: The lowest point over the entire domain of a function

More information

SUMMER MATH PACKET ALGEBRA TWO COURSE 229

SUMMER MATH PACKET ALGEBRA TWO COURSE 229 SUMMER MATH PACKET ALGEBRA TWO COURSE 9 MATH SUMMER PACKET INSTRUCTIONS MATH SUMMER PACKET INSTRUCTIONS Attached you will find a packet of exciting math problems for your enjoyment over the summer. The

More information

Curriculum Map: Mathematics

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

More information

Final Exam Study Guide Mathematical Thinking, Fall 2003

Final Exam Study Guide Mathematical Thinking, Fall 2003 Final Exam Study Guide Mathematical Thinking, Fall 2003 Chapter R Chapter R contains a lot of basic definitions and notations that are used throughout the rest of the book. Most of you are probably comfortable

More information

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

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

More information

Precalculus Summer Assignment 2015

Precalculus Summer Assignment 2015 Precalculus Summer Assignment 2015 The following packet contains topics and definitions that you will be required to know in order to succeed in CP Pre-calculus this year. You are advised to be familiar

More information

UNIT 4: RATIONAL AND RADICAL EXPRESSIONS. 4.1 Product Rule. Objective. Vocabulary. o Scientific Notation. o Base

UNIT 4: RATIONAL AND RADICAL EXPRESSIONS. 4.1 Product Rule. Objective. Vocabulary. o Scientific Notation. o Base UNIT 4: RATIONAL AND RADICAL EXPRESSIONS M1 5.8, M2 10.1-4, M3 5.4-5, 6.5,8 4.1 Product Rule Objective I will be able to multiply powers when they have the same base, including simplifying algebraic expressions

More information

Algebra 2 Segment 1 Lesson Summary Notes

Algebra 2 Segment 1 Lesson Summary Notes Algebra 2 Segment 1 Lesson Summary Notes For each lesson: Read through the LESSON SUMMARY which is located. Read and work through every page in the LESSON. Try each PRACTICE problem and write down the

More information

FOR STUDENTS WHO HAVE COMPLETED ALGEBRA 1 (Students entering Geometry)

FOR STUDENTS WHO HAVE COMPLETED ALGEBRA 1 (Students entering Geometry) FOR STUDENTS WHO HAVE COMPLETED ALGEBRA (Students entering Geometry) Dear Parent/Guardian and Student, Name: Date: Period: Attached you will find a review packet of skills which each student is expected

More information

HOSTOS COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS. MAT 010 or placement on the COMPASS/CMAT

HOSTOS COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS. MAT 010 or placement on the COMPASS/CMAT 1 HOSTOS COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 00 ELEMENTARY ALGEBRA CREDIT HOURS: 0.0 EQUATED HOURS: 4.5 CLASS HOURS: 4.5 + PREREQUISITE: REQUIRED TEXTS: DESCRIPTION: EXAMINATIONS: GRADES: MAT

More information

Evaluate the expression if x = 2 and y = 5 6x 2y Original problem Substitute the values given into the expression and multiply

Evaluate the expression if x = 2 and y = 5 6x 2y Original problem Substitute the values given into the expression and multiply Name EVALUATING ALGEBRAIC EXPRESSIONS Objective: To evaluate an algebraic expression Example Evaluate the expression if and y = 5 6x y Original problem 6() ( 5) Substitute the values given into the expression

More information

ALGEBRA I FORM I. Textbook: Algebra, Second Edition;Prentice Hall,2002

ALGEBRA I FORM I. Textbook: Algebra, Second Edition;Prentice Hall,2002 ALGEBRA I FORM I Textbook: Algebra, Second Edition;Prentice Hall,00 Prerequisites: Students are expected to have a knowledge of Pre Algebra and proficiency of basic math skills including: positive and

More information

Course Name: MAT 135 Spring 2017 Master Course Code: N/A. ALEKS Course: Intermediate Algebra Instructor: Master Templates

Course Name: MAT 135 Spring 2017 Master Course Code: N/A. ALEKS Course: Intermediate Algebra Instructor: Master Templates Course Name: MAT 135 Spring 2017 Master Course Code: N/A ALEKS Course: Intermediate Algebra Instructor: Master Templates Course Dates: Begin: 01/15/2017 End: 05/31/2017 Course Content: 279 Topics (207

More information

CURRICULUM GUIDE. Honors Algebra II / Trigonometry

CURRICULUM GUIDE. Honors Algebra II / Trigonometry CURRICULUM GUIDE Honors Algebra II / Trigonometry The Honors course is fast-paced, incorporating the topics of Algebra II/ Trigonometry plus some topics of the pre-calculus course. More emphasis is placed

More information

Intermediate Algebra

Intermediate Algebra Intermediate Algebra The purpose of this course is to strengthen students foundational conceptual and procedural skills in order to prepare students for college-and-career readiness. The course textbook,

More information

SUMMER MATH PACKET. Geometry A COURSE 227

SUMMER MATH PACKET. Geometry A COURSE 227 SUMMER MATH PACKET Geometry A COURSE 7 MATH SUMMER PACKET INSTRUCTIONS Attached you will find a packet of exciting math problems for your enjoyment over the summer. The purpose of the summer packet is

More information

How do you write and evaluate algebraic expressions? How can algebraic expressions and equations represent actual situations?

How do you write and evaluate algebraic expressions? How can algebraic expressions and equations represent actual situations? Topic: Expressions, Equations and Functions Days: 13 Key Learning: Expressions, equations, tables and graphs are used to model realworld situations. Unit Essential Question(s): How do you write and evaluate

More information

Chapter 1: Precalculus Review

Chapter 1: Precalculus Review : Precalculus Review Math 115 17 January 2018 Overview 1 Important Notation 2 Exponents 3 Polynomials 4 Rational Functions 5 Cartesian Coordinates 6 Lines Notation Intervals: Interval Notation (a, b) (a,

More information