Chapter 1. Expressions, Equations, and Functions

Size: px
Start display at page:

Download "Chapter 1. Expressions, Equations, and Functions"

Transcription

1 Chapter 1 Expressions, Equations, and Functions

2 1.1 Evaluate Expressions I can evaluate algebraic expressions and use exponents. CC.9-12.N.Q.1

3 Vocabulary: Variable a letter used to represent one or more numbers Algebraic expression expression that includes at least one variable

4 Evaluate an Algebraic Expression Substitute a number for each variable and simplify, if needed Example: Evaluate the expression when c = 4 a)4c b)8/c c)15 + c

5 Powers: Note: anything to the zero power = 1

6 Examples: Write the power in words and as a product. a)5 2 b) 1 2 3

7 Example: Evaluate the expression. A) n 5 when n = 3 B) d 2 when d = 9 5

8 HOMEWORK: p. 5 #1, 2, 4 48 even

9 1.2 Apply Order of Operations I can use order of operations to evaluate expressions. CC.9-12.A.SSE.1

10 In most languages, the meaning of words depend on the order: Ex. Sign the check Is not the same as Check the sign

11 Mathematics is a type of language with its own syntax and grammar. Ex X 2 What do we do first? Add or multiply? If we add first: X 2 If we multiply first: X 2 8 X Uh Oh! Which one is the correct answer?

12

13 What is PEMDAS? In order to make sure every person gets the same answer to a math problem, mathematicians came up with a rule called the order of operations Parenthesis ( ) [ ] Exponents 2 3 Multiplication X Division Addition + Subtraction - In order from left to right! In order from left to right!

14 Example: Evaluate (1 (-3)) 3 14

15 Example: Evaluate -4x 2 + 6x 5 when x = -3 15

16 HOMEWORK: p. 10 #1, 2, 4-34 even

17 1.3 Write Expressions I can translate verbal phrases into expressions. CC.9-12.A.SSE.1

18 Translate Verbal Expressions

19 Example: Translate the verbal phrase into an expression. a)8 times the quantity 4 plus a number n b)12 decreased by a number x c)the quotient of the square of a number w and 5

20 Vocabulary: Verbal model: describes real-world situations using words and math symbols Rate: fraction that compares two quantities measured in different units Unit rate: rate where the denominator is 1 unit

21 Example: A runner travel 730 yards in 5 minutes. Find the unit rate in feet per second. * Check your unit analysis!

22 HOMEWORK: p. 18 #1, 2, 4 28 even, 31, 32

23 1.4 Write Equations and Inequalities I can translate verbal sentences into equations or inequalities. CC.9-12.A.CED.1

24 Vocabulary: Equation: Inequality: Open sentence:

25 Symbol Meaning Words = < > Equal to Less than Less than or equal to Greater than Greater than or equal to The same as Fewer than At most, no more than More than At least, no less than

26 Example: Write an equation or inequality. a) The sum of twice a number r and 3 is 11. b) The quotient of a number n and 2 is at most 16. c) A number q is at least 5 and less than 17.

27 Solution of the equation or inequality: a number that makes the equation/inequality true. Example: check whether 5 is a solution of the equation or inequality a) 24 3d = 9 b) 4 + 3p > 19

28 HOMEWORK: p. 24 #1, 2, 4 36 even, pick 3 from #39-43

29 1.5 Use a Problem Solving Plan I can use a problem solving plan to solve problems. CC.9-12.A.CED.1

30 Vocabulary: Formula equation that relates two or more quantities. Examples:

31 4 Step Plan: 1)Understand 2)Plan 3)Solve 4)Check

32 A builder lays sod on the lawns of new homes. The installed cost for sod is $.38 per square foot. What is the cost of installing sod on a rectangular lawn that is 32 feet long and 18 feet wide?

33 Activity

34 HOMEWORK: p. 31 #1 10, 14-19

35 1.6 Use Precision and Measurement I can compare measurements for precision. CC.9-12.N.Q.3

36 Vocabulary: Precision level of detail that an instrument can measure Significant digits digits in a measurement that carry meaning that contributes to precision of measurement

37 Precision: Choose the more precise measurement a) 7 cm or 7.3 cm b) 0.2 gal or 6 qt c) 7 in or 2.02 ft

38 Significant Digits (figures): numbers that are important to precision of measurement All non zero digits (5 sig figs) Zeros to the right of the last nonzero digit and the decimal point (2 sig figs) Zeros between significant digits (4 sig figs)

39

40 Example: Determine the number of significant digits in each measurement. a) 250 b) c) 30.04

41 Rules for Sig Figs in Calculations: Addition/Subtraction: Round the answer to same place as last digit of the least precise measurement. Multiplication/Division: answer must have the same number of digits as the least precise measurement.

42 HOMEWORK: p. 38 #1-28

43 1.7 Represent Functions as Rules and Tables I can represent functions as rules and as tables. CC.9-12.A.CED.2

44 Vocabulary: Function: pairing of inputs with outputs so that each input is paired with exactly one output. Domain: set of all inputs Range: set of all outputs

45 Input Output Example: Look at the input value and determine what rule applies to get the output value

46 Example: Tell whether the pairing is a function.. a) Input output b) Input output

47 Function Rules: Independent variable input variable Dependent variable value depends on value of input; output

48 Example: The domain of the function is y = x + 4 is 0, 2, 3, 6, and 7. Make a table for the function. Identify the domain and range.

49 HOMEWORK: p. 44 #1 10, 14-21

50 1.8 Represent Functions as Graphs I can represent functions as graphs. CC.9-12.F.IF.4

51 perimeter Model: Let n = # of triangles Let p = the perimeter of each figure Table: Graph: Equation: n p Dependent p n # of triangles Dependent p = n + 2

52 This chart shows the price of sliced fruit platters. Platter Weight Price 1 lb. $ lb. $ lb. $ lb. $ lb. $8.10 3) How much would a 10 lb. platter cost? 1) How much would a 6 lb. platter cost? 2) Write an equation for the cost of a platter that weighs w lbs. Let p = price of platter p = 1.50 w Change Start Value

53 A taxi cab charges a flat rate of $2.50 and 15 cents per mile. Write a linear equation for the charge in terms of the number of miles driven. Then graph the function. Let C = charge in dollars Let m = # of miles driven

54 A car s fuel tank is filled at a rate of 1.6 gal/min. The tank held 5 gallons of gas before refueling. Let m = # of minutes Let V = Volume of gas in tank Equation: Table: m V Graph:

55 HOMEWORK: p. 52 #1 13, 15-17

Chapter 1 Expressions, Equations, and Functions

Chapter 1 Expressions, Equations, and Functions Chapter 1 Expressions, Equations, and Functions Sec 1.1 Evaluate Expressions Variable EX: Algebraic Expression a collection of,, and without an equal sign. EX: Evaluate an Expression to substitute a number

More information

Variable Expression: a collection of numbers, variables, and operations *Expressions DO NOT have signs. Ex: If x = 3 6x = Ex: if y = 9..

Variable Expression: a collection of numbers, variables, and operations *Expressions DO NOT have signs. Ex: If x = 3 6x = Ex: if y = 9.. Algebra 1 Chapter 1 Note Packet Name Section 1.1: Variables in Algebra Variable: a letter that is used to represent one or more numbers Ex: x, y, t, etc. (*The most popular one is x ) Variable Values:

More information

Expressions, Equations and Inequalities Guided Notes

Expressions, Equations and Inequalities Guided Notes Expressions, Equations and Inequalities Guided Notes Standards: Alg1.M.A.SSE.A.01a - The Highly Proficient student can explain the context of different parts of a formula presented as a complicated expression.

More information

MathB65 Ch 1 I,II,III, IV.notebook. August 23, 2017

MathB65 Ch 1 I,II,III, IV.notebook. August 23, 2017 Chapter 1: Expressions, Equations and Inequalities I. Variables & Constants II. Algebraic Expressions III. Translations IV. Introduction to Equations V. The Additive/Multiplication Principles VI. Strategy

More information

Chapter 1: Fundamentals of Algebra Lecture notes Math 1010

Chapter 1: Fundamentals of Algebra Lecture notes Math 1010 Section 1.1: The Real Number System Definition of set and subset A set is a collection of objects and its objects are called members. If all the members of a set A are also members of a set B, then A is

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

MATH 0030 Lecture Notes Section 2.1 The Addition Property of Equality Section 2.2 The Multiplication Property of Equality

MATH 0030 Lecture Notes Section 2.1 The Addition Property of Equality Section 2.2 The Multiplication Property of Equality MATH 0030 Lecture Notes Section.1 The Addition Property of Equality Section. The Multiplication Property of Equality Introduction Most, but not all, salaries and prices have soared over the decades. To

More information

Solving Equations. A: Solving One-Variable Equations. One Step x + 6 = 9-3y = 15. Two Step 2a 3 6. Algebra 2 Chapter 1 Notes 1.4 Solving Equations

Solving Equations. A: Solving One-Variable Equations. One Step x + 6 = 9-3y = 15. Two Step 2a 3 6. Algebra 2 Chapter 1 Notes 1.4 Solving Equations Algebra 2 Chapter 1 Notes 1.4 Solving Equations 1.4 Solving Equations Topics: Solving Equations Translating Words into Algebra Solving Word Problems A: Solving One-Variable Equations The equations below

More information

Multiplication and Division

Multiplication and Division UNIT 3 Multiplication and Division Skaters work as a pair to put on quite a show. Multiplication and division work as a pair to solve many types of problems. 82 UNIT 3 MULTIPLICATION AND DIVISION Isaac

More information

Evaluate algebraic expressions and use exponents. Translate verbal phrases into expressions.

Evaluate algebraic expressions and use exponents. Translate verbal phrases into expressions. Algebra 1 Notes Section 1.1: Evaluate Expressions Section 1.3: Write Expressions Name: Hour: Objectives: Section 1.1: (The "NOW" green box) Section 1.3: Evaluate algebraic expressions and use exponents.

More information

Ex.1 identify the terms and coefficients of the expression.

Ex.1 identify the terms and coefficients of the expression. Modeling with expressions An expression is a mathematical phrase that contains numbers or variables. Terms are the parts being added. Coefficient is the number in front of the variable. A constant is a

More information

Chapter 3. Equations and Inequalities. 10/2016 LSowatsky 1

Chapter 3. Equations and Inequalities. 10/2016 LSowatsky 1 Chapter 3 Equations and Inequalities 10/2016 LSowatsky 1 3-1B Write Equations Main Idea: Write algebraic equations from verbal sentences and problem situations. LSowatsky 2 Vocabulary: Equation mathematical

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

Algebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher

Algebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher Algebra 1 S1 Lesson Summaries For every lesson, you need to: Read through the LESSON REVIEW which is located below or on the last page of the lesson and 3-hole punch into your MATH BINDER. Read and work

More information

Equations and Inequalities. College Algebra

Equations and Inequalities. College Algebra Equations and Inequalities College Algebra Radical Equations Radical Equations: are equations that contain variables in the radicand How to Solve a Radical Equation: 1. Isolate the radical expression on

More information

Mini Lecture 1.1 Introduction to Algebra: Variables and Mathematical Models

Mini Lecture 1.1 Introduction to Algebra: Variables and Mathematical Models Mini Lecture. Introduction to Algebra: Variables and Mathematical Models. Evaluate algebraic expressions.. Translate English phrases into algebraic expressions.. Determine whether a number is a solution

More information

Algebra I Notes Unit Two: Variables

Algebra I Notes Unit Two: Variables Syllabus Objectives:. The student will use order of operations to evaluate expressions.. The student will evaluate formulas and algebraic expressions using rational numbers (with and without technology).

More information

OHS Algebra 1 Summer Packet

OHS Algebra 1 Summer Packet OHS Algebra 1 Summer Packet Good Luck to: Date Started: (please print student name here) 8 th Grade Math Teacher s Name: Complete each of the following exercises in this formative assessment. To receive

More information

Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression

Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression 1 Words to Review Give an example of the vocabulary word. Numerical expression 5 12 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression

More information

Math 9 Practice Final Exam #1

Math 9 Practice Final Exam #1 Class: Date: Math Practice Final Exam #1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the value of 0.64. a. 0.8 b. 0.08 0.4 d. 0.1 2. Which

More information

North Seattle Community College Math 084 Chapter 1 Review. Perform the operation. Write the product using exponents.

North Seattle Community College Math 084 Chapter 1 Review. Perform the operation. Write the product using exponents. North Seattle Community College Math 084 Chapter 1 Review For the test, be sure to show all work! Turn off cell phones. Perform the operation. Perform the operation. Write the product using exponents.

More information

OHS Algebra 1 Summer Packet

OHS Algebra 1 Summer Packet OHS Algebra 1 Summer Packet Good Luck to: Date Started: (please print student name here) 8 th Grade Math Teacher s Name: Complete each of the following exercises in this formative assessment. To receive

More information

ALGEBRA 1. Interactive Notebook Chapter 2: Linear Equations

ALGEBRA 1. Interactive Notebook Chapter 2: Linear Equations ALGEBRA 1 Interactive Notebook Chapter 2: Linear Equations 1 TO WRITE AN EQUATION: 1. Identify the unknown (the variable which you are looking to find) 2. Write the sentence as an equation 3. Look for

More information

Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Variable expression. Evaluate a variable expression

Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Variable expression. Evaluate a variable expression 1 Words to Review Give an example of the vocabulary word. Numerical expression 5 1 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression

More information

Name Date. Answers 1.

Name Date. Answers 1. Name Date Honors Algebra 2 Summer Work Due at Meet the Teacher Night Show all work. You will be graded on accuracy and completion. Partial credit will be given on problems where work is not shown. 1. Plot

More information

John L. Lehet

John L. Lehet New! Android App! SAT Mathematics Review Algebra John L. Lehet jlehet@mathmaverick.com www.mathmaverick.com SAT Math Daily Question Android App - new question each day - archive of over 200 questions -

More information

Rising 7th Grade Math. Pre-Algebra Summer Review Packet

Rising 7th Grade Math. Pre-Algebra Summer Review Packet Rising 7th Grade Math Pre-Algebra Summer Review Packet Operations with Integers Adding Integers Negative + Negative: Add the absolute values of the two numbers and make the answer negative. ex: -5 + (-9)

More information

Geometric Formulas (page 474) Name

Geometric Formulas (page 474) Name LESSON 91 Geometric Formulas (page 474) Name Figure Perimeter Area Square P = 4s A = s 2 Rectangle P = 2I + 2w A = Iw Parallelogram P = 2b + 2s A = bh Triangle P = s 1 + s 2 + s 3 A = 1_ 2 bh Teacher Note:

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

MAT Intermediate Algebra - Final Exam Review Textbook: Beginning & Intermediate Algebra, 5th Ed., by Martin-Gay

MAT Intermediate Algebra - Final Exam Review Textbook: Beginning & Intermediate Algebra, 5th Ed., by Martin-Gay MAT0 - Intermediate Algebra - Final Eam Review Tetbook: Beginning & Intermediate Algebra, 5th Ed., by Martin-Gay Section 2. Solve the equation. ) 9 - ( - ) = 2 Section 2.8 Solve the inequality. Graph the

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

Welcome to OSA Training 2015 Basic Math. By: Greg Hinckson Irena Nedeljkovic Iris Bishop Mitch Volk

Welcome to OSA Training 2015 Basic Math. By: Greg Hinckson Irena Nedeljkovic Iris Bishop Mitch Volk Welcome to OSA Training 2015 Basic Math By: Greg Hinckson Irena Nedeljkovic Iris Bishop Mitch Volk Curriculum I. WHOLE NUMBERS -Oder of Operations II. DECIMALS -Decimals to Percents to Fractions III. PERCENTS

More information

PRE-ALGEBRA SUMMARY WHOLE NUMBERS

PRE-ALGEBRA SUMMARY WHOLE NUMBERS PRE-ALGEBRA SUMMARY WHOLE NUMBERS Introduction to Whole Numbers and Place Value Digits Digits are the basic symbols of the system 0,,,, 4,, 6, 7, 8, and 9 are digits Place Value The value of a digit in

More information

Reference Page Math Symbols- + add - subtract x multiply divide = equal % percent $ dollar cent # at degree.

Reference Page Math Symbols- + add - subtract x multiply divide = equal % percent $ dollar cent # at degree. Reference Page Math Symbols- + add - subtract x multiply divide = equal % percent $ dollar cent # number/pound @ at degree. decimal point pi Roman Numerals Conversion I = 1 C = 100 V = 5 D = 500 X = 10

More information

7 = 8 (Type a simplified fraction.)

7 = 8 (Type a simplified fraction.) Student: Date: Assignment: Exponential and Radical Equations 1. Perform the indicated computation. Write the answer in scientific notation. 3. 10 6 10. 3. 4. 3. 10 6 10 = (Use the multiplication symbol

More information

Harbor Creek School District

Harbor Creek School District Numeration Unit of Study Big Ideas Algebraic Concepts How do I match a story or equation to different symbols? How do I determine a missing symbol in an equation? How does understanding place value help

More information

Math 4 Review for Quarter 1 Cumulative Test

Math 4 Review for Quarter 1 Cumulative Test Math 4 Review for Quarter 1 Cumulative Test Name: I. Unit Conversion Units are important in describing the world around us To convert between units: o Method 1: Multiplication/Division Converting to a

More information

Solve. Label any contradictions or identities. 1) -4x + 2(3x - 3) = 5-9x. 2) 7x - (3x - 1) = 2. 3) 2x 5 - x 3 = 2 4) 15. 5) -4.2q =

Solve. Label any contradictions or identities. 1) -4x + 2(3x - 3) = 5-9x. 2) 7x - (3x - 1) = 2. 3) 2x 5 - x 3 = 2 4) 15. 5) -4.2q = Spring 2011 Name Math 115 Elementary Algebra Review Wednesday, June 1, 2011 All problems must me done on 8.5" x 11" lined paper. Solve. Label any contradictions or identities. 1) -4x + 2(3x - 3) = 5-9x

More information

Section 2.1 Objective 1: Determine If a Number Is a Solution of an Equation Video Length 5:19. Definition A in is an equation that can be

Section 2.1 Objective 1: Determine If a Number Is a Solution of an Equation Video Length 5:19. Definition A in is an equation that can be Section 2.1 Video Guide Linear Equations: The Addition and Multiplication Properties of Equality Objectives: 1. Determine If a Number Is a Solution of an Equation 2. Use the Addition Property of Equality

More information

Mississippi College and Career Readiness Standards for Mathematics Scaffolding Document. Grade 6

Mississippi College and Career Readiness Standards for Mathematics Scaffolding Document. Grade 6 Mississippi College and Career Readiness Standards for Mathematics Scaffolding Document Grade 6 Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems

More information

DESCRIPTION OF COURSE:

DESCRIPTION OF COURSE: AIM HIGH SCHOOL Curriculum Map 29230 W. 12 Mile Road Farmington Hills, MI 48334 (248) 702-6922 www.aimhighschool.com COURSE TITLE: Algebra 1 PREREQUISITES: Pre-Algebra DESCRIPTION OF COURSE: Algebra 1

More information

Name Class Date. Essential question: How do you interpret, evaluate and write algebraic expressions that model real-world situations?

Name Class Date. Essential question: How do you interpret, evaluate and write algebraic expressions that model real-world situations? Name Class Date 1-1 1 Variables and Expressions Going Deeper Essential question: How do you interpret, evaluate and write algebraic expressions that model real-world situations? A-SSE.1.1a ENGAGE Interpreting

More information

Remember, you may not use a calculator when you take the assessment test.

Remember, you may not use a calculator when you take the assessment test. Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.

More information

HW: page 168 (12-24 evens, 25-28) Extra Credit # 29 & 31

HW: page 168 (12-24 evens, 25-28) Extra Credit # 29 & 31 Lesson 5-1 Rational Numbers pages 166-168 Review our number system and real numbers. Our Number System Real Complex Rational Irrational # Integers # Whole # Natural Rational Numbers the word "rational"

More information

Algebra I Notes Unit Two: Variables

Algebra I Notes Unit Two: Variables Syllabus Objectives:. The student will use order of operations to evaluate expressions.. The student will evaluate formulas and algebraic expressions using rational numbers (with and without technology).

More information

Exponents. Reteach. Write each expression in exponential form (0.4)

Exponents. Reteach. Write each expression in exponential form (0.4) 9-1 Exponents You can write a number in exponential form to show repeated multiplication. A number written in exponential form has a base and an exponent. The exponent tells you how many times a number,

More information

Grade 8 Please show all work. Do not use a calculator! Please refer to reference section and examples.

Grade 8 Please show all work. Do not use a calculator! Please refer to reference section and examples. Grade 8 Please show all work. Do not use a calculator! Please refer to reference section and examples. Name Date due: Tuesday September 4, 2018 June 2018 Dear Middle School Parents, After the positive

More information

1.1A: I can evaluate algebraic expressions by substituting in the given number for the variable.

1.1A: I can evaluate algebraic expressions by substituting in the given number for the variable. Purpose: This is a self-evaluation tool which will provide you and your teacher with information about what you already know and what you need to work on. Your teacher will then address any skills that

More information

How can you use multiplication or division to solve an inequality? ACTIVITY: Using a Table to Solve an Inequality

How can you use multiplication or division to solve an inequality? ACTIVITY: Using a Table to Solve an Inequality . Solving Inequalities Using Multiplication or Division How can you use multiplication or division to solve an inequality? 1 ACTIVITY: Using a Table to Solve an Inequality Work with a partner. Copy and

More information

Skills Check #1 ESM 1

Skills Check #1 ESM 1 Skills Check #1 ESM 1 I. Perform the operations; simplify completely. a) 40 5 10 4 8 3 4 c) 3 4 3 ( ) 1 413 d) (1 5) 1 5 e) 3 3 6 f) 6 40 5 9 g).16 7(0.3) h) 5.934.3 7.1 i) (31.8) 3.065 II. Simplify: (9)

More information

addend angle composite number capacity Vocabulary Flash Cards Review Review Review Review Review Review

addend angle composite number capacity Vocabulary Flash Cards Review Review Review Review Review Review addend angle area bar graph capacity composite number cubic units difference A figure formed by two rays with the same endpoint A number to be added to another number. 2 or 3 in the sum 2 + 3. A graph

More information

Part 1 - Pre-Algebra Summary Page 1 of 22 1/19/12

Part 1 - Pre-Algebra Summary Page 1 of 22 1/19/12 Part 1 - Pre-Algebra Summary Page 1 of 1/19/1 Table of Contents 1. Numbers... 1.1. NAMES FOR NUMBERS... 1.. PLACE VALUES... 3 1.3. INEQUALITIES... 4 1.4. ROUNDING... 4 1.5. DIVISIBILITY TESTS... 5 1.6.

More information

Algebra SUMMER PACKET Ms. Bank

Algebra SUMMER PACKET Ms. Bank 2016-17 SUMMER PACKET Ms. Bank Just so you know what to expect next year We will use the same text that was used this past year: published by McDougall Littell ISBN-13:978-0-6185-9402-3. Summer Packet

More information

Minnesota 7 th Grade 2007 Math Strands & Standards

Minnesota 7 th Grade 2007 Math Strands & Standards Minnesota 7 th Grade 2007 Math Strands & Standards Number & Operation Algebra Geometry & Measurement Data Analysis Read, write, represent and compare positive and negative rational numbers, expressed as

More information

Name: Date: Block: This test covers learning targets related to evaluating expressions, solving equations, and simplifying radicals.

Name: Date: Block: This test covers learning targets related to evaluating expressions, solving equations, and simplifying radicals. Algebra Test STUDY GUIDE A., A., A. Epressions, Equations, Radicals Name: Date: Block: This test covers learning targets related to evaluating epressions, solving equations, and simplifying radicals. Know

More information

South Carolina Alternate Assessments Performance Level Descriptors. Mathematics. Revised: June 29, 2018

South Carolina Alternate Assessments Performance Level Descriptors. Mathematics. Revised: June 29, 2018 South Carolina Alternate Assessments Performance Level Descriptors Mathematics Revised: June 29, 2018 Contents Standards Reference Number Abbreviations... 1 Grade 3... 2 Grade 4... 6 Grade 5... 9 Grade

More information

Solving Inequalities

Solving Inequalities Solving Inequalities Inequalities and Their Graphs Objective: To write, graph, and identify solutions of inequalities. Objectives I can write an inequality. I can identify solutions by evaluating inequalities.

More information

a) b) 1 c) 19 d) e) none of these 2.) 80 0 a) undefined b) 1 c) 80 d) 0 e) none of these Evaluate the expression 3.) a) b) c) d) e) none of these

a) b) 1 c) 19 d) e) none of these 2.) 80 0 a) undefined b) 1 c) 80 d) 0 e) none of these Evaluate the expression 3.) a) b) c) d) e) none of these Math 5 Review Practice Questions *Note 1: The actual Math 5 final exam may include, but is not limited to, the problems in this handout. Study your notes, past homework assignments, quizzes, and tests.

More information

5) ) y 20 y 10 =

5) ) y 20 y 10 = Name Class Date 7.N.4 Develop the laws of exponents for multiplication and division Directions: Rewrite as a base with an exponent. 1) 3 6 3-4 = 2) x 7 x 17 = 3) 10-8 10 3 = 5) 12-3 = -3 12 6) y 20 y 10

More information

Chapter 5 Inequalities

Chapter 5 Inequalities Chapter 5 Inequalities 5.1 Solve inequalities using addition and subtraction 1. Write and graph an inequality. 2. Solve inequalities using addition and subtraction. Review- Symbols to KNOW < LESS THAN

More information

Math Departmental Exit Assessment Review (Student Version)

Math Departmental Exit Assessment Review (Student Version) Math 006 - Departmental Exit Assessment Review (Student Version) Answer the question. 1) What does the digit 2 mean in the number 19,24? 2 thousands 2 hundreds 2 hundred thousands 2 tens Objective: (1.1)

More information

Sample Math Placement Exam Questions

Sample Math Placement Exam Questions Sample Math Placement Exam Questions This review is not intended to cover all of the material on the Math Placement Exam. Material on the Math Placement Exam that is not covered in this review includes:

More information

Unit One Algebraic Thinking (Part A Number Relationships) 1.2 Powers *I can write and understand numerical expressions involving

Unit One Algebraic Thinking (Part A Number Relationships) 1.2 Powers *I can write and understand numerical expressions involving 1.2 Powers *I can write and understand numerical expressions involving and Exponents whole number exponents. Discuss with your group how do you THINK you would find the value? Exponential Form: base 4

More information

Which one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x ) A) x = 5 B) x = -6 C) x = -5 D) x = 6

Which one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x ) A) x = 5 B) x = -6 C) x = -5 D) x = 6 Review for Final Exam Math 124A (Flatley) Name Which one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x - 14 1) A) x = 5 B) x = -6 C) x = -5 D) x = 6 Solve the linear equation.

More information

+ 37,500. Discuss with your group how do you THINK you would represent 40 degrees below 0 as an integer?

+ 37,500. Discuss with your group how do you THINK you would represent 40 degrees below 0 as an integer? 6.1 Integers *I can use positive and negative numbers to show amounts in real-world situations and explain what the number 0 means in those situations. *I can recognize opposite signs of numbers as indicating

More information

Contents. Introduction... 5

Contents. Introduction... 5 Contents Introduction... 5 The Language of Algebra Order of Operations... Expressions... Equations... Writing Expressions and Equations... Properties of The Four Operations... Distributive Property...

More information

Unit 1 Foundations of Algebra

Unit 1 Foundations of Algebra 1 Unit 1 Foundations of Algebra Real Number System 2 A. Real Number System 1. Counting Numbers (Natural Numbers) {1,2,3,4, } 2. Whole Numbers { 0,1,2,3,4, } 3. Integers - Negative and Positive Whole Numbers

More information

California 3 rd Grade Standards / Excel Math Correlation by Lesson Number

California 3 rd Grade Standards / Excel Math Correlation by Lesson Number California 3 rd Grade Standards / Lesson (Activity) L1 L2 L3 L4 L5 L6 L7 L8 Excel Math Lesson Objective Learning about the tens place and the ones place; adding and subtracting two-digit numbers; learning

More information

Math 90 Lecture Notes Chapter 1

Math 90 Lecture Notes Chapter 1 Math 90 Lecture Notes Chapter 1 Section 1.1: Introduction to Algebra This textbook stresses Problem Solving! Solving problems is one of the main goals of mathematics. Think of mathematics as a language,

More information

Unit Essential Questions. What are the different representations of exponents? Where do exponents fit into the real number system?

Unit Essential Questions. What are the different representations of exponents? Where do exponents fit into the real number system? Unit Essential Questions What are the different representations of exponents? Where do exponents fit into the real number system? How can exponents be used to depict real-world situations? REAL NUMBERS

More information

Math Review Packet. for Pre-Algebra to Algebra 1

Math Review Packet. for Pre-Algebra to Algebra 1 Math Review Packet for Pre-Algebra to Algebra 1 Epressions, Equations, Eponents, Scientific Notation, Linear Functions, Proportions, Pythagorean Theorem 2016 Math in the Middle Evaluating Algebraic Epressions

More information

Unit 3. Expressions. Unit 3 Calendar

Unit 3. Expressions. Unit 3 Calendar Unit 3 Expressions Exponents Order of Operations Evaluating Algebraic Expressions Translating Words to Math Identifying Parts of Exprsessions Evaluating Formulas Algebraic Properties Simplifying Expressions

More information

and 3 on a number line.

and 3 on a number line. EXAMPLE 1 Graph real numbers on a number line Graph the real numbers 5 4 and 3 on a number line. 5 Note that = 1.25. Use a calculator to approximate 3 4 to the nearest tenth: 3 1.7. (The symbol means is

More information

Write an equation for each relationship. Then make a table of input-output pairs and tell whether the function is proportional.

Write an equation for each relationship. Then make a table of input-output pairs and tell whether the function is proportional. Functions Reteaching 41 Math Course, Lesson 41 A function is a rule that identifies a relationship between a set of input numbers and a set of output numbers. A function rule can be described in words,

More information

MATH 081. Diagnostic Review Materials PART 2. Chapters 5 to 7 YOU WILL NOT BE GIVEN A DIAGNOSTIC TEST UNTIL THIS MATERIAL IS RETURNED.

MATH 081. Diagnostic Review Materials PART 2. Chapters 5 to 7 YOU WILL NOT BE GIVEN A DIAGNOSTIC TEST UNTIL THIS MATERIAL IS RETURNED. MATH 08 Diagnostic Review Materials PART Chapters 5 to 7 YOU WILL NOT BE GIVEN A DIAGNOSTIC TEST UNTIL THIS MATERIAL IS RETURNED DO NOT WRITE IN THIS MATERIAL Revised Winter 0 PRACTICE TEST: Complete as

More information

1-3: Algebraic Expressions

1-3: Algebraic Expressions 1-3: Algebraic Expressions Mr. Gallo Algebra Modeling Words with an Algebraic Expression What algebraic expression models the word phrase seven fewer than a number t? t 7 What algebraic expression models

More information

7.12 The student will represent relationships with tables, graphs, rules, and words.

7.12 The student will represent relationships with tables, graphs, rules, and words. 7.12 The student will represent relationships with tables, graphs, rules, and words. HINTS & NOTES Relation- is a set of ordered pairs. Remember to always start from the origin. Origin is (0,0) Move horizontally

More information

7) 24% of the lawyers in a firm are female. If there are 150 lawyers altogether, how many lawyers are female?

7) 24% of the lawyers in a firm are female. If there are 150 lawyers altogether, how many lawyers are female? Math 110 Sample Final Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the perimeter (or circumference) and area of the figure. 1) Give the exact

More information

Unit Essential Questions: How do variables help you model real-world situations?

Unit Essential Questions: How do variables help you model real-world situations? Unit Essential Questions: How do variables help you model real-world situations? How can you use properties of real numbers to simplify algebraic expressions? How do you solve an equation or inequality?

More information

FOR ALL STUDENTS TAKING ALGEBRA I SUMMER REVIEW PACKET

FOR ALL STUDENTS TAKING ALGEBRA I SUMMER REVIEW PACKET FOR ALL STUDENTS TAKING ALGEBRA I - SUMMER REVIEW PACKET Dear Student and Parent/Guardian, The math department at Central Dauphin School District wants ou to be successful in Algebra I. We also want ou

More information

Study Guide For use with pages 63 68

Study Guide For use with pages 63 68 2.1 For use with pages 63 68 GOAL Use properties of addition and multiplication. VOCABULARY Lesson 2.1 Commutative Property of Addition: In a sum, you can add the numbers in any order. Associative Property

More information

Chapter Solving Equations by Adding, Subtracting, Multiplying, and Dividing.notebook

Chapter Solving Equations by Adding, Subtracting, Multiplying, and Dividing.notebook Bellwork: Write as a fraction and reduce if you can: 1) 2.7 2) 0.325 Homework Questions??? Write each as a decimal, use repeating decimals when necessary: 3) 5/2 4) 6/8 Evaluate: 5) 2x + y; x = 4, y =

More information

Common Core Algebra Regents Review

Common Core Algebra Regents Review Common Core Algebra Regents Review Real numbers, properties, and operations: 1) The set of natural numbers is the set of counting numbers. 1,2,3,... { } symbol 2) The set of whole numbers is the set of

More information

Name Period Date DRAFT

Name Period Date DRAFT Name Period Date Equations and Inequalities Student Packet 4: Inequalities EQ4.1 EQ4.2 EQ4.3 Linear Inequalities in One Variable Add, subtract, multiply, and divide integers. Write expressions, equations,

More information

Review: Expressions and Equations

Review: Expressions and Equations Review: Expressions and Equations Expressions Order of Operations Combine Like Terms Distributive Property Equations & Inequalities Graphs and Tables Independent/Dependent Variables Constant: a number

More information

Writing and Graphing Inequalities

Writing and Graphing Inequalities 4.1 Writing and Graphing Inequalities solutions of an inequality? How can you use a number line to represent 1 ACTIVITY: Understanding Inequality Statements Work with a partner. Read the statement. Circle

More information

Student Self-Assessment of Mathematics (SSAM) for Intermediate Algebra

Student Self-Assessment of Mathematics (SSAM) for Intermediate Algebra Student Self-Assessment of Mathematics (SSAM) for Intermediate Algebra Answer key 1. Find the value of 3x 4y if x = -2 and y = 5 To find the value, substitute the given values in for x and y 3x -4y Substitute

More information

= = =

= = = . D - To evaluate the expression, we can regroup the numbers and the powers of ten, multiply, and adjust the decimal and exponent to put the answer in correct scientific notation format: 5 0 0 7 = 5 0

More information

Equation. A mathematical sentence formed by setting two expressions equal to each other. Example 1: 3 6 = 18 Example 2: 7 + x = 12

Equation. A mathematical sentence formed by setting two expressions equal to each other. Example 1: 3 6 = 18 Example 2: 7 + x = 12 Equation A mathematical sentence formed by setting two expressions equal to each other Example 1: 3 6 = 18 Example 2: 7 + x = 12 Variable A symbol, usually a letter, that is used to represent one or more

More information

UNIT 1 PACKET â PREREQ SKILLS

UNIT 1 PACKET â PREREQ SKILLS UNIT 1 PACKET â PREREQ SKILLS manipulations as use of the distributive property, simple factoring, and connecting... Simplifying using Distributive Property and Combining Like Terms:. UNIT 1 Math 621 Simplifying

More information

Relationships Between Quantities

Relationships Between Quantities Relationships Between Quantities MODULE 1? ESSENTIAL QUESTION How do you calculate when the numbers are measurements? CORE STANDARDS LESSON 1.1 Precision and Significant Digits CORE N.Q.3 LESSON 1.2 Dimensional

More information

Early Start: Worksheet #1 No calculator/phone use (11 16) (17 10)3

Early Start: Worksheet #1 No calculator/phone use (11 16) (17 10)3 Early Start: Worksheet #1 No calculator/phone use I. Perform the operations; simplify completely. a) 8 ( + 4) ( 7) + ( 1) b) (11 16) (17 10) c) 7 14 6 d) 1 6 5 e) 4 1 + f) 6 9() 10 + 5 5 1 5 4 g) 9 9 +

More information

WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5

WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5 May 06 VIRGINIA MATHEMATICS STANDARDS OF LEARNING CORRELATED TO MOVING WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5 NUMBER AND NUMBER SENSE 5.1 The student will a. read, write, and identify the place values

More information

SCIS-HIS. Teaching and Learning Standards January Mathematics Grades K - 5

SCIS-HIS. Teaching and Learning Standards January Mathematics Grades K - 5 SCIS-HIS Teaching and Learning Standards January 2015 Mathematics Grades K - 5 Table of Contents Introduction... 3 Kindergarten... 3 Counting & Cardinality... 3 Operations & Algebraic Thinking... 4 Number

More information

Simple Solutions Mathematics. Part A. Algebra I Part A. Help Pages & Who Knows

Simple Solutions Mathematics. Part A. Algebra I Part A. Help Pages & Who Knows Simple Solutions Mathematics Algebra I Part A & Who Knows 83 Vocabulary General Absolute Value the distance between a number, x, and zero on a number line; written as x. Example: 5 = 5 reads The absolute

More information

Free Pre-Algebra Lesson 57! page 1

Free Pre-Algebra Lesson 57! page 1 Free Pre-Algebra Lesson 57! page 1 Lesson 57: Review for Final Exam Section I. The Natural Numbers Comprehensive Practice Lessons 1-6 Lesson 1: Counting, Estimating, and Rounding Skill: Estimate the size

More information

Pre-Algebra Notes Unit Two: Solving Equations

Pre-Algebra Notes Unit Two: Solving Equations Pre-Algebra Notes Unit Two: Solving Equations Properties of Real Numbers Syllabus Objective: (.1) The student will evaluate expressions using properties of addition and multiplication, and the distributive

More information

Franklin Math Bowl Algebra I All answers are presented accurate to three decimal places unless otherwise noted. Good luck! c.

Franklin Math Bowl Algebra I All answers are presented accurate to three decimal places unless otherwise noted. Good luck! c. Franklin Math Bowl Algebra I 2009 All answers are presented accurate to three decimal places unless otherwise noted. Good luck! 1. Assuming that x 2 5x + 6 0, simplify x2 6x+9 x 2 5x+6. a. 3 x 2 b. x 2

More information

Solve Quadratic Equations by Completing the Square

Solve Quadratic Equations by Completing the Square 10.5 Solve Quadratic Equations by Completing the Square Before You solved quadratic equations by finding square roots. Now You will solve quadratic equations by completing the square. Why? So you can solve

More information

Willmar Public Schools Curriculum Map

Willmar Public Schools Curriculum Map Note: Problem Solving Algebra Prep is an elective credit. It is not a math credit at the high school as its intent is to help students prepare for Algebra by providing students with the opportunity to

More information