# Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 1 Real Numbers

Save this PDF as:

Size: px
Start display at page:

Download "Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 1 Real Numbers"

## Transcription

1 Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Please watch Section 1 of this DVD before working these problems. The DVD is located at: Page 1

2 Part 1: Real Numbers 1) Identify the real numbers below. 2) Identify the real numbers below. 3) Identify the real numbers below. Page 2

3 Part 2: Rational Numbers 4) Which of the following is a rational number? 5) Which of the following is a rational number? 6) Which of the following is a rational number? Page 3

4 Part 3: Irrational Numbers 7) Which of the following is an irrational number? 8) Which of the following is an irrational number? 10.10, 0.12, 18, π 9) Which of the following is an irrational number? 2, 30, , Page 4

5 Part 4: Integers 10) Which of the following is not an integer? 11) Which of the following is not an integer? 12) Which of the following is not an integer? Page 5

6 Part 5: Whole Numbers 13) Identify the whole number(s) below. 14) Identify the whole number(s) below. 15) Identify the whole number(s) below. Page 6

7 Part 6: Natural Numbers 16) Identify the natural number(s) below. 17) Identify the natural number(s) below. 18) Identify the natural number(s) below. Page 7

8 Part 7: Prime Numbers 19) Identify the prime number(s) below. 20) Identify the prime number(s) below. 21) Identify the prime number(s) below. Page 8

9 Part 8: Putting it all together For each of the numbers below, identify which group they belong to. (Real, Irrational, Rational, Integer, Whole, Natural and/or Prime number) Example: Is both a Real and a Rational number. 22) 23) 24) 25) Page 9

10 Question Answer 1) Identify the real numbers below. First, we need to remember the definition of a real number. This is any number that can be located on a number line. This excludes imaginary numbers. All of the numbers mentioned can be plotted onto a number line even if they are fractions or have numerous decimal places, they can still be plotted somewhere on a number line. All of them are real numbers Since all of the numbers meet the definition of a real number they are all by definition real numbers. Ans: All are considered real numbers Page 10

11 2) Identify the real numbers below. First, we need to remember the definition of a real number. This is any number that can be located on a number line. This excludes imaginary numbers. All of the numbers mentioned can be plotted onto a number line even if they are fractions or have numerous decimal places, they can still be plotted somewhere on a number line. All of them are real numbers Since all of these numbers meet the definition of a real number they are all by definition real numbers. Ans: All are considered real numbers Page 11

12 3) Identify the real numbers below. First, we need to remember the definition of a real number. This is any number that can be located on a number line. This excludes imaginary numbers. All of the numbers mentioned can be plotted onto a number line even if they are fractions or have numerous decimal places, they can still be plotted somewhere on a number line. All of them are real numbers Since all of these numbers meet the definition of a real number they are all by definition real numbers. Ans: All are considered real numbers Page 12

13 4) Which of the following is a rational number? First, we need to remember the definition of a rational number. This is any number that can be expressed as a fraction. We see as we express the numbers in fraction form that all but one can be expressed as a fraction. If we type the square root of two into a calculator we notice that the result is a non repeating decimal pattern. The rest of the numbers can be expressed as a fraction and therefore are rational numbers. Ans: Page 13

14 5) Which of the following is a rational number? First, we need to remember the definition of a rational number. This is any number that can be expressed as a fraction. We see as we express the numbers in fraction form that all but one can be expressed as a fraction. We notice right away that has a non repeating infinite pattern. Therefore, there is no way to express this number as a fraction. The rest of the numbers can be expressed as a fraction and therefore are rational numbers. Ans: Page 14

15 6) Which of the following is a rational number? First, we need to remember the definition of a rational number. This is any number that can be expressed as a fraction. We see as we express the numbers in fraction form that all but one can be expressed as a fraction. If we type into a calculator we notice that pi has a non repeating decimal pattern that goes on forever. Therefore, there is no way to express this number as a fraction. The rest of the numbers can be expressed as a fraction and therefore are rational numbers. Ans: Page 15

16 7) Which of the following is an irrational number? First, we need to remember the definition of an irrational number. This is any number that can t be expressed as a fraction. All of the numbers mentioned can be written as a fraction. Since all of these numbers can be expressed as fractions, none of these numbers are considered irrational Ans: None of the numbers listed are irrational numbers Page 16

17 8) Which of the following is an irrational number? 10.10, 0.12, 18, π First, we need to remember the definition of an irrational number. This is any number that can t be expressed as a fraction. The first three numbers mentioned can be written as a fraction. Since Pi = is an infinite non repeating decimal, it cannot be written as a fraction. π = Ans: Pi is an Irrational Number Page 17

18 9) Which of the following is an irrational number? 2, 30, , First, we need to remember the definition of an irrational number. This is any number that can t be expressed as a fraction. All of the numbers can be written as a fraction except for the infinite non repeating decimal. This is the only irrational number in our list Ans: is irrational Page 18

19 10) Which of the following is not an integer? First, we need to remember the definition of what an integer is. This is, any number that is positive, negative or zero, but has no decimal point.,-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 Right away, we look at the list of numbers and notice that all but one falls under this definition. Ans: Page 19

20 11) Which of the following is not an integer? First, we need to remember the definition of what an integer is. This is, any number that is positive, negative or zero, but has no decimal place.,-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 Right away, we look at the list of numbers and notice that all but one falls under this definition. The negative fraction will provide a result with a decimal place when we divide 15 by 16. Since the square root of 9 is exactly 3, this is an integer as well. Ans: Page 20

21 12) Which of the following is not an integer? First, we need to remember the definition of what an integer is. This is, any number that is positive, negative or zero, but has no decimal place.,-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 Right away, we look at the list of numbers and notice that all but one falls under this definition. Ans: Page 21

22 13) Identify the whole number(s) below. First, we need to remember the definition of what makes a whole number. A whole number is any positive number including zero that does not have a decimal place. By simply applying the definition we see that the two negative numbers are not whole numbers. Zero and one hundred do fit the definition. Ans: Page 22

23 14) Identify the whole number(s) below. First, we need to remember the definition of what makes a whole number. A whole number is any positive number including zero that does not have a decimal place. First we see that the negative number does not meet our definition. Then we see that the fraction will give us a decimal place as well as the square root of 2. The number fifteen is the only whole number. Ans: Page 23

24 15) Identify the whole number(s) below. First, we need to remember the definition of what makes a whole number. A whole number is any positive number including zero that does not have a decimal place. We see that 640 is both positive and does not contain a decimal place. The negative 640 however does not meet our definition so it is not a whole number. The one half will give us a decimal place, 0.5 so it is not a whole number. The number 1.1 is positive but has a decimal place and therefore is not a whole number. The only whole number from the list is 640. Ans: Page 24

25 16) Identify the natural number(s) below. First, we need to remember the definition of what makes a natural number. This is any number that can be used to physically count something. This includes: 1,2,3,4,5,6,7,8,9.. Based on our definition, we see that the negative numbers are not natural numbers because I can t physically count something I don t have so the negative numbers are not natural numbers. The last number to consider from the list is zero. If I have zero of something I can t naturally count it so zero is not a natural number. None. Since none of the numbers meet our criteria of what makes a natural number none of these are natural numbers Ans: None Page 25

26 17) Identify the natural number(s) below. First, we need to remember the definition of what makes a natural number. This is any number that can be used to physically count something. This includes: 1,2,3,4,5,6,7,8,9.. Based on our definition, we see that the negative numbers are not natural numbers because I can t physically count something I don t have so the negative numbers are not natural numbers. The square root of 9 is the same as 3, so I can physically count something if I have 3 apples or 3 pencils so the square root of 9 is a natural number. The last number to consider from the list is 26. I can definitely physically have 26 of something and count it so 26 is a natural numbers. Ans: Are natural numbers Page 26

27 18) Identify the natural number(s) below. First, we need to remember the definition of what makes a natural number. This is any number that can be used to physically count something. This includes: 1,2,3,4,5,6,7,8,9.. Based on our definition, we see that the negative numbers are not natural numbers because I can t physically count something I don t have so the negative numbers are not natural numbers. We are left with 640 and 0. If I have zero of something I can t naturally count it so zero is not a natural number. The number 640 however can be used to physically count something like the 640 pennies in my piggy bank. Therefore the number 640 is a natural number. The only natural number is the number 640. Ans: Page 27

28 19) Identify the prime number(s) below. First, we need to remember the definition of a prime number. This is a whole number other than zero and 1, which can only be divided by 1 and itself. When we say divided only by 1 and itself, we mean that those are the only numbers that will not give you a decimal place when you divide. The first number we have is 32. It is by definition a whole number and it is not zero or 1. However, 1 and 32 are not the only numbers I can divide 32 by. I can divide it by 2, 4, 8, and 16. So therefore it is not a prime number. The number 2 is a whole number that is not zero or 1. And I can only divide it by 1 and 2, so it is a prime number. The number zero already violates our definition so it is not a prime number. The number 16 is a whole number that is not zero or 1. However 1 and 16 are not the only numbers I can divide 16 by. I can divide it by 2, 4 and 8. So it is not a prime number. Ans: Page 28

29 20) Identify the prime number(s) below. First, we need to remember the definition of a prime number. This is a whole number other than zero and 1, which can only be divided by 1 and itself. When we say divided only by 1 and itself, we mean that those are the only numbers that will not give you a decimal place when you divide. The number 10 by definition a whole number and it is not zero or 1. However, 1 and 10 are not the only numbers I can divide 10 by. I can divide it by 2 and 5. So therefore it is not a prime number. The number 17 is a whole number and it is not zero or 1. When we try to divide 17 by something other than 1 or 17, we find that we can t do it without ending up with a decimal place. Therefore 17 is a prime number. The number 3 as well as 17 can only be divided by 1 and itself therefore it is a prime number. The number 1 violates our definition so it is not a prime number. Ans: Page 29

30 21) Identify the prime number(s) below. First, we need to remember the definition of a prime number. This is a whole number other than zero and 1, which can only be divided by 1 and itself. When we say divided only by 1 and itself, we mean that those are the only numbers that will not give you a decimal place when you divide. As we look at the first two numbers, -2 and 0.8, we notice they are not whole numbers which violates our definition of a prime number and therefore are not considered prime numbers. The number 15 is a whole number and it is not zero or 1. However, 1 and 15 are not the only numbers I can divide 15 by. I can divide it by the number 5 and still end up with a natural number (no decimal or zero). So it is not a prime number. The number 22 is a whole number and it is not zero or 1. However, 1 and 22 are not the only numbers I can divide 22 by. I can divide it by 2, and 11. So it is not a prime number. None. None of the numbers meet our definition of a prime number. Ans: None. Page 30

31 22) First, we need to remember our definitions and how each type of number is related to the other types of numbers. Remember that Real numbers is at the top of the umbrella. Everything else falls under it. Then it breaks off into Irrational and Rational numbers. Then under Rational numbers are Integers, Whole numbers, Natural numbers and Prime numbers. If I know a number is Irrational, then by definition it is not Rational or anything that falls under a Rational number. This number is a real number. Next we see if it is irrational or rational. Since I can write it as a fraction, then it is a rational number. Since it is has a decimal place, it is not an integer, a whole number, natural number or a prime number. Ans: Real number, Rational Page 31

32 23) number First, we need to remember our definitions and how each type of number is related to the other types of numbers. Remember that Real numbers is at the top of the umbrella. Everything else falls under it. Then it breaks off into Irrational and Rational numbers. Then under Rational numbers are Integers, Whole numbers, Natural numbers and Prime numbers. If I know a number is Irrational, then by definition it is not Rational or anything that falls under a Rational number. This number is a Real number. Next we see if it is Irrational or Rational. Just by looking at it, we see that it is Rational since we can write it as 7 over 1. It has no decimal place and it is positive so it is an Integer, a Whole number and a Natural number. We find that I can only divide this number by 1 and itself so it is a Prime number. Ans: Real number, Rational Number, Integer, Whole number, Natural number, and Prime Page 32

33 24) number First, we need to remember our definitions and how each type of number is related to the other types of numbers. Remember that Real numbers is at the top of the umbrella. Everything else falls under it. Then it breaks off into Irrational and Rational numbers. Then under Rational numbers are Integers, Whole numbers, Natural numbers and Prime numbers. If I know a number is Irrational, then by definition it is not Rational or anything that falls under a Rational number. This number is a Real number. Next we see if it is Irrational or Rational. Just by looking at it, we see that it has decimal places that are non repeatable and infer to go on forever. This means we can t represent it as a fraction and therefore is an Irrational number. Since it is an Irrational number it is not Rational and not any of the other types of numbers. Ans: Real number, Irrational Number Page 33

34 25) First, we need to remember our definitions and how each type of number is related to the other types of numbers. Remember that Real numbers is at the top of the umbrella. Everything else falls under it. Then it breaks off into Irrational and Rational numbers. Then under Rational numbers are Integers, Whole numbers, Natural numbers and Prime numbers. If I know a number is Irrational, then by definition it is not Rational or anything that falls under a Rational number. This number is a Real number. Next we see if it is Irrational or Rational. Just by looking at it, we see that it is Rational since we can write it as -2 over 1. We also notice that it has a negative sign but no decimal place. This number is still considered an Integer, but not considered a Whole number. Since it is not considered a whole number it can t be a Natural number or a Prime number by definition. Ans: Real number, Rational Number, and an Integer Page 34

### March 29, 2011. 171S4.4 Theorems about Zeros of Polynomial Functions

MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial

### x 4-1 = (x²)² - (1)² = (x² + 1) (x² - 1) = (x² + 1) (x - 1) (x + 1)

Factoring Polynomials EXAMPLES STEP 1 : Greatest Common Factor GCF Factor out the greatest common factor. 6x³ + 12x²y = 6x² (x + 2y) 5x - 5 = 5 (x - 1) 7x² + 2y² = 1 (7x² + 2y²) 2x (x - 3) - (x - 3) =

### 3. Add an Event: Alarm Alarm 0 a. Add an Action: Set Variable i. Applies to: Self ii. Variable: time_left iii. Value: +1 iv. Check the Relative box

Creating a Timer: You can have a timer that shows how long the player has been playing the game. 1. Create a new object and give it a name. This example is called object_timer. 2. Add an Event: Create

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

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

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

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

### Zeros of Polynomial Functions

Review: Synthetic Division Find (x 2-5x - 5x 3 + x 4 ) (5 + x). Factor Theorem Solve 2x 3-5x 2 + x + 2 =0 given that 2 is a zero of f(x) = 2x 3-5x 2 + x + 2. Zeros of Polynomial Functions Introduction

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

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

### Domain of a Composition

Domain of a Composition Definition Given the function f and g, the composition of f with g is a function defined as (f g)() f(g()). The domain of f g is the set of all real numbers in the domain of g such

### ALGEBRA 2 CRA 2 REVIEW - Chapters 1-6 Answer Section

ALGEBRA 2 CRA 2 REVIEW - Chapters 1-6 Answer Section MULTIPLE CHOICE 1. ANS: C 2. ANS: A 3. ANS: A OBJ: 5-3.1 Using Vertex Form SHORT ANSWER 4. ANS: (x + 6)(x 2 6x + 36) OBJ: 6-4.2 Solving Equations by

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

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

### PowerScore Test Preparation (800) 545-1750

Question 1 Test 1, Second QR Section (version 1) List A: 0, 5,, 15, 20... QA: Standard deviation of list A QB: Standard deviation of list B Statistics: Standard Deviation Answer: The two quantities are

### Arithmetic and Algebra of Matrices

Arithmetic and Algebra of Matrices Math 572: Algebra for Middle School Teachers The University of Montana 1 The Real Numbers 2 Classroom Connection: Systems of Linear Equations 3 Rational Numbers 4 Irrational

### GRADES 7, 8, AND 9 BIG IDEAS

Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for

Grades -8 Mathematics Training Test Answer Key 04 . Factor 6x 9. A (3x 9) B 3(x 3) C 3(3x ) D 6(x 9) Option A is incorrect because the common factor of both terms is not and the expression is not factored

### Title Location Date Start Time End Time Description

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

### Square Roots and Other Radicals

Radicals - Definition Radicals, or roots, are the opposite operation of applying exponents. A power can be undone with a radical and a radical can be undone with a power. For example, if you square 2,

### GMAT SYLLABI. Types of Assignments - 1 -

GMAT SYLLABI The syllabi on the following pages list the math and verbal assignments for each class. Your homework assignments depend on your current math and verbal scores. Be sure to read How to Use

### Functional Math II. Information CourseTitle. Types of Instruction

Functional Math II Course Outcome Summary Riverdale School District Information CourseTitle Functional Math II Credits 0 Contact Hours 135 Instructional Area Middle School Instructional Level 8th Grade

### Fractions Packet. Contents

Fractions Packet Contents Intro to Fractions.. page Reducing Fractions.. page Ordering Fractions page Multiplication and Division of Fractions page Addition and Subtraction of Fractions.. page Answer Keys..

### Online LEI Lesson 2. Lesson 2 Savings Accounts and U.S. Savings Bonds LEARNING, EARNING

Online LEI Lesson 2 Lesson 2 Savings Accounts and U.S. Savings Bonds On l i n e L E I 17 2 Savings Accounts and U.S. Savings Bonds LESS 2 SAVINGS ACCOUNTS U. S. SAVINGS BDS Time Required Lesson Description

### 6th Grade Lesson Plan: Probably Probability

6th Grade Lesson Plan: Probably Probability Overview This series of lessons was designed to meet the needs of gifted children for extension beyond the standard curriculum with the greatest ease of use

### Polynomials. Dr. philippe B. laval Kennesaw State University. April 3, 2005

Polynomials Dr. philippe B. laval Kennesaw State University April 3, 2005 Abstract Handout on polynomials. The following topics are covered: Polynomial Functions End behavior Extrema Polynomial Division

### The GMAT Guru. Prime Factorization: Theory and Practice

. Prime Factorization: Theory and Practice The following is an ecerpt from The GMAT Guru Guide, available eclusively to clients of The GMAT Guru. If you would like more information about GMAT Guru services,

Advanced GMAT Math Questions Version Quantitative Fractions and Ratios 1. The current ratio of boys to girls at a certain school is to 5. If 1 additional boys were added to the school, the new ratio of

### Main Question 1: How and where do you or your family use the Internet - whether on a computer or a cell phone? Follow up questions for INTERNET USERS

TABLE 1: Current Internet use Main Question 1: How and where do you or your family use the Internet - whether on a computer or a cell phone? Follow up questions for INTERNET USERS 1. What do you use to

### Big Ideas in Mathematics

Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards

### Find your new job through us

Sida: 1 av 7 Engelska New at the Employment Office (text version of the film on ny.arbetsformedlingen.se) Find your new job through us Welcome to the Employment Service Here you will find information about

### Chapter 13. Fractional Factorials. 13.1 Fractional replicates

244 Chapter 13 Fractional Factorials 13.1 Fractional replicates A factorial design is a fractional replicate if not all possible combinations of the treatment factors occur. A fractional replicate can

### Augmented reality enhances learning at Manchester School of Medicine

Augmented reality enhances learning at Manchester School of Medicine Welcome to the Jisc podcast. The University of Manchester is taking a unique approach to prescription training for its medical students

### Math 10 - Unit 3 Final Review - Numbers

Class: Date: Math 10 - Unit Final Review - Numbers Multiple Choice Identify the choice that best answers the question. 1. Write the prime factorization of 60. a. 2 7 9 b. 2 6 c. 2 2 7 d. 2 7 2. Write the

### 3 + 7 1 2. 6 2 + 1. 7 0. 1 200 and 30 100 100 10 10 10. Maths in School. Addition in School. by Kate Robinson

1 2. 6 2 + 1. 7 0 10 3 + 7 1 4. 3 2 1 231 200 and 30 100 100 10 10 10 Maths in School Addition in School by Kate Robinson 2 Addition in School Contents Introduction p.3 Adding in everyday life p.3 Coat

### How to Make the Most of Excel Spreadsheets

How to Make the Most of Excel Spreadsheets Analyzing data is often easier when it s in an Excel spreadsheet rather than a PDF for example, you can filter to view just a particular grade, sort to view which

### If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C?

Problem 3 If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Suggested Questions to ask students about Problem 3 The key to this question

### YOU CAN COUNT ON NUMBER LINES

Key Idea 2 Number and Numeration: Students use number sense and numeration to develop an understanding of multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and

### List the elements of the given set that are natural numbers, integers, rational numbers, and irrational numbers. (Enter your answers as commaseparated

MATH 142 Review #1 (4717995) Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Description This is the review for Exam #1. Please work as many problems as possible

### Mathematics Review for MS Finance Students

Mathematics Review for MS Finance Students Anthony M. Marino Department of Finance and Business Economics Marshall School of Business Lecture 1: Introductory Material Sets The Real Number System Functions,

### Coin Flip Questions. Suppose you flip a coin five times and write down the sequence of results, like HHHHH or HTTHT.

Coin Flip Questions Suppose you flip a coin five times and write down the sequence of results, like HHHHH or HTTHT. 1 How many ways can you get exactly 1 head? 2 How many ways can you get exactly 2 heads?

### ACCUPLACER. 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

### PHILOSOPHY OF THE MATHEMATICS DEPARTMENT

PHILOSOPHY OF THE MATHEMATICS DEPARTMENT The Lemont High School Mathematics Department believes that students should develop the following characteristics: Understanding of concepts and procedures Building

### A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions

A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions Marcel B. Finan Arkansas Tech University c All Rights Reserved First Draft February 8, 2006 1 Contents 25

### MATH 221 FIRST SEMESTER CALCULUS. fall 2007

MATH 22 FIRST SEMESTER CALCULUS fall 2007 Typeset:December, 2007 2 Math 22 st Semester Calculus Lecture notes version.0 (Fall 2007) This is a self contained set of lecture notes for Math 22. The notes

### Algebra 1 Course Title

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

### 1 Description of The Simpletron

Simulating The Simpletron Computer 50 points 1 Description of The Simpletron In this assignment you will write a program to simulate a fictional computer that we will call the Simpletron. As its name implies

### Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Section One: Terms Numerator: The number on top of a fraction which tells how many parts you have. Denominator: The number on the bottom of a fraction which tells how

### CAHSEE 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,

### 0.4 FACTORING POLYNOMIALS

36_.qxd /3/5 :9 AM Page -9 SECTION. Factoring Polynomials -9. FACTORING POLYNOMIALS Use special products and factorization techniques to factor polynomials. Find the domains of radical expressions. Use

### Successful 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:... 8-11 ABILITY LEVEL:... Basic DURATION:... 1 year CREDIT:... 5.0 per semester MEETS GRADUATION

### MBA Jump Start Program

MBA Jump Start Program Module 2: Mathematics Thomas Gilbert Mathematics Module Online Appendix: Basic Mathematical Concepts 2 1 The Number Spectrum Generally we depict numbers increasing from left to right

What You Need to Know Before Your Business Insurance Renews by Scott Kirby Shopping for commercial insurance is easy when prices are falling. Need to save money? Need broader coverage? Get another quote.

### Idea 1: Idea 2: Idea 1: Idea 2: Idea 3: Idea 4:

WHAT Idea 1: Use a barrier (bag, box) to hide materials of the activity from view. Talk about the fun things in the bag/box. If necessary, let the person hear/feel that there is stuff in there. Idea 2:

### MTH124: Honors Algebra I

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

### Math 181 Handout 16. Rich Schwartz. March 9, 2010

Math 8 Handout 6 Rich Schwartz March 9, 200 The purpose of this handout is to describe continued fractions and their connection to hyperbolic geometry. The Gauss Map Given any x (0, ) we define γ(x) =

### Welcome to Math 7 Accelerated Courses (Preparation for Algebra in 8 th grade)

Welcome to Math 7 Accelerated Courses (Preparation for Algebra in 8 th grade) Teacher: School Phone: Email: Kim Schnakenberg 402-443- 3101 kschnakenberg@esu2.org Course Descriptions: Both Concept and Application

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

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

### Grade 4 - Module 5: Fraction Equivalence, Ordering, and Operations

Grade 4 - Module 5: Fraction Equivalence, Ordering, and Operations Benchmark (standard or reference point by which something is measured) Common denominator (when two or more fractions have the same denominator)

### Descriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics

Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics (or inductive statistics),

### What to Expect on the Compass

What to Expect on the Compass What is the Compass? COMPASS is a set of untimed computer adaptive tests created by the American College Test (ACT) Program. Because COMPASS tests are "computer adaptive,"

### Integrated Skills in English ISE II

Integrated Skills in English Reading & Writing exam Sample paper 4 10am 12pm Your full name: (BLOCK CAPITALS) Candidate number: Centre: Time allowed: 2 hours Instructions to candidates 1. Write your name,

### MATH 289 PROBLEM SET 4: NUMBER THEORY

MATH 289 PROBLEM SET 4: NUMBER THEORY 1. The greatest common divisor If d and n are integers, then we say that d divides n if and only if there exists an integer q such that n = qd. Notice that if d divides

### Why should we learn this? One real-world connection is to find the rate of change in an airplane s altitude. The Slope of a Line VOCABULARY

Wh should we learn this? The Slope of a Line Objectives: To find slope of a line given two points, and to graph a line using the slope and the -intercept. One real-world connection is to find the rate

### Excel Formatting: Best Practices in Financial Models

Excel Formatting: Best Practices in Financial Models Properly formatting your Excel models is important because it makes it easier for others to read and understand your analysis and for you to read and

### Principles of Mathematics MPM1D

Principles of Mathematics MPM1D Grade 9 Academic Mathematics Version A MPM1D Principles of Mathematics Introduction Grade 9 Mathematics (Academic) Welcome to the Grade 9 Principals of Mathematics, MPM

### CRLS 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

### Change Number Stories Objective To guide children as they use change diagrams to help solve change number stories.

Number Stories Objective To guide children as they use change diagrams to help solve change number stories. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

### C Major F Major G Major A Minor

For this task you will create a 16 bar composition with a Ground Bass Accompaniment. REMINDER A chord is built on the notes 1 3 5 of a scale. e.g. chord of C would have the notes C E G. The first note

### A power series about x = a is the series of the form

POWER SERIES AND THE USES OF POWER SERIES Elizabeth Wood Now we are finally going to start working with a topic that uses all of the information from the previous topics. The topic that we are going to

### Student Guide and Syllabus for MAT100 Introductory Algebra

Course Information: MAT100 Introductory Algebra Section: 05C Section: 06C Section: 07C* Classroom: 341 Main Building Classroom: 341 Main Building Classroom: 341 Main Building Meeting Dates: Monday Thursday

### 2013 MBA Jump Start Program

2013 MBA Jump Start Program Module 2: Mathematics Thomas Gilbert Mathematics Module Algebra Review Calculus Permutations and Combinations [Online Appendix: Basic Mathematical Concepts] 2 1 Equation of

### Drawing a histogram using Excel

Drawing a histogram using Excel STEP 1: Examine the data to decide how many class intervals you need and what the class boundaries should be. (In an assignment you may be told what class boundaries to

### Time Value of Money 1

Time Value of Money 1 This topic introduces you to the analysis of trade-offs over time. Financial decisions involve costs and benefits that are spread over time. Financial decision makers in households

### REPUTATION MANAGEMENT SURVIVAL GUIDE. A BEGINNER S GUIDE for managing your online reputation to promote your local business.

REPUTATION MANAGEMENT SURVIVAL GUIDE A BEGINNER S GUIDE for managing your online reputation to promote your local business. About Main Street Hub: Main Street Hub is the voice for more local businesses

### 380.760: Corporate Finance. Financial Decision Making

380.760: Corporate Finance Lecture 2: Time Value of Money and Net Present Value Gordon Bodnar, 2009 Professor Gordon Bodnar 2009 Financial Decision Making Finance decision making is about evaluating costs

### Natural Law and John Austin

University of California, Irvine Nature of Law What is a law? Law and Morality Natural Law Theory Napoleonic Code Which are these behaviors are illegal? Cold blooded murder Violating a contract Lying in

### INSTRUCTIONS FOR FILING BANKRUPTCY (for Assistance Ddesk visitor)

BEFORE you file: INSTRUCTIONS FOR FILING BANKRUPTCY (for Assistance Ddesk visitor) 1. You must take a credit counseling course. This is required by law. The cost of the class is between \$10 and \$50. See

### Prentice Hall Connected Mathematics 2, 7th Grade Units 2009

Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Grade 7 C O R R E L A T E D T O from March 2009 Grade 7 Problem Solving Build new mathematical knowledge through problem solving. Solve problems

### A 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

### A. Factoring out the Greatest Common Factor.

DETAILED SOLUTIONS AND CONCEPTS - FACTORING POLYNOMIAL EXPRESSIONS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you!

### Napa Valley College Fall 2015 Math 106-67528: College Algebra (Prerequisite: Math 94/Intermediate Alg.)

1 Napa Valley College Fall 2015 Math 106-67528: College Algebra (Prerequisite: Math 94/Intermediate Alg.) Room 1204 Instructor: Yolanda Woods Office: Bldg. 1000 Rm. 1031R Phone: 707-256-7757 M-Th 9:30-10:35

### Lesson 9: Radicals and Conjugates

Student Outcomes Students understand that the sum of two square roots (or two cube roots) is not equal to the square root (or cube root) of their sum. Students convert expressions to simplest radical form.

### Bystander Intervention

Bystander Intervention T Y P E S 1 Common Components 2 What is Bystander Intervention 3 Techniques to Try 4 Steps to Action 5 Who you can contact for more information regarding bystander intervention and

### Florida Math for College Readiness

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

### Math at a Glance for April

Audience: School Leaders, Regional Teams Math at a Glance for April The Math at a Glance tool has been developed to support school leaders and region teams as they look for evidence of alignment to Common

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

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

### Descriptive statistics; Correlation and regression

Descriptive statistics; and regression Patrick Breheny September 16 Patrick Breheny STA 580: Biostatistics I 1/59 Tables and figures Descriptive statistics Histograms Numerical summaries Percentiles Human

### Average producers can easily increase their production in a larger office with more market share.

The 10 Keys to Successfully Recruiting Experienced Agents by Judy LaDeur Understand whom you are hiring. Don t make the mistake of only wanting the best agents or those from offices above you in market

### 4.1. COMPLEX NUMBERS

4.1. COMPLEX NUMBERS What You Should Learn Use the imaginary unit i to write complex numbers. Add, subtract, and multiply complex numbers. Use complex conjugates to write the quotient of two complex numbers

### Unit 6: Polynomials. 1 Polynomial Functions and End Behavior. 2 Polynomials and Linear Factors. 3 Dividing Polynomials

Date Period Unit 6: Polynomials DAY TOPIC 1 Polynomial Functions and End Behavior Polynomials and Linear Factors 3 Dividing Polynomials 4 Synthetic Division and the Remainder Theorem 5 Solving Polynomial

### Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:

Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours

### EAP/GWL Rev. 1/2011 Page 1 of 5. Factoring a polynomial is the process of writing it as the product of two or more polynomial factors.

EAP/GWL Rev. 1/2011 Page 1 of 5 Factoring a polynomial is the process of writing it as the product of two or more polynomial factors. Example: Set the factors of a polynomial equation (as opposed to an

### The Commission Cutting Report

The Commission Cutting Report Why they re being cut and what you can do about it! By Mike Ferry Page 1 of 17 THE COMMISSION CUTTING REPORT Why am I writing a report of this type? Why is a report of this

### This loop prints out the numbers from 1 through 10 on separate lines. How does it work? Output: 1 2 3 4 5 6 7 8 9 10

Java Loops & Methods The while loop Syntax: while ( condition is true ) { do these statements Just as it says, the statements execute while the condition is true. Once the condition becomes false, execution

### Precalculus Orientation and FAQ

Precalculus Orientation and FAQ MATH 1011 (Precalculus) is a four hour 3 credit course that prepares a student for Calculus. Topics covered include linear, quadratic, polynomial, rational, exponential,

### Primes. Name Period Number Theory

Primes Name Period A Prime Number is a whole number whose only factors are 1 and itself. To find all of the prime numbers between 1 and 100, complete the following exercise: 1. Cross out 1 by Shading in

### What we will cover. Types of orders How to place an order Instruc8ons from the DPR So>ware and what they mean

What we will cover Types of orders How to place an order Instruc8ons from the DPR So>ware and what they mean What is a STOP Order? This type of order is what we use at How Do I Trade Stock.com regularly

### The Easy Picture Guide to banking xxxx. Choosing xxxxxxxxxxxxxxxxxxxxx a xxxxxxxxxxxxxxxxxxxxx. bank account

The Easy Picture Guide to banking xxxx Choosing xxxxxxxxxxxxxxxxxxxxx and opening a xxxxxxxxxxxxxxxxxxxxx bank account The Easy Picture Guide to xxxx a bank account The Easy Picture Guide to Money for