# Using Casio Graphics Calculators

Size: px
Start display at page:

Transcription

1 Using Casio Graphics Calculators (Some of this document is based on papers prepared by Donald Stover in January 2004.) This document summarizes calculation and programming operations with many contemporary Casio calculators (among them the fx-9750g Plus, CFX-9850G Plus, CFX- 9850GB Plus, CFX-9950GB Plus, FX-9860G and FX-7400G Plus). In what follows, key labels are in bold-face type, with parentheses indicating labels above keys. For example, to access the left square bracket, the keystrokes would be indicated as SHIFT + ([). Although every effort is made to make this section answer all problems related to, it may be necessary to refer to your calculator User s Guide. General Operation Most multiplications are indicated by simple juxtaposition; the " key is needed only between numbers. To indicate negative numbers, use the ( ) key, not the key, which represents subtraction as in A - B. The letters A through Z appear in red above the keys; to type one, first type the ALPHA key. (SHIFT ALPHA locks in this mode; another ALPHA cancels it.) Note that you can enter the letter X by pressing the X, ",T key. Notice too that your cursor changes from _ to A, indicating alpha mode. The functions directly above or above left are obtained with the SHIFT key. Thus ALPHA " represents the letter S, while SHIFT " represents the left curly bracket, {. In this document these would be shown as ALPHA " ( S) and SHIFT " ({) respectively. Powers are done with the " key. Internal calculations are carried to 15 digits. The calculator comes on displaying a main menu of icons for 15 different modes. You can later access this screen by pressing the MENU key. focuses attention on only three of those modes: PRGM, MAT and GRAPH. The MAT mode is for matrices, not math. Normal arithmetic calculation is done in the RUN mode, not discussed here. Movement around any screen is accomplished by the cursor movement keys. These are the corresponding (up, down, left, right) corners of the black area located in the mid-right area of the calculator face. The area is labeled REPLAY in tiny black-on-black print. To choose a mode on the menu screen, use the cursor movement keys to find that mode and then press EXE. Alternatively, simply press the number or letter in the lower right corner of the mode desired. For example, press the 5 key to enter graph mode, the log (B) key (you don't have to press ALPHA) to enter program mode. Within a mode, various labels usually appear at the bottom of the screen, above some or all of the gray F1, F2, F3, F4, F5 and F6 keys. (Such displays also appear when you use any of the keys SHIFT, ALPHA, OPTN, VARS. or SHIFT VARS (PRGM).) A labeled F key may perform a single function, but in many situations it results in a new set of F key labels in effect, a submenu. Using EXE to choose a highlighted option on the screen is another way you may reach a submenu. To back up through layers of submenus, use the EXIT key. SHIFT EXIT (QUIT) skips back to the initial screen of the current mode. In highlighting screen options using the cursor Page 1 of 8

4 F2 (Goto) Goto F4 (?)? Input data F5 ( ") " Output data F6 F3 (Rel) F1 (=) = F2 ( ) F3 (>) > F4 (<) < F5 ( ) F6 ( ) F6 (SYBL) or ALPHA F1 (') ' F2 (") " OPTN F2 (Mat) Matrices F1 (Mat) Matrix F6 F2 (Dim) Dimension F6 F4 (NUM) F1 (Abs) Absolute Value F5 (Intg) Greatest Integer Function F6 F6 F4 (LOGIC) F1 (And) And F2 (Or) Or F3 (Not) Not Program Control Structures Unless otherwise instructed a program proceeds line by line in the order they are entered. Control structures (listed under SHIFT VARS (PRGM) F1 (COM)while in editing mode) change this order of program operation in specific ways or stop program operation. In this book we will use many of these keys. IEnd and WEnd As you will see in the following examples, these instructions send control back to the preceding control structure. Ends are like parentheses. When one loop is embedded inside another, that loop's End occurs first. If <test> Then <instruction> A test, for example If X=5, determines whether the Then instruction is performed. When the test is true (in this case if X does equal five) then the following single program line beginning with Then is performed. When the test is false, that line is skipped. (No IfEnd is necessary in this case although it will not make a difference if it is included.) Page 4 of 8

5 If <test> Then <instruction 1> <instruction 2>... IEnd In this case you want the If test to govern more than one line of code. You then write those program lines between Then and IEnd. For is a counting instruction. It applies a series of steps one at a time 1 within indicated limits. Here is an example of a For loop: 0 " A For N " 1 To 5 A + N " A Next In this example, before we enter the For loop A is set equal to 0. There is only one instruction between the For and Next lines but there could have been many. The For command line establishes a variable, N, that will take on the values successively between the numbers that follow. In this case the successive values are N = 1, 2, 3, 4, and 5. Each time one of these values of N is set the instruction or instructions that follow until Next are processed. Thus the For loop here is a short way of processing the following five steps: " A 'A is now " A 'A is now " A 'A is now " A 'A is now " A 'A is now 15 At this point the program leaves the For loop and any following statements are processed with A = 15. (Note that N = 5 as well.) While is a loop that is processed until the test included in the While statement fails. In other words, the While instruction is saying "While this is true, do the following until you reach Wend, then repeat the test. When the test fails, jump to the line after the Wend." Here is a simple example of a While loop: 1 " N While N < 12 N " 2 " N WEnd The instruction in this loop will be processed until N is no longer less than 12. Here are the lines that will b processed: 1 " 2 " N 'N is now 2 2 " 2 " N 'N is now 4 4 " 2 " N 'N is now 8 8 " 2 " N 'N is now 16 After this final step it is no longer true that N < 12. At this point the loop is exited and any instructions following it are processed with N = It is possible to modify this by including a step size. Two examples: in For I " 1 To 9 Step 2 N would jump 2 each time, performing the loop for N = 1, 3, 5, 7 and 9; in For I " 5 To 3 Step - 1, N would reduce one each time, processing N = 5, 4 and 3. Page 5 of 8

6 Lbl allows you to set a target line for a Goto instruction. Include a number in this line as in Lbl 1. Goto sends program control to the designated Lbl line. For example, the instruction Goto 1 would send program control to Lbl 1, even if this means jumping out of a loop. Although this and other instructions can be useful, they can create endless loops. In that case you must manually stop program operation by pressing AC/ ON. 2 Input and Output in Programs Here are the instructions that allow you to enter and retrieve data.? If you want to have the program user enter a number N at some point in the program (usually at or near the beginning) enter the line: "N"? " N When the program is run, it will stop at that line and display N?. You would then type a value and press EXE. The program would then continue with N set equal to the value you typed.. " This symbol gives a way to present information. If you want to have the program show the value of N, simply enter the line: 3 Matrices N " This output line is useful for other purposes as well. For example, you can use lines like this entered at various points in your program to print data values as an aid to debugging programmer's lingo for finding and correcting errors. First, let's understand what a matrix is. It is an array of numbers arranged in rows and columns. 4 For example, you might have the array: This is a 3 by 4 matrix. (Note that you always use the order row, then column.) Arbitrarily, we refer to matrix dimensions and matrix entries in the order horizontal row then vertical column. If 2 Early programmers used Goto instructions extensively until a computer scientist named Dykstra severely criticized such use because they created programs that looked like spider webs and were very difficult to interpret and debug. Since then the control structure has been rarely used. There are, however, situations when it best serves the programmer's purpose. Goto is used only a few times in appropriate places in this text. 3 Once a program has been run, you can also access any value that occurred in that program by typing its name followed by EXE. You could, for example, have omitted an N" line from a program and after the program has been run type N EXE. 4 Matrices (that's the plural of matrix) are very useful mathematical structures that can be manipulated in many ways by well established rules: by addition and multiplication, for example. In this book we will be working only with single matrices and only to store and change value entries. Those matrix applications appear in Appendix 5-1 and Chapter 9. Page 6 of 8

7 we name this matrix Mat A, we can refer to individual entries. For example Mat A[3,4] is 2, the number in the 3rd row and 4th column. We can also enter or change entries in a matrix. For example, the program line: 5 " Mat A[1,4] would change the 3 in that matrix example to 5. Keying a matrix entry may be confusing at first, because you must use the MAT then the Mat keys. Here are the key strokes that you would use to enter Mat A[1,4] broken down into separate parts: First to get Mat: OPTN F2 (MAT) F1 (Mat) Next to get the A: ALPHA X, ",T (A) And finally to get the [1,4]: SHIFT + ([) 1, 4 SHIFT (]) Preparing a Matrix for Program Use Apparently there is no way to establish a matrix size within a CASIO program. 5 For the few programs involving matrices used in and in these web-based supplements, you can simply set up a matrix large enough to include any calculation you will be doing. The Casio calculators allow very large matrices with up to 255 rows and 255 columns. The program BIGMULT of Appendix 6-1 calls for a matrix, A, with three rows and a number of columns depending on the size of the multiplicands. The program BIGDIV of this website calls for a matrix, A, with five rows and a number of columns depending on the divisor, dividend and quotient. To serve those programs we need only set up a matrix A with plenty of columns. Most will choose to do so with, say, 50 columns (enough to process 200 digit numbers since four digits are entered in each matrix element. It is possible, however, to use all 255 columns in order to process numbers with over 1000 digits, 4 digits at a time, or over digits, 10 at a time. Here is how you can establish a matrix, A, with 6 rows and 50 columns. From the menu, choose MAT. That will take you to the Matrix screen where Mat A will be highlighted. If there is already a listing of rows and columns in the form: Mat A : 6 " 7 you will need to delete this. To do so use: F1 (DEL) or F2 (DEL A) and then F1 (YES). Whether or not you had to do this, you are now ready to indicate the 6 rows and 50 columns. To do so, in the Matrix screen simply key: 6 EXE 50 EXE This is all it takes to set up your 5 by 50 matrix A, which is filled with zeros. 5 If any reader knows how to set up a matrix within a program, please inform the author and this section will immediately reflect that information. Page 7 of 8

8 You are now ready to use matrix A in your program. But you should be careful when you do so to see that when you enter your program data that you fill the rest of the lines you will be using with zeros so that old data does not mess up your calculation. Page 8 of 8

### Activity 6 Graphing Linear Equations

Activity 6 Graphing Linear Equations TEACHER NOTES Topic Area: Algebra NCTM Standard: Represent and analyze mathematical situations and structures using algebraic symbols Objective: The student will be

### SYSTEMS OF EQUATIONS AND MATRICES WITH THE TI-89. by Joseph Collison

SYSTEMS OF EQUATIONS AND MATRICES WITH THE TI-89 by Joseph Collison Copyright 2000 by Joseph Collison All rights reserved Reproduction or translation of any part of this work beyond that permitted by Sections

### Basic Use of the TI-84 Plus

Basic Use of the TI-84 Plus Topics: Key Board Sections Key Functions Screen Contrast Numerical Calculations Order of Operations Built-In Templates MATH menu Scientific Notation The key VS the (-) Key Navigation

### For another way to generate recursive sequences, see Calculator Note 1D.

!"# If you want to do further calculation on a result you ve just found, and that result is the first number in the expression you now want to evaluate, you can simply continue the expression. For example,

### Calculator Notes for the TI-89, TI-92 Plus, and Voyage 200

CHAPTER 1 Note 1A Reentry Calculator Notes for the TI-89, TI-92 Plus, and Voyage 200 If you want to do further calculation on a result you ve just found, and that result is the first number in the expression

Operators Lecture 2 Mathcad Basics + Addition, - Subtraction, * Multiplication, / Division, ^ Power ( ) Specify evaluation order Order of Operations ( ) ^ highest level, first priority * / next priority

### Microsoft Excel 2010 Part 3: Advanced Excel

CALIFORNIA STATE UNIVERSITY, LOS ANGELES INFORMATION TECHNOLOGY SERVICES Microsoft Excel 2010 Part 3: Advanced Excel Winter 2015, Version 1.0 Table of Contents Introduction...2 Sorting Data...2 Sorting

### Chapter Table & Graph

Chapter Table & Graph The Table & Graph menu makes it possible to generate numeric tables from functions stored in memory. You can also use multiple functions to generate tables. Since Table & Graph uses

### Sample Table. Columns. Column 1 Column 2 Column 3 Row 1 Cell 1 Cell 2 Cell 3 Row 2 Cell 4 Cell 5 Cell 6 Row 3 Cell 7 Cell 8 Cell 9.

Working with Tables in Microsoft Word The purpose of this document is to lead you through the steps of creating, editing and deleting tables and parts of tables. This document follows a tutorial format

### Calculator Notes for the CFX-9850GB Plus

CHAPTER 1 Calculator Notes for the Note 1A Entering Lists The calculator contains six folders, each with six preset lists. You can enter 255 elements into a list if enough memory is available. You can

### The Center for Teaching, Learning, & Technology

The Center for Teaching, Learning, & Technology Instructional Technology Workshops Microsoft Excel 2010 Formulas and Charts Albert Robinson / Delwar Sayeed Faculty and Staff Development Programs Colston

### Getting to know your TI-83

Calculator Activity Intro Getting to know your TI-83 Press ON to begin using calculator.to stop, press 2 nd ON. To darken the screen, press 2 nd alternately. To lighten the screen, press nd 2 alternately.

### FX 115 MS Training guide. FX 115 MS Calculator. Applicable activities. Quick Reference Guide (inside the calculator cover)

Tools FX 115 MS Calculator Handouts Other materials Applicable activities Quick Reference Guide (inside the calculator cover) Key Points/ Overview Advanced scientific calculator Two line display VPAM to

### Introductory Handbook for the TI-89 Titanium

Introductory Handbook for the TI-89 Titanium Note: This handbook will, for the most part, work for the standard TI-89 as well. The color-coding used on the TI-89 differs from the color-coding used on the

### MICROSOFT EXCEL FORMULAS

MICROSOFT EXCEL FORMULAS Building Formulas... 1 Writing a Formula... 1 Parentheses in Formulas... 2 Operator Precedence... 2 Changing the Operator Precedence... 2 Functions... 3 The Insert Function Button...

Intro to Excel spreadsheets What are the objectives of this document? The objectives of document are: 1. Familiarize you with what a spreadsheet is, how it works, and what its capabilities are; 2. Using

### Linear Algebra and TI 89

Linear Algebra and TI 89 Abdul Hassen and Jay Schiffman This short manual is a quick guide to the use of TI89 for Linear Algebra. We do this in two sections. In the first section, we will go over the editing

### This activity will show you how to draw graphs of algebraic functions in Excel.

This activity will show you how to draw graphs of algebraic functions in Excel. Open a new Excel workbook. This is Excel in Office 2007. You may not have used this version before but it is very much the

### Introduction to the TI-Nspire CX

Introduction to the TI-Nspire CX Activity Overview: In this activity, you will become familiar with the layout of the TI-Nspire CX. Step 1: Locate the Touchpad. The Touchpad is used to navigate the cursor

### A.2. Exponents and Radicals. Integer Exponents. What you should learn. Exponential Notation. Why you should learn it. Properties of Exponents

Appendix A. Exponents and Radicals A11 A. Exponents and Radicals What you should learn Use properties of exponents. Use scientific notation to represent real numbers. Use properties of radicals. Simplify

### Getting started Texas Instruments TI-85 and TI-86 calculators

Getting started Texas Instruments TI-85 and TI-86 calculators Overview: Your graphing calculator or computer is a powerful and flexible tool, which you would probably be able to use fairly well without

### 2 SYSTEM DESCRIPTION TECHNIQUES

2 SYSTEM DESCRIPTION TECHNIQUES 2.1 INTRODUCTION Graphical representation of any process is always better and more meaningful than its representation in words. Moreover, it is very difficult to arrange

### Graphing Calculator Workshops

Graphing Calculator Workshops For the TI-83/84 Classic Operating System & For the TI-84 New Operating System (MathPrint) LEARNING CENTER Overview Workshop I Learn the general layout of the calculator Graphing

### Using Parametric Equations in SolidWorks, Example 1

Using Parametric Equations in SolidWorks, Example 1 (Draft 4, 10/25/2006, SW 2006) Introduction In this example the goal is to place a solid roller on a solid wedge. Their relationship will be governed

### xn. x must be written as x^(2n) and NOT as x^2n. Writing x^2n means 4x y would be written as 4 x^2 y^3 or with the multiplication mark as 4*x^2*y^3.

Writing Mathematical Epressions in Plain Tet Eamples and Cautions Copyright 009 Sally J. Keely. Mathematical epressions can be typed online in a number of ways including plain tet, ASCII codes, HTML tags,

### Formulas, Functions and Charts

Formulas, Functions and Charts :: 167 8 Formulas, Functions and Charts 8.1 INTRODUCTION In this leson you can enter formula and functions and perform mathematical calcualtions. You will also be able to

### How to test and debug an ASP.NET application

Chapter 4 How to test and debug an ASP.NET application 113 4 How to test and debug an ASP.NET application If you ve done much programming, you know that testing and debugging are often the most difficult

### EL-9650/9600c/9450/9400 Handbook Vol. 1

Graphing Calculator EL-9650/9600c/9450/9400 Handbook Vol. Algebra EL-9650 EL-9450 Contents. Linear Equations - Slope and Intercept of Linear Equations -2 Parallel and Perpendicular Lines 2. Quadratic Equations

### TI-83/84 Plus Graphing Calculator Worksheet #2

TI-83/8 Plus Graphing Calculator Worksheet #2 The graphing calculator is set in the following, MODE, and Y, settings. Resetting your calculator brings it back to these original settings. MODE Y Note that

### FREE FALL. Introduction. Reference Young and Freedman, University Physics, 12 th Edition: Chapter 2, section 2.5

Physics 161 FREE FALL Introduction This experiment is designed to study the motion of an object that is accelerated by the force of gravity. It also serves as an introduction to the data analysis capabilities

### Quick Reference ebook

This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

### Binomial Probability Distribution

Binomial Probability Distribution In a binomial setting, we can compute probabilities of certain outcomes. This used to be done with tables, but with graphing calculator technology, these problems are

### Review of Fundamental Mathematics

Review of Fundamental Mathematics As explained in the Preface and in Chapter 1 of your textbook, managerial economics applies microeconomic theory to business decision making. The decision-making tools

### Application. Outline. 3-1 Polynomial Functions 3-2 Finding Rational Zeros of. Polynomial. 3-3 Approximating Real Zeros of.

Polynomial and Rational Functions Outline 3-1 Polynomial Functions 3-2 Finding Rational Zeros of Polynomials 3-3 Approximating Real Zeros of Polynomials 3-4 Rational Functions Chapter 3 Group Activity:

### Visual Logic Instructions and Assignments

Visual Logic Instructions and Assignments Visual Logic can be installed from the CD that accompanies our textbook. It is a nifty tool for creating program flowcharts, but that is only half of the story.

### VB.NET Programming Fundamentals

Chapter 3 Objectives Programming Fundamentals In this chapter, you will: Learn about the programming language Write a module definition Use variables and data types Compute with Write decision-making statements

### 5: Magnitude 6: Convert to Polar 7: Convert to Rectangular

TI-NSPIRE CALCULATOR MENUS 1: Tools > 1: Define 2: Recall Definition --------------- 3: Delete Variable 4: Clear a-z 5: Clear History --------------- 6: Insert Comment 2: Number > 1: Convert to Decimal

### Basic Formulas in Excel. Why use cell names in formulas instead of actual numbers?

Understanding formulas Basic Formulas in Excel Formulas are placed into cells whenever you want Excel to add, subtract, multiply, divide or do other mathematical calculations. The formula should be placed

### PTC Mathcad Prime 3.0 Keyboard Shortcuts

PTC Mathcad Prime 3.0 Shortcuts Swedish s Regions Inserting Regions Operator/Command Description Shortcut Swedish Area Inserts a collapsible area you can collapse or expand to toggle the display of your

### Computational Mathematics with Python

Boolean Arrays Classes Computational Mathematics with Python Basics Olivier Verdier and Claus Führer 2009-03-24 Olivier Verdier and Claus Führer Computational Mathematics with Python 2009-03-24 1 / 40

### 3 Some Integer Functions

3 Some Integer Functions A Pair of Fundamental Integer Functions The integer function that is the heart of this section is the modulo function. However, before getting to it, let us look at some very simple

### Accentuate the Negative: Homework Examples from ACE

Accentuate the Negative: Homework Examples from ACE Investigation 1: Extending the Number System, ACE #6, 7, 12-15, 47, 49-52 Investigation 2: Adding and Subtracting Rational Numbers, ACE 18-22, 38(a),

### How to make a line graph using Excel 2007

How to make a line graph using Excel 2007 Format your data sheet Make sure you have a title and each column of data has a title. If you are entering data by hand, use time or the independent variable in

### ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers Basic Math 1.2 - The Number Line Basic Math 1.3 - Addition of Whole Numbers, Part I

ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers 1) Read whole numbers. 2) Write whole numbers in words. 3) Change whole numbers stated in words into decimal numeral form. 4) Write numerals in

### Excel 2007 Basic knowledge

Ribbon menu The Ribbon menu system with tabs for various Excel commands. This Ribbon system replaces the traditional menus used with Excel 2003. Above the Ribbon in the upper-left corner is the Microsoft

### MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS

MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS Systems of Equations and Matrices Representation of a linear system The general system of m equations in n unknowns can be written a x + a 2 x 2 + + a n x n b a

### Excel 2003 A Beginners Guide

Excel 2003 A Beginners Guide Beginner Introduction The aim of this document is to introduce some basic techniques for using Excel to enter data, perform calculations and produce simple charts based on

### Multiplying and Dividing Signed Numbers. Finding the Product of Two Signed Numbers. (a) (3)( 4) ( 4) ( 4) ( 4) 12 (b) (4)( 5) ( 5) ( 5) ( 5) ( 5) 20

SECTION.4 Multiplying and Dividing Signed Numbers.4 OBJECTIVES 1. Multiply signed numbers 2. Use the commutative property of multiplication 3. Use the associative property of multiplication 4. Divide signed

### Excel Level Two. Introduction. Contents. Exploring Formulas. Entering Formulas

Introduction Excel Level Two This workshop introduces you to formulas, functions, moving and copying data, using autofill, relative and absolute references, and formatting cells. Contents Introduction

### ECDL. European Computer Driving Licence. Spreadsheet Software BCS ITQ Level 2. Syllabus Version 5.0

European Computer Driving Licence Spreadsheet Software BCS ITQ Level 2 Using Microsoft Excel 2010 Syllabus Version 5.0 This training, which has been approved by BCS, The Chartered Institute for IT, includes

### 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

### Q&As: Microsoft Excel 2013: Chapter 2

Q&As: Microsoft Excel 2013: Chapter 2 In Step 5, why did the date that was entered change from 4/5/10 to 4/5/2010? When Excel recognizes that you entered a date in mm/dd/yy format, it automatically formats

### Display Format To change the exponential display format, press the [MODE] key 3 times.

Tools FX 300 MS Calculator Overhead OH 300 MS Handouts Other materials Applicable activities Activities for the Classroom FX-300 Scientific Calculator Quick Reference Guide (inside the calculator cover)

### Introduction to Microsoft Excel 2010

Introduction to Microsoft Excel 2010 Screen Elements Quick Access Toolbar The Ribbon Formula Bar Expand Formula Bar Button File Menu Vertical Scroll Worksheet Navigation Tabs Horizontal Scroll Bar Zoom

### Training Manual. Pre-Employment Math. Version 1.1

Training Manual Pre-Employment Math Version 1.1 Created April 2012 1 Table of Contents Item # Training Topic Page # 1. Operations with Whole Numbers... 3 2. Operations with Decimal Numbers... 4 3. Operations

### EET 310 Programming Tools

Introduction EET 310 Programming Tools LabVIEW Part 1 (LabVIEW Environment) LabVIEW (short for Laboratory Virtual Instrumentation Engineering Workbench) is a graphical programming environment from National

### . 0 1 10 2 100 11 1000 3 20 1 2 3 4 5 6 7 8 9

Introduction The purpose of this note is to find and study a method for determining and counting all the positive integer divisors of a positive integer Let N be a given positive integer We say d is a

### SAMPLE. Computer Algebra System (Classpad 330 using OS 3 or above) Application selector. Icolns that access working zones. Icon panel (Master toolbar)

A P P E N D I X B Computer Algebra System (Classpad 330 using OS 3 or above) B.1 Introduction For reference material on basic operations of the calculator, refer to the free downloadable documentation

### Indicator 2: Use a variety of algebraic concepts and methods to solve equations and inequalities.

3 rd Grade Math Learning Targets Algebra: Indicator 1: Use procedures to transform algebraic expressions. 3.A.1.1. Students are able to explain the relationship between repeated addition and multiplication.

### Linear Algebra: Vectors

A Linear Algebra: Vectors A Appendix A: LINEAR ALGEBRA: VECTORS TABLE OF CONTENTS Page A Motivation A 3 A2 Vectors A 3 A2 Notational Conventions A 4 A22 Visualization A 5 A23 Special Vectors A 5 A3 Vector

### SPSS INSTRUCTION CHAPTER 1

SPSS INSTRUCTION CHAPTER 1 Performing the data manipulations described in Section 1.4 of the chapter require minimal computations, easily handled with a pencil, sheet of paper, and a calculator. However,

### 3.2. Solving quadratic equations. Introduction. Prerequisites. Learning Outcomes. Learning Style

Solving quadratic equations 3.2 Introduction A quadratic equation is one which can be written in the form ax 2 + bx + c = 0 where a, b and c are numbers and x is the unknown whose value(s) we wish to find.

### 6.4 Normal Distribution

Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under

### Excel 2007 A Beginners Guide

Excel 2007 A Beginners Guide Beginner Introduction The aim of this document is to introduce some basic techniques for using Excel to enter data, perform calculations and produce simple charts based on

### VISUAL GUIDE to. RX Scripting. for Roulette Xtreme - System Designer 2.0

VISUAL GUIDE to RX Scripting for Roulette Xtreme - System Designer 2.0 UX Software - 2009 TABLE OF CONTENTS INTRODUCTION... ii What is this book about?... iii How to use this book... iii Time to start...

### PROG0101 Fundamentals of Programming PROG0101 FUNDAMENTALS OF PROGRAMMING. Chapter 3 Algorithms

PROG0101 FUNDAMENTALS OF PROGRAMMING Chapter 3 1 Introduction to A sequence of instructions. A procedure or formula for solving a problem. It was created mathematician, Mohammed ibn-musa al-khwarizmi.

### Statgraphics Getting started

Statgraphics Getting started The aim of this exercise is to introduce you to some of the basic features of the Statgraphics software. Starting Statgraphics 1. Log in to your PC, using the usual procedure

### Calculator Notes for the TI-82

CHAPTER 0 Calculator Notes for the Note 0A Fractions This calculator will convert a decimal number to a fraction. Enter the decimal number and press MATH 1 ( Frac) ENTER. This is the convert to fraction

### Computational Mathematics with Python

Computational Mathematics with Python Basics Claus Führer, Jan Erik Solem, Olivier Verdier Spring 2010 Claus Führer, Jan Erik Solem, Olivier Verdier Computational Mathematics with Python Spring 2010 1

### VISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University

VISUAL ALGEBRA FOR COLLEGE STUDENTS Laurie J. Burton Western Oregon University VISUAL ALGEBRA FOR COLLEGE STUDENTS TABLE OF CONTENTS Welcome and Introduction 1 Chapter 1: INTEGERS AND INTEGER OPERATIONS

### CBA Fractions Student Sheet 1

Student Sheet 1 1. If 3 people share 12 cookies equally, how many cookies does each person get? 2. Four people want to share 5 cakes equally. Show how much each person gets. Student Sheet 2 1. The candy

### Intermediate PowerPoint

Intermediate PowerPoint Charts and Templates By: Jim Waddell Last modified: January 2002 Topics to be covered: Creating Charts 2 Creating the chart. 2 Line Charts and Scatter Plots 4 Making a Line Chart.

### Continued Fractions and the Euclidean Algorithm

Continued Fractions and the Euclidean Algorithm Lecture notes prepared for MATH 326, Spring 997 Department of Mathematics and Statistics University at Albany William F Hammond Table of Contents Introduction

### Academic Support Center. Using the TI-83/84+ Graphing Calculator PART II

Academic Support Center Using the TI-83/84+ Graphing Calculator PART II Designed and Prepared by The Academic Support Center Revised June 2012 1 Using the Graphing Calculator (TI-83+ or TI-84+) Table of

### Excel. Microsoft Office s spreadsheet application can be used to track. and analyze numerical data for display on screen or in printed

Excel Microsoft Office s spreadsheet application can be used to track and analyze numerical data for display on screen or in printed format. Excel is designed to help you record and calculate data, and

### Excel Tutorial. Bio 150B Excel Tutorial 1

Bio 15B Excel Tutorial 1 Excel Tutorial As part of your laboratory write-ups and reports during this semester you will be required to collect and present data in an appropriate format. To organize and

### Microsoft Excel Basics

COMMUNITY TECHNICAL SUPPORT Microsoft Excel Basics Introduction to Excel Click on the program icon in Launcher or the Microsoft Office Shortcut Bar. A worksheet is a grid, made up of columns, which are

### Polynomial and Rational Functions

Polynomial and Rational Functions Quadratic Functions Overview of Objectives, students should be able to: 1. Recognize the characteristics of parabolas. 2. Find the intercepts a. x intercepts by solving

### MATLAB Workshop 3 - Vectors in MATLAB

MATLAB: Workshop - Vectors in MATLAB page 1 MATLAB Workshop - Vectors in MATLAB Objectives: Learn about vector properties in MATLAB, methods to create row and column vectors, mathematical functions with

### Chapter 9 Creating Reports in Excel

Chapter 9 Creating Reports in Excel One of the most powerful features of Standard & Poor s Research Insight is its ability to communicate with Microsoft Excel through Active-X Technology. Excel requests

### Paramedic Program Pre-Admission Mathematics Test Study Guide

Paramedic Program Pre-Admission Mathematics Test Study Guide 05/13 1 Table of Contents Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page

### 26 Integers: Multiplication, Division, and Order

26 Integers: Multiplication, Division, and Order Integer multiplication and division are extensions of whole number multiplication and division. In multiplying and dividing integers, the one new issue

### Creating Advanced Reports with the SAP Query Tool

CHAPTER Creating Advanced Reports with the SAP Query Tool In this chapter An Overview of the SAP Query Tool s Advanced Screens 86 Using the Advanced Screens of the SAP Query Tool 86 86 Chapter Creating

### Excel Basics By Tom Peters & Laura Spielman

Excel Basics By Tom Peters & Laura Spielman What is Excel? Microsoft Excel is a software program with spreadsheet format enabling the user to organize raw data, make tables and charts, graph and model

### TabletWorks Help Index 1

TabletWorks Help Index 1 When the driver for your tablet type has been installed, the TabletWorks Control Panel is set up on the Windows Control Panel. The TabletWorks Control Panel is divided into several

### fx-92b Collège 2D+ User s Guide http://edu.casio.com http://edu.casio.com/forum/ CASIO Worldwide Education Website CASIO EDUCATIONAL FORUM

E fx-92b Collège 2D+ User s Guide CASIO Worldwide Education Website http://edu.casio.com CASIO EDUCATIONAL FORUM http://edu.casio.com/forum/ Contents Important Information... 2 Sample Operations... 2 Initializing

### Microsoft Excel 2013 Tutorial

Microsoft Excel 2013 Tutorial TABLE OF CONTENTS 1. Getting Started Pg. 3 2. Creating A New Document Pg. 3 3. Saving Your Document Pg. 4 4. Toolbars Pg. 4 5. Formatting Pg. 6 Working With Cells Pg. 6 Changing

### How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

### Part V: Texas Instruments TI-92, TI-92 Plus, Voyage 200

Part V: Texas Instruments TI-92, TI-92 Plus, Voyage 200 V.1 Getting started with the TI-92, TI-92 Plus, Voyage 200 Note: All keystroke sequences given for the Voyage 200 are applicable to the TI-92 and

### What Is Singapore Math?

What Is Singapore Math? You may be wondering what Singapore Math is all about, and with good reason. This is a totally new kind of math for you and your child. What you may not know is that Singapore has

### AFN-FixedAssets-062502

062502 2002 Blackbaud, Inc. This publication, or any part thereof, may not be reproduced or transmitted in any form or by any means, electronic, or mechanical, including photocopying, recording, storage

### SAP Business Intelligence ( BI ) Financial and Budget Reporting. 7.0 Edition. (Best Seller At Least 43 copies Sold)

SAP Business Intelligence ( BI ) Financial and Budget Reporting 7.0 Edition (Best Seller At Least 43 copies Sold) November 2011 Table of Contents Log In... 3 Initial Variable Screen... 5 Multiple / Single

### This web-based report provides information for single funds centers. The report can be run for one funds center or multiple single funds centers.

Budget Status Report This web-based report provides information for single funds centers. The report can be run for one funds center or multiple single funds centers. The report includes the following

### Adding and Subtracting Positive and Negative Numbers

Adding and Subtracting Positive and Negative Numbers Absolute Value For any real number, the distance from zero on the number line is the absolute value of the number. The absolute value of any real number

### Windows XP Pro: Basics 1

NORTHWEST MISSOURI STATE UNIVERSITY ONLINE USER S GUIDE 2004 Windows XP Pro: Basics 1 Getting on the Northwest Network Getting on the Northwest network is easy with a university-provided PC, which has

### 1.6 The Order of Operations

1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative

### 9 Control Statements. 9.1 Introduction. 9.2 Objectives. 9.3 Statements

9 Control Statements 9.1 Introduction The normal flow of execution in a high level language is sequential, i.e., each statement is executed in the order of its appearance in the program. However, depending

### POLYNOMIAL FUNCTIONS

POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a