Mentor Products, Inc.

TABLE OF CONTENTS

 1   WHAT IS THE MENTOR MATHEMATICS ADVISOR?
 2   HOW DO I USE THE MENTOR MATHEMATICS ADVISOR?
 3   START THE MENTOR MATHEMATICS ADVISOR
 4   ENTERING SYMBOLS, EXPRESSIONS, AND EQUATIONS
 5   STARTING A SESSION
 6   START A PROBLEM
    6.1   Start a Problem Dialog
    6.2   The Variables Dialog
    6.3   The Find Equations Dialog
    6.4   The Enter Two Points Dialog
    6.5   The Enter Two Intercepts Dialog
    6.6   The Enter a Point and a Slope Dialog
 7   MENTOR MESSAGE WINDOWS
    7.1   Mentor Reminds
    7.2   Mentor Says
    7.3   Mentor Warns
8    SYSTEMS OF EQUATIONS
9    USING THE MOUSE
10   THE MENTOR GRAPHING TOOL
    10.1    The Mentor Graph Display File Menu
    10.2    The Mentor Graph Display Graph Menu
    10.3    The Mentor Graph Display View Menu
    10.4    Transfer to the Mentor Graphing Tool 
11   WHAT NOT TO EXPECT
Appendix A The Greek Alphabet
Appendix B Installation

The Mentor Mathematics Advisor is a program carefully designed to help users learn to work algebraic problems. As you work your algebra problem using the Mentor Mathematics Advisor, you will be advised step by step as to the correctness of your work and, if a step is incorrect, you will often be advised about what you did wrong.

By constantly reinforcing your correct steps and stopping you immediately if you make a mistake, the Mentor Mathematics Advisor will help you develop sure and efficient procedures for working algebra problems.

If a step is incorrect, it will tell you. In many situations, it can tell you what mistake you have made. After advising you that a mistake has been made, it will paint the incorrect step red and let you edit the step.

A Mentor Mathematics Advisor work session consists of entering one or more problems. You can give each problem a label or you can accept the Mentor Mathematics Advisor's default problem numbering. Solving a problem consists of entering steps leading to the solution. Generally, a step is one line. An exception is simultaneous equation problems where a step will generally have two or more lines. The Mentor Mathematics Advisor will open a window after you have entered each step and comment on your work. If the step in not correct, the Mentor Mathematics Advisor will not let you continue with the problem until you have corrected your mistake. You may hide a problem, a step, or a line.

If a problem, a step, or a line is marked hidden, it will not be displayed unless you turn on the Toggle Hidden switch under the View menu item.

The Advisor icon should be on your desktop. If not, check the installation steps once again. The icon shows a candle. Our purpose is to shed light on the solution of algebraic problems. Double click on the Advisor icon to start your session.

You should now see an empty white screen below the three top lines of the program. If you look at the screen, you can see the top line shows the candle icon to the left of "Untitled - Mentor Mathematics Advisor". This is called the title bar.

If you move your cursor to this bar and press the left mouse button you can move the Mentor window around on the desktop. Release the mouse button when the Advisor's display is positioned where you want it. There are three buttons on the right side of the title bar. These buttons are the same as in other windows programs.

The left of the three buttons lets you minimize the program. This means make it leave the desktop. You can see that the program is still active by looking at the bar at the bottom of your Windows screen that shows all active programs that are currently running. Clicking on the Mentor Mathematics Advisor button in this bar and the normal display returns to the desktop.

The middle button maximizes the Advisor window or returns the Advisor window to normal size if it is already maximized.

The third button can be used to terminate the Advisor session.

The second line of the Advisor window is called the menu bar. It contains five drop-down menus: File, Edit, View, Problem, and Help. Some of the menu items that will drop down are not in use at this time. These inactive menu items appear faded and clicking on them produces no actions.

File has eight menu items: New, Open, Save, Save As, Print, Print Preview, Print Setup and Exit. These menu items work similar to other programs written for Windows. New clears any work in the current session leaving you ready to start a new session. Open allows you to return to previous sessions that you have saved. Save saves the current session for future use. Save As lets you specify a name for the current session and then saves the current session under that name. You should use Save AS to save and name a new session the first time it is saved and use Save thereafter. The names of the most recent sessions that have been saved will appear between the Print Setup and the Exit menu item. These sessions can be loaded by clicking on a name or through the Open menu item. Clicking on Print will print your session if your computer is connected to a printer. Print Preview shows you the format of the printed page. This may be formatted differently from the view on your screen. Print Setup accesses the profile dialog for your printer and lets you modify print options in the same manner as many other programs.. Clicking on Exit terminates the program. Under Edit, there are no active menu items.

View has four active items, Status Bar, Reminder, Toggle Step Numbers, and Toggle Hidden Lines. The status bar is the last line at the bottom of the Advisor Window. Status messages and other information may be shown here. You have the option of not showing the status bar. Clicking on the Status Bar menu item turns the status bar off and on. The Reminder Window will be discussed later. If a Reminder Window is hidden, clicking on the Reminder menu item will make the Reminder Window visible. If the reminder Window is visible, clicking on the Reminder menu item will hide it. You have the option of displaying step numbers and can turn this facility on and off by clicking on Toggle Step Numbers. If you make a mistake working a problem, the Mentor Mathematics Advisor will tell you and require a correction before allowing you to continue. Once you correct the mistake, the step in error is removed from the display. You may also elect to remove a step if you think that it is unnecessary. With Toggle Hidden Lines you can display all of your work. This can be useful in reviewing your work to avoid making the same mistake again.

Problem has one menu item, Start Problem. Clicking on this menu item has the same effect as clicking on the box with the green M in the bar below the menu bar. Ctrl-M, holding the Control Key down while pressing the M key, also has the same effect. Starting a Session and starting a problem will be discussed in detail shortly.

Help has two menu items, About Mentor and Banner. The Banner menu item displays a welcome banner from the developer. This banner will be visible for about 30 seconds and then disappear. While the banner is visible, clicking on the Banner menu item will send it away.

The third bar on the Advisor window is called the toolbar. The first item on the toolbar is a button with a green S. Then there is a white input box. You will learn how to use these tools shortly.

The Mentor Mathematics Advisor understands the letters of the alphabet as variables or symbolic constants. An upper case letter and a lower case letter are two distinct symbols. It also understands the Greek alphabet. Greek letters are entered with two keystrokes. The first keystroke is a backslash, . The second keystroke must be a letter of the alphabet except for the letters j, J, v, or V. Appendix A defines the Greek alphabet and the keystrokes to display it.

After leaving the Problem dialog box the focus will be in the Math Input box in the toolbar. In Windows, the focus means the location in a window where action is expected. By moving the mouse and clicking elsewhere, the focus can often be changed. If you do this and wish to return the focus to the Math Input box use the mouse to move the cursor back to the Math Input box and click.

While an expression or an equation must be entered as a string of characters, the Mentor Mathematics Advisor will display your mathematics in the main window looking as mathematics should look. The rules are very simple and soon you will not have to think about how to enter your mathematics. The elements that you can enter:

• Integers: Enter the digits of the integer with an optional minus sign, -, in front. The Mentor Mathematics Advisor limits you to no more than 28 digits an a given number.
• Decimal: Decimal numbers such as 3.14159 can be entered starting with a sign or a digit. If the first character is a sign, it must be followed by a digit. Thus .5 should be entered as 0.5 with a leading zero. The Mentor Mathematics Advisor will insert a zero digit for you if necessary.
• Scientific Notation: This allows you to express very large or very small numbers. You may enter a number in scientific notation by entering an decimal number followed by the letter e (upper or lower case) followed by an integer. This signifies that the decimal number is multiplied by 10 raised to the power of the integer. For example, -12.3e4 means -12.3 times 10 to the 4^th power.
• Mixed Numbers: Although mixed numbers do not have a proper place in algebra, they are used extensively in grade school and middle school. You may enter a mixed number by typing an integer followed by a space then an unsigned integer followed by the divide symbol, "/" and then another unsigned integer.
• Symbols: Any single letter of the alphabet, lower case or upper case, can be used as a symbol. In some situations, the symbol I, upper or lower case, may be reserved to mean the square root of -1. Also, e may be reserved to mean the base of the natural logarithms. Greek letters are entered with two characters. For example an alpha, a, is entered by typing a. i and v are not permitted. Symbols are used to denote variables. Sometimes symbols are used to denote constants. For example, the Greek letter, p, is used to represent the ratio of the circumference of a circle to its diameter.
• Addition/Subtraction: This is entered just as you would write addition in a mathematical expression. For example, or . These examples are shown with space between the symbols and the plus and the minus. It is not necessary to enter space in the Math Input box.
• Parentheses: Parentheses are used just as they are in algebra, to cause the expression within the parentheses to be treated as a single mathematical object, i.e. a number.
• Multiplication: If you enter the Mentor Mathematics Advisor will understand that x is multiplied by y. Likewise means times . The expression, does not mean The symbols, , are understood to mean the number, thirty-two. You may enter to force the multiplication of the and the . You may, however, enter or in these two examples without changing their meaning. Parentheses are used with multiplication just as you do in algebra. For example, means times x times the sum of x and y.
• Division: The / is used for division. To divide enter a mathematical expression followed by / followed by another mathematical expression. As with multiplication, parentheses can be used to denote a complicated expression.
• Exponentiation: The ^ is used for exponents. The term, , would be entered, x^2. A more complicated exponent can be entered using parentheses. For example, entering x^(u + v) causes the sum, u+v, to be the exponent of x or
  

• Functions:
• To enter square root, , type sqrt(x).
• To enter the natural logarithm of x, type ln(x).
• To enter the logarithm of x base 10, type log(x).
• To enter the absolute value of x, , type abs(x).

If you are working with expressions or single equations, each step consists of a single line. After you have entered the line and pressed the Enter key, the Mentor Mathematics Advisor will know that you have finished the current step. If you are solving simultaneous equation, a step may contain from one to and many lines as there are variables in the problem. If the step contains less lines than the number of variables, you must tell the Mentor Mathematics Advisor that you have completed the current step by entering the symbol, ;.

If you enter something that the Mentor Advisor cannot interpret, you will be informed and permitted to edit your entry in the Math Input box. You can edit your expression or equation by using the left and right arrow keys, the delete key, and the backspace key. When you have finished typing your expression or equation press the Enter key. If you are solving an equation, see the section, The Variables Dialog, to understand what happens next.

Otherwise, if this is the first step in your problem, your entry will be evaluated to insure that it is a valid entry for the objective that you have chosen. You can continue by entering the next step.

After the second step, or a subsequent step, is entered a window called Mentor Says will open with comments on your entry for the step.

After starting the Mentor Mathematics Advisor, you will have a blank work space below the toolbar. The next step would be to begin working on a problem set. To do this, first click on the "M" in the toolbar or click on Start Problem under the Problem menu or press Ctrl_M. Any of these actions will show you a dialog with the title "Start Mentor Math Advisor Session". Here you have an opportunity to name your work session to identify the assignment or problem set that you are going to work. For example, you could enter

        Practice on Oct. 5, 2001

or

        Homework due February 20, 2001

If you do not need to have a particular identifier such as this, you can accept the default name that consists of the time and date that you start your session by pressing the Enter key or by clicking on OK in the Session dialog box without entering a session name.

Once you are finished with the Session dialog, you are ready to start a problem. To do this, again either click on the "M" button on the toolbar or click on the Problem menu item followed by the Start Problem menu item or press Ctrl-M. This will open a dialog box titled "Start a Problem".

Upon entering this dialog, control is given to the Enter Problem Label window. For example, if you are working problem 12 in section 3 of chapter 5 in your algebra book, you might wish to label the problem with something like

5.3.12

Or, if simply numbering the problems is satisfactory, leave the label field blank and the Mentor Mathematics Advisor will label problems for you. After you click on a problem objective you may press Enter or click on OK to begin working the problem. You may change the problem objective if you wish.

Six types of problem are shown with this version:

• Solve equation. This tells the Mentor Mathematics Advisor that you will enter a problem with variables for which you wish to solve. You can use symbols for constants in your equations. You will see how to do this when the Variable dialog box is discussed in 6.2. Systems of equations have some special considerations that will be explained in a separate section.
• Find equation meeting conditions. This is used to advise you as you find an equation that has characteristics that you specify. Clicking on these options opens the Find Equation dialog that lets you specify characteristics. See the section, Finding Equations, for a discussion of the options available for this type of problem.
• Expand/Simplify algebraic expression. As you enter successive steps, the Mentor Mathematics Advisor can determine if each step is correct or incorrect. Best form is in the eye of the beholder, however. You must understand the form that your teacher desires and that it may be different from Mentor's notion.
• Factor algebraic expression. Many modern algebra classes do not emphasis the factoring of algebraic expressions. However, your algebra education is not complete until you are skilled at factoring. The MMA will let you know when you are correct and will even tell you if you are partially correct.
• Evaluate numeric expression. Use this objective to simplify a numeric expression, no character symbols, to an integer or fraction.
• Evaluate numeric equation. Use this objective to simplify a numeric equation to the simplest integer or fractional equation. The equation may or may not be true.

For most algebra the answer is expected to be "exact", i.e. integers and integer fractions are used to represent numbers. It is necessary in some cases, however, to represent numbers with decimal representation or scientific notation. By clicking on the Precision button, the Precision dialog will open so that you can specify precision required for your answer.

Upon choosing the objective, press Enter or click on OK to complete problem setup. Or, should you wish a different size font, click on Set Font Size. If you enter the Font Size dialog, you can select from a choice of sizes and click on OK to return to the Problem dialog. Then click on OK to exit the Problem dialog.

If your objective is to solve an equation, the Mentor Mathematics Advisor will open the Variable dialog box after you enter the problem. This box will show the symbols that you have used in your equation. These symbols will be shown in an input box that you can edit. Suppose that you have entered the equation

and you wish to solve for x. The Variable Dialog box contains x, which is the variable you want. Press Enter to accept this.

Now suppose that you want to solve

and you wish to solve for y. The Variable Dialog box will contain both x and y. Edit the input box so that only y is shown and then press Enter or click on FINISHED. The x will now be treated as a constant symbol and not a variable.

The variables of a problem are specified. Any other variable symbols introduced during the solution steps will be treated as constant symbols.

This dialog allows you to specify the horizontal and the vertical variables and two points that define your line. The default variables are x and y. Points are entered in the form, (x,y). The coordinates of the points can be any expression that the Mentor Mathematics Advisor can understand except expressions containing either the horizontal or the vertical variables. Clicking on Cancel allows you to leave the dialog without entering the required information. Clicking on OK before the required information is entered has no effect.

This dialog allows you to specify the horizontal and the vertical variables and the two intercepts that define your line. The intercepts can be any expression that the Mentor Mathematics Advisor can understand except expressions containing either the horizontal or the vertical variables. Clicking on Cancel allows you to leave the dialog without entering the required information. Clicking on OK before the required information is entered has no effect.

This dialog allows you to specify the horizontal and the vertical variables and two points that define your line. The default variables are x and y. A point is entered in the form, (x,y). The slope can be any expression. The coordinates of the point and the slope can each be any expression that the Mentor Mathematics Advisor can understand except expressions containing either the horizontal or the vertical variables. Clicking on Cancel allows you to leave the dialog without entering the required information. Clicking on OK before the required information is entered has no effect.>

Three special information windows are provided by the Mentor Mathematics Advisor has three special information windows.

The Mentor Mathematics Advisor will show you the specifications that you provide for an equation that you are to find in this window. If you wish to move this window, click anywhere in the window and, while holding the mouse key down, use the mouse to move the window to the place that you want it. Then release the mouse key. Clicking on Hide sends Mentor Reminds away. You can bring it back by clicking on View on the Menu Bar and then clicking on Reminder. Clicking on Reminder in the View menu would also hide Mentor Reminds, if it is visible, just as does clicking on the Hide button.

After each step of a problem, the Mentor Says window will open with comments about your progress. It may be as simple as saying that you are right or wrong or may provide more complex information.

If Mentor Says is in the way of what you want to see in the main window, Mentor Says can be moved by left clicking anywhere in Mentor Says, holding the left mouse key down, and moving Mentor Says to the position you would like it to be. Releasing the left mouse key stops the movement of Mentor Says.

If you do not move Mentor Says, pressing Enter sends Mentor Says away and returns the focus to the Math Input box for the next step. Unless, of course, you have finished the problem correctly. Then the last step will be highlighted and when you terminate Mentor Says, you will be ready to start the next problem.

If the Continue button in Mentor Says has lost the focus (you moved the window or happened to click somewhere outside of Mentor Says) just click on the Continue button. The Continue button follows Mentor's comments and may be below the bottom of the Mentor Says window. If this happens, you can scroll down to the button. You would want to do this anyway to see all of Mentor's comments.

If you are entering mathematical expressions or relations and enter something that the Mentor Mathematics Advisor cannot interpret as valid input, Mentor Warns tells you. When this happens, press Enter and control is returned to the input dialog that has the error. You can use the arrow and backspace keys to correct the error.

If you continue entering new information without correcting the error, Mentor Warns will return with every character that you enter. This may irritate you as well as Mentor so correct input errors when they occur.

To solve a system of equations click the Solve option in the Problem Dialog. After you enter the first equation, the Variables dialog will ask you to specify the problem variables. Here, you must show all of the problem's variables even if they do not appear in the first equation. The Mentor Mathematics Advisor will now expect as many equations as the problem has variables. As you type in the equations of a step, the equations appear in the work space. When the last equation is entered, the equations of the step will be moved into their position in the problem. Depending on your method for solving the equations, a step may have fewer equations that the number of variable. For example, if you are solving three equations in x, y, and z, you might first eliminate z giving you two equations in x and y. To tell the Mentor Mathematics Advisor that the two equations complete a step, enter a semicolon after the last equation before pressing Enter.

As you find the answer to each variable, Mentor Says will tell you that you have found a solution but that there are more to find. When all have been found, Mentor Says will tell you that the problem is finished.

Nonlinear systems of equations have an added complexity. They may have multiple answers. For example, one solution to the system of equations

is and . The other solution is and . In order for the Mentor Mathematics Advisor to understand your answers, the answer for all variables must be entered in one step.

You can use your mouse to click on any problem, step, or line that you have entered. If you left click, the problem, step, or line becomes current and is given a darker background for emphasis. The Mentor Says and Mentor Reminds windows are displayed to help you review your work. Right clicking will give you a menu with Edit Line, Insert Step, Hide Problem, Hide Step, and Hide Line. Some of these menu items may not be displayed in some cases.

The fourth menu item on the Mentor Mathematics Advisor menu bar is Graph. Clicking on this menu item opens the Mentor Graphing Tool's Mentor Graph Display window. This window has menu items of its own: File, Graph, and View. You can resize the Mentor Graph Display window by left clicking on an edge or corner and dragging the edge or corner to a different location.

The File menu item acts in the same manner as the File menu item in the Mentor Mathematics Advisor. The Mentor Graph Display window File options are: New, Open, Close, Save, Save As, Print, and Exit. The action of these menu items apply to the Mentor Graphing Tool and not to the Mentor Mathematics Advisor's main window and contents.

The Graph menu item lets you add, delete, edit, or change the scale of a graph. Clicking on the Graph menu item in the Mentor Graph Display window and then on Input/Scale displays the Graph Property Sheets with two tabs: Graph Input and Editing and Graph Scale. Click on OK at the bottom of Graph Property Sheets to close the property sheets.

				10.2.1	Graph Input and Editing

Use the Graph Input and Editing dialog to enter a graph, delete a graph, or to edit a graph. The spin box to the right of Equation # displays the number of the current equation. If you are graphing multiple equations, you can select from your list of equations by clicking up or down in the spin box. To the left of the Equation # spin box are the New, Apply, and Delete buttons. The New button sets you up to enter a new graph. Delete removes the current graph. Apply sets changes in the Graph Type or Graph Variables.

Graph Type gives you the option of plotting an equation as a Cartesian plot or a Polar plot. A Cartesian plot is the default. You may also change the default independent and dependent variable, x and y. It is important that the Graph Variables agree with the variables that you enter in the Equation/Expression Input Box.

To enter a graph, change the Graph Type and Graph Variables if desired. Then click on the New button. The input focus goes to the white Input Box just below "Equation/Expression". Enter an equation in the independent and dependent variables or an expression in the independent variable. When your equation or expression has been entered, press the Enter key to display the graph.

You may display graphs with different variables on the Mentor Graph Display. The dependent variable will be displayed on the vertical axis and all of the graphs will have the same scale.

				10.2.2	Graph Scale

By default, the Mentor Graph Display graphs both the horizontal and vertical axes from -10 to 10 with 10 partitions each for grid labels. If you change the graph limits of Left, Right, Bottom, or Top or if you change the Number of Partitions for the horizontal or vertical grid, the Restore Defaults button will change the graph back to the defaults. The Apply button causes any changes that you have made to be implemented in the Mentor Graph Display.

The graph limits may be entered as a number or as an expression containing p. Horizontal axes are often displayed in terms of p when plotting trigonometric functions. If you want to use p in scaling an axis, you must remember to enter p as p. You must also enter the graph limits in one of the following forms:

where can be any integer and can be any positive integer (without sign entered).

You may vary the number of grid partitions from 1 to 20. Show Grid extends the label tic marks across the entire graph. You have the option of 2, 5, or 10 for a Zoom Factor, see section 10.3.2 for addition discussion of Zoom.

The Polar Scale gives you control of the domain of the independent variable for Polar Graphs. The default is from 0 to .

				10.3.1	Show Equations

The equations or expressions that you are graphing are displayed in a Mentor Graphs window. Like Mentor Reminds, you can hide this window by clicking on the Hide button in the Mentor Graphs window and you can bring it back by clicking on View and then Show Equations in the Mentor Graph Display menu bar. Each equation is in a different color and is color coded to its graph color.

				10.3.2	Zoom

The Mentor Graph Display View menu item also contains Zoom In and Zoom Out. This is a technique to allow you to rapidly change the scale of your graph. The Zoom Factor controls how rapidly the scale changes and Zoom In and Zoom Out changes the direction of change. For example, if the Zoom Factor is 10 and you click on Zoom In, the scale of the graph will change from [-10,10] to [-1,1] on both the horizontal and the vertical axes. Had you clicked on Zoom Out instead, the scale would have changed to [-100,100].

Often you want to change the graph scales so that the origin is no longer in the center of the graph. You can do this by using Graph Scale discussed above. You can also do this buy using Zoom with the mouse. If you move the mouse cursor onto the Mentor Graph Display you will see the graph coordinates of the cursor displayed at the bottom of the display. Point the mouse to the intersection of two graphs that you have entered and right click the mouse. You will see the coordinates of the mouse displayed and a menu that pops up containing Zoom In and Zoom Out. Clicking on either Zoom In or Zoom Out changes the scale in the same proportion to the Zoom Factor and the menu item zooms and also centers the graph on the mouse point. This is particularly useful in using the Mentor Graphing Tool to approximate solutions to equations.

If you use Zoom on a polar graph you may find it necessary to adjust the domain of the polar graph.

If you are working in the Mentor Mathematics Advisor, the previous directions in Section 10 tell you how you may enter a graph. But if you have already entered an expression or an equation, you can transfer that expression or equation to the Mentor Graphing Tool directly as follows.

First, right click on the expression or equation that you wish to graph. A menu will pop up with the menu option, Graph Line. Clicking on Graph Line brings up the Graph Input and Editing dialog with the expression or equation that you selected transferred to the Equation Input Box. Pressing Enter or clicking on the Apply Button then adds the new graph to the display.

The Mentor Mathematics Advisor does not work problems for you. Mentor Products, Inc. believes that it is important for you to develop the capability of solving algebraic problems on your own. We believe that telling you that your work is correct helps you learn and that pointing out errors helps you learn. But giving you answers does not help you at all.

Good luck as you progress through algebra. Algebra is the gateway to all science, engineering, and technology.

1. Decide were you wish to place the Advisor. By default, the directory "Mentor Products, Inc" will be placed under "Program Files" on the "C:" drive. You may place it elsewhere if you wish..

2. Insert Mentor Disk 1 in the A: drive.

In a DOS window, enter A:MMA

or

in the Windows Explorer, double click on the MMA application

or

in the Start menu, click on run and enter A:\MMA.

Now follow the instructions given by WinZip and InstallShield..

3. Mentor Disk 2 should now be in the A: drive. Remove it and put it with Mentor Disk 1 in a safe place.

4. Setup is now complete.

UPDATE - Floppy Disk Version

UPDATE - Email Version

1. Save the email attachment, MMA.exe for possible future reinstallation.

2. Double click on MMA.exe and follow the instructions given by WinZip and InstallShield.

• Setup is now complete..

Return to the Mentor home page.