HP 40gs User Manual

hp40g+.book Page i Friday, December 9, 2005 1:03 AM

HP 40gs graphing calculator

user's guide

Edition1 Part Number F2225AA-90001

title.fm Page ii Friday, February 17, 2006 9:48 AM

Notice

THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE.

HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN.

Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws.

Hewlett-Packard Company 4995 Murphy Canyon Rd, Suite 301 San Diego, CA 92123

Printing History

Edition 1 April 2005

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Contents

Preface

Manual conventions .............................................................. P-1

Notice ................................................................................. P-2

1 Getting started

On/off, cancel operations......................................................1-1

The display ..........................................................................1-2

The keyboard .......................................................................1-3

Menus .................................................................................1-8

Input forms ...........................................................................1-9

Mode settings.....................................................................1-10

Setting a mode...............................................................1-11

Aplets (E-lessons).................................................................1-12

Aplet library ..................................................................1-16

Aplet views....................................................................1-16

Aplet view configuration..................................................1-18

Mathematical calculations ....................................................1-19

Using fractions....................................................................1-25

Complex numbers ...............................................................1-29

Catalogs and editors ...........................................................1-30

2 Aplets and their views

Aplet views ..........................................................................2-1

About the Symbolic view ...................................................2-1

Defining an expression (Symbolic view) ..............................2-1

Evaluating expressions ......................................................2-3

About the Plot view...........................................................2-5

Setting up the plot (Plot view setup).....................................2-5

Exploring the graph..........................................................2-7

Other views for scaling and splitting the graph ..................2-13

About the numeric view...................................................2-16

Setting up the table (Numeric view setup) ..........................2-16

Exploring the table of numbers.........................................2-17

Building your own table of numbers..................................2-19

“Build Your Own” menu keys...........................................2-20

Example: plotting a circle ................................................2-20

3 Function aplet

About the Function aplet ........................................................3-1

Getting started with the Function aplet.................................3-1

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Function aplet interactive analysis........................................... 3-9

Plotting a piecewise-defined function ................................ 3-12

4 Parametric aplet

About the Parametric aplet .................................................... 4-1

Getting started with the Parametric aplet............................. 4-1

5 Polar aplet

Getting started with the Polar aplet ......................................... 5-1

6 Sequence aplet

About the Sequence aplet...................................................... 6-1

Getting started with the Sequence aplet .............................. 6-1

7 Solve aplet

About the Solve aplet............................................................ 7-1

Getting started with the Solve aplet .................................... 7-2

Use an initial guess............................................................... 7-5

Interpreting results ................................................................ 7-6

Plotting to find guesses .......................................................... 7-7

Using variables in equations ................................................ 7-10

8 Linear Solver aplet

About the Linear Solver aplet ................................................. 8-1

Getting started with the Linear Solver aplet.......................... 8-1

9 Triangle Solve aplet

About the Triangle Solver aplet .............................................. 9-1

Getting started with the Triangle Solver aplet....................... 9-1

10 Statistics aplet

About the Statistics aplet...................................................... 10-1

Getting started with the Statistics aplet.............................. 10-1

Entering and editing statistical data ...................................... 10-6

Defining a regression model.......................................... 10-12

Computed statistics ........................................................... 10-14

Plotting............................................................................ 10-15

Plot types .................................................................... 10-16

Fitting a curve to 2VAR data ......................................... 10-17

Setting up the plot (Plot setup view) ................................ 10-18

Trouble-shooting a plot ................................................. 10-19

Exploring the graph ..................................................... 10-19

Calculating predicted values ......................................... 10-20

11 Inference aplet

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About the Inference aplet .....................................................11-1

Getting started with the Inference aplet .............................11-1

Importing sample statistics from the Statistics aplet..............11-4

Hypothesis tests ..................................................................11-8

One-Sample Z-Test..........................................................11-8

Two-Sample Z-Test ..........................................................11-9

One-Proportion Z-Test....................................................11-10

Two-Proportion Z-Test ....................................................11-11

One-Sample T-Test ........................................................11-12

Two-Sample T-Test ........................................................11-14

Confidence intervals..........................................................11-15

One-Sample Z-Interval...................................................11-15

Two-Sample Z-Interval ...................................................11-16

One-Proportion Z-Interval...............................................11-17

Two-Proportion Z-Interval ...............................................11-17

One-Sample T-Interval ...................................................11-18

Two-Sample T-Interval....................................................11-19

12 Using the Finance Solver

Background........................................................................12-1

Performing TVM calculations ................................................12-4

Calculating Amortizations................................................12-7

13 Using mathematical functions

Math functions....................................................................13-1

The MATH menu ............................................................13-1

Math functions by category ..................................................13-2

Keyboard functions.........................................................13-3

Calculus functions...........................................................13-6

Complex number functions...............................................13-7

Constants ......................................................................13-8

Conversions...................................................................13-8

Hyperbolic trigonometry..................................................13-9

List functions ................................................................13-10

Loop functions..............................................................13-10

Matrix functions ...........................................................13-11

Polynomial functions .....................................................13-11

Probability functions......................................................13-12

Real-number functions ...................................................13-14

Two-variable statistics....................................................13-17

Symbolic functions........................................................13-17

Test functions ...............................................................13-19

Trigonometry functions ..................................................13-20

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Symbolic calculations........................................................ 13-20

Finding derivatives....................................................... 13-21

Program constants and physical constants ........................... 13-24

Program constants........................................................ 13-25

Physical constants ........................................................ 13-25

14 Computer Algebra System (CAS)

What is a CAS? ................................................................. 14-1

Performing symbolic calculations .......................................... 14-1

An example .................................................................. 14-2

CAS variables.................................................................... 14-4

The current variable ....................................................... 14-4

CAS modes ....................................................................... 14-5

Using CAS functions in HOME ............................................. 14-7

Online Help....................................................................... 14-8

CAS functions in the Equation Writer .................................... 14-9

ALGB menu................................................................. 14-10

DIFF menu................................................................... 14-16

REWRI menu ............................................................... 14-28

SOLV menu................................................................. 14-33

TRIG menu .................................................................. 14-38

CAS Functions on the MATH menu ..................................... 14-45

Algebra menu ............................................................. 14-45

Complex menu ............................................................ 14-45

Constant menu ............................................................ 14-46

Diff & Int menu ............................................................ 14-46

Hyperb menu .............................................................. 14-46

Integer menu ............................................................... 14-46

Modular menu............................................................. 14-51

Polynomial menu ......................................................... 14-55

Real menu................................................................... 14-60

Rewrite menu .............................................................. 14-60

Solve menu ................................................................. 14-60

Tests menu .................................................................. 14-61

Trig menu ................................................................... 14-61

CAS Functions on the CMDS menu ..................................... 14-62

15 Equation Writer

Using CAS in the Equation Writer ....................................... 15-1

The Equation Writer menu bar......................................... 15-1

Configuration menus ...................................................... 15-3

Entering expressions and subexpressions............................... 15-5

How to modify an expression ....................................... 15-11

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Accessing CAS functions....................................................15-12

Equation Writer variables .................................................15-16

Predefined CAS variables .............................................15-16

The keyboard in the Equation Writer ..............................15-17

16 Step-by-Step Examples

Introduction .......................................................................16-1

17 Variables and memory management

Introduction ........................................................................17-1

Storing and recalling variables .............................................17-2

The VARS menu ..................................................................17-4

Memory Manager...............................................................17-9

18 Matrices

Introduction ........................................................................18-1

Creating and storing matrices...............................................18-2

Working with matrices.........................................................18-4

Matrix arithmetic.................................................................18-6

Solving systems of linear equations ...................................18-8

Matrix functions and commands..........................................18-10

Argument conventions...................................................18-10

Matrix functions ...........................................................18-10

Examples .........................................................................18-13

19 Lists

Displaying and editing lists...................................................19-4

Deleting lists ..................................................................19-6

Transmitting lists .............................................................19-6

List functions .......................................................................19-6

Finding statistical values for list elements ................................19-9

20 Notes and sketches

Introduction ........................................................................20-1

Aplet note view...................................................................20-1

Aplet sketch view ................................................................20-3

The notepad.......................................................................20-6

21 Programming

Introduction ........................................................................21-1

Program catalog ............................................................21-2

Creating and editing programs.............................................21-4

Using programs ..................................................................21-7

Customizing an aplet...........................................................21-9

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Aplet naming convention .............................................. 21-10

Example ..................................................................... 21-10

Programming commands ................................................... 21-13

Aplet commands.......................................................... 21-14

Branch commands ....................................................... 21-17

Drawing commands ..................................................... 21-19

Graphic commands...................................................... 21-21

Loop commands .......................................................... 21-23

Matrix commands ........................................................ 21-24

Print commands ........................................................... 21-25

Prompt commands........................................................ 21-26

Stat-One and Stat-Two commands.................................. 21-29

Stat-Two commands ..................................................... 21-30

Storing and retrieving variables in programs ................... 21-31

Plot-view variables ....................................................... 21-31

Symbolic-view variables................................................ 21-38

Numeric-view variables ................................................ 21-40

Note variables............................................................. 21-43

Sketch variables .......................................................... 21-43

22 Extending aplets

Creating new aplets based on existing aplets......................... 22-1

Using a customized aplet................................................ 22-3

Resetting an aplet ............................................................... 22-3

Annotating an aplet with notes............................................. 22-4

Annotating an aplet with sketches......................................... 22-4

Downloading e-lessons from the web .................................... 22-4

Sending and receiving aplets............................................... 22-4

Sorting items in the aplet library menu list.............................. 22-6

Reference information

Glossary.............................................................................. R-1

Resetting the HP 40gs ........................................................... R-3

To erase all memory and reset defaults ............................... R-3

If the calculator does not turn on ........................................ R-4

Operating details ................................................................. R-4

Batteries ......................................................................... R-4

Variables............................................................................. R-6

Home variables ............................................................... R-6

Function aplet variables.................................................... R-7

Parametric aplet variables................................................. R-8

Polar aplet variables ........................................................ R-9

Sequence aplet variables ................................................ R-10

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Solve aplet variables.......................................................R-11

Statistics aplet variables ..................................................R-12

MATH menu categories .......................................................R-13

Math functions ...............................................................R-13

Program constants ..........................................................R-15

Physical Constants ..........................................................R-16

CAS functions ................................................................R-17

Program commands........................................................R-19

Status messages..................................................................R-20

Limited Warranty

Service.......................................................................... W-3

Regulatory Notices ......................................................... W-5

Index

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hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM

Preface

The HP 40gs is a feature-rich graphing calculator. It is also a powerful mathematics learning tool, with a built-in computer algebra system (CAS). The HP 40gs is designed so that you can use it to explore mathematical functions and their properties.

You can get more information on the HP 40gs from Hewlett-Packard’s Calculators web site. You can download customized aplets from the web site and load them onto your calculator. Customized aplets are special applications developed to perform certain functions, and to demonstrate mathematical concepts.

Hewlett Packard’s Calculators web site can be found at:

http://www.hp.com/calculators

Manual conventions

The following conventions are used in this manual to represent the keys that you press and the menu options that you choose to perform the described operations.

• Key presses are represented as follows: , , , etc.

• Shift keys, that is the key functions that you access by

pressing the key first, are represented as follows:

CLEAR, MODES, ACOS, etc.

• Numbers and letters are represented normally, as

follows: 5, 7, A, B, etc.

• Menu options, that is, the functions that you select

using the menu keys at the top of the keypad are represented as follows:

, , .

• Input form fields and choose list items are represented

as follows: Function, Polar, Parametric

• Your entries as they appear on the command line or

within input forms are represented as follows:

2*X

-3X+5

P-1

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Notice

This manual and any examples contained herein are provided as-is and are subject to change without notice. Except to the extent prohibited by law, Hewlett-Packard Company makes no express or implied warranty of any kind with regard to this manual and specifically disclaims the implied warranties and conditions of merchantability and fitness for a particular purpose and Hewlett-Packard Company shall not be liable for any errors or for incidental or consequential damage in connection with the furnishing, performance or use of this manual and the examples herein.

Hewlett-Packard Development Company, L.P.

The programs that control your HP 40gs are copyrighted and all rights are reserved. Reproduction, adaptation, or translation of those programs without prior written permission from Hewlett-Packard Company is also prohibited.

P-2

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Getting started

On/off, cancel operations

To turn on Press to turn on the calculator.

To cancel When the calculator is on, the key cancels the

current operation.

To turn off Press OFF to turn the calculator off.

To save power, the calculator turns itself off after several minutes of inactivity. All stored and displayed information is saved.

If you see the ((•)) annunciator or the Low Bat message, then the calculator needs fresh batteries.

HOME HOME is the calculator’s home view and is common to all

aplets. If you want to perform calculations, or you want to quit the current activity (such as an aplet, a program, or an editor), press . All mathematical functions are available in the HOME. The name of the current aplet is displayed in the title of the home view.

Protective cover The calculator is provided with a slide cover to protect the

display and keyboard. Remove the cover by grasping both sides of it and pulling down.

You can reverse the slide cover and slide it onto the back of the calculator. this will help prevent you losing the cover while you are using the calculator.

To prolong the life of the calculator, always place the cover over the display and keyboard when you are not using the calculator.

Getting started 1-1

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The display

To adjust the contrast

Simultaneously press and (or ) to increase (or decrease) the contrast.

To clear the display • Press CANCEL to clear the edit line.

• Press display history.

CLEAR to clear the edit line and the

Parts of the display

History

Edit line

Menu key or soft key labels. The labels for the menu keys’ current meanings. is the label for the first menu key in this picture. “Press ” means to press the first menu key, that is, the leftmost top-row key on the calculator keyboard.

Edit line. The line of current entry. History. The HOME display ( ) shows up to four

lines of history: the most recent input and output. Older lines scroll off the top of the display but are retained in memory.

Title. The name of the current aplet is displayed at the top of the HOME view. RAD, GRD, DEG specify whether Radians, Grads or Degrees angle mode is set for HOME.

T and S symbols indicate whether there is more

The history in the HOME display. Press the and to scroll in the HOME display.

Title

Menu key labels

1-2 Getting started

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Annunciators. Annunciators are symbols that appear above the title bar and give you important status information.

Annunciator Description

α Alpha in effect for next keystroke.

((•)) Low battery power.

Data is being transferred.

The keyboard

Shift in effect for next keystroke. To cancel, press again.

To cancel, press again.

Busy.

HP 40gs Graphing Calculator

Menu Key Labels

Menu Keys

Aplet Control Keys

Alpha Key

Shift Key

Getting started 1-3

Cursor Keys

Enter Key

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Menu keys

• On the calculator keyboard, the top row of keys are called menu keys. Their meanings depend on the context—that’s why they are blank. The menu keys are sometimes called “soft keys”.

• The bottom line of the display shows the labels for the menu keys’ current meanings.

Aplet control keys

The aplet control keys are:

Key Meaning

Displays the Symbolic view for the current aplet. See “Symbolic view” on page 1-16.

Displays the Plot view for the current aplet. See “Plot view” on page 1-16.

Displays the Numeric view for the current aplet. See “Numeric view” on page 1-17.

Displays the HOME view. See “HOME” on page 1-1.

Displays the Aplet Library menu. See “Aplet library” on page 1-16.

Displays the VIEWS menu. See “Aplet views” on page 1-16.

1-4 Getting started

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Entry/Edit keys

The entry and edit keys are:

Key Meaning

(

CANCEL)

CLEAR

, , ,

Cancels the current operation if the calculator is on by pressing . Pressing , then

OFF turns the

calculator off. Accesses the function printed in blue

above a key. Returns to the HOME view, for

performing calculations. Accesses the alphabetical

characters printed in orange below a key. Hold down to enter a string of characters.

Enters an input or executes an operation. In calculations, acts like “=”. When or is present as a menu key, acts the same as pressing or

Enters a negative number. To enter –25, press 25. Note: this is not

the same operation that the subtract button performs ().

Enters the independent variable by inserting X, T, θ, or N into the edit line, depending on the current active aplet.

Deletes the character under the cursor. Acts as a backspace key if the cursor is at the end of the line.

Clears all data on the screen. On a settings screen, for example Plot Setup, CLEAR returns all settings to their default values.

Moves the cursor around the display. Press first to move to the beginning, end, top or bottom.

Getting started 1-5

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Key Meaning (Continued)

CHARS Displays a menu of all available

characters. To type one, use the arrow keys to highlight it, and press

select each and press , then press .

Shifted keystrokes

There are two shift keys that you use to access the operations and characters printed above the keys: and .

Key Description

Press the key to access the operations printed in blue above the keys. For instance, to access the Modes screen, press , then press . (MODES is labeled in blue above the key). You do not need to hold down when you press HOME. This action is depicted in this manual as “press

To cancel a shift, press again.

. To select multiple characters,

MODES.”

The alphabetic keys are also shifted keystrokes. For instance, to type Z, press Z. (The letters are printed in orange to the lower right of each key.)

To cancel Alpha, press again.

For a lower case letter, press

For a string of letters, hold down

while typing.

1-6 Getting started

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HELPWITH The HP 40gs built-in help is available in HOME only. It

provides syntax help for built-in math functions. Access the HELPWITH command by pressing

SYNTAX and then the math key for which you require

syntax help.

Example Press SYNTAX

Note: Remove the left parenthesis from built-in functions such as sine, cosine, and tangent before invoking the HELPWITH command.

Note: In the CAS system, pressing the SYNTAX will show the CAS help menu.

Math keys HOME ( ) is the place to do non-symbolic

calculations. (For symbolic calculations, use the computer algebra system, referred throughout this manual as CAS).

Keyboard keys. The most common operations are available from the keyboard, such as the arithmetic (like

) and trigonometric (like ) functions. Press to complete the operation: 256 displays 16.

MATH menu. Press

to open the MATH menu. The MATH menu is a comprehensive list of math functions that do not appear on the keyboard. It also includes categories for all other functions and constants. The functions are grouped by category, ranging in alphabetical order from Calculus to Trigonometry.

• The arrow keys scroll through the list ( , )

and move from the category list in the left column

to the item list in the right column ( , ).

• Press to insert the selected command onto the

edit line.

• Press to dismiss the MATH menu without

selecting a command.

Getting started 1-7

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• Pressing displays the list of Program Constants. You can use these in programs that you develop.

• Pressing displays a menu of physical constants from the fields of chemistry, physics, and quantum mechanics. You can use these constants in calculations. (pSee “Physical constants” on page 13-25 for more information.)

• Pressing takes you to the beginning of the MATH menu.

See “Math functions by category” on page 13-2 for details of the math functions.

HINT

When using the MATH menu, or any menu on the HP 40gs, pressing an alpha key takes you straight to the first menu option beginning with that alpha character. With this method, you do not need to press first. Just press the key that corresponds to the command’s beginning alpha character.

Note that when the MATH menu is open, you can also access CAS commands. You do this by pressing . This enables you to use CAS commands on the HOME screen, without opening CAS. See Chapter 14 for details of CAS commands.

Program commands

Pressing CMDS displays the list of Program Commands. See “Programming commands” on page 21-13.

Inactive keys If you press a key that does not operate in the current

context, a warning symbol like this appears. There is no beep.

Menus

A menu offers you a choice of items. Menus are displayed in one or two columns.

• The arrow in the display means more items below.

• The arrow in the display means more items above.

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To search a menu • Press or to scroll through the list. If you press

or , you’ll go all the way to

the end or the beginning of the list. Highlight the item you want to select, then press (or ).

• If there are two columns, the left column shows general categories and the right column shows specific contents within a category. Highlight a general category in the left column, then highlight an item in the right column. The list in the right column changes when a different category is highlighted.

Press or when you have highlighted your selection.

• To speed-search a list, type the first letter of the word. For example, to find the Matrix category in ,

press , the Alpha “M” key.

• To go up a page, you can press . To go down a page, press .

To cancel a menu Press (for CANCEL) or . This cancels the

current operation.

Input forms

An input form shows several fields of information for you to examine and specify. After highlighting the field to edit, you can enter or edit a number (or expression). You can also select options from a list ( ). Some input forms include items to check ( ). See below for examples input forms.

Reset input form values

Getting started 1-9

To reset a field to its default values in an input form, move the cursor to that field and press . To reset all default field values in the input form, press CLEAR.

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Mode settings

You use the Modes input form to set the modes for HOME.

HINT

Although the numeric setting in Modes affects only HOME, the angle setting controls HOME and the current aplet. The angle setting selected in Modes is the angle setting used in both HOME and current aplet. To further configure an aplet, you use the and ).

SETUP keys (

Press

MODES to access the HOME MODES input

form.

Setting Options

Angle Measure

Angle values are:

Degrees. 360 degrees in a circle. Radians. 2π radians in a circle. Grads. 400 grads in a circle.

The angle mode you set is the angle setting used in both HOME and the current aplet. This is done to ensure that trigonometric calculations done in the current aplet and HOME give the same result.

Number Format

The number format mode you set is the number format used in both HOME and the current aplet.

Standard. Full-precision display. Fixed. Displays results rounded to a

number of decimal places. Example:

123.456789 becomes 123.46 in Fixed 2 format.

Scientific. Displays results with an exponent, one digit to the left of the decimal point, and the specified number of decimal places. Example:

123.456789 becomes 1.23E2 in Scientific 2 format.

1-10 Getting started

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Setting Options (Continued)

Engineering. Displays result with an exponent that is a multiple of 3, and the specified number of significant digits beyond the first one. Example:

123.456E7 becomes 1.23E9 in Engineering 2 format.

Fraction. Displays results as fractions based on the specified number of decimal places. Examples:

123.456789 becomes 123 in Fraction 2 format, and .333 becomes 1/3 and 0.142857 becomes 1/7. See “Using fractions” on page 1-25.

Mixed Fraction. Displays results as mixed fractions based on the specified number of decimal places. A mixed fraction has an integer part and a fractional part. Examples:

123.456789 becomes 123+16/35 in Fraction 2 format, and 7÷ 3 returns 2+1/3. See “Using fractions” on page 1-25.

Decimal Mark

Dot or Comma. Displays a number as 12456.98 (Dot mode) or as 12456,98 (Comma mode). Dot mode uses commas to separate elements in lists and matrices, and to separate function arguments. Comma mode uses periods (dot) as separators in these contexts.

Setting a mode

This example demonstrates how to change the angle measure from the default mode, radians, to degrees for the current aplet. The procedure is the same for changing number format and decimal mark modes.

1. Press form.

Getting started 1-11

MODES to open the HOME MODES input

chapter-1.fm Page 12 Friday, December 9, 2005 1:26 AM

The cursor (highlight) is in the first field, Angle Measure.

2. Press to display a list of choices.

3. Press to select Degrees,

and press

. The angle measure

changes to degrees.

4. Press to return to HOME.

HINT

Whenever an input form has a list of choices for a field, you can press to cycle through them instead of using

Aplets (E-lessons)

Aplets are the application environments where you explore different classes of mathematical operations. You select the aplet that you want to work with.

Aplets come from a variety of sources:

• Built-in the HP 40gs (initial purchase).

• Aplets created by saving existing aplets, which have

been modified, with specific configurations. See “Creating new aplets based on existing aplets” on page 22-1.

• Downloaded from HP’s Calculators web site.

• Copied from another calculator.

Aplets are stored in the Aplet library. See “Aplet library” on page 1-16 for further information.

You can modify configuration settings for the graphical, tabular, and

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symbolic views of the aplets in the following table. See “Aplet view configuration” on page 1-18 for further information.

Aplet

Use this aplet to explore:

name

Function Real-valued, rectangular functions y in

terms of x. Example: .

y 2x23x 5++=

Inference Confidence intervals and Hypothesis

tests based on the Normal and Students-t distributions.

Parametric Parametric relations x and y in terms of

t. Example: x = cos(t) and y = sin(t).

Polar Polar functions r in terms of an angle θ.

Example: .

r 24θ()cos=

Sequence Sequence functions U in terms of n, or

in terms of previous terms in the same or another sequence, such as and

. Example: , and

n 2–

U10= U21=

n1–

Solve Equations in one or more real-valued

variables. Example: .

x 1+ x

n 1–

x–2–=

Finance Time Value of Money (TVM)

calculations.

Linear Solver

Solutions to sets of two or three linear equations.

Triangle Solver

Unknown values for the lengths and angles of triangles.

Statistics One-variable (x) or two-variable (x and

y) statistical data.

In addition to these aplets, which can be used in a variety of applications, the HP 40gs is supplied with two teaching aplets: Quad Explorer and Trig Explorer. You cannot modify configuration settings for these aplets.

A great many more teaching aplets can be found at HP’s web site and other web sites created by educators, together with accompanying documentation, often with student work sheets. These can be downloaded free of

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charge and transferred to the HP 40gs using the provided Connectivity Kit.

Quad Explorer aplet

HINT

The Quad Explorer aplet is used to investigate the behaviour of as the values of a, h and

yaxh+()

v+=

v change, both by manipulating the equation and seeing the change in the graph, and by manipulating the graph and seeing the change in the equation.

More detailed documentation, and an accompanying student work sheet can be found at HP’s web site.

Press , select Quad Explorer, and then press

. The Quad Explorer aplet opens in mode, in which the arrow keys, the and keys, and the key are used to change the shape of the graph. This changing shape is reflected in the equation displayed at the top right corner of the screen, while the original graph is retained for comparison. In this mode the graph controls the equation.

It is also possible to have the equation control the graph. Pressing displays a sub-expression of your equation.

Pressing the and key moves between subexpressions, while pressing the and key changes their values.

Pressing allows the user to select whether all three sub-expressions will be explored at once or only one at a time.

A button is provided to evaluate the student’s knowledge. Pressing displays a target quadratic graph. The student must manipulate the equation’s parameters to make the equation match the target graph. When a student feels that they have correctly chosen the parameters a button evaluates the answer and provide feedback. An

button is provided for those who give up!

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Trig Explorer aplet The Trig Explorer aplet is used to investigate the

behaviour of the graph of as the values of a, b, c and d change, both by manipulating the equation and seeing the change in the graph, or by manipulating the graph and seeing the change in the equation.

Press , select Trig Explorer, and then press

to display the screen

shown right.

In this mode, the graph controls the equation. Pressing the and

keys transforms the graph, with these transformations reflected in the equation.

The button labelled is a toggle between and . When is chosen, the ‘point of control’ is at the origin (0,0) and the and keys control vertical and horizontal transformations. When is chosen the ‘point of control’ is on the first extremum of the graph (i.e. for the sine graph at .

ya bxc+()d+sin=

Origin

π 21,⁄()

The arrow keys change the amplitude and frequency of

Extremum

the graph. This is most easily seen by experimenting.

Pressing displays the equation at the top of the screen. The equation is controlled by the graph. Pressing the and keys moves from parameter to parameter. Pressing the or key changes the parameter’s values.

The default angle setting for this aplet is radians. The angle setting can be changed to degrees by pressing

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Aplet library

Aplets are stored in the Aplet library.

To open an aplet Press to display the Aplet library menu. Select the

aplet and press or . From within an aplet, you can return to HOME any time

by pressing .

Aplet views

When you have configured an aplet to define the relation or data that you want to explore, you can display it in different views. Here are illustrations of the three major aplet views (Symbolic, Plot, and Numeric), the six supporting aplet views (from the VIEWS menu), and the two user-defined views (Note and Sketch).

Note: some aplets—such as the Linear Solver aplet and the Triangle Solver aplet—only have a single view, the Numeric view.

Symbolic view Press to display the aplet’s Symbolic view.

You use this view to define the function(s) or equation(s) that you want to explore.

See “About the Symbolic view” on page 2-1 for further information.

Plot view Press to display the aplet’s Plot view.

In this view, the functions that you have defined are displayed graphically.

See “About the Plot view” on page 2-5 for further information.

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Numeric view Press to display the aplet’s Numeric view.

In this view, the functions that you have defined are displayed in tabular format.

See “About the numeric view” on page 2-16 for further information.

Plot-Table view The VIEWS menu contains the Plot-Table view.

Select Plot-Table Splits the screen into the plot

and the data table. See “Other views for scaling and splitting the graph” on page 2-13 for futher information.

Plot-Detail view The VIEWS menu contains the Plot-Detail view.

Select Plot-Detail Splits the screen into the plot

and a close-up. See “Other views for scaling and splitting the graph” on

page 2-13 for further information.

Overlay Plot view

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The VIEWS menu contains the Overlay Plot view.

Select Overlay Plot Plots the current

expression(s) without erasing any pre-existing plot(s).

See “Other views for scaling and splitting the graph” on page 2-13 for further information.

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Note view Press NOTE to display the aplet’s note view.

This note is transferred with the aplet if it is sent to another calculator or to a PC. A note view contains text to supplement an aplet.

See “Notes and sketches” on page 20-1 for further information.

Sketch view Press SKETCH to display the aplet’s sketch view.

Displays pictures to supplement an aplet.

See “Notes and sketches” on page 20-1 for further information.

Aplet view configuration

You use the SETUP keys ( , and

) to configure the aplet. For example, press

SETUP-PLOT ( ) to display the input form for

setting the aplet’s plot settings. Angle measure is controlled using the

Plot Setup Press SETUP-PLOT.

Sets parameters to plot a graph.

Numeric Setup Press SETUP-NUM. Sets

parameters for building a table of numeric values.

Symbolic Setup This view is only available in

the Statistics aplet in mode, where it plays an important role in choosing data models. Press

MODES view.

SETUP-SYMB.

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