HP 39g+ Graphing Calculator User Manual
hp 39g+ graphing calculator
Mastering the hp 39g+
A guide for teachers, students and other
users of the hp 39g+, hp 39g & hp 40g
Edition 1.1
HP part number F2224-90010
Printed Date: 2005/10/11
Table of Contents
Introduction.................................................................................................12
How to use this Manual..............................................................................13
Early High School.........................................................................................................13
Pre-Calculus.................................................................................................................14
Calculus........................................................................................................................14
Where’s the ON button?.............................................................................15
Some Keyboard Examples.........................................................................16
Keys & Notation Conventions...................................................................17
Some essential keys .......................................................................................................17
The SHIFT key .............................................................................................................17
The ALPHA key............................................................................................................18
The Screen keys ..........................................................................................................18
Pop-up menus & short-cuts..........................................................................................18
Everything revolves around Aplets! .........................................................21
Some typical aplet views .............................................................................................. 22
The HOME view...........................................................................................25
What is the HOME view?.................................................................................................25
Exploring the keyboard...................................................................................................26
The screen keys ........................................................................................................... 26
Aplet related keys.........................................................................................................26
The arrow keys.............................................................................................................26
The SYMB, PLOT and NUM keys....................................................................................27
Intro to the VIEWS menu ..............................................................................................28
The VARS key ............................................................................................................... 28
The SETUP views .........................................................................................................30
The MODES view ...........................................................................................................30
Numeric formats ........................................................................................................... 31
The ANS key .................................................................................................................32
The negative key .......................................................................................................... 33
The CHARS key............................................................................................................ 33
The DEL and CLEAR keys ............................................................................................34
Angle and Numeric settings...........................................................................................35
Memory Management......................................................................................................37
The MEMORY MANAGER view................................................................................... 37
Downloaded aplets & memory .....................................................................................38
The GRAPHICS MANAGER ........................................................................................ 39
The LIBRARY MANAGER............................................................................................ 39
Fractions on the hp 39g+................................................................................................40
Pitfalls to watch for .......................................................................................................42
The HOME History.............................................................................................................43
COPYing calculations................................................................................................... 43
Clearing the History......................................................................................................44
SHOWing results..........................................................................................................44
Storing and Retrieving Memories..................................................................................45
Referring to other aplets from the HOME view...............................................................46
An introduction to the MATH Menu...............................................................................47
Resetting the calculator..................................................................................................48
Soft reboot....................................................................................................................48
Soft reboot (Hardware).................................................................................................49
Hard reboot (with memory wipe) .................................................................................. 49
Summary ..........................................................................................................................50
2
The Function Aplet.....................................................................................51
∫
Choose the aplet ..........................................................................................................51
The SYMB view .............................................................................................................52
The XTθ button ............................................................................................................. 52
ing your function ...............................................................................................52
The NUM view................................................................................................................ 53
The PLOT view .............................................................................................................53
Auto Scale........................................................................................................................54
The PLOT SETUP view....................................................................................................55
Detail vs. Faster............................................................................................................ 55
Simultaneous................................................................................................................ 56
Connect ........................................................................................................................ 56
Axes.............................................................................................................................. 56
Labels ...........................................................................................................................56
Grid...............................................................................................................................56
The default axis settings ................................................................................................57
The Bar...............................................................................................................57
The MENU toggle.........................................................................................................57
The Menu Bar functions..................................................................................................58
Trace ............................................................................................................................58
Defn ..............................................................................................................................58
Goto..............................................................................................................................59
The Zoom Sub-menu ...................................................................................................60
Center...........................................................................................................................60
In/Out............................................................................................................................60
Box…............................................................................................................................61
X-Zoom In/Out x4 and Y-Zoom In/Out x4 ....................................................................62
Square ..........................................................................................................................62
Auto Scale, Decimal, Integer and Trig .........................................................................62
The FCN menu.................................................................................................................63
Root ..............................................................................................................................63
Intersection...................................................................................................................64
Slope ............................................................................................................................64
Signed area… ..............................................................................................................65
Definite integrals........................................................................................................... 65
Tracing the integral in PLOT ......................................................................................... 66
Areas between and under curves ................................................................................67
Extremum ..................................................................................................................... 68
Tips & Tricks - Function.............................................................................69
Finding a suitable set of axes....................................................................................... 69
Composite functions.....................................................................................................71
Using functions in the HOME view ...............................................................................72
Differentiating ...............................................................................................................73
Circular functions.......................................................................................................... 74
Trig functions................................................................................................................76
Retaining calculated values.......................................................................................... 77
The NUM view revisited ..............................................................................................77
ZOOM...........................................................................................................................78
Integration: The definite integral using the
function ............................................... 80
Integration: The algebraic indefinite integral ................................................................ 81
The hp 40g Computer Algebra System........................................................................82
Integration: The definite integral using PLOT variables ............................................... 83
Piecewise defined functions .........................................................................................85
‘Nice’ scales..................................................................................................................86
Use of brackets in functions ......................................................................................... 87
3
Problems when evaluating limits..................................................................................88
Gradient at a point........................................................................................................90
Finding and accessing polynomial roots ...................................................................... 91
The VIEWS menu........................................................................................92
Plot-Detail.....................................................................................................................93
Plot-Table ..................................................................................................................... 94
Overlay Plot..................................................................................................................95
Auto Scale .................................................................................................................... 96
Decimal, Integer & Trig................................................................................................. 97
Downloaded Aplets from the Internet ...........................................................................99
Curve Areas..................................................................................................................99
Linear Programming.....................................................................................................99
The Parametric Aplet................................................................................100
Choose XRng, YRng & TRng..................................................................................... 100
The effect of TRng...................................................................................................... 101
TStep controls smoothness........................................................................................101
Tips & Tricks - Parametric equations .....................................................103
Fun and games..............................................................................................................103
Example 1...................................................................................................................103
Example 2...................................................................................................................103
Vectors ...........................................................................................................................104
Example 1...................................................................................................................104
Example 2...................................................................................................................105
The Polar Aplet.........................................................................................106
Choose XRng, YRng & θRng ..................................................................................... 106
θStep and smoothness............................................................................................... 106
Changing the default for θStep................................................................................... 106
Circular circles ............................................................................................................106
The Sequence Aplet .................................................................................107
Recursive or non-recursive ........................................................................................107
First, second & general terms ....................................................................................107
Convenient screen keys provided .............................................................................. 108
Tips & Tricks - Sequences & Series........................................................110
Defining a generalized GP and the sum to n terms. ..................................................110
Solving sequence problems ....................................................................................... 110
Modeling loans ...........................................................................................................112
The Solve Aplet.........................................................................................113
Equations vs. expressions.......................................................................................... 113
Entering the equation ................................................................................................. 113
Solving for a missing value.........................................................................................114
The INFO report ......................................................................................................... 114
Multiple solutions and the initial guess.......................................................................115
Graphing in Solve.......................................................................................................116
Transferring approximate solutions............................................................................116
Referring to functions from other aplets ..................................................................... 117
A detailed explanation of PLOT in Solve.................................................................... 118
The meaning of messages..............................................................................120
Tips & Tricks - Solve ................................................................................121
Easy problems............................................................................................................ 121
Harder problems......................................................................................................... 121
4
The Stats Aplet - Univariate Data............................................................122
Uni vs. Bi-variate data ................................................................................................ 122
Clearing data .............................................................................................................. 122
Sorting data ................................................................................................................ 123
The STATS key .......................................................................................................... 123
Functions of columns .................................................................................................124
Registering columns as ‘in use’.................................................................................. 124
Working with frequency tables ...................................................................................125
Auto scale...................................................................................................................125
Plot Setup options ......................................................................................................126
Box and whisker graphs .............................................................................................126
The effect of HRng ..................................................................................................... 127
Grouped data & HWidth ............................................................................................. 127
Tips & Tricks - Univariate Data................................................................129
New columns as functions of old................................................................................129
Simulating Dice ..........................................................................................................129
Simulating Random Variables....................................................................................130
The Stats Aplet - Bivariate Data ..............................................................132
Uni vs. Bi-variate data ................................................................................................ 132
Clearing data .............................................................................................................. 132
Entering data as ordered pairs...................................................................................133
Adjusting the symbols used to plot points ..................................................................133
The cursor ..................................................................................................................133
Sorting paired columns............................................................................................... 134
Specifying the fit model .............................................................................................. 134
Multiple data sets .......................................................................................................134
Choosing from available fit models ............................................................................135
The User Defined model ............................................................................................135
Connected data .......................................................................................................... 136
Two Variable Statistics ...............................................................................................137
Showing the line of best fit .........................................................................................138
Predicting using PREDY..............................................................................................140
Predicting using the PLOT view..................................................................................140
RelErr as a measure of non-linear fit....................................................................... 141
Tips & Tricks - Bivariate Data..................................................................143
New columns as functions of old................................................................................143
Using values from in calculations ..................................................................143
Obtaining coefficients from the fit model ....................................................................145
Finding Fit Coefficients...............................................................................................145
Correct interpretation of the PREDX function ............................................................146
Assigning rank orders to sets of data .........................................................................147
Using Stats to find equations from point data ............................................................148
The Inference aplet...................................................................................150
Using the Chi2 test on a frequency table ................................................................... 150
Hypothesis test: T-Test 1-µ ....................................................................................... 151
Confidence interval: T-Int 1-µ .................................................................................... 153
Hypothesis test: T-Test µ1 -µ
Hypothesis test: Z-Test 1-µ ....................................................................................... 156
.....................................................................................154
2
Tips & Tricks - Inference..........................................................................158
Importing from a frequency table ...............................................................................158
5
The Finance aplet .....................................................................................160
Parameters.................................................................................................................160
Straightforward compound interest ............................................................................ 161
Annuity........................................................................................................................162
Loan calculations........................................................................................................ 162
Amortization................................................................................................................163
The Quad Explorer teaching aplet ..........................................................164
Objectives...................................................................................................................164
Choosing the level......................................................................................................164
GRAPH mode............................................................................................................. 164
SYMB mode ...............................................................................................................165
Self test mode ............................................................................................................166
The Trig Explorer teaching aplet.............................................................167
Objectives...................................................................................................................167
SIN vs. COS ............................................................................................................... 167
SYMB vs. GRPH mode ..............................................................................................167
Using Matrices on the hp 39g+................................................................170
The MATRIX Catalog ................................................................................................ 170
Matrix calculations in the HOME view ..........................................................................171
Solving a system of equations....................................................................................172
Finding an inverse matrix ........................................................................................... 174
The dot product ..........................................................................................................175
Using Lists on the hp 39g+......................................................................176
The list variables ........................................................................................................176
Operations on lists...................................................................................................... 176
Statistical columns as lists.......................................................................................... 176
List functions...............................................................................................................177
Editing a list ................................................................................................................ 177
Operations on elements .............................................................................................177
Using the Notepad Catalog......................................................................178
Aplet notes vs. independent notes ............................................................................. 178
Independent Notes and the Notepad Catalog..........................................................179
Transferring notes using IR ........................................................................................180
Editing software..........................................................................................................180
Software .........................................................................................................................181
For the hp 38g, hp 39g & hp 40g................................................................................181
For the hp 39g+ ..........................................................................................................181
Creating a Note..............................................................................................................182
Locking ALPHA mode ................................................................................................. 182
The CHARS view .........................................................................................................183
Corrupting notes.........................................................................................................183
Using the aplet Sketchpad.......................................................................184
Adding text to a sketch ............................................................................................... 184
The DRAW menu ...........................................................................................................185
DOT+..........................................................................................................................185
LINE............................................................................................................................185
BOX ............................................................................................................................185
CIRCLE ......................................................................................................................186
Cut and paste (sort of…)............................................................................................186
Capturing the PLOT screen ....................................................................................... 187
6
Using, Copying & Creating aplets...........................................................189
Creating a copy of a Standard aplet............................................................................190
Copying and adding to the Function aplet.................................................................. 190
Copying and adding to the Stats aplet ....................................................................... 191
Some examples of saved aplets..................................................................................192
The Triangles aplet..................................................................................................... 192
The Prob. Distributions aplet......................................................................................192
The Transformer aplet................................................................................................194
Copying from hp 39g+ to hp 39g+ via the infra-red link............................................197
The infra-red port........................................................................................................ 197
Time out...................................................................................................................... 199
Attached programs ..................................................................................................... 199
Downloading aplets from the Internet.........................................................................200
Finding aplets ............................................................................................................. 200
Organizing your collection ..........................................................................................201
Software for the hp 38g, hp 39g & hp 40g .................................................................202
Software for the hp 39g+............................................................................................203
The HPGComm Connectivity Program ......................................................................204
Deleting downloaded aplets from the calculator ........................................................207
Saving notes, aplets and sketches via the Connectivity Kit ....................................... 208
Capturing screens using the Connectivity Kit............................................................. 210
Editing Notes with the Aplet Development Kit............................................................211
Programming the hp 39g+ .......................................................................212
The design process.......................................................................................................212
An overview................................................................................................................212
Choosing the parent aplet .......................................................................................... 212
Naming conventions...................................................................................................213
Planning the VIEWS menu..........................................................................................214
The SETVIEWS command .......................................................................................... 214
Special entries in the SETVIEWS command...............................................................216
The ‘Start’ entry .......................................................................................................... 217
Example aplet #1........................................................................................................ 217
Example aplet #2........................................................................................................ 222
Example aplet #3........................................................................................................ 224
Example aplet #4........................................................................................................ 226
Programming Commands........................................................................233
The Aplet commands....................................................................................................233
CHECK & UNCHECK................................................................................................ 233
SELECT...................................................................................................................... 233
SETVIEWS.................................................................................................................234
The Branch commands.................................................................................................234
IF THEN [ELSE] END............................................................................................... 234
CASE..........................................................................................................................234
IFFERR THEN [ELSE] END......................................................................................234
RUN............................................................................................................................235
STOP..........................................................................................................................235
The Drawing commands...............................................................................................235
ARC ............................................................................................................................235
BOX ............................................................................................................................235
ERASE .......................................................................................................................236
FREEZE .....................................................................................................................236
LINE............................................................................................................................236
PIXON and PIXOFF .................................................................................................. 236
TLINE .........................................................................................................................236
7
The Graphics commands .............................................................................................237
The Loop commands ....................................................................................................237
FOR <var> = <start> TO <end> [STEP] <statements> END ..................................... 237
DO UNTIL................................................................................................................... 237
WHILE REPEAT......................................................................................................... 237
BREAK .......................................................................................................................238
The Matrix commands...................................................................................................238
EDITMAT....................................................................................................................238
REDIM ........................................................................................................................238
The Print commands.....................................................................................................239
PRDISPLAY ...............................................................................................................239
PRHISTORY...............................................................................................................239
PRVAR ....................................................................................................................... 239
The Prompt commands.................................................................................................240
BEEP ..........................................................................................................................240
CHOOSE …. ..............................................................................................................240
DISP ........................................................................................................................... 241
DISPXY ......................................................................................................................241
DISPTIME................................................................................................................... 241
GETKEY .....................................................................................................................241
INPUT.........................................................................................................................242
MSGBOX.................................................................................................................... 242
PROMPT .................................................................................................................... 242
WAIT........................................................................................................................... 242
The MATH menu functions......................................................................243
The ‘Real’ group of functions.......................................................................................246
CEILING ..................................................................................................................... 246
DEG RAD ................................................................................................................ 246
FLOOR ....................................................................................................................... 246
FNROOT ....................................................................................................................247
FRAC..........................................................................................................................247
HMS ........................................................................................................................248
HMS........................................................................................................................248
INT..............................................................................................................................249
MANT .........................................................................................................................249
MAX............................................................................................................................249
MIN .............................................................................................................................250
MOD ........................................................................................................................... 250
% ................................................................................................................................250
%CHANGE.................................................................................................................251
%TOTAL.....................................................................................................................251
RAD DEG ................................................................................................................ 251
ROUND ......................................................................................................................252
SIGN...........................................................................................................................252
TRUNCATE................................................................................................................253
XPON .........................................................................................................................253
The ‘Stat-Two’ group of functions...............................................................................254
PREDY ....................................................................................................................... 254
PREDX ....................................................................................................................... 254
The ‘Symbolic’ group of functions..............................................................................255
The = ‘function’ ...........................................................................................................255
ISOLATE ....................................................................................................................255
LINEAR?..................................................................................................................... 256
QUAD ......................................................................................................................... 256
QUOTE.......................................................................................................................257
The | function..........................................................................................................258
8
The ‘Tests’ group of functions.....................................................................................259
The ‘Trigonometric’ & ‘Hyperbolic’ groups of functions...........................................259
COT, SEC etc............................................................................................................. 259
EXP ............................................................................................................................260
ALOG.......................................................................................................................... 260
EXPM1 .......................................................................................................................260
LNP1...........................................................................................................................261
The ‘Calculus’ group of functions...............................................................................261
The ‘Complex’ group of functions...............................................................................262
ABS ............................................................................................................................263
SIGN...........................................................................................................................263
ARG............................................................................................................................264
CONJ..........................................................................................................................264
IM & RE ...................................................................................................................... 264
The ‘List’ group of functions........................................................................................265
CONCAT ....................................................................................................................265
∆LIST..........................................................................................................................266
MAKELIST..................................................................................................................266
πLIST ..........................................................................................................................267
POS ............................................................................................................................267
SIZE............................................................................................................................ 268
ΣLIST..........................................................................................................................268
REVERSE ..................................................................................................................268
SORT.......................................................................................................................... 268
The ‘Loop’ group of functions .....................................................................................269
ITERATE ....................................................................................................................269
RECURSE..................................................................................................................270
Σ (SUMMATION)........................................................................................................270
The ‘Matrix’ group of functions....................................................................................271
COLNORM ................................................................................................................. 271
COND .........................................................................................................................271
CROSS.......................................................................................................................271
DET ............................................................................................................................272
DOT ............................................................................................................................272
EIGENVAL..................................................................................................................272
EIGENVV.................................................................................................................... 272
IDENTMAT ................................................................................................................. 272
INVERSE.................................................................................................................... 273
LQ...............................................................................................................................273
LSQ ............................................................................................................................274
LU ...............................................................................................................................274
MAKEMAT..................................................................................................................274
QR .............................................................................................................................. 274
RANK.......................................................................................................................... 274
ROWNORM................................................................................................................ 274
RREF..........................................................................................................................274
SCHUR.......................................................................................................................275
SIZE............................................................................................................................ 275
SPECNORM............................................................................................................... 275
SPECRAD .................................................................................................................. 275
SVD ............................................................................................................................ 275
SVL.............................................................................................................................275
TRACE .......................................................................................................................276
TRN ............................................................................................................................ 276
9
The ‘Polynomial’ group of functions...........................................................................277
POLYCOEF................................................................................................................277
POLYEVAL................................................................................................................. 277
POLYFORM ...............................................................................................................278
POLYROOT................................................................................................................279
The ‘Probability’ group of functions............................................................................280
COMB.........................................................................................................................280
The ! function.............................................................................................................. 280
PERM ......................................................................................................................... 281
RANDOM....................................................................................................................281
RANDSEED................................................................................................................281
UTPN..........................................................................................................................282
UTPC..........................................................................................................................283
UTPF .......................................................................................................................... 283
UTPT .......................................................................................................................... 283
Appendix A: Worked Examples...............................................................284
Finding the intercepts of a quadratic..........................................................................284
Method 1 - Using the QUAD function in HOME. ............................................................284
Method 2 - Using the Function aplet. ......................................................................... 284
Method 3 - Using the POLYROOT function..................................................................285
Finding complex solutions to a complex equation....................................................285
Method 1 - Using the QUAD function.........................................................................285
Method 2 - Using POLYROOT...................................................................................285
Finding critical points and graphing a polynomial....................................................286
Solving simultaneous equations.................................................................................288
Method 1 - Graphing the lines....................................................................................288
Second method - using a matrix.................................................................................288
Third method - using the 3x3 Solver aplet ................................................................289
Expanding polynomials................................................................................................290
Exponential growth.......................................................................................................291
Solution of matrix equations........................................................................................293
Inconsistent systems of equations .............................................................................294
Using the RREF function............................................................................................294
Finding complex roots..................................................................................................295
Analyzing vector motion and collisions......................................................................296
Circular Motion and the Dot Product...........................................................................297
Inference testing using the Chi2 test...........................................................................299
Appendix B: Teaching Calculus with an hp 39g+..................................301
Investigating
Domains and Composite Functions............................................................................302
Gradient at a Point.........................................................................................................303
Gradient Function..........................................................................................................304
The Chain Rule ..............................................................................................................305
Optimization...................................................................................................................305
Area Under Curves........................................................................................................306
Fields of Slopes and Curve Families...........................................................................306
Inequalities.....................................................................................................................307
Rectilinear Motion .........................................................................................................307
Limits..............................................................................................................................307
Piecewise Defined Functions.......................................................................................308
Sequences and Series ..................................................................................................308
Transformations of Graphs..........................................................................................309
n
yx= for n an integer..........................................................................301
10
Appendix C: The hp 40g & its CAS .........................................................310
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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.
© Copyright 1993-1998, 2005 Hewlett-Packard Development Company, L.P.
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
Acknowledgements
Hewlett-Packard would like to thank the author Colin Croft.
Printing History
Edition 1 February 2004
Edition 2 September 2005
Notice
Introduction....................................................................................................................310
What is a CAS? .......................................................................................................... 310
What is the difference between the hp 39g, hp 40g & hp 39g+? ...............................312
Using the CAS................................................................................................................313
Entering and editing an expression............................................................................313
In-line editing mode .................................................................................................... 316
Erasing, copying, cutting and pasting ........................................................................316
Cursor mode............................................................................................................... 317
The CAS HOME History.............................................................................................317
The PUSH and POP commands................................................................................318
Pasting to an aplet...................................................................................................... 319
Evaluating algebraic expressions............................................................................... 320
Using functions in the CAS..........................................................................................321
E.g. 1 Using LIMIT.................................................................................................... 321
E.g. 2 Factorizing expressions ................................................................................. 322
E.g. 3 Solving equations........................................................................................... 323
E.g. 4 Solving simultaneous equations ....................................................................323
E.g. 5 Solving a simultaneous integration ................................................................ 325
E.g. 6 Defining a user function ................................................................................. 327
On-line help....................................................................................................................328
Configuring the CAS.....................................................................................................329
Tips & Tricks - CAS.......................................................................................................330
11
I
NNTTRROODDUUCCTTIIOON
I
This booklet is intended to help you to master your hp 39g+ calculator but is
also aimed at users of the hp 39g and hp 40g. These are very sophisticated
calculators, having more capabilities than a mainframe computer of the ’70s,
so don’t expect to come to grips with its abilities in one or two sessions.
However, if you persevere you will gain efficiency and confidence.
The majority of readers may only have used a Scientific calculator before so
explanations are as complete as possible. However it is not the purpose of
this book to teach mathematics so knowledge will be assumed. Those who
are already familiar with another brand or type, may find that a quick skim is
sufficient, perhaps with detailed reading of the “Tips and Tricks” sections.
The impact these calculators are having on the topics taught and even more,
the way they are taught is proving to be profound. The inventiveness and
flexibility of teachers of mathematics is being stretched to the limit as we
gradually change the face of teaching in the light of these machines.
N
For those concerned with the impact of a graphical calculator on the
‘fundamentals’ of mathematics, it should be recalled that the same fears were
held for scientific calculators when they were introduced earlier. History has
shown that these fears were generally groundless. Students are learning
topics in high school that their parents did not cover until university years. In
particular, the scientific calculator proved to be a great boon to students of
middle to lower ability in mathematics, relieving them of the burden of tedious
calculations and allowing them to concentrate on the concepts. This is also
the case with graphical calculators.
This manual is not intended to replace the one supplied with the calculator. It
fills in the holes, and also provides tips to make your work smother and more
confident. Happy calculating.
About the author
Colin Croft is a teacher at St. Hilda’s Anglican School for Girls in Perth,
Western Australia. Colin has worked extensively with Hewlett Packard on the
graphic calculator family of which the hp 39g+ is a member, and was part of
the team which created the hp 39g & hp 40g in 2000. He maintains an
extensive website of material for the hp 39g/40g/39g+ series called The HP
Home view, at http://www.hphomeview.com.
12
H
OOWW TTOO UUSSEE TTHHIISS
H
It has been attempted to design this manual to cover the full use of the
hp 39g+ calculator. This means explanations which will be useful to anyone
from a student who is just beginning to use algebra seriously, to one who is
coming to grips with advanced calculus, and also to a teacher who is already
familiar with some other brand of graphic calculator.
Readers may encounter one of two difficulties. Firstly, the information in here
will be beyond the needs of some readers and secondly, the explanations
may be too detailed for more advanced users.
For students who don’t yet need the more advanced capabilities, suggestions
on which parts of the manual to read are given below. For more advanced
users, it is suggested that you read the sections on the Function, Sequence,
Statistics, Inference, Finance and Solve aplets, and also read the ‘Tips and
Tricks’ sections which follow many of the chapters.
M
AANNUUAAL
M
L
Early High School
Typical topics covered include…
Solving linear equations, graphing linear equations and possibly
simple quadratics, examining number patterns, multiplying
polynomials, factoring simple polynomials, calculations involving
powers (
positives and negatives, scientific notation, indices, systems of
equations and inequalities, parallel and perpendicular lines, dividing
polynomials, solving quadratics, rational expressions and equations.
Suggestions…
Read about the Function aplet in full, ignoring any sections that seem
to advanced. Learn about Intersection and Root in the menu
and make sure you know how the menu, Autoscale and PLOT
SETUP work. Learn to Build Your Own in the NUM view because it
lets you find values for rules easily. Learn to use the HOME view for
routine calculations, the MODES view, and how to use the calculator’s
memories. Read about the Solve aplet and how to use it to solve
equations. Read about the Statistics aplet and how to use it to find
23
, ,......xx ), square roots, cube roots, order of operations,
13
means and to display histograms. In the MATH menu, read about the
functions ROUND, POLYFORM and POLYROOT. Make sure you
know how to save and transfer aplets. Learn about the Sketch view
and the Notes catalog for a bit of fun.
Pre-Calculus
Typical topics covered include…
Solving complex linear and non-linear simultaneous equations, and
trig, exponential & complex quadratic equations, factoring of any
quadratic, use and re-arrangement of formulas, indices, trigonometry,
some statistics, absolute value and greatest integer functions,
matrices, logarithms and parametric equations.
Suggestions…
Cover all of the material mentioned for high school students. Read the
suggestions on how to deal with graphs whose shape you don’t know
in advance. Learn how to use the Parametric aplet. Your teacher
might best advise on which portions of the Statistics aplet will be
relevant to you. In the MATH menu, also learn about functions
CEILING, ABS and FLOOR, POLYCOEF, and POLYEVAL. Read the
section covering the Matrices catalog and the functions DET, RREF,
INVERSE, and TRN.
Calculus
Topics covered here will vary according to which course students undertake
but there are very few skills covered in this manual which will not be of use at
some time. It is suggested that students skim the whole manual, and then
re-read it at intervals as material is covered in their courses and they begin to
see which parts of the manual are particularly relevant.
14
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Let’s begin by looking at the fundamentals - the layout of the keyboard and
which are the important keys that are used frequently. The sketch below
shows most of the important keys. These are the ones which control the
operation of the calculator - others are used to do calculations once the
important keys have set up the environment to do it in.
The NUM key gives you a
tabular view of your
function, sequence or data.
The PLOT key displays the
graph view for any given
environment.
These six screen keys change their
function in different contexts. The
bar at the bottom of the screen labels
them. Check this bar for special
functions in an
These are the cursor (or
arrow) keys. They let you
move within a window.
iven context.
The SYMB key nearly
always takes you to a
view in which you can
The VIEWS key gives a
different menu in each aplet.
It can be very useful, and is
always worth checking.
HOME is where you will do
most of your calculations. It
is shared by all the aplets
and oversees them all.
The APLET key is central.
This key allows you to choose
which mathematical
environment you wish to
working.
So where is the ON button?
Examples of the effects of each of these keys and many more are shown on
the pages that follow.
15
S
OOMMEE
S
Shown below are snapshots of some typical screens you might see when
you press each of the keys shown on the previous page. Exactly what you
see depends on which aplet is active at the time.
The aplet used below to illustrate this is the Function aplet, which is used to
graph and analyze Cartesian functions. Notice how the meanings of the row
of blank screen keys under the screen changes in different views.
The SYMB key - in this case it is set to graph
K
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the function
E
XXAAMMPPLLEES
E
32
76yx x x=−−+.
The PLOT key - used to graph the function.
S
The NUM key showing a tabular view of the
function.
The MATH key gives access to more than a
hundred extra functions, grouped by category.
The view shown right is currently showing the
Probability section.
The APLET key is used to choose which aplet
is active. There are 10 aplets provided with
the calculator and more can be downloaded
from the internet.
16
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There are a number of types of keys/buttons that are used on the hp 39g+.
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The basic keys are those that you see on any
calculator including scientific ones, such as the
numeric operators and the trig keys. Most of these
keys have two or more functions.
All references to keys, whether they need the SHIFT key or not, are written in
this typeface: KEY.
The SHIFT key
The SHIFT key gives you the second function for each
key. In the case of the COS key, the second function is
ACOS, sometimes referred to as arc-cos or cos-1 or
inverse cos. Most keys have these second functions that
are obtained via the SHIFT key.
When I want you to use one of these keys that needs to
have the SHIFT key pressed first I usually won’t say so.
It seems to me that you’re intelligent enough to work out
for yourself when the SHIFT key needs to be pressed.
Take for example the COS key shown left. If
you just press the key, you get the COS function.
However above left of the key and below right
you will see two additional meanings assigned
via the SHIFT and ALPHA keys.
17
The ALPHA key
The next modifier key is the ALPHA key. This is used to type alphabetic
characters, and these appear in orange just below most keys.
The Screen keys
A special type of key unique to the hp 39g+ and family is the row of blank
keys directly under the screen. These keys change their function depending
on what you are doing at the time. The easiest
way to see this is to press the APLET key. As
you can see right, the functions are listed at
the bottom of the screen. All you have to is to
press the key under the screen definition you
want to use.
All references to keys of this type are shown
as images of the label. For example, if I want
you to press the key under the SORT label it
would be written as . Do it now and you’ll
see the screen shown on the right. Notice that
the keys have now changed function. Press
the one under .
Pop-up menus & short-cuts
Sometimes pressing a key pops up a menu on the screen as you just saw.
You use the up/down arrow keys to move the highlight through the menu and
make choices by pressing the ENTER key. Choices that are listed in a menu
will usually be written using italics. As an example, I might say to press
and choose Chronologically. The manual you are given with your calculator
uses a different convention.
As mentioned before, the third way a key can be used is to get letters of the
alphabet. This is not so that you can write letters to your friends (although
you can do that with the Notepad) but so that you can use variables like X
and Y or A and B. The key above the SHIFT key labeled ALPHA is used
to type in letters of the alphabet. Lower case letters are obtained by pressing
the SHIFT key before the ALPHA key. If you want to type in more than just a
single letter, hold down the ALPHA key. Unfortunately, this doesn't work for
lowercase.
18
Try this…
If you haven’t already, out of the menu from the
previous screen. Press the HOME key to see the
screen on the right. Yours may not be blank like mine
but that doesn’t matter.
Press 12 and then press the screen key labeled
. Now press the ALPHA key and then the
alphabetic D key (on the XTθ key). Finally, press the
ENTER key. Your screen should look like mine on the
right. You have now stored the value 12 into memory
D. Each alpha key can be used as a memory.
You can also use these memories in calculations.
Type in the following (not forgetting the ALPHA key
before the D)…. (3+D)/5 ENTER
The calculator will use the value of 12 stored earlier in
D to evaluate the expression (see right). In case you
haven’t worked it out for yourself, the / symbol
comes from the divide key ( ) and the * symbol from the multiply key.
More information on memories and detailed information on the HOME view in
general is given on pages 45.
The calculator also comes with a large number of mathematical functions that
are very useful. They can all be obtained via menus
through the MATH key. Try pressing the MATH key now
and you should find your screen looks like the screen
shot on the right.
The MATH menu is covered in detail on pages 243 but
we will have a brief look now.
The left side of the menu lists the categories of
functions. As you use the up/down arrows to scroll
through the topics, you’ll see the actual list on the right
change. Move down through the menu until you reach
Prob. (short for Probability) and then one step more
and you’ll find yourself back at Real. Now press the
right arrow key and your highlight will move into the
right hand menu (see above). Move the highlight down through this menu
until you reach Round. Press ENTER.
19
You should now be back HOME, with the function
ROUND( entered in the display as shown right. You
can also achieve the same effect by using ALPHA to
type in the word letter by letter. Some people prefer
to do it that way.
Now type in: 4+D/18,3) and press ENTER
As you can see, the effect was to round off the answer
of 4.666666.. to 3 decimal places.
There are shortcuts for obtaining things from the MATH
menu that are covered later (see page 47).
20
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A set of “aplets” is provided in the APLET view on the hp 39g+. This
effectively mean that it is not just one calculator but nine (or more), changing
capabilities according to which aplet is chosen.
The best way to think of these aplets is as “environments” or “rooms” within
which you can work. Although these environments may seem dissimilar at
first, they all have things in common, such as that the PLOT key produces
graphs, that the SYMB key puts you into a screen used to enter equations and
rules, and that the NUM key displays the information in tabular form.
There are ten standard aplets available via the APLET key. More can be
created by you or obtained via the Internet (see pages 212 & 200)
A
PPLLEETTS
A
S
!
!
The Function aplet (see page 51)
Provides f(x) style graphs, calculus functions etc. It will not only
graph but find intercepts, intersections, areas and turning
points.
The Inference aplet (see page 150)
Allows the investigation of inferential statistics via hypothesis
testing and confidence intervals. This was not available on the
hp 38g, the original calculator upon which the hp 39g+ was
based.
The Parametric aplet (see page 100)
Handles x(t), y(t) style graphs. Can also be used to help with
vector motion.
The Finance aplet (see page 160)
Performs calculations involving time/value of money.
The Polar aplet (see page 106)
Handles r(θ) style graphs. Quite apart from their mathematical
use, they produce some really lovely patterns!
21
The Quadratic Explorer aplet (see page 164)
=
This is a teaching aplet, allowing the student to investigate the
properties of quadratic graphs.
The Sequence aplet (see page 107)
Handles sequences such as
23;2
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+= or
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−
T−= .
n
Allows you to explore recursive and non-recursive sequences.
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The Solve aplet (see page 113)
Solves equations for you. Given an equation such as
2Arrh
π
=+ it will solve for any variable if you tell it the
()
values of the others.
The Statistics aplet (see page 122 & 132)
Handles descriptive statistics really well. Data entry is easy, as
is editing. It analyzes univariate and bivariate data, drawing
scatter graphs, histograms and box & whisker graphs.
The Trig Explorer aplet (see page 167)
This is a teaching aplet, allowing the student to investigate the
properties of sine and cosine graphs.
The Function aplet is probably the easiest to understand and also the one
you will use most often, so we will have a very quick look at this aplet.
Some typical aplet views
The APLET key is used to list all the aplets and start,
reset or save them.
The SYMB view is used to enter equations….
It can store up to ten functions.
The NUM view shows the function in table form…
22
The PLOT view is used to display the function as a
graph…
The key gives access to a number of other
useful tools allowing further analysis of the function.
Although these views are superficially different in other aplets, the basic idea
is usually similar.
Having said that aplets are best thought of as “working environments”, it is
equally true that aplets are essentially programs, with the standard ones
simply being built into the calculator. This is a programmable calculator,
having its own programming language and able to perform quite
sophisticated tasks.
Unless you particularly want to learn about the programming language, there
is no reason why you should worry about it. The standard aplets will cover all
of your normal requirements in mathematics.
However one of the great strengths of the hp 39g+ is its ability to “download”
additional aplets from other calculators, from a PC or Mac and from the
Internet. See page 200.
A cable and software were provided with your hp 39g+ which you can use to
connect your PC or Mac to your calculator and then download aplets from the
computer to the calculator or to save your work to the computer. If you have
an hp 38g, hp 39g or hp 40g then you need to buy the cable separately.
If you are using an hp 39g+ then the cable connects to the USB port on your
computer. If you are using an hp 39g or an hp 40g then you will need to
purchase the cable and download the software from Hewlett-Packard’s
website.
More information on this can be found on pages 200 - 226.
Calculator Tip
Search on the web using the key word “hp 39g” and you
will find a variety of sites which contain information and
aplets.
23
Once an aplet is transferred onto any one calculator, transferring it to another
takes only seconds using the built in infra-red link at the top of each
calculator. This is exactly like the remote control of a VCR, and allows two
calculators to talk to each other. In the interests of security in examinations
the distance over which they can communicate is limited to about 8 - 10cm
(about 3 - 4 inches). See page 197 for details on this process.
Aplets are available to do many mathematical tasks such as statistical
simulations, time series analysis and many tasks called for in calculus,
physics and chemistry. There are a number of web sites which offer aplets.
The Hewlett-Packard site is found at…
http://www.hp.com/calculators/
(follow the links to graphical calculators and then to the library
of aplets)
In addition to this you should check the site called The HP HOME view which
can be found at…
http://www.hphomeview.com
(contains not only aplets and games, but also a huge amount of
detailed information on the calculator.)
Calculator Tip
The aplets for an hp 39g, hp 40g and hp 39g+ are
interchangeable but not those of an hp 38g. If you load an
aplet from an hp 38g onto an older model then the
download will appear to be successful but the calculator
will “crash” when the aplet is run.
The entire topic of aplets is discussed in more detail in the chapter entitled
“Using, copying & creating aplets” on page 189.
24
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In addition to these aplets, there is also the HOME view, which can best be
thought of as a scratch pad for all the others. This is accessed via the HOME
key (just below the APLET key) and is the view in which you will do your
routine calculations such as working out 5% of $85, or finding √35. The
HOME view is the view that you will most often use, so we will explore that
view first.
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This is the HOME base for the calculator. All other
aplets can be accessed from it and affect it to varying
degrees, and all mathematical functions are available
in this view. Learn to use this view as efficiently as
possible, since a great deal of work will be done here.
We will explore the HOME view in the following order:
1. Exploring the Keyboard
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2. Angle and numeric settings
3. Memory management
4. Fractions on the hp 39g+
5. The HOME History
6. Storing and retrieving memories
7. Referring to other aplets from the HOME view
8. An introduction to the MATH menu
9. Resetting the calculator
25
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It is worth familiarizing yourself with the mathematical functions available on
the keyboard. If we examine them row by row, you will see that they tend to
fall into two categories - those which are specific to the use of aplets, and
those which are commonly used in mathematical calculations.
The screen keys
The first row of blank keys are context defined. The
reason they have no label is that their meaning is
redefined in different situations - they are the
‘screen keys’. The current meaning of each key is
listed in the row of boxes at the bottom of the
screen.
A common abbreviation used for these keys is SK1
or SK2 etc (for “screen key 1” ). In the PLOT view
shown above, some of the screen keys are labeled,
such as the key. When you press this the row of screen keys labels
appear or disappear. To see another view where all the keys are in use,
change to the APLET view.
Calculator Tip
Develop the habit of checking the screen to see if any of
those keys have been given meanings. In many views, the
screen keys have been set up with useful shortcuts and
functions.
Aplet related keys
The next two rows of keys and part of the
third are mainly aplet related, so we’ll deal
with them as a group.
The arrow keys
The arrow keys on the right are used in
most views, usually to move the cursor (a
small cross) or the highlight around on the
screen.
26
The APLET key is used to choose between the
various different aplets available. Everything in the
calculator revolves around aplets, which you can
think of either as miniature programs or as
environments within
which you can work.
The hp 39g+ comes with ten standard aplets -
Finance, Function, Inference, Parametric,
Polar, Quadratic Explorer, Sequence, Solve,
Statistics and Trig Explorer. Which one you
want to work with is chosen via the APLET key.
Calculator Tip
The name of the active aplet is shown at the top of the
screen, as above. It is important to bear this in mind
because the angle and numeric settings are tied to the
active aplet. Changing aplets may therefore cause these
settings to change in HOME too.
See page 35 for more details on this.
In addition to the standard ten, covered in great detail in the chapters
following, many more aplets are available from the Internet written by other
programmers. Once these are downloaded into your calculator they can also
be accessed via the APLET key. For more detail on this type of aplet, see
the brief summary later in this section, and the chapter entitled “Programming
the hp 39g+” on page 212.
The
SYMB, PLOT
and
NUM
keys
The SYMB, PLOT and NUM keys are used within aplets to
move from view to view. In most aplets the PLOT view
shows the graph, the SYMB view shows the equations and
the NUM view shows the equations in tabular (numeric)
format.
The VIEWS key pops up a menu from which you can
choose various options. Part of the VIEWS menu for
the Function aplet is shown right. See page 92 for
more information.
27
The VIEWS menu is provided for two purposes…
Intro to the
VIEWS
menu
Firstly, within the standard aplets (Function, Sequence, Solve etc.) it provides
a list of special views available to enhance the PLOT view.
For example the standard PLOT screen provides a
graph, but the VIEWS menu lets you use a split screen
such as shown right. Information on the VIEWS menu
is given in the chapter dealing with the Function aplet.
In addition to this, the VIEWS key also has a critical role when using aplets
which have been downloaded from the Internet. When a programmed aplet
is created for the hp 39g+, a menu is provided by the programmer to let you
control and use it. This menu is tied to the VIEWS key,
replacing the menu normally found on the key. For
example, the snapshot shown right is of a VIEWS
menu taken from an aplet designed to analyze and
graph Time Series data.
The next important key is the HOME key. It allows you
to change into the HOME view from wherever you are.
Above it is the MODES key, accessed by pressing
SHIFT first. Far more detailed information on these
two views follows later.
The
VARS
key
The VARS key is used (mainly by programmers) to
access all the different variables stored by the
calculator.
Shown right are two views of the VARS screen, the first
from the HOME list showing the graphic variables
(memories) G1, G2…. and the next from the APLET
list showing some of the variables in the set controlling
PLOT.
The VARS key is not generally used much, and you may not have followed
this explanation. Don’t worry. The VARS key is mostly used by programmers
who want to produce aplets of their own and is discussed in more detail in
the chapter entitled “Programming on the hp 39g+” on page 212. Uses are
also detailed in the Function aplet’s “Tips and Tricks” section on page 69.
28
The MATH key next to VARS provides access to a
library of mathematical functions. The more
common functions have keys of their own, but there
is a limit to the number of keys that one can put on a
calculator before it takes too long to find the key
required.
The MATH menu lists all those functions that would not fit onto the keyboard
plus some which also appear on the keyboard. Shown in the screen
snapshot above is a small selection of the total list. For a listing of almost all
the functions, with examples of their use, see the chapter entitled “The MATH
Menu” on page 243.
Most of the keys have another function in light blue above the
key. The hp 39g+ gets twice the action from each key by
having this second function.
The second function is accessed via the SHIFT key on the left side of
the calculator. Although this book will sometimes tell you explicitly to press
this key, in most cases it will be assumed that you are intelligent enough to
work out for yourself when it is necessary to press it.
The ALPHA key gives alphabetical characters, shown below right of
most keys. Pressing SHIFT ALPHA gives lower case. If you press
and hold down the ALPHA key you can ‘lock’ alpha mode but this
doesn’t work for lower case. Many people use this to type in
functions by hand rather than using the MATH menu.
Calculator Tip
You can use the ALPHA button to type in functions by
hand instead of going through the MATH menu. This is
often faster.
29
The
SETUP
views
The SETUP views, above PLOT, SYMB and NUM,
are used to customize their respective views. For
example, the PLOT SETUP screen controls things
like axes, labels etc. Their use changes in
different aplets, so for more information see the
explanations in the chapters dealing with the various aplets, particularly with
the Function aplet on page 55.
In particular, the SYMB SETUP key is only used in one place, which is to
choose the data model for bivariate statistics in the Statistics aplet. It is not
available in the other aplets and trying to access it will result only in a quick
flash of an exclamation mark on the screen to say “You’ve done something
wrong!”.
Information on the use of the SKETCH and NOTE keys
(above APLET and VEIWS) can be found in the
chapters “Using the Sketchpad” and “Using the Notepad Catalog” on pages
184 & 178. Briefly, any aplet (except for the Quad & Trig Explorer aplets)
has a note and a sketch associated with it, which are usually blank unless
you have added to them.
The main use for them comes with aplets downloaded from the Internet.
Instructions for using the aplet are sometimes included with the aplet in note
form, and sometimes as an accompanying sketch.
The
MODES
view
The MODES view (see right) controls the
numeric format used in displaying numbers
and angles in aplets. At the bottom of the
screen you will see that one of the screen keys
has been given the function
. Pressing
this key pops up a menu of choices from which
you can select the option which suits you. The
default angle setting is radians.
Calculator Tip
If you don’t want to use the menu then, rather than
pressing , highlight the field and then press the ‘+’
key repeatedly. This will cycle through the choices without
popping up a menu. This can be much faster if the menu
has only a few choices.
30
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