Hp Prime User Manual

HP Prime Graphing Calculator
© Copyright 2015–2017 HP Development Company, L.P.
The information contained herein is subject to change without notice. The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services. Nothing herein should be construed as constituting an additional warranty. HP shall not be liable for technical or editorial errors or omissions contained herein.
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this product.
Third Edition: December 2017
First Edition: July 2015
Document Part Number: 813269-003
Table of contents
1 Preface ......................................................................................................................................................... 1
Manual conventions ............................................................................................................................................... 1
2 Getting started ............................................................................................................................................. 2
Before starting ....................................................................................................................................................... 2
On/o, cancel operations ...................................................................................................................................... 3
To turn on ............................................................................................................................................. 3
To cancel .............................................................................................................................................. 3
To turn o ............................................................................................................................................ 3
The Home View .................................................................................................................................... 3
The CAS View ....................................................................................................................................... 3
Protective cover ................................................................................................................................... 3
The display ............................................................................................................................................................. 4
Adjusting the brightness ..................................................................................................................... 4
Clearing the display ............................................................................................................................. 4
Sections of the display ........................................................................................................................ 4
The Quick Settings menu .................................................................................................................... 5
Navigation .............................................................................................................................................................. 6
Touch gestures .................................................................................................................................... 7
The keyboard ....................................................................................................................................... 7
Context-sensitive menu ...................................................................................................................... 8
Entry and edit keys ................................................................................................................................................ 9
Shift keys ........................................................................................................................................... 10
Adding text ........................................................................................................................................ 11
Math keys .......................................................................................................................................... 11
Math template ................................................................................................................. 13
Math shortcuts ................................................................................................................ 14
Fractions ......................................................................................................................... 15
Hexagesimal numbers .................................................................................................... 15
EEX key (powers of 10) ................................................................................................... 16
Menus ................................................................................................................................................................... 17
Selecting from a menu ...................................................................................................................... 17
Shortcuts ........................................................................................................................................... 18
Closing a menu .................................................................................................................................. 18
Toolbox menus .................................................................................................................................. 18
Input forms .......................................................................................................................................................... 18
iii
Resetting input form elds ............................................................................................................... 19
System-wide settings .......................................................................................................................................... 19
Home settings ................................................................................................................................... 20
Page 1 .............................................................................................................................. 20
Page 2 .............................................................................................................................. 21
Page 3 .............................................................................................................................. 21
Page 4 .............................................................................................................................. 22
Specifying a Home setting .............................................................................................. 22
Mathematical calculations .................................................................................................................................. 23
Where to start ................................................................................................................................... 24
Choosing an entry type ..................................................................................................................... 24
Entering expressions ......................................................................................................................... 24
Example .......................................................................................................................... 25
Parentheses .................................................................................................................... 25
Algebraic precedence ................................................................................... 26
Negative numbers ........................................................................................................... 26
Explicit and implied multiplication ................................................................................. 26
Large results ................................................................................................................... 27
Reusing previous expressions and results ....................................................................................... 27
Using the clipboard ......................................................................................................... 27
Reusing the last result .................................................................................................... 28
Reusing an expression or result from the CAS ............................................................... 29
Storing value in a variable ................................................................................................................. 29
Complex numbers ................................................................................................................................................ 30
Copy and paste ..................................................................................................................................................... 31
Sharing data ......................................................................................................................................................... 33
General procedure ............................................................................................................................. 33
Using Memory Manager ....................................................................................................................................... 34
Backups catalog ................................................................................................................................ 34
Online help ........................................................................................................................................................... 36
3 Reverse Polish Notation (RPN) ...................................................................................................................... 38
History in RPN mode ............................................................................................................................................ 39
Reusing results .................................................................................................................................. 40
Sample calculations ............................................................................................................................................. 41
Manipulating the stack ........................................................................................................................................ 42
PICK .................................................................................................................................................... 43
ROLL ................................................................................................................................................... 43
Swap .................................................................................................................................................. 43
Stack .................................................................................................................................................. 43
DROPN ............................................................................................................................. 43
iv
DUPN ............................................................................................................................... 44
Echo ................................................................................................................................. 44
LIST .............................................................................................................................. 45
Show an item ..................................................................................................................................... 45
Delete an item ................................................................................................................................... 45
Delete all items .................................................................................................................................. 46
4 Computer algebra system (CAS) .................................................................................................................... 47
CAS view ............................................................................................................................................................... 47
CAS calculations ................................................................................................................................................... 48
Example 1 .......................................................................................................................................... 49
Example 2 .......................................................................................................................................... 50
Settings ................................................................................................................................................................ 50
Page 1 ................................................................................................................................................ 51
Page 2 ................................................................................................................................................ 52
Setting the form of menu items ........................................................................................................ 52
Using an expression or result from Home view ................................................................................ 52
Using a Home variable in CAS ............................................................................................................ 53
5 Exam Mode .................................................................................................................................................. 54
Using Basic Mode ................................................................................................................................................. 54
Modifying the default conguration ................................................................................................................... 55
Creating a new conguration .............................................................................................................................. 57
Activating exam mode ......................................................................................................................................... 58
Cancelling exam mode ...................................................................................................................... 60
Modifying congurations .................................................................................................................................... 60
Changing a conguration .................................................................................................................. 60
Returning to the default conguration ............................................................................................. 60
Deleting congurations ..................................................................................................................... 61
6 Introduction to HP apps ............................................................................................................................... 62
Application library ............................................................................................................................................... 63
Opening an app .................................................................................................................................. 63
Resetting an app ............................................................................................................................... 63
Sorting apps ...................................................................................................................................... 64
Deleting an app ................................................................................................................................. 64
Other options ..................................................................................................................................... 64
App views ............................................................................................................................................................. 64
Symbolic view .................................................................................................................................... 65
Symbolic Setup view ......................................................................................................................... 66
v
Plot view ............................................................................................................................................ 66
Plot Setup view .................................................................................................................................. 67
Numeric view ..................................................................................................................................... 67
Numeric Setup view ........................................................................................................................... 68
Quick example ................................................................................................................................... 68
Opening the app .............................................................................................................. 68
Symbolic view ................................................................................................................. 69
Symbolic Setup view ....................................................................................................... 70
Plot view .......................................................................................................................... 70
Plot Setup view ............................................................................................................... 71
Numeric view ................................................................................................................... 71
Numeric Setup view ........................................................................................................ 72
Common operations in Symbolic view ................................................................................................................ 72
Adding a denition ............................................................................................................................ 72
Modifying a denition ....................................................................................................................... 73
Denitional building blocks ............................................................................................................... 73
Evaluating a dependent denition .................................................................................................... 74
Selecting or deselecting a denition to explore ............................................................................... 75
Choosing a color for plots ................................................................................................................. 75
Deleting a denition .......................................................................................................................... 75
Symbolic view: Summary of menu buttons ...................................................................................... 76
Common operations in Symbolic Setup view ...................................................................................................... 77
Overriding system-wide settings ...................................................................................................... 77
Restoring default settings ................................................................................................................ 77
Common operations in Plot view ......................................................................................................................... 78
Zoom .................................................................................................................................................. 78
Zoom factors ................................................................................................................... 78
Zoom options .................................................................................................................. 79
Zoom gestures ................................................................................................................ 79
Zoom keys ....................................................................................................................... 79
Zoom menu ..................................................................................................................... 79
Box zoom ........................................................................................................................ 80
Views menu ..................................................................................................................... 81
Testing a zoom with split-screen viewing ...................................................................... 81
Zoom examples ............................................................................................................... 82
Zoom In ......................................................................................................... 83
Zoom Out ...................................................................................................... 83
X In ................................................................................................................ 84
X Out ............................................................................................................. 84
Y In ................................................................................................................ 85
Y Out ............................................................................................................. 86
vi
Square ........................................................................................................... 86
Autoscale ...................................................................................................... 87
Decimal ......................................................................................................... 88
Integer .......................................................................................................... 88
Trig ................................................................................................................ 89
Trace .................................................................................................................................................. 89
Selecting a plot ............................................................................................................... 89
Evaluating a function ...................................................................................................... 90
Turning tracing on or o ................................................................................................. 90
Plot view: Summary of menu buttons .............................................................................................. 91
Copy-and-paste operations in Plot view ........................................................................................... 91
Common operations in Plot Setup view .............................................................................................................. 91
Conguring Plot view ........................................................................................................................ 91
Page 1 .............................................................................................................................. 92
Page 2 .............................................................................................................................. 93
Page 3 .............................................................................................................................. 93
Graphing methods ............................................................................................................................. 94
Restoring default settings ................................................................................................................ 96
Common operations in Numeric view ................................................................................................................. 97
Zoom .................................................................................................................................................. 97
Zoom options .................................................................................................................. 98
Zoom gestures ................................................................................................................ 98
Zoom keys ....................................................................................................................... 98
Zoom menu ..................................................................................................................... 98
Evaluating .......................................................................................................................................... 99
Custom tables ................................................................................................................................. 100
Deleting data ................................................................................................................ 101
Copy and paste in Numeric view ..................................................................................................... 101
Copying and pasting a cell ............................................................................................ 101
Copying and pasting a row ............................................................................................ 101
Copying and pasting an array of cells ........................................................................... 102
Numeric view: Summary of menu buttons ..................................................................................... 102
More menu .................................................................................................................... 103
Common operations in Numeric Setup view ..................................................................................................... 103
Restoring default settings .............................................................................................................. 104
Combining Plot and Numeric Views ................................................................................................................... 104
Adding a note to an app ..................................................................................................................................... 105
Creating an app .................................................................................................................................................. 105
Example ........................................................................................................................................... 105
App functions and variables .............................................................................................................................. 107
Functions ......................................................................................................................................... 107
vii
Variables .......................................................................................................................................... 107
Qualifying variables ........................................................................................................................ 108
7 Function app ............................................................................................................................................. 109
Getting started with the Function app .............................................................................................................. 109
Opening the Function app ............................................................................................................... 109
Dening the expressions ................................................................................................................ 110
Setting up a plot .............................................................................................................................. 111
Plotting a function .......................................................................................................................... 111
Tracing a graph ................................................................................................................................ 112
Changing the scale .......................................................................................................................... 113
Displaying Numeric view ................................................................................................................. 113
Setting up Numeric view ................................................................................................................. 115
Exploring Numeric view .................................................................................................................. 116
Navigating a table ......................................................................................................... 116
Going directly to a value ............................................................................................... 117
Accessing the zoom options ......................................................................................... 117
Other options ................................................................................................................ 117
Analyzing functions ........................................................................................................................................... 117
Displaying the Plot view menu ........................................................................................................ 118
Sketching functions ...................................................................................................... 118
Modifying function graphs ........................................................................................... 119
Finding a root of a quadratic equation ......................................................................... 120
Finding an intersection of two functions ..................................................................... 122
Finding the slope of a quadratic equation .................................................................... 123
Finding the signed area between two functions .......................................................... 124
Finding the extremum of the quadratic equation ........................................................ 126
Adding a tangent to a function ..................................................................................... 126
Function variables ............................................................................................................................................. 127
Accessing function variables ........................................................................................................... 127
Summary of FCN operations ............................................................................................................................. 129
Dening functions in terms of derivatives or integrals .................................................................................... 129
Functions dened by derivatives .................................................................................................... 129
Functions dened by integrals ........................................................................................................ 132
8 Advanced Graphing app .............................................................................................................................. 134
Getting started with the Advanced Graphing app ............................................................................................. 136
Opening the Advanced Graphing app .............................................................................................. 136
Dening an open sentence .............................................................................................................. 137
Setting up the plot .......................................................................................................................... 137
Plotting the selected denitions ..................................................................................................... 139
viii
Exploring the graph ......................................................................................................................... 139
Trace in Plot view .......................................................................................................... 142
Numeric view ................................................................................................................................... 143
Displaying Numeric view .............................................................................................. 143
Exploring Numeric view ................................................................................................ 144
Numeric Setup view ...................................................................................................... 144
Trace in Numeric view ................................................................................................... 145
Edge ............................................................................................................ 146
PoI ............................................................................................................... 147
Zoom in Numeric view .................................................................................................. 147
Plot Gallery ........................................................................................................................................................ 148
Exploring a plot from the Plot Gallery ............................................................................................ 148
9 Graph 3D app ............................................................................................................................................. 149
Getting started with the Graph 3D app ............................................................................................................. 149
Opening the Graph 3D app .............................................................................................................. 149
Dening an expression .................................................................................................................... 149
Setting up the plot .......................................................................................................................... 150
Plotting the expression ................................................................................................................... 153
Plot view: summary of menu buttons .......................................................................... 155
Zooming in Plot view .................................................................................................... 155
Displaying a table ............................................................................................................................ 156
Numeric view: summary of menu buttons ................................................................... 157
Zooming in Numeric view ............................................................................................. 157
Setting up a table ............................................................................................................................ 158
10 Geometry ................................................................................................................................................ 160
Getting started with the Geometry app ............................................................................................................ 160
Preparation ...................................................................................................................................... 160
Opening the app and plotting the graph ........................................................................................ 160
Adding a constrained point ............................................................................................................. 161
Adding a tangent ............................................................................................................................. 162
Creating a derivative point .............................................................................................................. 163
Adding some calculations ............................................................................................................... 165
Calculations in Plot view ................................................................................................................. 167
Trace the derivative ......................................................................................................................... 167
Plot view in detail .............................................................................................................................................. 168
Selecting objects ............................................................................................................................. 169
Hiding names ................................................................................................................................... 169
Moving objects ................................................................................................................................ 169
Coloring objects ............................................................................................................................... 170
ix
Filling objects .................................................................................................................................. 170
Clearing an object ............................................................................................................................ 170
Clearing all objects .......................................................................................................................... 171
Gestures in Plot view ....................................................................................................................... 171
Zooming .......................................................................................................................................... 171
Plot view: buttons and keys ............................................................................................................ 172
The Options menu ........................................................................................................................... 173
Using the slopeeld command ....................................................................................................... 173
Plot Setup view ................................................................................................................................ 174
Symbolic view in detail ...................................................................................................................................... 175
Creating objects .............................................................................................................................. 176
Reordering entries .......................................................................................................................... 176
Hiding an object ............................................................................................................................... 176
Deleting an object ........................................................................................................................... 177
Symbolic Setup view ....................................................................................................................... 177
Numeric view in detail ....................................................................................................................................... 177
Listing all objects ............................................................................................................................ 180
Displaying calculations in Plot view ................................................................................................ 180
Editing a calculation ........................................................................................................................ 180
Deleting a calculation ...................................................................................................................... 181
Plot view: Cmds menu ....................................................................................................................................... 181
Point ................................................................................................................................................ 181
Point .............................................................................................................................. 181
Point On ......................................................................................................................... 181
Midpoint ........................................................................................................................ 182
Center ............................................................................................................................ 182
Intersection ................................................................................................................... 182
Intersections ................................................................................................................. 182
Random Points .............................................................................................................. 182
Line .................................................................................................................................................. 182
Segment ........................................................................................................................ 182
Ray ................................................................................................................................ 183
Line ................................................................................................................................ 183
Parallel .......................................................................................................................... 183
Perpendicular ................................................................................................................ 183
Tangent ......................................................................................................................... 183
Median ........................................................................................................................... 183
Altitude .......................................................................................................................... 183
Angle bisector ............................................................................................................... 184
Polygon ............................................................................................................................................ 184
Triangle ......................................................................................................................... 184
x
Isosceles Triangle ......................................................................................................... 184
Right Triangle ................................................................................................................ 185
Quadrilateral ................................................................................................................. 185
Parallelogram ............................................................................................................... 185
Rhombus ....................................................................................................................... 185
Rectangle ...................................................................................................................... 185
Polygon ......................................................................................................................... 186
Regular Polygon ............................................................................................................ 186
Square ........................................................................................................................... 186
Curve ................................................................................................................................................ 186
Circle .............................................................................................................................. 186
Circumcircle ................................................................................................................... 187
Excircle .......................................................................................................................... 187
Incircle ........................................................................................................................... 187
Ellipse ............................................................................................................................ 188
Hyperbola ..................................................................................................................... 188
Parabola ........................................................................................................................ 188
Conic .............................................................................................................................. 188
Locus ............................................................................................................................. 189
Plot .................................................................................................................................................. 189
Function ........................................................................................................................ 190
Parametric .................................................................................................................... 190
Polar .............................................................................................................................. 190
Sequence ....................................................................................................................... 191
Implicit .......................................................................................................................... 191
Slopeeld ...................................................................................................................... 191
ODE ................................................................................................................................ 191
List ................................................................................................................................. 191
Slider ............................................................................................................................. 192
Transform ........................................................................................................................................ 192
Translation .................................................................................................................... 192
Reection ...................................................................................................................... 193
Rotation ........................................................................................................................ 194
Dilation .......................................................................................................................... 194
Similarity ....................................................................................................................... 195
Projection ...................................................................................................................... 195
Inversion ....................................................................................................................... 196
Reciprocation ................................................................................................................ 196
Cartesian ......................................................................................................................................... 197
Abscissa ........................................................................................................................ 197
Ordinate ........................................................................................................................ 197
xi
PointComplex ............................................................................................................ 197
Coordinates ................................................................................................................... 197
Equation of .................................................................................................................... 197
Parametric .................................................................................................................... 198
Polar coordinates .......................................................................................................... 198
Measure ........................................................................................................................................... 198
Distance ........................................................................................................................ 198
Radius ........................................................................................................................... 198
Perimeter ...................................................................................................................... 198
Slope ............................................................................................................................. 198
Area ............................................................................................................................... 198
Angle ............................................................................................................................. 198
Arc Length ..................................................................................................................... 198
Tests ................................................................................................................................................ 199
Collinear ........................................................................................................................ 199
On circle ......................................................................................................................... 199
On object ....................................................................................................................... 199
Parallel .......................................................................................................................... 199
Perpendicular ................................................................................................................ 199
Isosceles ........................................................................................................................ 199
Equilateral ..................................................................................................................... 199
Parallelogram ............................................................................................................... 200
Conjugate ...................................................................................................................... 200
Geometry functions and commands ................................................................................................................. 200
Symbolic view: Cmds menu ............................................................................................................ 200
Point .............................................................................................................................. 200
Point ........................................................................................................... 200
Point on ...................................................................................................... 201
Midpoint ...................................................................................................... 201
Center ......................................................................................................... 201
Intersection ................................................................................................ 201
Intersections ............................................................................................... 201
Line ................................................................................................................................ 202
Segment ..................................................................................................... 202
Ray .............................................................................................................. 202
Line ............................................................................................................. 202
Parallel ........................................................................................................ 202
Perpendicular ............................................................................................. 203
Tangent ....................................................................................................... 203
Median ........................................................................................................ 203
Altitude ....................................................................................................... 203
xii
Bisector ....................................................................................................... 204
Polygon ......................................................................................................................... 204
Triangle ....................................................................................................... 204
Isosceles Triangle ....................................................................................... 204
Right Triangle ............................................................................................. 204
Quadrilateral .............................................................................................. 204
Parallelogram ............................................................................................. 205
Rhombus ..................................................................................................... 205
Rectangle .................................................................................................... 205
Polygon ....................................................................................................... 205
Regular Polygon ......................................................................................... 206
Square ......................................................................................................... 206
Curve ............................................................................................................................. 206
Circle ........................................................................................................... 206
Circumcircle ................................................................................................ 206
Excircle ........................................................................................................ 206
Incircle ........................................................................................................ 207
Ellipse ......................................................................................................... 207
Hyperbola ................................................................................................... 207
Parabola ..................................................................................................... 207
Conic ........................................................................................................... 208
Locus ........................................................................................................... 208
Plot ................................................................................................................................ 208
Function ...................................................................................................... 208
Parametric .................................................................................................. 208
Polar ........................................................................................................... 208
Sequence .................................................................................................... 209
Implicit ........................................................................................................ 209
Slopeeld .................................................................................................... 209
ODE ............................................................................................................. 209
List .............................................................................................................. 209
Slider ........................................................................................................... 210
Transform ..................................................................................................................... 210
Translation ................................................................................................. 210
Reection ................................................................................................... 210
Rotation ...................................................................................................... 210
Dilation ....................................................................................................... 210
Similarity .................................................................................................... 210
Projection ................................................................................................... 211
Inversion ..................................................................................................... 211
Reciprocation .............................................................................................. 211
xiii
Numeric view: Cmds menu .............................................................................................................. 211
Cartesian ....................................................................................................................... 211
Abscissa ...................................................................................................... 211
Ordinate ...................................................................................................... 212
Coordinates ................................................................................................. 212
Equation of ................................................................................................. 212
Parametric .................................................................................................. 212
Polar Coordinates ....................................................................................... 212
Measure ......................................................................................................................... 212
Distance ...................................................................................................... 212
Radius ......................................................................................................... 213
Perimeter .................................................................................................... 213
Slope ........................................................................................................... 213
Area ............................................................................................................. 213
Angle ........................................................................................................... 213
Arc Length ................................................................................................... 214
Tests .............................................................................................................................. 214
Collinear ...................................................................................................... 214
On circle ...................................................................................................... 214
On object ..................................................................................................... 214
Parallel ........................................................................................................ 214
Perpendicular ............................................................................................. 215
Isosceles ..................................................................................................... 215
Equilateral .................................................................................................. 215
Parallelogram ............................................................................................. 215
Conjugate .................................................................................................... 215
Other Geometry functions .............................................................................................................. 215
aix ............................................................................................................................... 215
barycenter ..................................................................................................................... 216
convexhull ..................................................................................................................... 216
distance2 ....................................................................................................................... 216
division_point ............................................................................................................... 216
equilateral_triangle ...................................................................................................... 216
exbisector ..................................................................................................................... 217
extract_measure .......................................................................................................... 217
harmonic_conjugate ..................................................................................................... 217
harmonic_division ........................................................................................................ 217
isobarycenter ................................................................................................................ 218
is_harmonic .................................................................................................................. 218
is_harmonic_circle_bundle ........................................................................................... 218
is_harmonic_line_bundle ............................................................................................. 218
xiv
is_orthogonal ................................................................................................................ 218
is_rectangle .................................................................................................................. 218
is_rhombus ................................................................................................................... 219
is_square ....................................................................................................................... 219
LineHorz ........................................................................................................................ 219
LineVert ......................................................................................................................... 219
open_polygon ............................................................................................................... 219
orthocenter ................................................................................................................... 219
perpendicular bisector .................................................................................................. 220
point2d .......................................................................................................................... 220
polar .............................................................................................................................. 220
pole ............................................................................................................................... 220
power_pc ....................................................................................................................... 220
radical_axis ................................................................................................................... 221
vector ............................................................................................................................ 221
vertices .......................................................................................................................... 221
vertices_abca ................................................................................................................ 221
11 Spreadsheet ............................................................................................................................................ 222
Getting started with the Spreadsheet app ........................................................................................................ 222
Basic operations ................................................................................................................................................ 227
Navigation, selection, and gestures ............................................................................................... 227
Cell references ................................................................................................................................. 227
Cell naming ...................................................................................................................................... 228
Method 1 ....................................................................................................................... 228
Method 2 ....................................................................................................................... 228
Using names in calculations ......................................................................................... 228
Entering content .............................................................................................................................. 228
Direct entry ................................................................................................................... 229
Importing data .............................................................................................................. 230
External functions ........................................................................................................ 230
Copy and paste ................................................................................................................................ 232
Using the CHOOSE command ............................................................................................................................ 232
External references ........................................................................................................................................... 232
Referencing variables ...................................................................................................................... 233
Using the CAS in spreadsheet calculations ....................................................................................................... 234
Buttons and keys ............................................................................................................................................... 234
Formatting options ............................................................................................................................................ 235
Format parameters ......................................................................................................................... 236
Spreadsheet functions ...................................................................................................................................... 237
xv
12 Statistics 1Var app ................................................................................................................................... 238
Getting started with the Statistics 1Var app ..................................................................................................... 238
Symbolic view: menu items ............................................................................................................ 241
Entering and editing statistical data ................................................................................................................. 245
Numeric view: menu items .............................................................................................................. 245
More menu .................................................................................................................... 245
Editing a data set ............................................................................................................................ 246
Deleting data ................................................................................................................................... 246
Inserting data .................................................................................................................................. 246
Generating data ............................................................................................................................... 246
Sorting data values ......................................................................................................................... 247
Computed statistics ........................................................................................................................................... 247
Plotting .............................................................................................................................................................. 248
Plotting statistical data ................................................................................................................... 248
Plot types ........................................................................................................................................ 249
Histogram ..................................................................................................................... 249
Box-and-whisker plot ................................................................................................... 250
Normal probability plot ................................................................................................ 250
Line plot ........................................................................................................................ 251
Bar graph ...................................................................................................................... 251
Pareto chart .................................................................................................................. 252
Control chart ................................................................................................................. 252
Dot plot ......................................................................................................................... 253
Stem and leaf plot ......................................................................................................... 253
Pie chart ........................................................................................................................ 254
Setting up the plot .......................................................................................................................... 254
Exploring the graph ......................................................................................................................... 254
Plot view: menu items .................................................................................................. 255
13 Statistics 2Var app ................................................................................................................................... 256
Getting started with the Statistics 2Var app ..................................................................................................... 256
Opening the Statistics 2Var app ...................................................................................................... 256
Entering data ................................................................................................................................... 257
Choosing data columns and t ........................................................................................................ 258
Exploring statistics .......................................................................................................................... 259
Setting up the plot .......................................................................................................................... 260
Plotting the graph ........................................................................................................................... 261
Displaying the equation .................................................................................................................. 262
Predicting values ............................................................................................................................. 262
Entering and editing statistical data ................................................................................................................. 263
Numeric view: menu items .............................................................................................................. 264
xvi
More menu .................................................................................................................... 264
Dening a regression model ............................................................................................................................. 264
Choosing a t ................................................................................................................................... 265
Fit types ........................................................................................................................................... 265
Dening your own t ....................................................................................................................... 265
Computed statistics ........................................................................................................................................... 266
Plotting statistical data ..................................................................................................................................... 267
Tracing a scatter plot ...................................................................................................................... 268
Tracing a curve ................................................................................................................................ 268
Tracing order ................................................................................................................................... 269
Plot view: menu items ..................................................................................................................... 269
Function menu .............................................................................................................. 269
Sketch ......................................................................................................... 269
Plot Setup view ................................................................................................................................ 270
Predicting values ............................................................................................................................. 270
Plot view ........................................................................................................................ 270
Home view .................................................................................................................... 271
Troubleshooting a plot .................................................................................................................... 271
14 Inference app .......................................................................................................................................... 272
Sample data ....................................................................................................................................................... 272
Getting started with the Inference app ............................................................................................................. 272
Opening the Inference app .............................................................................................................. 273
Symbolic view options .................................................................................................................... 273
Selecting the inference method ...................................................................................................... 275
Entering data ................................................................................................................................... 276
Displaying the test results .............................................................................................................. 277
Plotting the test results .................................................................................................................. 277
Importing statistics ........................................................................................................................................... 278
Opening the Statistics 1Var app ...................................................................................................... 278
Clearing unwanted data .................................................................................................................. 278
Entering data ................................................................................................................................... 279
Calculating the statistics ................................................................................................................. 280
Opening the Inference app .............................................................................................................. 280
Selecting the inference method and type ...................................................................................... 281
Importing the data .......................................................................................................................... 281
Displaying results numerically ........................................................................................................ 283
Displaying results graphically ......................................................................................................... 283
Hypothesis tests ................................................................................................................................................ 283
One-Sample Z-Test .......................................................................................................................... 284
Menu name ................................................................................................................... 284
xvii
Inputs ............................................................................................................................ 284
Results .......................................................................................................................... 284
Two-Sample Z-Test .......................................................................................................................... 284
Menu name ................................................................................................................... 284
Inputs ............................................................................................................................ 285
Results .......................................................................................................................... 285
One-Proportion Z-Test .................................................................................................................... 285
Menu name ................................................................................................................... 285
Inputs ............................................................................................................................ 286
Results .......................................................................................................................... 286
Two-Proportion Z-Test .................................................................................................................... 286
Menu name ................................................................................................................... 286
Inputs ............................................................................................................................ 286
Results .......................................................................................................................... 288
One-Sample T-Test .......................................................................................................................... 288
Menu name ................................................................................................................... 288
Inputs ............................................................................................................................ 288
Results .......................................................................................................................... 289
Two-Sample T-Test .......................................................................................................................... 289
Menu name ................................................................................................................... 289
Inputs ............................................................................................................................ 289
Results .......................................................................................................................... 290
Condence intervals .......................................................................................................................................... 290
One-Sample Z-Interval .................................................................................................................... 290
Menu name ................................................................................................................... 290
Inputs ............................................................................................................................ 290
Results .......................................................................................................................... 290
Two-Sample Z-Interval ................................................................................................................... 291
Menu name ................................................................................................................... 291
Inputs ............................................................................................................................ 291
Results .......................................................................................................................... 291
One-Proportion Z-Interval .............................................................................................................. 292
Menu name ................................................................................................................... 292
Inputs ............................................................................................................................ 292
Results .......................................................................................................................... 292
Two-Proportion Z-Interval .............................................................................................................. 292
Menu name ................................................................................................................... 292
Inputs ............................................................................................................................ 292
Results .......................................................................................................................... 293
One-Sample T-Interval .................................................................................................................... 293
Menu name ................................................................................................................... 293
xviii
Inputs ............................................................................................................................ 293
Results .......................................................................................................................... 293
Two-Sample T-Interval ................................................................................................................... 294
Menu name ................................................................................................................... 294
Inputs ............................................................................................................................ 294
Results .......................................................................................................................... 294
Chi-square tests ................................................................................................................................................ 295
Goodness of t test ......................................................................................................................... 295
Menu name ................................................................................................................... 295
Inputs ............................................................................................................................ 295
Results .......................................................................................................................... 295
Menu keys ..................................................................................................................... 295
Two-way table test ......................................................................................................................... 296
Menu name ................................................................................................................... 296
Inputs ............................................................................................................................ 296
Results .......................................................................................................................... 296
Menu keys ..................................................................................................................... 296
Inference for regression .................................................................................................................................... 297
Linear t-test ..................................................................................................................................... 297
Menu name ................................................................................................................... 297
Inputs ............................................................................................................................ 297
Results .......................................................................................................................... 297
Menu keys ..................................................................................................................... 297
Condence interval for slope .......................................................................................................... 298
Menu name ................................................................................................................... 298
Inputs ............................................................................................................................ 298
Results .......................................................................................................................... 298
Menu keys ..................................................................................................................... 298
Condence interval for intercept .................................................................................................... 299
Menu name ................................................................................................................... 299
Inputs ............................................................................................................................ 299
Results .......................................................................................................................... 299
Menu keys ..................................................................................................................... 299
Condence interval for a mean response ....................................................................................... 300
Menu name ................................................................................................................... 300
Inputs ............................................................................................................................ 300
Results .......................................................................................................................... 300
Menu keys ..................................................................................................................... 300
Prediction interval ........................................................................................................................... 301
Menu name ................................................................................................................... 301
Inputs ............................................................................................................................ 301
xix
Results .......................................................................................................................... 301
Menu keys ..................................................................................................................... 301
ANOVA ................................................................................................................................................................ 302
Menu name ...................................................................................................................................... 302
Inputs ............................................................................................................................................... 302
Results ............................................................................................................................................. 302
Menu keys ........................................................................................................................................ 302
15 Solve app ................................................................................................................................................ 304
Getting started with the Solve app ................................................................................................................... 304
One equation ................................................................................................................................... 304
Opening the Solve app .................................................................................................. 305
Clearing the app and dening the equation ................................................................. 305
Entering known variables ............................................................................................. 306
Solving for the unknown variable ................................................................................ 307
Plotting the equation .................................................................................................... 307
Several equations ........................................................................................................................... 308
Opening the solve app .................................................................................................. 309
Dening the equations ................................................................................................. 309
Entering a seed value ................................................................................................... 309
Solving the unknown variables .................................................................................... 310
Limitations ...................................................................................................................................... 310
Solution information ......................................................................................................................................... 311
16 Linear Solver app ..................................................................................................................................... 312
Getting started with the Linear Solver app ....................................................................................................... 312
Opening the Linear Solver app ........................................................................................................ 312
Dening and solving the equations ................................................................................................ 313
Solving a two-by-two system ......................................................................................................... 314
Menu items ........................................................................................................................................................ 314
17 Parametric app ........................................................................................................................................ 315
Getting started with the Parametric app .......................................................................................................... 315
Opening the Parametric app ........................................................................................................... 315
Dening the functions ..................................................................................................................... 316
Setting the angle measure .............................................................................................................. 316
Setting up the plot .......................................................................................................................... 317
Plotting the functions ..................................................................................................................... 318
Exploring the graph ......................................................................................................................... 318
Displaying the Numeric view ........................................................................................................... 319
xx
18 Polar app ................................................................................................................................................. 320
Getting started with the Polar app .................................................................................................................... 320
Opening the Polar app .................................................................................................................... 320
Dening the function ...................................................................................................................... 320
Setting the angle measure .............................................................................................................. 321
Setting up the plot .......................................................................................................................... 322
Plotting the expression ................................................................................................................... 322
Exploring the graph ......................................................................................................................... 323
Displaying the Numeric view ........................................................................................................... 324
19 Sequence app .......................................................................................................................................... 325
Getting started with the Sequence app ............................................................................................................ 326
Opening the Sequence app ............................................................................................................. 326
Dening the expression .................................................................................................................. 326
Setting up the plot .......................................................................................................................... 327
Plotting the sequence ..................................................................................................................... 328
Exploring the graph ......................................................................................................................... 329
Displaying Numeric view ................................................................................................................. 329
Exploring the table of values .......................................................................................................... 330
Setting up the table of values ......................................................................................................... 331
Another example: Explicitly dened sequences ............................................................................................... 331
Dening the expression .................................................................................................................. 331
Setting up the plot .......................................................................................................................... 332
Plotting the sequence ..................................................................................................................... 332
Exploring the table of values .......................................................................................................... 333
20 Finance app ............................................................................................................................................. 334
Getting started with the Finance app ................................................................................................................ 334
Opening the Finance app ................................................................................................................. 334
Symbolic view options .................................................................................................................... 335
Time value of money (TVM) ............................................................................................................................... 335
Using TVM ........................................................................................................................................ 335
Cash ow diagrams ......................................................................................................................... 337
TVM variables .................................................................................................................................. 339
Another example: balloon payment ............................................................................................... 340
Amortizations .................................................................................................................................. 341
Calculating amortizations ............................................................................................ 341
Amortization for a home mortgage example .............................................................. 341
Amortization graph ....................................................................................................... 343
Amortization variables ................................................................................................. 343
xxi
Interest conversion ............................................................................................................................................ 343
Using interest conversion ............................................................................................................... 343
Interest conversion variables .......................................................................................................... 344
Date calculation ................................................................................................................................................. 344
Using date calculation ..................................................................................................................... 345
Date calculation variables ............................................................................................................... 346
Cash ow ............................................................................................................................................................ 347
Using cash ow ............................................................................................................................... 347
Cash ow variables ......................................................................................................................... 348
Another example: MIRR and FMRR .................................................................................................. 349
Exploring cash ow in Plot view ..................................................................................................... 350
Plot view: menu items ..................................................................................................................... 352
Sample cash ows ........................................................................................................................... 353
Depreciation ...................................................................................................................................................... 353
Using depreciation .......................................................................................................................... 354
Depreciation variables .................................................................................................................... 355
Depreciation types .......................................................................................................................... 356
Another example: declining balance .............................................................................................. 356
Break-even ......................................................................................................................................................... 357
Using break-even ............................................................................................................................ 357
Break-even variables ...................................................................................................................... 358
Percent change .................................................................................................................................................. 358
Using percent change ...................................................................................................................... 359
Percent change variables ................................................................................................................ 360
Percent change types ...................................................................................................................... 360
Another example: part/total calculation ........................................................................................ 360
Bond ................................................................................................................................................................... 361
Using bond ....................................................................................................................................... 361
Bond variables ................................................................................................................................. 362
Black-Scholes ..................................................................................................................................................... 363
Using Black-Scholes ........................................................................................................................ 363
Black-Scholes variables .................................................................................................................. 364
Another example: annual inputs ..................................................................................................... 364
21 Triangle Solver app .................................................................................................................................. 366
Getting started with the Triangle Solver app .................................................................................................... 366
Opening the Triangle Solver app ..................................................................................................... 366
Setting the angle measure .............................................................................................................. 367
Specify the known values ............................................................................................................... 367
Solving for the unknown values ..................................................................................................... 368
Choosing triangle types ..................................................................................................................................... 368
xxii
Special cases ...................................................................................................................................................... 369
Indeterminate case ......................................................................................................................... 369
No solution with given data ............................................................................................................ 369
Not enough data .............................................................................................................................. 370
22 Explorer app ............................................................................................................................................ 371
Getting started with the Explorer app .............................................................................................................. 371
Opening the Explorer app ............................................................................................................... 371
Exploring linear functions ................................................................................................................................. 371
Exploring quadratic functions ........................................................................................................................... 372
Exploring cubic functions .................................................................................................................................. 374
Exploring exponential functions ....................................................................................................................... 375
Exploring logarithmic functions ........................................................................................................................ 376
Exploring trigonometric functions .................................................................................................................... 377
23 Functions and commands ......................................................................................................................... 379
Keyboard functions ........................................................................................................................................... 381
.................................................................................................. 381
........................................................................................................................................... 381
(ex) ...................................................................................................................... 381
........................................................................................................................................... 382
(10x) .................................................................................................................... 382
................................................................................................................ 382
(ASIN) ................................................................................................................... 382
(ACOS) .................................................................................................................. 382
(ATAN) ................................................................................................................... 383
........................................................................................................................................... 383
............................................................................................................................. 383
........................................................................................................................................... 383
............................................................................................................................. 383
xxiii
............................................................................................................................. 383
........................................................................................................................................... 384
(|x|) ....................................................................................................................... 384
........................................................................................................................................... 384
............................................................................................................................. 384
........................................................................................................................................... 385
........................................................................................................................... 385
.......................................................................................................................... 385
.......................................................................................................................... 385
.......................................................................................................................... 385
Math menu ......................................................................................................................................................... 386
Numbers .......................................................................................................................................... 386
Ceiling ............................................................................................................................ 386
Floor .............................................................................................................................. 386
IP ................................................................................................................................... 386
FP .................................................................................................................................. 386
Round ............................................................................................................................ 386
Truncate ........................................................................................................................ 387
Mantissa ........................................................................................................................ 387
Exponent ....................................................................................................................... 387
Arithmetic ........................................................................................................................................ 387
Maximum ...................................................................................................................... 387
Minimum ....................................................................................................................... 388
Modulus ......................................................................................................................... 388
Find Root ....................................................................................................................... 388
Percentage .................................................................................................................... 388
Arithmetic – Complex ...................................................................................................................... 388
Argument ...................................................................................................................... 388
Conjugate ...................................................................................................................... 388
Real Part ........................................................................................................................ 389
Imaginary Part .............................................................................................................. 389
Unit Vector .................................................................................................................... 389
xxiv
Arithmetic – Exponential ................................................................................................................ 389
ALOG .............................................................................................................................. 389
EXPM1 ........................................................................................................................... 389
LNP1 .............................................................................................................................. 389
Trigonometry .................................................................................................................................. 389
CSC ................................................................................................................................ 390
ACSC .............................................................................................................................. 390
SEC ................................................................................................................................ 390
ASEC .............................................................................................................................. 390
COT ................................................................................................................................ 390
ACOT .............................................................................................................................. 390
Hyperbolic ....................................................................................................................................... 390
SINH ............................................................................................................................... 390
ASINH ............................................................................................................................ 390
COSH .............................................................................................................................. 390
ACOSH ............................................................................................................................ 390
TANH .............................................................................................................................. 391
ATANH ............................................................................................................................ 391
Probability ....................................................................................................................................... 392
Factorial ........................................................................................................................ 392
Combination .................................................................................................................. 392
Permutation .................................................................................................................. 392
Probability – Random ...................................................................................................................... 392
Number ......................................................................................................................... 392
Integer ........................................................................................................................... 392
Normal .......................................................................................................................... 393
Seed .............................................................................................................................. 393
Probability – Density ....................................................................................................................... 393
Normal .......................................................................................................................... 393
T .................................................................................................................................... 393
χ2 ................................................................................................................................... 393
F ..................................................................................................................................... 393
Binomial ........................................................................................................................ 394
Geometric ...................................................................................................................... 394
Poisson .......................................................................................................................... 394
Probability – Cumulative ................................................................................................................. 394
Normal .......................................................................................................................... 394
T .................................................................................................................................... 394
X2 .................................................................................................................................. 395
F ..................................................................................................................................... 395
Binomial ........................................................................................................................ 395
xxv
Geometric ...................................................................................................................... 395
Poisson .......................................................................................................................... 395
Probability – Inverse ....................................................................................................................... 396
Normal .......................................................................................................................... 396
T .................................................................................................................................... 396
χ2 ................................................................................................................................... 396
F ..................................................................................................................................... 396
Binomial ........................................................................................................................ 396
Geometric ...................................................................................................................... 397
Poisson .......................................................................................................................... 397
List ................................................................................................................................................... 397
Matrix .............................................................................................................................................. 397
Special ............................................................................................................................................. 397
Beta ............................................................................................................................... 397
Gamma .......................................................................................................................... 397
Psi .................................................................................................................................. 397
Zeta ............................................................................................................................... 397
erf .................................................................................................................................. 398
erfc ................................................................................................................................ 398
Ei .................................................................................................................................... 398
Si .................................................................................................................................... 398
Ci .................................................................................................................................... 398
CAS menu ........................................................................................................................................................... 398
Algebra ............................................................................................................................................ 399
Simplify ......................................................................................................................... 399
Collect ........................................................................................................................... 399
Expand .......................................................................................................................... 399
Factor ............................................................................................................................ 399
Substitute ..................................................................................................................... 399
Partial Fraction ............................................................................................................. 399
Algebra – Extract ............................................................................................................................. 400
Numerator ..................................................................................................................... 400
Denominator ................................................................................................................. 400
Left Side ........................................................................................................................ 400
Right Side ...................................................................................................................... 400
Calculus ........................................................................................................................................... 400
Dierentiate .................................................................................................................. 400
Integrate ....................................................................................................................... 401
Limit .............................................................................................................................. 401
Series ............................................................................................................................ 401
Summation ................................................................................................................... 401
xxvi
Calculus – Dierential ..................................................................................................................... 402
Curl ................................................................................................................................ 402
Divergence .................................................................................................................... 402
Gradient ........................................................................................................................ 402
Hessian .......................................................................................................................... 402
Calculus – Integral ........................................................................................................................... 402
By Parts u ...................................................................................................................... 402
By Parts v ...................................................................................................................... 403
F(b)–F(a) ........................................................................................................................ 403
Calculus – Limits .............................................................................................................................. 403
Riemann Sum ................................................................................................................ 403
Taylor ............................................................................................................................ 403
Taylor of Quotient ......................................................................................................... 403
Calculus – Transform ....................................................................................................................... 404
Laplace .......................................................................................................................... 404
Inverse Laplace ............................................................................................................. 404
FFT ................................................................................................................................. 404
Inverse FFT .................................................................................................................... 404
Solve ................................................................................................................................................ 404
Solve .............................................................................................................................. 404
Zeros ............................................................................................................................. 405
Complex Solve ............................................................................................................... 405
Complex Zeros .............................................................................................................. 405
Numerical Solve ............................................................................................................ 406
Dierential Equation .................................................................................................... 406
ODE Solve ...................................................................................................................... 406
Linear System ............................................................................................................... 406
Rewrite ............................................................................................................................................ 406
lncollect ......................................................................................................................... 406
powexpand ................................................................................................................... 407
texpand ......................................................................................................................... 407
Rewrite – Exp & Ln .......................................................................................................................... 407
ey*lnx xy ................................................................................................................... 407
xyey*lnx .................................................................................................................... 407
exp2trig ......................................................................................................................... 407
expexpand .................................................................................................................... 408
Rewrite – Sine .................................................................................................................................. 408
asinxacosx ................................................................................................................ 408
asinxatanx ................................................................................................................ 408
sinxcosx*tanx ........................................................................................................... 408
Rewrite – Cosine .............................................................................................................................. 408
xxvii
acosxasinx ................................................................................................................ 408
acosxatanx ................................................................................................................ 408
cosxsinx/tanx ............................................................................................................ 409
Rewrite – Tangent ........................................................................................................................... 409
atanxasinx ................................................................................................................ 409
atanxacosx ................................................................................................................ 409
tanxsinx/cosx ............................................................................................................ 409
halftan ........................................................................................................................... 409
Rewrite – Trig .................................................................................................................................. 410
trigxsinx .................................................................................................................... 410
trigxcosx ................................................................................................................... 410
trigxtanx ................................................................................................................... 410
atrig2ln ......................................................................................................................... 410
tlin ................................................................................................................................. 410
tcollect .......................................................................................................................... 410
trigexpand ..................................................................................................................... 411
trig2exp ......................................................................................................................... 411
Integer ............................................................................................................................................. 411
Divisors ......................................................................................................................... 411
Factors .......................................................................................................................... 411
Factor List ..................................................................................................................... 411
GCD ................................................................................................................................ 412
LCM ................................................................................................................................ 412
Integer – Prime ................................................................................................................................ 412
Test if Prime .................................................................................................................. 412
Nth Prime ...................................................................................................................... 412
Next Prime .................................................................................................................... 412
Previous Prime .............................................................................................................. 412
Euler .............................................................................................................................. 413
Integer – Division ............................................................................................................................ 413
Quotient ........................................................................................................................ 413
Remainder ..................................................................................................................... 413
anMOD p ........................................................................................................................ 413
Chinese Remainder ....................................................................................................... 413
Polynomial ...................................................................................................................................... 414
Find Roots ..................................................................................................................... 414
Coeicients ................................................................................................................... 414
Divisors ......................................................................................................................... 414
Factor List ..................................................................................................................... 414
GCD ................................................................................................................................ 414
LCM ................................................................................................................................ 414
xxviii
Polynomial – Create ........................................................................................................................ 415
Poly to Coef ................................................................................................................... 415
Coef to Poly ................................................................................................................... 415
Roots to Coef ................................................................................................................. 415
Roots to Poly ................................................................................................................. 415
Random ......................................................................................................................... 415
Minimum ....................................................................................................................... 416
Polynomial – Algebra ...................................................................................................................... 416
Quotient ........................................................................................................................ 416
Remainder ..................................................................................................................... 416
Degree ........................................................................................................................... 416
Factor by Degree ........................................................................................................... 416
Coef. GCD ....................................................................................................................... 417
Zero Count ..................................................................................................................... 417
Chinese Remainder ....................................................................................................... 417
Polynomial – Special ....................................................................................................................... 417
Cyclotomic ..................................................................................................................... 417
Groebner Basis .............................................................................................................. 417
Groebner Remainder ..................................................................................................... 418
Hermite ......................................................................................................................... 418
Lagrange ....................................................................................................................... 418
Laguerre ........................................................................................................................ 418
Legendre ....................................................................................................................... 418
Chebyshev Tn ................................................................................................................ 419
Chebyshev Un ............................................................................................................... 419
Plot .................................................................................................................................................. 419
Function ........................................................................................................................ 419
Contour ......................................................................................................................... 419
App menu ........................................................................................................................................................... 419
Finance app functions ..................................................................................................................... 420
TVM functions ............................................................................................................... 420
Main variables ............................................................................................. 420
Optional variables ...................................................................................... 420
TvmFV ......................................................................................................... 421
TvmIPYR ...................................................................................................... 421
TvmNbPmt .................................................................................................. 421
TvmPMT ...................................................................................................... 421
TvmPV ......................................................................................................... 421
Interest conversion functions ....................................................................................... 421
IntConvNom ................................................................................................ 422
IntConvE ................................................................................................... 422
xxix
IntConvCPYR ............................................................................................... 422
Date calculation functions ............................................................................................ 422
DateDays .................................................................................................... 422
Cash ow functions ...................................................................................................... 422
CashFlowIRR ............................................................................................... 422
CashFlowMIRR ............................................................................................ 423
CashFlowFMRR ........................................................................................... 423
CashFlowTotal ............................................................................................ 423
CashFlowNPV .............................................................................................. 423
CashFlowNFV .............................................................................................. 423
CashFlowNUS .............................................................................................. 424
CashFlowPB ................................................................................................ 424
Depreciation functions ................................................................................................. 424
Depreciate .................................................................................................. 424
Break-even functions ................................................................................................... 425
BrkEvFixed .................................................................................................. 425
BrkEvQuant ................................................................................................. 425
BrkEvCost ................................................................................................... 425
BrkEvPrice .................................................................................................. 425
BrkEvProt ................................................................................................. 425
Percent change functions ............................................................................................. 426
ChangePrice ................................................................................................ 426
ChangeCost ................................................................................................. 426
PercentMargin ............................................................................................ 426
PercentMarkup ........................................................................................... 426
ChangeOld .................................................................................................. 426
ChangeNew ................................................................................................. 427
PercentTotal ............................................................................................... 427
PercentChange ........................................................................................... 427
Bond functions .............................................................................................................. 427
BondYield .................................................................................................... 427
BondPrice .................................................................................................... 428
Black Scholes functions ................................................................................................ 428
BlackScholes ............................................................................................... 428
Solve app functions ......................................................................................................................... 428
SOLVE ............................................................................................................................ 428
Spreadsheet app functions ............................................................................................................. 428
SUM ............................................................................................................................... 429
AVERAGE ....................................................................................................................... 430
AMORT ........................................................................................................................... 430
STAT1 ............................................................................................................................. 430
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