Instruction/ maintenance manual of the product NW280AAABA HP (Hewlett-Packard)
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HP Pr ime Gr aphing C alc ulator User G uid e.
Ed i t io n 1 P art Number NW2 80 - 200 1 Legal Notices This manual and an y e xamples con tained here in are pr ov ided "as is" and ar e subject t o change w ithout notice .
Cop yri ght © 20 1 3 Hewlett-P ac kar d Dev elopment Compan y , L .P . Repr oduction , adaptatio n, or tr anslation of this manual is pr ohibited w ithout pr ior wr itten per- mission o f Hewlett-P ac kar d Compan y , ex cept as allow ed under the copy right la ws.
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Contents 1 Contents Preface Manual conventions ................ ................ ................. ............... 9 Notice ................ ................ ................ ................ ................. 10 1 Getting started Before starting ....
2 Con tents 4 Exam Mode Modifying the default co nfiguration .... ................... .............. 62 Creating a new c onfiguration ..... .................... ................ .... 63 Activating Exam Mode ................ ................... .......
Contents 3 6 Function app Getting started with the Fu nction app ............ ................... ..... 111 Analyzing functions .................... ................. ................ ........ 118 The Function Variables ... ................. .........
4 Con tents Plot types ................. ................ ................ ................. ..... 219 Setting up the plot (Plot Setup view) ....... ................... ......... 2 21 Exploring the graph ......................... ................ ....
Contents 5 15 Parametric app Getting started with the Parametric app ............... .................. 271 16 Polar app Getting started with the Polar ap p .......... .................... ........... 277 17 Sequence app Getting started with the Seq uence app .
6 Con tents App menu .................... ................ ................ ................. ..... 347 Function app functions ............ ................................ ......... 348 Solve app functions ... ................................ .......
Contents 7 24 Lists Create a list in the List Catalog ........... ................ ................ .. 45 1 The List Editor ........... ................. ................ ................ ..... 453 Deleting lists . .................... ...............
8 Con tents 28 Basic integer arithmetic The default base ......... ................ ................ ................ ......... 5 82 Changing the default b ase ................... ................ ............ 583 Examples of integer arithmetic ......
Preface 9 Pref ace Manual conventions The following conventions ar e used in this manual to represent the keys that you pres s and the menu options that you choose to perform operations. • A ke y that initiates an unshifted functio n is re presented b y an image of that key : e , B , H , etc.
10 Preface • Items y ou can select fr om a list , and character s on the entry line , are se t in a non-propo r tio nal font , as follo ws : Function , Polar , Parametric , Ans , etc.
Getting started 11 1 Gett in g s ta rted The HP Pr ime Gr aphing Calc ulator is an eas y- to -use y et po werf ul graphing calc ulator desig ned for secondary mathemati cs educati on and be yond . It off ers h undreds o f functi ons and command s, and includes a computer algebr a sy stem (CA S) for s ymboli c calculati ons.
12 Getting started When the calc ulator is on, a battery symbol appears in the titl e bar of the screen . Its app earance w ill indicate how muc h po wer the batte r y has.
Getting started 13 The Home View Home v iew is the starting point f or many calculations . Most ma thematical func tions ar e av ailable in the Home v iew .
14 Getting started Sections of the display Home v ie w has four s ections (sho wn abov e) . The title bar s h ow s e i t h e r t h e s cre e n n a m e o r t h e n a m e o f t h e a p p yo u are c urr ently using— Function in the e xample abo ve .
Getting started 15 CAS [White] Y ou ar e wor king in CAS v ie w , not Home v iew . [orange] In Home view The A lpha ke y is activ e. The c harac - ter show n in orange on a k ey w ill be entered in upper case wh e n a k ey is pr esse d. See “ Adding tex t” on page 2 3 f or more inf ormation .
16 Getting started Navigation The HP Pr ime offer s two modes of na vig ation: touch and k ey s. In many ca ses, y ou can tap on an icon , field , menu , or obj ect to select (o r deselect) it . F or ex ample , you can open the F unction app by tapping once on its i con in the Appli cation L ibrary .
Getting started 17 Touch gestures In addition to selecti on by tapping , there ar e other touch- r elated operations a vailable to y ou: T o qui ckly mo ve fr om page to page , flick : P lace a finger on the sc ree n and quickl y sw ipe it in the desire d di r ection (up or dow n) .
18 Getting started The keyboard The n umbers in the legend be low r efe r to the parts of the k ey board de scr ibed in the illustr ation on the ne xt page.
Getting started 19 Context-sensitive menu A conte xt-sensitive men u occup ies the bottom line of the screen. The opti ons available depend on the context , that is, the vi ew y ou are in.
20 Getting started The re ar e two types o f buttons on the conte xt-sensiti ve menu: • menu button: tap to displa y a pop-up menu . These buttons hav e squar e corners alo ng their top (such as in the illustr ation abo ve). • command button: tap to initiate a command .
Getting started 21 Sv Relations palette: Display s a palet te of compar ison operator s and Bool- ean operators . Sr Spec ial sy mbols palette: Displa ys a palette of common math and Gr eek cha rac te rs. Sc Automati cal ly inserts the d egree , minute , or second s ymbol accor d- ing to the conte xt.
22 Getting started Shift keys The re ar e two shift k ey s that you use to access the operati ons and characters pr inted on th e bottom of the keys : S and A . Sa Displa ys all the av ailable characters . T o enter a character , use the c ursor k ey s to highlight it , and then tap .
Getting started 23 Adding text The text y ou can enter directly is sho wn by the orange char acters on the k ey s. The se char acters can only be enter ed in conjuncti on with the A and S keys. B ot h upper case and lowe rcase c haracters can be entered , and the method is ex actly the oppos ite in CAS vi ew than in Home v ie w .
24 Getting started Math keys The mo st common math functi ons have their ow n ke ys o n the k ey board (or a k ey in comb ination w ith the S key ) . Ex am ple 1 : T o calc ulate SIN( 1 0) , pr ess e 10 a n d pres s E . The ans wer displa yed is –0.
Getting started 25 Example : Suppose y ou want t o find the c ube r oot of 94 5 : 1 . In Home v iew , pres s F . 2. S e l e c t . The skeleton or frame work for y our calculation now appears on the entry line: 3 . E ach box on the templ ate needs to be completed: 3 > 94 5 4.
26 Getting started degrees; and enters ″ if the pr ev iou s entry is a value in minutes. Thus enter ing : 36 Sc 40 Sc 20 Sc yie l d s 36 ° 4 0 ′ 20 ″ . See “Hexagesimal numbers ” on page 2 6 for mo re in form a ti on. Fractions The fra ct io n key ( c ) cyc les t hrough thee vari eties of fr actional dis play .
Getting started 27 Note that the degr ee and minut e entri es must be in tegers, and the minute and second entries m ust be positiv e. Dec imals are not allo w ed, e xcept in the seconds . Note too that the HP Prime tr eats a value in hexgesimal f ormat as a single entity .
28 Getting started 5. P re s s E Th e re s ul t i s 8.0000 E 15 . This is equi valent t o 8 × 1 0 15 . Menus A menu off ers y ou a ch o i c e of i t e m s .
Getting started 29 To close a menu A menu w ill close a utomaticall y when yo u select an item fr om it . If you w ant to clos e a menu witho ut selecting anything f rom it , pr ess O or J . Toolbox menus The Tool b ox m en us ( D ) ar e a collection o f menus offe ring func tions and commands use ful in mathematics and progr amming.
30 Getting started Reset input form fields T o r eset a f ield to its def ault value , highli ght the fie ld and pres s C . T o r eset all fields to the ir default v alues, pres s SJ (Clear ) .
Getting started 31 Page 1 Settin g Options Angl e Me asu re Degrees : 36 0 degrees in a c irc le . Rad ian s : 2 r adians in a cir cle . The angle mode y ou set is the angle s e t t i n g u s e d i n b o t h H o m e vi e w a n d the curr ent app .
32 Getting started Entry T ex tbook : An ex pres sion is en te red in mu ch th e sa me way as i f y ou wer e writing it on paper (w ith some ar guments abo ve or belo w others) . In oth er words, y our ent ry could be two -dimensional. Algebraic : An e xpressi on is enter ed on a single li ne .
Getting started 33 Page 2 Dec imal Mark Dot or Comma . Display s a number as 1 2 4 5 6. 98 (dot mode) or a s 1 2 4 5 6, 98 (comma mode). Dot mode uses commas to s eparate elements in lists and mat ri ces, and to separate function arguments. Comma mode us es semicolons as separators in these contexts.
34 Getting started Page 3 Pa g e 3 o f t h e Home Settings in put form is f or setting Exam mode . This mode enable s cer tain functi ons of the calc ulator to be disabled for a set per iod, w ith the disabling contro lled by a pass wor d.
Getting started 35 Specifying a Home setting This e xam ple demonstrate s how to c hange the number for mat from the de fault setting—St anda r d—to Scientif ic w ith t wo dec imal places. 1 . Press SH (Settings) to open the Home Settings input form.
36 Getting started Mathematical calculations The mo st commonly used math oper ations ar e av ailable fr om the ke yboar d (see “Math ke ys ” on page 2 4). Access to the re st of the math functi ons is via v ario us menus (see “Menus ” on page 2 8) .
Getting started 37 • RPN ( Revers e P ol i sh N ota t io n ) . [Not av ailable in CA S view . ] The ar guments o f the expr ession ar e ente red f irst follo wed by the oper ator . The entry of an operator automaticall y evaluates w hat has alread y been entered .
38 Getting started If y ou make a mistak e while ent ering an e xpres sion, y ou can: • delete the c haracte r to the left of the cur sor by pres sing C • delete the c haracte r to the righ t of the curs or by pres sing S C • clear the entire entry line by pr essing O or J .
Getting started 39 The f ollo wing e xamples sho w the use of par entheses, and the use of t he cursor ke ys to mov e out side a group of obje cts encl osed with in paren the ses. Algebraic precedence The H P Prime calc ulates accor ding to the follo wi ng order of pr ecedence.
40 Getting started Explicit and implied multiplication Implied mu ltiplication t akes place w hen two oper ands appear with no operator between them . If you enter AB , fo r exa mp l e, t h e res u l t i s A*B . Noti ce in the ex ample on page 3 8 that we ent ered 1 4 Sk 8 with out the multip lication operator af ter 1 4.
Getting started 41 Tip Pressing S= takes you straight to the very first entry in history, and pressing S takes you straight to the most recent entry. Using the clipboard Y our la st four e xpre ssions ar e alw ay s copied t o the clipboar d and can easily be r etrie ved b y pressing SZ .
42 Getting started Y ou can repeat the pr ev ious calc ulation simply b y pressing E . This can be usef ul if the pre viou s calculatio n inv olv ed Ans . F or ex ample , suppos e you w ant to calc ulate the n th root of 2 when n is 2 , 4, 8 , 1 6, 3 2 , and so on .
Getting started 43 Example : T o assign 2 to to the var iable A : Szj AaE Yo u r s t o r e d v a l u e appe ars as shown at t he ri ght. If y ou then wanted to multiply your stored val u e by 5 , you co ul d enter: Aas 5 E . Y ou can also c reat e your o wn v ari ables in Home v iew .
44 Getting started Complex numbers Y ou can per form ar ithmetic operations using complex numbers. Complex numbers can be entered in the fol lowin g form s, where x is the real part , y is the imagina.
Getting started 45 scr een with as a menu item, y ou c an select an item on that sc reen to se nd it to another HP Prime . Y ou use one o f the supplied USB cables to send obj ects fr om one HP Prime to another . This is the mi cr o - A–mic ro B U SB cable.
46 Getting started Online Help Pres s W to open the online help . The help initiall y pro v ided is conte xt -sensiti ve , that is, it is al way s about the cur rent v ie w and its menu items . F or ex ample , to get help on the Functi on app , pr ess I , select F unction , and press W .
Reverse Polish Notation (RPN) 47 2 Re v erse P olish Notation (RPN) The HP Prime pro vides y ou with three way s of entering objects in Home v iew : • Te x t b o o k An e xpres sion is enter ed in much the same w ay was if y ou w ere wr iting it on paper (w ith some arguments abo ve or below o thers) .
48 Reverse Polish Notation (RPN) The same entr y-line editing tools ar e av ailable in RPN mode as in algebr aic and te xtbook mode: • Pres s C to delete the character to the left of the cursor . • Pres s SC to delete the char acter to the r ight of the cu rs or .
Reverse Polish Notation (RPN) 49 bottom . In RPN mode, y our history is or dered c hron ologically b y defa ult, but y ou can change the or der of the items in his tory . (This is explained in “Manipulating the stack ” on page 5 1.) Re-using results Ther e are two w ay s to re-use a result in history .
50 Reverse Polish Notation (RPN) Ho we ver , y ou could also ha ve ent ere d the arguments s eparat ely and then, w ith a blank entr y line, enter ed the operator ( s ). Y our histor y would look like this befor e entering the o perator : If there are no entr ies in history and you enter an operator or functi on, an err or message appears.
Reverse Polish Notation (RPN) 51 Manipulating the stack A number of stack -manipulation options ar e av ailable. Most appear as menu items acros s t he bottom the scr een. T o see these items, y ou must f irst select an item in history: PICK Cop ies the selec ted item to stac k lev el 1 .
52 Reverse Polish Notation (RPN) DUPN Duplicates all items betw een (and including) the hi ghlighted item and the item on stack lev el 1 . If , for e xample , you ha ve selected the item on stac k lev.
Computer algebra system (CAS) 53 3 Computer algebra s y stem (CAS) A computer algebra sy stem (CAS) enables you to perform sy mbolic calc ulations . By def ault , CAS w orks in e xact mode , giv ing y ou infinite pr ecisi on.
54 Computer algebra system (CAS) The menu buttons in CA S vie w are: • : assigns an ob ject to a v aria ble • : applies common simplificati on rules to r educe an ex pres sion to its simples t form . F or ex ample , simplify(e a + LN( b *e c ) ) yi e l d s b *E X P ( a )* EXP( c ) .
Computer algebra system (CAS) 55 Example 1 T o f ind the roots o f 2 x 2 + 3 x – 2: 1 . With the CA S menu open , select P olynomial and then Fin d Ro ot s . The function proot() appears on the entry line. 2 . Between the parentheses , enter: 2 Asj+ 3 Asw 2 3 .
56 Computer algebra system (CAS) Page 1 Setting Pur pose Angle Measur e Se lect the units for ang le measure- ments: Radians or Degrees . Number F ormat (firs t drop-do wn list) Select the number form.
Computer algebra system (CAS) 57 Page 2 Com plex Selec t this to allow co mplex r esults in var iables. Use √ If chec ked, s econd order poly no - mials ar e factor iz ed in comple x mode or in r eal mode if the dis- cr iminant is positiv e.
58 Computer algebra system (CAS) Setting the form of menu items One setting that aff ects the CAS is made ou tside the CAS Settings scr een. This setting determines whether the commands on the CA S menu ar e pre sented de scr iptiv ely or b y their command name .
Computer algebra system (CAS) 59 functi ons to be pre sented by the ir command name, deselec t the Menu Display opti on on the second page of the Ho me Settings scr een (see “Home settin gs ” on page 30) .
60 Computer algebra system (CAS).
Exam Mode 61 4 Ex am Mod e The HP Pr ime can be pr ecis ely conf igur ed for an e xaminatio n, w ith any number of f eatures or f unctions disabled for a set per iod of time. C onfigur ing a HP Prime for an e xaminatio n is ca lled ex am mode configur ation .
62 Exam Mode Modifying the default configuration A conf igur ation named Default Exam a ppears w hen yo u first acces s the Exam Mode scr een. Thi s con figuration has no functions disabled. If onl y one configurati on is needed, y ou can simply modify the default ex am confi guration .
Exam Mode 63 An e xpand box at the left of a f eature indicates that it is a categor y with sub-items that y ou can ind i viduall y disable . (Notice that there is an e xpan d bo x beside S ystem Apps in the ex ample show n abov e .) T ap on the ex pand box to s ee the sub-items .
64 Exam Mode 5 . T ap , select Copy from the menu and enter a name for the new configuration. See “ Adding t ext” on page 2 3 if you need help with entering alphabetic c haracters . 6. T ap tw ice . 7 . T ap . The Ex am Mode Configuration scr een appears.
Exam Mode 65 T o act iva te ex am mode: 1. I f t h e Ex am Mode screen is not sho wing , pres s SH , tap and tap . 2 . I f a con figu ration other t han Default Exam is r equired , choose it f rom the Configuration list . 3 . Selec t a time -out period f rom the Timeout list.
66 Exam Mode mode , with the spec ifi ed disabled feature s not accessible to the user of that calculator . 9 . Repeat f rom s tep 7 for eac h calculator that needs t o hav e its functi onality limited.
Exam Mode 67 To return to the default configuration 1. P r e s s SH . T he Home Setting s screen appears. 2. Ta p . 3. Ta p . The Ex am Mode scr een appea rs . 4. Choos e Default Exam from t he Configu ration list . 5. Ta p , selec t Reset from the menu and tap to confirm your intention to return the configuration to its default settings.
68 Exam Mode.
An introduction to HP apps 69 5 An intr oduc tion to HP apps M u c h o f t h e f u n c t i o n a l i t y o f t h e H P P r i m e i s p ro vi d e d i n p a c ka g e s called HP apps.
70 An introduction to HP apps As y ou use an app to explore a les son or solve a pr oblem, y ou add data and def initions in one or mor e of the app ’s vie ws . All this info rmation is a utomaticall y sav ed in the app. Y ou can co me back t o the app at any time and all the infor mation is still ther e .
An introduction to HP apps 71 With one ex ception , all the apps mentioned abov e are desc ribed in detail in this user guide . The ex ception is the DataStr eamer app . A brie f introduc tion to this app is gi ven in the HP Prime Qu ick St ar t Gu ide .
72 An introduction to HP apps Y ou can change the sort order of the built-in apps to: • Alphabeticall y The app icons are so rted alphabetically by n ame, and in ascending order: A to Z. • Fix e d Apps are displayed in their default order: Function, Advanced Graphing, Geometry … Polar, a nd Sequence.
An introduction to HP apps 73 App views Most a pps have three maj or vi ew s: Sy mbolic , Plo t, and Numer ic. Thes e vie ws ar e based on the s ymboli c, gr aphic, and numer ic repr esentations of mathematical obj ects. The y are accessed thr ough the Y , P , and M k ey s near the top left of the k eyboar d.
74 An introduction to HP apps Symbolic Setup view The S y mbolic Setup v iew is the same for eac h app. It enables you to o ver ride the sy stem-wi de settings for angle measur e , number for mat, and comple x- number entry . The ov err ide applies only to the c urrent app .
An introduction to HP apps 75 Plot view The table belo w outlines w hat is done i n the P lot vie w of eac h app. App Use t he Plot vie w to: Advanc ed Gra phing Plot and explor e the o pen sentences selected in S ymbolic v ie w . F inance Display an amorti z ation gr aph.
76 An introduction to HP apps Plot Setup view The table below outlines what is done in the P lot Setup vi ew of each app . App Use t he Plot Setup vie w to: Advanc ed Graphing Modify the appearance of plots and the plot env i r onm ent . F inance Not used F unction Modify the appearance of plots and the plot env i r onm ent .
An introduction to HP apps 77 Numeric view The table belo w outlines w hat is don e in the Numeri c vie w of each app . App Use the Numeric vie w to: Advanc ed Gra phing Vi ew a table of numbers gener ated by the open sentences se lected in S ymboli c vie w .
78 An introduction to HP apps Numeric Setup view Th e t a b l e b e l ow o u t l i n es wh a t i s d o n e i n t h e N u m e r ic S e t u p vi e w of each ap p. T ri angle Solv er Enter know n data about a tr iangle and solve for the un known data. T ri g Explorer Not used App Use the Numeric v iew to: (Cont .
An introduction to HP apps 79 Quick example The fo llow ing ex ample uses all six app vi ew s and should give y ou an idea of the typ ical w orkflo w inv olv ed in wor king with an app . The P ol ar app is used as the sample app. Open the app 1 . Open the Appli cation Libr ary by pr essing I .
80 An introduction to HP apps Symbolic Setup view 4. Press SY . 5. S e l e c t Radians from th e Angl e Measure menu . Plot view 6. Press P . A graph of the equation is plotted. However, as the illustration at the right shows, only a part of the petals is visible.
An introduction to HP apps 81 Numeric View The values generated b y the equation can be seen in Numer ic vi ew . 10 . P r e s s M . Suppos e you w ant to see j ust whol e nu mb ers fo r ; in other word s, yo u wa n t t h e i n cre me n t betw een consec uti ve v alues in the column to be 1 .
82 An introduction to HP apps Add a definition With the e xcepti on of the P arametr ic app , there ar e 1 0 f ields fo r entering def initions. In the P ar ametric app ther e are 20 fi elds, two for eac h paired def inition . 1 . Highlight an empt y field y ou want to use, e ith er by tapping on it or scr olling to it .
An introduction to HP apps 83 • F rom Home v ari ables Some Home variables can be incorporated into a symbolic definition. To access a Home variable, press a , tap , select a category of va riable, and select the variable of interest. Thus you could ha ve a definition that reads F1(X)=X 2 +Q .
84 An introduction to HP apps • Fro m a p p fu n ct io n s Some of the functions on the App menu can be incorporated into a definition . The App menu is one of the Toolbox menus ( D ). The following definition incorporates the app function PredY : F9(X)=X 2 + Statistics_2Var.
An introduction to HP apps 85 Y ou can tell if a def inition is selec ted by the tic k (or chec kmark) beside it . A checkmark is added b y default as soon as y ou cr eate a def inition . So if y ou don ’t w ant to plot or e valua te a partic ular def inition , highlight it and t ap .
86 An introduction to HP apps Symbolic view: Summa ry of menu buttons Button P ur pose Cop ies the highligh ted definitio n to the entry line for editing . T ap when done. T o add a ne w definiti on—ev en one that is r eplacing an e xis ting one—highlight the fi eld an d just st ar t entering y our new definiti on.
An introduction to HP apps 87 Common operations in Symbolic Setup view [Scope: all apps] The S ymboli c Setup vi ew is the same for all apps . Its primary purpose is to allow y ou to ov erri de t hree of the sy stem-wide settings specifi ed on the Home Settings wi n d ow .
88 An introduction to HP apps Common operations in Plot view Plo t view f un c t io na l i t y t h a t i s c om m o n to m a ny ap p s is d e scri b e d in detail in this section . Functi onalit y that is available onl y in a particular app is desc ribed in the chapter dedicated to that app.
An introduction to HP apps 89 Zoom keys Ther e are two z oom k eys: pr essing + z ooms in and pressing w z ooms out . The e xtent of the scaling is determined by the ZOOM FAC TOR settings (explained a bove). Zoom menu In Plot v iew , tap and tap an option .
90 An introduction to HP apps Box zoom A b o x zo o m e n a b l e s y o u t o zo o m i n o n a n a r e a o f t h e s c r e e n t h a t you sp e cif y . 1 . With the P lot v iew menu open , tap and select Box . 2 . T ap one corner of the area y ou want to zoom in on and then tap .
An introduction to HP apps 91 Views menu The most commonl y used z oom options a re als o availa ble on the View s menu. T hese are: • Auto sca l e • Dec ima l • Integer • Tr i g . The se optio ns—whi ch can be appli ed what ev er vi ew y ou ar e cur rentl y working in—ar e explained in th e table immediately above .
92 An introduction to HP apps Note that ther e is an Unzoom option on the Zoo m menu . Use t h i s t o re t u r n a p l o t t o i t s p r e -zo o m s t a t e .
An introduction to HP apps 93 Y Out Y Out Square Square Notice that in this ex ample , the plot on left has had a YI n z oom applied to it . The Square z oom has r eturned the plot to its default state wher e t he X and Y scales are eq ual.
94 An introduction to HP apps Tri g Trig Trace [Scope: Ad vanced Gra phing, F unction , P arametr ic , P olar , Sequence , Solv e, S tatistics 1 V ar , and Statistics 2V ar .] The tr acing f unctionality enables yo u to mov e a cur sor (the trace cur so r ) along the curr ent g raph .
An introduction to HP apps 95 To evaluate a definition One of the pr imary uses of the tr ace func tionality is to ev aluate a plot ted definit ion. Suppose in S ymbolic view y ou h ave def in ed F1(X) as (X – 1) 2 –3 . Suppos e further that you w ant to know what the v alue of that functi on is when X is 2 5.
96 An introduction to HP apps Plot view: Summary of menu buttons Common operations in Plot Setup view This sec tion cov ers onl y operatio ns common to the apps mentioned . See the chapter dedicated to an app for the a pp- specif ic operations done in P lot Setup vie w .
An introduction to HP apps 97 confi guration opti ons are spr ead acr oss two pages. T ap to mo ve fr om the fir st to the second page, and to r eturn to the f irst page . Tip When you go to Plot view to see the graph of a definition selected in Symbolic view, th er e may be no graph shown.
98 An introduction to HP apps Page 2 S * MAR K [St ats 2 V ar only] Sets the gr aphic that w ill be used t o r ep r esent a data point in a scat ter plot. A differ ent graphic can be used for each of the fi ve analy ses that can be plot ted together .
An introduction to HP apps 99 Graphing methods The HP Pr ime giv es you the option o f choosing one of thr ee gra phing methods. The methods ar e descr ibed below , w ith each applied to the functi on f(x) = 9*sin(e x ). • adaptiv e : th i s g ives ve r y acc urate r esults and is us ed by de fault .
100 An introduction to HP apps Restore default settings [Scope: Ad vanced Gra phing, F unction , P arametr ic , P olar , Sequence , Solv e, S tatistics 1 V ar , Statistic s 2V ar , Geometry .] T o r estor e one field to its def ault setting: 1 . Select t he field .
An introduction to HP apps 101 x- values w ill be 1 0, 1 0. 1 , 1 0.2 , 1 0. 3, 1 0.4, etc . (Zoo ming out does the opposite: 1 0, 1 0.4, 1 0, 8 , 1 1 .2 etc. becomes1 0, 1 1 .6, 1 3.2 , 1 4.8, 1 6.4 , etc.). Zoom options In Numeri c vie w , z oom options are a vailable fr om tw o source s: • the k ey board • the menu in Numeri c vie w .
102 An introduction to HP apps The z oom op tions are explained i n the following table. Evaluating Y ou can step thr ough the table of e valuations in Nume ric v ie w by pr essing = or . Y ou can also q uickl y jump to an e valuatio n by enter ing the independent var iable of inter est in the independent vari able column and tapping .
An introduction to HP apps 103 3. Tap . Numeric view is refreshed, with the value you entered in the first row and the result of the evaluation in a cell to the right.
104 An introduction to HP apps Numeric view: Summary of menu buttons Button P urp ose T o modify the incr ement between consecuti ve values of the independ ent var iable in the table of evaluati ons. See page 1 00. [Build Y ourOwn only] T o edit the v alue in the select ed cell.
An introduction to HP apps 105 Common operations in Numeric Setup view [Scope: Adv anced Graphing , Fu nction , P arametr ic, P olar , Sequence] Pres s SM to open Numeric Setup v ie w .
106 An introduction to HP apps T o help y ou set a starti ng number and increment that matches the c urr ent P lot vie w , tap . Restore default settings T o r estor e one field to its def ault setting: 1 . Select t he field . 2 . Press C . T o re store all default settings, pr ess SJ .
An introduction to HP apps 107 T o add a note to an app: 1. O p e n t h e a p p . 2. P re s s SI (Info) . If a note has already been crea ted for this app, its contents are displayed.
108 An introduction to HP apps Lik e built -i n apps, customiz ed apps c an be sent to anot her H P Prime calculator . This is explained in “Sharing data” on page 44. Customi z ed apps can also be rese t, deleted, and sorted ju st as built-i n apps can (as e xplained earlier in this chapter ) .
An introduction to HP apps 109 Seque nce app—see c hapter 1 7, “Seq uence app ” , beginning on page 2 8 1. As we ll as cloning a built -in app—as descr ibed abo ve—y ou can modify the internal w orkings of a c ustomi z ed app using the HP Prime pr ogr amming language.
110 An introduction to HP apps Suppose y ou are in Home vi ew and want to r etrie ve the mean of a data set r ecently calc ulated in the S tatistics 1V ar app. 1 . Press a . This opens the Variables menu . From here you can access Home variables, user-defi ned variables, and app vari ables.
Function app 111 6 Function app The F uncti on app enables y ou to explor e up to 1 0 r eal- valued , r ectangular func tions of y in ter ms of x; for exa m p l e, an d .
112 Function app Open the Function app 1 . Open the F uncti on app. I Select Function Recall that you can open an ap p just by tapping its icon. You can also open it by using the cursor keys to highlight it and then pressing E . The Function app starts in Symbolic view.
Function app 113 5. D e ci d e i f y o u w a n t t o : – giv e one or mor e function a c ustom colo r when it is plotted – ev aluate a dependent function – deselec t a definiti on that you do n’t w ant to exp l ore – incorpor ate var iables, math commands and CA S commands in a def inition.
114 Function app Trace a graph By de fault , the trace f unctionality is acti ve . This enable s y ou to mov e a cursor along a gr aph. If mor e than two gr aphs are sho wn , the gra ph that is the highest in the list of func tions in S ymboli c vie w is the gra ph that will be traced by def ault.
Function app 115 • Use opti ons on the Zoom menu to z oom in or out , hor iz on tally or verti cally , or both , etc. • Use option s on the Vi e w menu ( V ) to se lect a pre- def ined vie w . Note that the Autoscale option attempts to pro vide a best fit, sho w in g as man y of the cr itical f eature s of each plo t as possible .
116 Function app Y ou can also choose w hether the table of data in Numeri c vie w is automaticall y populated or whether it is populated by y ou t yp ing in the pa rtic ular x -va lues y ou are in tere sted in. T hese opti ons— Automatic or BuildYourOwn —are available fr om the Num Ty p e list.
Function app 117 ex pressi ons selected in S y mbolic v iew : 1–x and ( x–1 ) 2 –3 . Y ou can also scr oll through the columns of the depe ndant var iables (la beled F1 and F2 in the illustr ation abo ve). You can also scroll the table vertically or horizontally using tap and drag gestures.
118 Function app Analyzing functions The Fun ct ion menu ( ) in P lot vi ew enable s you t o find r oots, inters ections, slopes , signed areas , and ex trema f or any f unction def ined in the Func tion app . If y ou have mor e than one func tion plotted, y ou ma y need to choo se the functi on of inter est befo rehand .
Function app 119 Note the button. If you tap this button, vertical and horizontal dotted lines are drawn through the current position of the tracer to highlight its position. Use this feature to draw attention to the cursor location. You can also choose a blinking cursor in Plot Setup.
120 Function app 3 . Choo se the functi on who se point of inte rsecti on with the c urren tly selec ted functi on yo u wish to f ind. The coordinates of the intersection are displayed at the bottom of the screen. Tap on the screen near the intersection, and repeat from step 2.
Function app 121 To find the signed area between the two functions W e ’ll no w find the area betw een the two f unctions in the ran g e . 1. T a p and select Signed area . 2. Spec ify the start val u e fo r x : Tap and press Q 1 . 3 E . 3. Ta p . 4.
122 Function app Shortc ut : When the Goto opti on is available , y ou can display the Go T o sc r e e n s i m p l y b y t y p i n g a n u m b e r. T h e number y ou t ype appears on the entry line. Jus t tap to accept it. To find the extremum of the quadratic 1 .
Function app 123 To access Function variables The Fun ct io n v aria bles are a vailable in Home v ie w and in the CAS, w here they can be included as arguments in calculati ons. The y ar e also available in S ymboli c vi ew . 1 . T o access the var iables, press a , tap and select Function .
124 Function app Summary of FCN operations Operation Description Root Select Root to f ind the root of the cur rent f unction near est to the tr acing cursor . If no root is found, b ut only an extr emum, then the r esult is labeled Extremum instead o f Root .
Advanced Graph ing app 125 7 Adv anced Graphing app The A dvanced Gr aphing app enables yo u to define and explor e the gr aphs of symboli c open sentences in x , y , both or neither . Y ou can plot conic secti ons, poly nomials in standard or gener al form , inequalities, and f unctions.
126 Advanced Graphin g app Getting started with the Advanced Graphing app The A dv anced Graphing app u ses the c ustomary app vi ew s: S ymbolic , P lot, and Numer ic descr ibed in chapter 5.
Advanced Graph ing app 127 Open the app 1 . Open the Ad vanced Gra phing app: I Select Advanced Graphing The app opens in the Symbolic view. Define the open sentence 2.
128 Advanced Graphin g app Set up the plot Y ou can change the r ange of the x - and y -ax es and the spac ing of the interval marks along the ax es. 4. Display Plot Setup view: SP (Setup) Fo r t h i s ex a m p l e, y o u c a n leav e the plot settings at the ir defa ult values .
Advanced Graph ing app 129 8. Tap . The definition as you entered it in Symbolic view appears at the botto m of the sc reen. 9. Tap . The definition is now editable. 10. Change the < to = and tap . Notice that the graph changes to match the new definition.
130 Advanced Graphin g app The tr acer does no t extend be yo nd the curr ent P lot v iew w indow . The table belo w contains brief des cripti ons of each option .
Advanced Graph ing app 131 Numeric view The Numer ic vi ew of mo st HP apps is designed to e xplore 2 - var iable r elations using n umeri cal tables. Becau se the Adv anced Gra phing app expands this.
132 Advanced Graphin g app Numeric Setup Although y ou can configur e the X- and Y -values show n in Numeri c vie w by enter ing values and z o oming in or out , y ou can also dir ectl y set the values show n using Numeri c setup.
Advanced Graph ing app 133 Trace Edge 16. Tap and select Edge . No w the table show s (if possible) pairs of value s that mak e the relation tr ue. By de fault , the fir st column is the Y -column and ther e are multiple X-columns in case more than one X-v al ue can be pair ed w ith the Y -value to mak e the relation tr ue.
134 Advanced Graphin g app Plot Gallery A gallery of interesting gr aphs—and the equations that gener ated them—is pro v ided with the calc ulator . Y ou open t he galler y from Pl o t vi ew : 1 . W ith Plot v ie w open, pres s the Menu key . Note that y ou pr ess the Menu k e y here , not the Menu touch button on th e scr een.
Geometry 135 8 Geo met ry The Geometry app enables yo u to draw and e xplore geometr ic constru ctions . A geometri c constructi on can be composed of any n umber of geometri c objects , such as points , lines, pol ygons , curves , tangents, and so o n.
136 Geometry Preparation 1. P r e s s SH . 2. O n t h e Home Setting scr een set the number for mat to Fixed and the number of dec imal places to 3 . Open the app and plot the graph 3. P re s s I and selec t Geometry . If there are objects showing that you don’t need, p ress SJ and confirm your intention b y tapping .
Geometry 137 Add a tangent 8. W e w ill now add a tange nt to the curv e, making poin t B the point of ta ngency: > More > Tangent 9 . T ap o n point B , press E and then pre ss J . A tangent is drawn through point B . (Depending on where you placed point B , your illustration might be different from the one at the rig ht.
138 Geometry finger completes the mo ve and dese lects the point . In this case t h e re i s no way t o c a n c e l t h e m ove un l e s s yo u h av e a ct i va t e d k ey board shortc uts, whi ch pr ov ides y ou with an undo functi on. (Shortcuts ar e descr ibed on page 1 4 7.
Geometry 139 point B (referred to as GB in Symbolic view) and the later is to constrained to the slope of C (referred to as GC in Symbolic view). 19 . Yo u s h o u l d h a v e point() on the entry line.
140 Geometry tangent changes in Plot view, the value of the slope is automatically updated in Numeric view. 2 6 . With the new calc ulation highli ghted in Numeri c vie w , tap . Selecting a calculation in Numeric view means that it will also be displayed in Plot vi ew.
Geometry 141 Trace the derivative Po i n t D is t he point whos e ordinate value matches the der iv ativ e of the curv e at point B . It is easi er to see how the deri vati ve c hanges by looking at a plot of it rather than compar ing subsequent calc ulations .
142 Geometry Creating or s electing an objec t alwa ys in vol ves at least tw o steps: tap and pr ess E . Only b y pressing E do y ou confirm y our intenti on to cr eate the point or select an objec t. When cr eating a point , you can tap on the sc reen and then us e the cur sor k ey s to acc uratel y position the point bef or e pre ssing E .
Geometry 143 four v ert ice s are named D , E , G, and H . Mor eov er , eac h of the si x segments is also giv en a name: I, J , K, L , M, and N. The se names are not dis playe d in Plot v ie w , but y ou can see t h e m i f y o u g o t o S y m b o l i c v i e w ( s e e “ S y m b o l i c v i e w i n d e t a i l ” on page 1 48).
144 Geometry Coloring objects An obj ect is colored black b y default (and cy an when it is selec ted) . If you w ant to change the color of an ob ject: 1 . S elect the obj ect wh ose color y ou w ant to c hange. 2. P r e s s Z . 3. S e l e c t Change Color .
Geometry 145 Clearing an object T o c lear one objec t, se lect it and tap C . N o t e t h a t a n o b j e c t is distinct fr om the points y ou enter ed to cr eate it. Th us deleting the obj ect does not delete the po ints that define it . Tho se points r emain in the app .
146 Geometry Plot view: buttons and keys Plot Setup view The P lot Set up v iew enables y ou to conf igur e the appear ance of P lot v ie w and to take adv antage of k eyb oard shortcuts . But ton or k ey Pur pose V ar ious scaling options . See “Zoom ” on page 8 8.
Geometry 147 The f ields and options are: • X Rng : T w o fields for enter ing th e minimum and max imum x-v alues, ther eby gi ving the defa ult hori z ontal ra nge. As w ell as c hanging this range on the Geomet r y Pl ot S e t up scr een, yo u can change it by panning and z ooming.
148 Geometry Symbolic view in detail Ev er y object—whether a point , segment, line , poly gon, or c ur ve—is gi ven a name, and its de finition is display ed in S ymboli c vie w ( Y ). The name is the name for it y ou see in P lot v iew , but pr efi xed b y “G” .
Geometry 149 Note Calculations referencing geomet ry variables can be made in the CAS or in the Numeric view of the Geometry app (explained below on page 150). Y ou can change the definiti on of an object b y selecting it , tapping , and altering one or mor e of its def ining paramet ers.
150 Geometry Deleting an object As w ell as deleting an object in P lot v ie w (see page 1 45) you can delete an object in S ymboli c vie w . 1 . H ighlight the def inition of the ob ject y ou want t o delete. 2 . T ap or pr ess C . T o delet e all objects , press SJ .
Geometry 151 You could have entered the comma nd and object name manually, that is, without choosing them from menus. If you enter object names manu ally, remember that the name of the object in Plot view must be given a “G” prefix if it is used in any calculation.
152 Geometry grouped accor ding to their type , with each gr oup gi ven its own m e n u. If yo u are building a calculati on, y ou can select an obje ct fr om one of the se var iables me nus. T he name of the se lected obj ect is placed at the insertion po int on the entry line.
Geometry 153 Geometric objects The geome tric ob jects disc uss ed in this section ar e thos e that can be cr eated in Plot v ie w . Objects can also be cr eated in S ymbolic view—more , in fact, than in Plot vi ew—but these are discu ssed in “Geometr y functions and commands ” on page 1 6 5.
154 Geometry placed on a c irc le will r emain on that c ir cle r egardles s of how y ou mov e the point . If ther e is no object w her e you t ap, a po int is cr eated if you then press E . Midpoint T ap wher e you w ant one point to be and press E .
Geometry 155 Erase Trace Eras es all trace lines , but leav es the definitio n of the trace points in S ymbo lic vie w . While a T r ace definition is s till in S ymboli c vie w , if you mo ve the point again , a new tr ace line is cr eate d. Center T ap a cir cle and pr ess E .
156 Geometry Line Segment T ap where y ou want one endp oint to be and p res s E . T ap w here y ou want the other endpoint to be and pres s E . A segment is dra wn between the tw o end p oints . Key b o a rd s h o r t cu t : r Ray T ap w here y ou want the endpoint to be and pr ess E .
Geometry 157 Parallel T ap on a point ( P ) and pr ess E . T ap on a line ( L ) and pr ess E . A ne w line is dra w parallel t o L and passing thr ough P . Perpendicular T ap on a point ( P ) and pr ess E . T ap on a line ( L ) and pr ess E . A ne w line is dra w perpendic ular to L and passing thr ough P .
158 Geometry fo ur vertices ar e automati cally calc ulated and the r egular hex agon is dr aw n. Special Eq. trian gle Pr oduces an eq uilateral tr iangle . T ap at one v ertex and pr ess E . T ap at another verte x and pr ess E . T he location o f the third v ertex is a utomaticall y calculated and the tri angle is dra wn .
Geometry 159 Special Circumcircle A circu m ci rcl e i s th e ci rcl e that passes thr ough eac h of the tri angle’s thr ee vertic es, thus enc losing the tri angle. T ap at each v ertex of the tri angle, pr essing E after e ach tap . Incircle An incir cle is a c irc le that is tangent to each of a pol ygon ’s sides .
160 Geometry Locus T ak es two points as its argumen ts: the firs t is the point w hose possible locati ons form the loc us; the second is a po int on an objec t. T his second po int dri v es the firs t through its loc us as the second mo ves on its objec t.
Geometry 161 Geometric transformations The Tr a n s f o r m menu—d isplay ed by tapping —pr ov ides nume rou s tools for y ou to perfo rm tr ansformati ons on geometr ic obj ects in P lot vi ew .
162 Geometry Reflection A reflecti on is a tr ansformati on whi ch maps an object or set of point s onto its mirr or image, w here the mir ror is either a po int or a line.
Geometry 163 Rotation A r otation is a mapping that rotates each point b y a fix ed angle ar ound a cent er point . The angle is de fined using the angle() command , wi th the verte x of the angle as the fir st argumen t. Suppose you w ish to rotate the squar e (GC) arou nd point K (GK) thr ough ∡ LKM in the figu re to th e righ t.
164 Geometry lengths of the co rre sponding segments . If k=1 , then the lengths CA and CA ’ are r ecipr ocals. S u p p o s e yo u w i s h t o fi n d t h e i n v e r s i o n o f a c i r c l e ( G C ) w i t h a point on the c ir cle (GD) as center . 1 .
Geometry 165 Geometry functions and commands The lis t of geometry-specif ic functi ons and commands in this section co ve rs those that can be f ound by ta pping in both S ymbo lic and Numer ic v ie w and those that ar e only av ailable fr om the Catlg men u .
166 Geometry center R eturns the center of a c ir cle . center(circle) Example: center(circle(x 2 +y 2 –x–y)) giv es point(1/2,1/2) division_point F or two points A and B, and a numeri cal factor k , r eturn s a point C suc h that C-B= k *(C-A).
Geometry 167 isobarycenter Retur ns the hy pothetical cent er of mass of a set o f points. W orks lik e barycenter but assume s that all poin ts have eq ual weig h t. isobarycenter(point1, point2, …,pointn) Exam ple: isobarycenter(–3,3,3* √ 3*i) ret u rn s poin t(3* √ 3*i/3) , whi ch is equi valent to (0, √ 3).
168 Geometry point2d Randoml y re-distributes a set of points suc h that, fo r each point , x ∈ [–5,5] and y ∈ [–5 ,5]. An y further move ment of one of the po ints will r andomly r e -distribute all o f the points w ith each tap or directi on ke y press .
Geometry 169 bisector Gi ven thr ee points , cr eates the bisec tor of the angle def ined by the thr ee poin ts whos e verte x is at the first po int. T he angle does not ha ve to be dra wn in the P lot vi ew . bisector(point1, point2, point3) Exam ples: bisector(A,B,C) dra ws the b isector of ∡ BAC.
170 Geometry median_line Gi ven thr ee poin ts that define a tr iangle , cr eates the median of the tr iangle that pas ses thr ough the firs t point and co ntains the midpoi nt of the segment def ined by the other tw o points.
Geometry 171 perpendicular Dra ws a line thr ough a giv en point that is perpendic ular to a gi ven line . The line may be de fined b y its name, tw o points, or an expr essi on in x and y . perpendicular(point, line) or perpendicular(point1, point2, point3) Exam ples: perpendicular(GA, GD) dr aw s a line per pendic ular to line D through po int A.
172 Geometry Polygon equilateral_triangle Dr aw s an equilater al tria ngle defined b y one of its side s; that is, b y two consec utiv e vertices . The third po int is calculated automaticall y , but is not def ined symboli cally .
Geometry 173 isosceles_triangle Dra ws an isosceles tr iangle defined by t wo of its v ertices and an angle. T he ve r tices def ine one of the tw o sides equal in length and the angle def ines the angle betw een the two sides of equal length .
174 Geometry polygon Dr aw s a poly gon fr om a set of v ertices . polygon(point1, point2, …, pointn) Example: polygon(GA, GB, GD) dr aw s Δ ABD quadrilateral Dra ws a quadrilater al fr om a set of fo ur points. quadrilateral(point1, point2, point3, point4) Example: quadrilateral(GA, GB, GC, GD) dr aws quadr ilateral ABCD .
Geometry 175 Exam ple rhombus(GA, GB, angle(GC, GD, GE)) dr a ws a rhombus on segment AB such that th e angle at vertex A has the same measure a s ∡ DCE .
176 Geometry Curve function Dra ws the plot o f a function , giv en an expr ession in the independent var iable x. Note the use of lo w ercase x . plotfunc(Expr) Example: Example: plotfunc(3*sin( x) ) dr aws the gr aph of y =3*sin( x ).
Geometry 177 ellipse Dra ws an ellipse , giv en the foc i and either a point on the ellipse or a scalar that is one half the constan t sum of the distances f rom a poin t on the ellipse to each o f the foc i.
178 Geometry incircle Dr aws the incir cle of a tri angle, the c ir cle tangent t o all three sides o f the triangle . incircle(point1, point2, point3) Example: incircle(GA, GB, GC) dr aw s the inc irc le of Δ ABC.
Geometry 179 inversion Dr aws the in versi on of a point , w ith res pect to another po int, by a scale f actor . inversion(point1, realk, point2) Exam ple: inversion(GA, 3, GB) dr aw s point C on line AB suc h that AB*A C=3 . In this case , point A is the cente r of the inv ersi on and the scale fac tor is 3 .
180 Geometry rotation Rotates a geometric object , about a giv en center point, thr ough a giv en angle . rotate(point, angle, object) Example: rotate(GA, angle(GB, GC, GD),GK) r otates the geometri c object labeled K, abou t point A, through an angle equal to ∡ CBD .
Geometry 181 Measure Plot angleat Used in S ymbolic v iew . Gi ven the three points of an angle and a fo ur th point as a location, display s the measure of the angle def ined by the f irst thr ee points . The measur e is displa yed , wi th a label, at the locati on in the P lot vi ew gi ven b y the fo ur th point .
182 Geometry distanceatraw W orks the same as distanceat, but w ithout the label. perimeterat Used in S ymboli c vi ew . Display s the perimeter of a pol ygon or c irc le . The measur e is display ed, w ith a label , at the gi ven po i nt i n Pl ot vi ew .
Geometry 183 affix Retur ns the coordinat es of a point or both the x - and y -l engths of a ve ctor as a comple x number . affix(point) or affix(vector) Exam ple: if G A is a point at ( 1 , –2) , then affix(GA) retu rns 1–2i . angle Returns the measure of a directed angle.
184 Geometry Examples: If G A is defined to be the unit c irc le, then area(GA) ret u rn s . area(4-x^2/4, x=-4..4) ret ur n s 1 4. 666 … coordinates Gi ven a v ector o f points, r eturns a matr ix co ntaining the x - and y-coor dinates of tho se points .
Geometry 185 equation Retur ns the Cartesian eq uation of a c ur ve in x and y , or the Cartesian coor dinates of a point . equation(curve) or equation(point) Exam ple: If G A is the point at (0, 0), GB is the point at ( 1 , 0) , and GC is def ined as cir cle(G A, GB-G A), then equation(GC) ret u r ns x 2 + y 2 = 1 .
186 Geometry If G A is the point at (0, 0), GB is the point at ( 1 , 0) , and GC is def ined as square(G A, GB-G A ) , then perimeter(GC) re t u rn s 4 .
Geometry 187 is_element T est s if a poin t is on a geometr ic ob ject . R eturns 1 if it is and 0 otherw ise is_element(point, object) Exam ple: is_element(point , circle(0,1)) ret u rn s 1 . is_equilateral T ak es three points and te sts whether o r not they are v ertices of a single equilater al tri angle.
188 Geometry is_parallel T ests w hether or not two lines ar e parallel . Retur ns 1 if they are and 0 otherw ise. is_parallel(line1, line2) Example: is_parallel(line(2x+3y=7),line(2x+ 3y=9) re t u rn s 1 . is_parallelogram T ests w hether or no t a set of fo ur points ar e vertices o f a parallelogr am .
Geometry 189 is_square T ests w hether or not a set o f four points ar e v ertices of a squar e. R eturns 1 if the y ar e and 0 otherwise . is_square(point1, point2, point3, point4) Exam ple: is_square(point(0,0), point(4,2), point(2,6), point(-2,4)) ret u r n s 1 .
190 Geometry Example: harmonic_division(point(0, 0), point (3, 0), point(4, 0), p) ret u rn s point(12/5, 0) and stor es it in the var iable p is_harmonic T ests w hether or not 4 points ar e in a harmonic di visi on or ra nge. Re turns 1 if they ar e or 0 otherwise .
Geometry 191 LineHorz Dra ws the horiz ontal line y=a. LineHorz(a) Exam ple: LineHorz(-2) dra ws the hor iz ontal line who se equation is y = –2 LineVert Draws th e ver t ic al li n e x = a.
192 Geometry pole R eturns the pole of the gi ven line w ith re spect to the gi ven ci rcl e . pole(circle, line) Example: pole(circle(x^2+y^2=1), line(x=3)) re t u rn s point(1/3, 0) powerpc Gi ven a.
Geometry 193 single_inter Retur ns the inters ection of curv e1 and curve2 that is closes t to point . single_inter(curve1, curve2, point) Exam ple: single_inter(line(y=x),circle(x^2+y^2=1) , point(1,1)) ret u rn s point(((1+i)* √ 2)/2) vector Creates a vector fr om point1 to point2 .
194 Geometry.
Spreadsheet 195 9 Spre adsh eet The S preadsheet app pro vi des a grid of cells for y ou to enter content (such a s numbers, te xt, e xpressions , and so on) and to perform certain oper ations on wha t yo u e nt e r . T o open the Spr eadsheet app , pre ss I and selec t Spreadsheet .
196 Spreadsheet 3. E n t e r PRICE and tap . Y ou have named the entire firs t c o lu mn PRICE . 4. Select column B . E ither tap on B or us e the cur sor k ey s to highligh t the B cell. 5 . Enter a f ormula fo r your commissi on (being 1 0% o f the pr ice of each it em sold): S.
Spreadsheet 197 1 1 . T o delete the dummy v alues, selec t cell A1 , tap , pres s until all the dummy value s are se lected, and the n pres s C . 1 2 . Select cell C1 . 1 3. Enter a la bel for y our taking s: S.AN TA K I N G S E Notice that t ext str ings, but not name s, need to be enc losed w ithin quotation marks .
198 Spreadsheet 2 3 . Enter a label for y our fi xed costs: S.AN COS TS E 2 4. In cell D5 , enter 1 00. This is what y ou hav e to pay the landow ner for r enting the space for y our stall. 2 5. Enter the label PROFIT in cell C7 . 2 6 . I n cell D7 , enter a formula to calc ulate y our pro fit: S.
Spreadsheet 199 3 2 . T ap and select Color . 3 3 . Choose a color f or the contents o f the selected cells . 34. T ap and select Fill . 3 5 . Choose a color f or the back gr ound of the selec ted cells. The mo st important cells in the s preadsheet w ill no w stand out from the rest.
200 Spreadsheet Cell references Y ou can re fer to the value o f a cell in for mulas as if it w ere a var iable . A cell is re fer enced by its column and r ow coor dinates, and references can be absolute or relative . An absol ute r efe re nce is wr itte n as $C$R ( wh ere C is the column number and R the r ow number ) .
Spreadsheet 201 The f ollo wing is a mor e comple x ex ample in vol ving the naming of an entir e column. 1 . S elect cell A (that is the header cell f or column A). 2. E n t e r COST and tap . 3 . Selec t cell B (that is the header cell f or column B) .
202 Spreadsheet underl ying fo rmula that generates the v alue, mo ve y our cursor to the cell . The entry line show s a for mula if ther e is one. A single for mula can add conte nt to ev ery cell in a column or r ow . F or ex ample, mo ve t o C (the heading cell for column C), enter S.
Spreadsheet 203 The column is f illed with the dat a from the s tatistic s app, starting w ith the cell selected at step 1 . An y data in that column will be o verwr itten by the data being imported. Y ou can also export data from the Spr eadsheet app to a statisti cs app.
204 Spreadsheet The re ar e additio nal spre adsheet functi ons that y ou can use (mostl y related to f inanc e and statistics calc ulations). See “Spr eadsheet a pp func tions ” on pa ge 34 9 . Copy and paste T o cop y one or mor e cells, selec t them and pre ss SV (Cop y).
Spreadsheet 205 Referencing variables An y var iable can be inserted in a cell. This inc ludes Home var iables, App v ariables , CAS var iables and user v ariables .
206 Spreadsheet Using the CAS in spreadsheet calculations Y ou can for ce a spr eadsheet calc ulation t o be perfor med b y the CAS , thereb y ensuring that r esults ar e sy mbolic (and thus e xact). F or ex ample , the for mula = √ Row in r ow 5 gi ves 2.
Spreadsheet 207 Buttons and keys Button or ke y P urpose Ac tivat es the entry line for y ou to edit the obj ect in the select ed cell. (Onl y visible if the selec ted cell has content .) Con verts the te xt y ou hav e enter ed on the entry line to a name .
208 Spreadsheet Formatting options The f ormatting opti ons appear when y ou tap . The y apply to w hatever is c urrentl y select ed: a cell, block , column, r ow , or the entir e spre adsheet.
Spreadsheet 209 Format Parameters E ach for mat at tribute is r epresented b y a parameter that can be refere nc ed i n a fo rmu la. For exam pl e, =D1(1) retur ns the fo rmula in cell D1 (or no thing if D1 has no for mula). The attribut es that can be retr iev ed in a for mulas b y ref ere ncing its assoc iated parameter ar e listed belo w .
210 Spreadsheet r e l e v a n t c e l l . F o r e x a m p l e , w h e r e v e r i t i s p l a c e d g5(1):=6543 enters 6543 in cell g5 . An y pre viou s content in g5 is replaced . Similarl y , B3(5 ) :=2 for ces the contents of B3 to be display ed in medium fon t siz e .
Statistics 1Var app 211 10 Statistics 1V ar app The S tatistics 1V ar app can stor e up to ten data sets at one time . It can per for m one -vari able statistical anal ysis o f one or mor e sets of data. The S tatistics 1V ar app star ts w ith the Numeric v iew which is used to enter data.
212 Statistics 1Var app 2 . Enter the measur ement data in column D1 : 16 0 E 16 5 E 17 0 E 17 5 E 18 0 E 3 . F ind the mean of the sample. T ap to see the statis tics calc ulated fr om the sample data in D1 . Th e m ea n (x _ )i s 1 7 0 . Ther e are more statisti cs than can be display ed on one scr een.
Statistics 1Var app 213 re presen t the data in Plot v ie w: Histogr am , Box and Whisk er , Normal Proba bility , L ine, Bar , or P ar eto . Symbolic view: menu items The menu items you can tap on in.
214 Statistics 1Var app 7 . Ent er the name of the column that yo u will contain the fr equenc ies (in this exam p le, D2 ): 2 8 . I f y o u w a n t t o c h o o s e a color for the gr aph of the data in P lot vi ew , see “Choose a color fo r plots” on page 8 5.
Statistics 1Var app 215 1 3. Configur e a histogr am plot for the data. S P ( ( Setup ) Enter parameters appropriate to y our data. Th ose show n at the r ight w ill ensure that all the data in this particular ex ample are displa yed in Plot v iew . 14 .
216 Statistics 1Var app 1V ar app open, r eturn to Home v ie w and enter Spreadsheet.A1:A10 D7 E . Whic hev er method y ou use, the dat a you enter is automati cally sa ved . Y ou can lea ve this app and come b a ck t o i t l a t e r. Y o u wi l l fi n d t h a t t h e d a t a yo u l a s t e n t e r e d is still a vailable .
Statistics 1Var app 217 Delete data • T o delete a data item, highli ght it and pres s C . The values be low the deleted cell w ill scr oll up one r o w . • T o delete a column of data , highlight an entry in that column and pres s SJ (Clear). Selec t the column and tap .
218 Statistics 1Var app y ou want to sort by income , then y ou make C2 the independent column and C1 the depend ent column. 4. Spec ify an y fr equency dat a column. 5 . T ap . The independent column is sorted as spec ified and any o ther columns are sorted to match the independent column .
Statistics 1Var app 219 Plotting Yo u c a n p l o t : • Histo grams • Box -and- Whisker plots • Normal Probab ilit y plots • Lin e p l o ts • Bar gra phs • Pa r e t o c h a r t s Once y ou have entered y our data and def ined your data set , you can plot y our data .
220 Statistics 1Var app that bin is 6 . The data set is def ined by H3 in S ymboli c v iew . Y ou can see inf ormation abo ut other bins b y pres sing > or < . Box-and-Whisker plot The l ef t wh is ker m a rks the minimum data v alue. The bo x mar ks the firs t quartile , the median , and the third q uartile.
Statistics 1Var app 221 Pareto chart A par eto chart places the data in descending or der and displa ys ea ch w ith its perce ntage of the who l e. Setting up the plot (Plot Setup view) The Pl ot S et up view ( SP ) enables y ou to s pecify many of the same plotting parameters as other app s (such as X Rng and Y Rng ).
222 Statistics 1Var app Plot view: menu items The men u items you can tap on in P lot vi ew ar e: But ton Purpose Display s the Z oom menu . T urns tr ace mode on or off . See “Z oom ” on page 1 00.) Display s the def inition of the c urr ent statistical plot .
Statistics 2Var app 223 11 Statistics 2V ar app The S tatistics 2V ar app can stor e up to ten data sets at one time. It can perf orm two -var iable statistical anal ysis of one or mor e sets of data. The S tatistics 2V ar app star ts w ith the Numeric v iew which is used to enter data.
224 Statistics 2Var app Open the Statistics 2Var app 1 . Open the Statisti cs 2V ar app: I Select Statistics 2Var . Enter data 2 . Enter the advertising minutes d ata in column C1 : 2 E 1 E 3 E 5 E 5 E 4 E 3.
Statistics 2Var app 225 5. S e l e c t a fi t : Fro m t h e Ty p e 1 fi eld select a fit . In this ex ample , select Linear . 6. I f you w an t t o choo se a color for the gr aph of the data in P lot vie w , see “Choo se a color for plo ts” on page 8 5.
226 Statistics 2Var app 1 0. Find the mean sales () . The mean sales , , is appro x imately $1 , 7 9 6 . Pres s to re turn to Numer ic vi ew . Setup plot 1 1 . Change the plotting range to ensur e that all the data points ar e plotted (and to select a differ ent data -point indicator , if you w ish) .
Statistics 2Var app 227 Display the equation 1 3. Return to the S y mbolic vi ew . Y Note the expressi on in the Fit1 fie l d. I t sho ws that the slope ( m ) of th e regression line is 4 2 5 .8 7 5 and the y -inter cept ( b ) is 37 6 . 2 5 . Predict values L et’s now predic t the sales figur e if adv er tising w ere to go up to 6 minutes.
228 Statistics 2Var app The cu rsor jumps from w hatever data point it w as on to the regr ession c ur ve . 1 6. T ap on the regr ession line near x = 6 (near the r ight edge of th e display) . Then pr ess > until x = 6 . If the x -value is not sho w n at the bottom left of the sc reen , tap .
Statistics 2Var app 229 Whic hev er method y ou use , the data yo u enter is automaticall y saved . Y o u can leav e this app and come back to it later . Y ou will find that the data you last enter ed is still av ailable. After entering the d ata, y ou must define da ta sets—and the wa y they ar e to be plotted—in S ymboli c vie w .
230 Statistics 2Var app Delete data • T o delete a data item, highli ght it and p r ess C . The value s below the delete d cell will sc roll u p one ro w . • T o delete a column of dat a, highligh t an entry in that column and press SJ (Clear). Se lect the column and tap .
Statistics 2Var app 231 Defining a regression model Y ou define a r egr ession model in S ymboli c vie w . Ther e are three w ays to do so: • Accept the def ault option to f it the data to a str aight line . • Choose a pr e -defined fit ty pe (logarithmic , exponential , and so on) .
232 Statistics 2Var app To define your own fit 1. P r e s s Y to display the S ymbo lic vie w . 2 . F or the anal ysis y ou are in tere sted in (S1 thr ough S5), select the Ty p e fi el d. 3 . T ap the f ield again to see a menu of fit types . 4. Select User Defined fr om the menu .
Statistics 2Var app 233 Computed statistics When y ou tap , three sets o f statistics become av ailable. B y default , the statisti cs inv olv ing both the independent and depend ent columns are sho wn . T ap to see the st atistics in vol ving j ust the independent column or to displa y the statisti cs der iv ed fr om the dependent column .
234 Statistics 2Var app The statisti cs display ed when you tap are: The statisti cs display ed when you tap are: Plotting statistical data Once you hav e entered your data, selected the da ta set to analyz e and spec ified y our fit model, y ou can plot y our data .
Statistics 2Var app 235 necessary), the X Rng and Y Rng fields in Plot Setup view . ( SP ). 3. P re s s P . If the data set and regr ession line ar e not ideally positio ned, Pr ess V and se lect Autoscale . Autos cale can be relied upon to giv e a good star ting scale w hich can the n be adjusted lat er in the Plo t Setup view .
236 Statistics 2Var app pres s a fourth time , you w ill re turn to the S1 scatter plot . If you ar e confused as to w hat yo u are tr acing , just tap to see the definiti on of the object (scatter plo t or f it) curr entl y being tr aced.
Statistics 2Var app 237 Predicting values PredX is a func tion that pr edicts a va lue for X giv en a val u e fo r Y . Lik ew ise , PredY is a functi on that predi cts a val u e fo r Y g iven a val u e fo r X . In both cases , the pr edictio n is based on the equati on that best fits the data according to the spec ifi ed fit type .
238 Statistics 2Var app Tip In cases where more than one fit curve is displayed, the PredX and PredY functions use the first act ive fit defined in Symbolic view. Troubleshooting a plot If y ou hav e problems plotting, c heck the f ollow ing: • The f it (that is, r egres sion model) that y ou int ended to select is the o ne selected .
Inference app 239 12 Infer ence app The Inf er ence app enable s you to calc ulate conf idence intervals and undertake h ypothesis tests bas ed on the Normal Z -distributi on or Student’s t -distribution .
240 Inference app Symbolic view options The table belo w summari z es the options available in S ymbolic v ie w for the two inf erence methods: h ypothesis test and confi dence inter val . If y ou choo se one of the h ypothesis tes ts, y ou can choo se an alternativ e hypothesis to test against the null h ypothesis .
Inference app 241 Select the inference method 2. Hypothesis Test is the def ault infer ence method . If it is not select ed, tap on t he Method f ield and select it. 3. C h o o s e t h e t y p e o f test . In this case , select Z–Test: 1 fr o m th e Ty p e menu .
242 Inference app The Nume ric v ie w is wher e yo u enter the sample statis tics and population parameters fo r the situation you ar e ex amining . The sa mple data supplie d here belo ng to the case in w hich a s tudent has generated 5 0 pseudo-random numbers o n his graphing calc ulator .
Inference app 243 Importing statistics The Inf ere nce app can c alc ulate confidence in ter vals and test h ypothese s based on data in the Statistics 1V ar and Statisti cs 2V ar apps. T he follo wing e xample illustr ates the proces s. A ser ies of si x e xperiment s giv es the follo w ing values as the boiling point of a liq uid: 8 2 .
244 Inference app Calculate statistics 4. Calc ulate statistics: Th e s ta ti s ti cs calc ulated will no w be imported into the Infer ence app . 5 . T ap to close the statis tics w indow . Open the Inference app 6. Open the Infere nce app and clear the cu rre nt s e t t i ng s.
Inference app 245 1 1. F r o m t h e App fie ld select the stat istics app that has the data y ou want to impo r t . 12 . I n t h e Column fiel d spec ify the column in that app wher e the data is stor ed. (D1 is the defa ult.) 13 . T a p . 14 . S p e c i f y a 9 0 % confi dence inter val in the C fie ld.
246 Inference app The HP Pr ime h ypothesis tes ts use the Normal Z - distributi on or the Student’s t -distribution to calc ulate probab ilities. If y ou wish to use other distributi ons, please use the Home v ie w and the distributi ons found w ithin the Probab ilit y cate gory of th e Math menu.
Inference app 247 Results The r esults ar e: Two-Sample Z-Test Menu name Z- T e s t : 1 – 2 On the basis of two samples , each fr om a separate populatio n, this test meas ures the str ength of the e vi dence fo r a selected h y pothesis against the n ull hy pothesis.
248 Inference app Results The r esults ar e: One-Proportion Z-Test Menu name Z- T e s t : On the basis of s tatistic s fro m a single sample , this test measur es the str ength of the ev idence f or a selected hy pothesis against the n ull hy pothesis.
Inference app 249 Results The r esults ar e: Two-Proportion Z-Test Menu name Z- T e s t : 1 – 2 On the basis of statisti cs from tw o samples, each fr om a differ ent populati on, this tes t measur es the str ength of the ev idence f or a selec ted hy pothesis against the null h ypothesis .
250 Inference app Results The r esults ar e: One-Sample T-Test Menu name T-T e st : 1 This test is used when the population standar d devi ation is not kno wn . On the basis of s tatistics f rom a single s ample, this test mea sures the st rength of the e vi dence for a select ed hy pothesis against the null h y pothesis.
Inference app 251 Inputs The in puts are: Results The r esults ar e: Two-Sample T-Test Menu name T-T e st : 1 – 2 This te st is used w hen the population standard de vi ation is not kno w n.
252 Inference app Inputs T he inputs ar e: Results The r esults ar e: Fie ld name Definition Sample 1 mean Sample 2 mean s 1 Sample 1 standard de viati on s 2 Sample 2 standard de viati on n 1 Sampl e.
Inference app 253 Confidence intervals The co nfidence int erval calculati ons that the HP Prime can perform ar e based on the Normal Z -distr ibution or Studen t’s t -distr ibution .
254 Inference app Inputs T he inputs ar e: Results The r esults ar e: One-Proportion Z-Interval Menu name Z- I n t : 1 This option use s the Normal Z -distr ibution to calc ulate a confi dence interval f or the pr oportion of succes ses in a population f or the case in w hich a s ample of si z e n has a number of su ccesses x .
Inference app 255 Results The r esults ar e: Two-Proportion Z-Interval Menu name Z- I n t : 1 – 2 This option us es th e Normal Z -distributi on to calculate a confidence interval for the differ ence between the proportions o f successes in two populati ons.
256 Inference app One-Sample T-Interval Menu name T-I n t : 1 This option use s the Student’s t-distr ibution to calc ulate a confi dence inter val f or , the tr ue mean of a population, for the ca se in whic h the true population s tandard dev iation , , is unknow n.
Inference app 257 Inputs The in puts are: Results The r esults ar e: Result Def inition Sample 1 mean Sample 2 mean s 1 Sample 1 standard de viati on s 2 Sample 2 standard de viati on n 1 Sample 1 siz.
258 Inference app.
Solve app 259 13 Solv e app The Solv e app en ables you to def in e up to ten equations or expr essions eac h with as man y var iables a s you lik e. Y ou can sol ve a single equati on or ex pres sion fo r one of its var iable s, based o n a seed va lue.
260 Solve app One equation Suppose y ou w ant to f ind the accelerati on needed to inc rea se the speed of a car fr om 1 6.6 7 m/s (6 0 kph) to 2 7 .7 8 m/s ( 1 00 kph) ov er a distance of 1 00 m. The equ ation to sol ve is: V 2 = U 2 +2 AD . whe re V = f inal speed, U = initial s peed, A = acceler ation needed, and D = distance .
Solve app 261 Enter known variables 4. Display the Numer ic v ie w . M Here y ou spec ify the value s of the know n var iables, highligh t the vari able that yo u want to sol ve f or , and tap . 5 . Enter the v alues for the know n var iables. 2 7 . 7 8 E 1 6 .
262 Solve app Plot the equation The P lot v iew s how s one graph f or each si de of the sol ved equation . Y ou can choose an y of the v ariable s to be the independent var iable by selecting it in Numeric v iew . So in this ex ample make sur e that A is highligh ted.
Solve app 263 Note By dragging a finger horizontally or vertically across the sc reen, you can quickly see parts of the pl ot that are initially out side the x and y ranges you set. Several equations Y ou can define up to ten equations and e xpressions in Sy mbolic vie w and se lect those you want to solve tog eth er as a sy stem.
264 Solve app var iables, or let the calc ulator pro vi de a solution . (T yp ically a seed v alue is a value that dir ects the calc ulator t o pro vi de, if possible , a solutio n that is closes t to it rather than some o ther value .) In this e xample , let’s look f or a solut ion in the v icinity of X = 2 .
Solve app 265 Solution information When y ou are sol ving a single equation , the button appears on the menu after y ou tap . T apping disp lays a me ssage giving you som e in format ion ab out t he soluti ons found (if an y) . T ap to clear the message .
266 Solve app Cannot find solution No values satisfy the selected equation or expression. Bad Guess(es) The initial guess lies outsid e the domain of the equation. Therefore, the solution was not a real number or it caused an error. Constant? The value of the e quation is the same at every point sampled.
Linear Solver app 267 14 Li n e a r S ol ve r a p p The L inear Sol ver app enable s you to s olve a set of linear equati ons. T he set can contain tw o or thr ee linear equations. In a two-equation set , each equati on must be in the form . In a thr ee -equation set , eac h equation mu st be in the for m .
268 Linear Solver app Note If the last time you used the Linear Solver app you solved for two equations, the two-equation input form is displayed. To solve a thr ee-equation set, tap ; now the input form displays three equations. Define and solve the equations 2 .
Linear Solver app 269 Solve a two-by- two system If the thr ee -equation input fo rm is display ed and you wan t t o s ol ve a t wo - equation set, tap . Note You can enter any expression th at resolves to a numerical result, including variables. Just enter the name of a variable.
270 Linear Solver app.
Parametric app 271 15 Pa r a m e t r i c a p p The P arametr ic app ena bles you to e xplor e parametr ic equati ons. T hese ar e equations in w hic h both x and y are defined as f unctions of t .
272 Parametric app The graphical and numerical data you see in Plot view and Numeric view are derived from the symbolic functions defined here. Define the functions The re a re 2 0 fie ld s for de fin in g fun ct ion s. Thes e a re labelled X1(T) thr ough X9(T) and X0(T ) , and Y1(T) thr ough Y9(T) and Y0(T) .
Parametric app 273 Set the angle measure Set the angle meas ure to de grees: 5. S Y (Settings) 6. T a p t h e Angle Measure fi el d and select Degrees . Yo u c o u l d a l s o hav e set the angle measur e on the Home Settings scr een. Ho we ver , Home settings ar e sy stem-w ide .
274 Parametric app Explore the graph The men u but ton gi ves y ou access to common tools f or ex ploring plo ts: : displays a range of z oom options. (The + and w ke ys can als o be used to z oom in and ou t.
Parametric app 275 Display the numeric view 15 . D i s p l a y t h e Numeri c vie w: M 1 6. W ith the cur sor in the T column , t ype a new v alue and tap . The table scrolls to the val u e yo u en te red. Y ou ca n also zoom in or out on the inde pendent variable (thereb y decr easing or increasing the incr ement bet ween consecuti ve values).
276 Parametric app.
Polar app 277 16 Po l a r a p p The P olar app enables y ou to explore polar eq uations. P olar equations ar e equations in whi ch r —the distance a point is f rom the or igin: (0, 0)—is defined in terms o f , the angle a segment f rom the po int to the ori gin makes w ith the pola r axis.
278 Polar app 3 . Define the e xpression 5 cos( /2)cos ( ) 2 . 5 Szf dn 2 >> fd > j E Notice how the d key en t e rs wha teve r va ria bl e is re levant to the c urr ent app . In this app the r eleva nt vari ab l e i s . 4. If y ou wish, c hoose a color f or the plot other than its default .
Polar app 279 8. Set up the plot by specifying appropriate graphing options. In this example, set the upper limit of the range of the independ ent variable to 4 : Select the 2nd Rng field and enter 4 Sz ( The re ar e numer ous wa ys o f confi guring the appear ance of Plot v ie w .
280 Polar app If only one polar equa tion is pl otted, you can see th e equation that ge nerated the plot b y tapping . If ther e are se ver al equati ons plotted, mo ve the tr acing c ursor to the plo t you ar e inter ested—b y pres sing = or —and then tap .
Sequence app 281 17 Sequence app The S equence app pro vides y ou w ith var ious w ays to explor e sequences. Y ou can define a sequence named , for e xample , U1 : • in terms of n • in terms of U1( n –1 ) • in terms of U1( n –2) • in terms o f another sequence, f or ex ample , U2( n ) or • in an y combination of the abo ve .
282 Sequence app Open the Sequence app 1 . Open the Sequ ence app: I Sele ct Sequence The ap p o pe n s i n S ymbolic v ie w . Define the expression 2 .
Sequence app 283 6. Select Stairstep from th e Seq Plot menu . 7 . S et the X Rng maxim um, and the YR n g maximu m, to 8 (as show n at the rig h t ) . Plot the sequence 8. P lot the Fibonacc i seque nce : P 9 . Return to Plot Setup view ( S P ) and select Cobweb , fr om the Seq P lot menu .
284 Sequence app Display Numeric view 1 1 . Displa y Numeri c view: M 12 . W i t h t h e c u r s o r anyw here in the N column, type a ne w value and tap . The table of v alues sc rolls to the v alue yo u e n t ere d. Y o u c a n then see the corr esponding value in the sequence.
Sequence app 285 Set up the table of values The N u me ric S et u p view pro vi des o ptions common to mos t of the graphing apps , although there is no z oom factor as the domain for the sequences is the set of counting numbers. See “Common oper ations in Numer ic Setup v iew ” on pa ge 1 05 for m ore in form a ti on.
286 Sequence app Plot the sequence 6. Pl ot t h e se q u en c e : P Pres s E to see the dotted lines in the fi gure to the righ t. P res s i t a g ai n to hide the do tted lines. Explore the table of sequence values 7 . Vie w the table : M 8. T ap and select 1 t o see the sequence v alues.
Finance app 287 18 Finance app The F inance app e nables you t o solv e time -value -of-mone y (TVM) and amor ti z ation pr oblems. Y ou can use the app to do compound interest calculations and to cr eate amorti zati on tables . Comp ound interest is accumulati ve inter est , that is, intere st on inter est alr eady earned .
288 Finance app 3. I n t h e I%/YR fie ld, t yp e 5.5— t h e i n te res t rat e — an d pres s E . 4. In PV fi eld, type 1 9 500 w 3000 and pre ss E . This is the pr esent v alue of the loan, be ing the purc hase pr ice less the deposit . 5. L e a v e P/YR and C/YR both at 12 (their def ault value s) .
Finance app 289 The P V va l u e i s calculated as 1 5, 7 05 .8 5, this being the max imum you c an b o r row . Th us, w ith yo ur $3, 000 deposit, y ou can affor d a car with a p ri c e t a g o f u p t o $ 1 8,7 05. 85. Cash flow diagrams TVM transactions can be r epresented in cash flo w diagr ams .
290 Finance app The f ollow ing cash flo w diagra m shows a loan f rom the lender's point of v iew : Time value of money (TVM) Time-value -of-money (TVM) calc ulations make u se of the notio n that a dollar today w ill be w orth more than a dollar sometime in the f uture .
Finance app 291 The re ar e sev en TVM vari ables: TVM calculations: Another example Suppose y ou hav e taken ou t a 30 -year , $ 1 50, 000 house mortgage at 6.
292 Finance app pay ment . Find the si z e of the balloon pay ment—that is , the value o f the mortgage after 1 0 y ears of pa yment . The f ollo wing cash flo w diagr am illustr ates the case o f a mortgage with balloon pa yment: 1 . S tart the Fi nance app: I Select Finance 2 .
Finance app 293 Calculating amortizations Amorti z ation calc ulations de termine the amoun ts applied to war ds the principal and inter est in a pay ment , or series of pa yments. T hey also use TVM var iables. To calculate amortizations: 1 . S tart the Finance app .
294 Finance app 2 . T ap . 3 . Sc ro ll dow n the table to pay ment group 1 0. Note that after 1 0 y e a r s , $ 22,8 35 . 53 has been paid off the pri ncipal and $90, 9 36 .4 7 paid in inter est, lea ving a balloon pay ment due of $1 2 7 ,1 6 4 . 4 7 .
Finance app 295.
Triangle Solver app 295 19 T riangle Solver app The T riangle S olv er app enables y ou to calc ulate the le ng th of a si de of a t ria ng l e, o r t he s iz e of an a ng le i n a triangle, fr om in formation you supply about th e other lengths, angle s, or both.
296 Triangle Solve r app 2 . If ther e is unwanted data fr om a prev ious calc ulation, y ou can clear it all b y pressing SJ (Clear ). Set angle measure Mak e sure that your angle measur e mode is appr opri ate. By de fault , the app starts in degree mode .
Triangle Solver app 297 Solve for the unknown values 4. T ap . The app d ispl ays the values of the unknow n vari abl es. A s t h e illustr ation at the r ight sho ws, the length of the unknow n side in our e xample is 3 .2 2 9 6 7… The other tw o angles hav e also been calculated .
298 Triangle Solve r app Special cases The indeterminate case If two sides and an adjacent acute angle ar e entered and ther e are tw o soluti ons, only one w ill be displa yed initi ally . In this case , the button is display ed (as in this ex ample).
Triangle Solver app 299.
The Explorer apps 299 20 T he Explorer apps Ther e are thr ee e xplorer apps. T hese ar e designed for y ou to explore the relationships between the p arameters of a functi on and the shape of the gr aph of that functi on.
300 The Explorer apps fo rm of the equati on being ex plored at the top and, belo w it, the cur rent eq uation of that for m. The ke ys y ou can use to manipulate the graph or equation appear belo w the equatio n. T he x- and y-int ercepts are gi ven at the bottom.
The Explorer apps 301 Equation mode T ap to enter equation mode . A dot w ill appear on t he Eq button at the bottom of the scr een. In equation mode , you use the c urso r ke ys to mov e between par ameters in the equation and change their values, obser ving the ef fect on t he g raph dis played.
302 The Explorer apps Quadratic Explorer app The Quadrati c Explorer app can be used to in vesti gate the behavi or of as t he values of a , h and v cha n ge. Open the app Press I and selec t Quadratic Explorer . The left half o f the display sho ws the gr aph of a quadr atic func tion.
The Explorer apps 303 Choose a gener al for m by tapping the L eve l button— , and so on—until the for m you want is dis played . The k eys a vailable to y ou to manipulate the gr aph vary from le vel t o level . Equation mode T ap to mov e to equation mode .
304 The Explorer apps Trig Explorer app The T ri g Explorer app can be used to in vestigate the behav ior of the gr aphs and as th e values of a , b , c and d cha n ge.
The Explorer apps 305 Graph mode The app opens in graph mode . In graph mode , you m a n i p u l a t e a c op y of the graph b y pre ssing the cur s or keys . Al l fo u r key s are a vailable . The original graph—conv er ted to dotted lines—remains in place for y ou to easily see the r esult of yo ur manipulations.
306 The Explorer apps Test mode T ap to enter test mod e. In test mode you test y our skill at matching an eq uation to the gr aph sho wn. T est mode is lik e equation mode in that y ou use the c urso r ke ys t o s e l e c t a n d c h a n g e t h e v a l u e o f o n e o r m o r e p a r a m e t e r s in the equation .
Functions and command s 307 21 Fu nc tions and commands Many mathemati cal functions ar e av ailable from the calculator ’s ke yboar d. Thes e are desc ribed in “K ey board functi ons ” on page 309. Other func tions and commands ar e collected together i n the T oolbox menus ( D ) .
308 Functions and commands – used in pr ogramming – used in the Matr ix E ditor – used in the L ist E ditor – and some add itional fun ctions and c ommands See “Ctlg menu” on page 378.
Functions and command s 309 Abbreviations used in this chapter In desc ribing the s ynt ax of functi ons and commands, the follo w ing abbrev iations and con venti ons are used: Eqn: an equation Expr .
310 Functions and commands The e xam ples below sho w the r esults yo u would get in Home v iew . If y ou ar e in the CAS , the r esults are giv en in simplifi ed s ymboli c format . F or e xample: Sj 32 0 r e t u r n s 17.88854382 in Home vie w , and 8* √ 5 in the CAS .
Functions and command s 311 efg Sine, cosine, tangent. Inputs and outputs de pend on the current angle format: degrees or radians. SIN ( val ue ) COS ( val ue ) TAN ( val ue ) Example: TAN(45) ret u rn s 1 (degrees mode) Se ( ASIN )A r c s i n e : s i n –1 x.
312 Functions and commands Sj Square root. Also accepts complex numbers. ) √ val u e Example: √ 32 0 r e t u r n s 17.88854382 k x raised to the power of y . Also accepts complex numbers. val u e pow er Example: 2 8 ret u rn s 256 Sk The n th root of x .
Functions and command s 313 Math menu Pr ess D to open the T oolbox menus (one of which is the Math menu). The functi ons and commands av ailable on the Math menu are listed as they ar e categori z ed on the menu . Numbers Ceiling Small est integer greater tha n or equal to val ue .
314 Functions and commands ROUND can also r ound to a number of significant di gits if places is a negativ e integer (as sho wn in the se cond ex ample below). Examples: ROUND(7.8676,2) ret u rn s 7.87 ROUND(0.0036757,-3) ret u rn s 0.00368 Truncate Tr u n c a t e s va lu e to decimal places .
Functions and command s 315 pr ess K . This opens the computer algebra sy stem. If y ou wan t to return t o Home vie w to mak e further calculations , pr ess H . Minimum Minimum. The lesser of tw o values. MIN(value1,value2) Exam ple: MIN(210,25) ret u rn s 25 Modulus Modulo .
316 Functions and commands Real Part Re a l pa r t x , of a comple x number , ( x+y*i ). RE(x+y*i) Example: RE(3+4*i) re t u rn s 3 Imaginary Part Imaginary part, y, of a complex nu mber , ( x+y*i ). IM(x+y*i) Example: IM(3+4*i) re t u rn s 4 Unit Vector Sign of val u e .
Functions and command s 317 SEC Secant: 1/cos x . SEC(value) ASEC Ar c secant. ASEC(value) COT Cot ang en t: cos x /sin x . COT(value) ACOT Arc cota ng ent. ACOT(value) Hyperbolic The hy perbolic trigonometr y functions ca n also take complex numbers as ar guments.
318 Functions and commands Combination The n umber of combinations ( without r egard to or der) of n things tak en r at a time . COMB(n,r) Exam ple: Suppose yo u want to kno w ho w many w ay s fiv e things can be combined two at a time . COMB(5,2) ret u r ns 10.
Functions and command s 319 Seed Sets the seed value on whic h th e random f unctions operate . By s pecify ing the same seed value on tw o or more calc ulators , yo u ensure that the same r a ndom numbers app ear on each calc ulator when the r andom functi ons are e xec uted .
320 Functions and commands Binomial Binomial pr obabilit y density function. C omputes the probab ilit y of k success es out of n tr ials, eac h with a probab ilit y of success of p . Retur ns Comb(n,k) if ther e is no third ar gument. Note that n and k ar e integers w ith .
Functions and command s 321 Cum ulativ e distr ibution fu nction . Retur ns the low er - tail probabili ty of th e probabilit y dens it y function for th e value x , gi ve n n degrees o f free dom. CHISQUARE_CDF(n,k) Exam ple: CHISQUARE_CDF ( 2,6.1 ) ret u rn s 0.
322 Functions and commands T Inv erse cumulati ve S tudent's t distr ibution f unction . Retur ns the val u e x such that the S tudent's- t low er - tail probab ility of x , w ith n degrees of fr eedom, is p . STUDENT_ICDF(n,p) Example: STUDENT_ICDF ( 3,0.
Functions and command s 323 Matrix The se functi ons wor k on matri x data stor ed in matri x var iables. T hey ar e explained in detail in cha pter 2 5, “Matri ces ” , beginning on page 46 3. Special Beta Retur ns the value of the bet a function ( for t wo n um be rs a and b .
324 Functions and commands CAS menu Press D to open the T o olbo x menus (one of w hich is the CAS men u) . The func tions on the CAS men u are those mo st commonl y use d. Man y mor e func tions are available . See “Ctlg menu ” , beginning on p a g e 378 .
Functions and command s 325 Substitute Subs titutes a value f or a var iable in an e xpr ession . Syntax: subst(Expr,Var=value) Exam ple: subst(x/(4-x^2),x=3) ret u rn s -3/5 Partial Fraction P erforms pa rtial fr a ction decomposi tion on a fraction.
326 Functions and commands Calculus Differentiate With one expr ession as ar gument , returns de ri vativ e of the expr ession w ith res pect to x . W ith one expression and one var iable as arguments , retur ns the deri vati ve or partial deri v ative of the expr essi on with r espec t to the vari able.
Functions and command s 327 Series Returns the ser ies expansion of an e xpression in the v ic init y of a gi ven equality var iable . With the opti onal third and fo ur th ar guments y ou can spec ify the or der and dir ection o f the seri es expansion.
328 Functions and commands Gradient Retur ns the gradi ent of an e xpre ssion . With a list of v aria bles as second ar gument, r eturns the v ector of partial der ivati ve s. grad(Expr,LstVar) Example: grad(2*x^2*y-x*z^3,[x,y,z]) gi ves [2*2*x*y- z^3,2*x^2,-x*3*z^2] Hessian R eturns the Hessian matr ix o f an expr essio n.
Functions and command s 329 F(b)–F(a) Ret u rns F ( b )–F( a ). preval(Expr(F( var)),Real(a) ,Real(b),[Var ]) Exam ple: preval(x^2-2,2,3) gi ves 5 Limits Riemann Sum Returns in the ne ighborh ood .
330 Functions and commands Inverse Laplace Ret urns th e i nverse Lapl ace tran sform of an expression. invlaplace(Expr,[Var],[IlapVar]) Example: ilaplace(1/(x^2+1)^2) ret u rn s ((-x)*cos(x))/ 2+sin(x)/2 FFT With one ar gument (a vec tor), retur ns the discr ete F our ier transf orm in R .
Functions and command s 331 Zeros W ith an expr essio n as argumen t, r eturns the r eal z er os of the expr essi on; that is, the solu tions whe n the expr essio n is set equal to z ero .
332 Functions and commands Differential Equation R eturns the soluti on to a differ ential equati on. deSolve(Eq,[TimeVar],Var) Example: desolve(y''+y=0,y) ret u rn s G_0*cos(x)+G_1*sin(x) ODE Solve Ordinary D iffer ential Equati on solver .
Functions and command s 333 texpand Expands a transcendental e xpressi on. texpand(Expr) Exam ple: texpand(sin(2*x)+exp(x+y)) ret u rn s exp(x)*exp(y)+ 2*cos(x)*sin(x)) Exp & Ln e y*lnx → x y Returns an expr essio n of the fo rm e n*ln(x ) re wr itten as a power of x.
334 Functions and commands asinx → atanx Retur ns an expr essi on w ith asin( x ) re wr itten as: asin2atan(Expr) Example: asin2atan(2*asin(x)) ret u rn s sinx → cosx*tanx R eturns an e xpre ssion w ith sin( x ) r ew ritten as co s( x )*tan( x ).
Functions and command s 335 Tangent atanx → asinx Retur ns an expr ession w ith atan( x ) re wr itten as: atan2asin(Expr) Exam ple: atan2asin(atan(2*x)) ret ur n s atanx → acosx Retur ns an expr ession w ith atan( x ) re wr itten as: atan2acos(Expr) tanx → sinx/cosx R eturns an e xpression w ith tan( x ) re wr itten as si n( x )/cos( x ).
336 Functions and commands trigx → cosx R eturns an e xpres sion simplif ied using the f ormula s sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x) . Cos(x) is gi ven pr ecedence ov er sin(x) and tan(x) in the r esult .
Functions and command s 337 trigexpand Retur ns a tri gonometric expr ession in expanded for m. trigexpand(Expr) Exam ple: trigexpand(sin(3*x)) gi ves (4*cos(x)^2- 1)*sin(x) trig2 exp Retur ns an expr essio n with tr igonometr ic func tions r ewr itten as comple x exponenti als (with out lineari z ation).
338 Functions and commands GCD Re turns the great est common di visor of tw o or more int egers. gcd(Intgr1, Intgr2,…) Example: gcd(32,120,636) ret u rn s 4 LCM R eturns the low est co mmon multiple of two or inte gers.
Functions and command s 339 Division Quotient Retur ns the integer quoti ent of the E ucli dean div ision of tw o integ ers . iquo(Intgr1, Intgr2) Exam ple: iquo(63, 23) ret u rn s 2 Remainder R eturns the integer r emainder fr om the Eu clidean di visi on of tw o in teg er s.
340 Functions and commands Coefficients Gi ven a poly nomial in x, r eturns a vector containing the coeff ici ents. If the poly nomial is in a var iable other than x , then declar e the vari able as the second argument .
Functions and command s 341 Create Poly to Coef Giv en a polynomi al, r eturns a vector containing the coeffi ci ents of the polyn omial. W ith a vari able as second ar gument, r eturns t he coeffi ci ents of a pol ynomi al with r espec t to the var iable.
342 Functions and commands Random Returns a vector of the c oeffic ients of a poly nom ial of deg ree Integer and w here the coe ffic ie nts are r andom integ ers in the range –9 9 thr ough 99 w ith unifor m distribution or in an interval spec ified b y Interval .
Functions and command s 343 Degree Retur ns the degre e of a poly nomial . degree(Poly) Exam ple: degree(x^3+x) gi ves 3 Factor by Degree For a gi ven pol ynomial in x of degr ee n , factors out x n and r eturns the r esulting produ ct. factor_xn(Poly) Exam ple: factor_xn(x^4-1) gi ves x^4*(1-x^-4) Coef.
344 Functions and commands Special Cyclotomic R eturns the list of coe ffic ien ts of the cy clotomic polyno mial of an integer . cyclotomic(Integer) Example: cyclotomic(20) gi ves [1 0 –1 0 1 0 –.
Functions and command s 345 Lagrange Giv en a vector of abscissas and a vector of ordinates, returns the Lagr ange pol ynomial f or the points s pecif ied in the two vect ors. T his functi on can also take a matr i x as argument , w ith the fir st ro w cont aining the absc issas and the second r ow containing the or dinates.
346 Functions and commands Plot Function Used t o define a func tion gra ph in the Sy mbolic v ie w of the Geometr y ap p . Plots t he graph of an expr ession wr it ten in terms of the independent vari able x . Not e that the va riable is lo wer case .
Functions and command s 347 ODE Used in the S ymboli c vie w of the Geometry app . Dra ws the soluti on of the differ enti al equation y ’=f( x , y ) that contains as initial condition the po int (x 0 , y 0 ) .
348 Functions and commands Function app functions The F uncti on app func tions pro v ide the same func tionality found in the F uncti on app's P lot v ie w under the FCN me nu . All the se oper ations work on func tions. The functi ons may be expr essions in X or the name s of the F uncti on app v ari ables F0 thro ugh F9 .
Functions and command s 349 Solve app functions The S olv e app has a single functi on that sol ves a gi ven equation or e xpr ession f or one of its va riables . En may be an equation o r expr ession , or it may be the name o f one of the Sol ve S ymbolic vari ables E0–E9 .
350 Functions and commands The s yn tax for man y , but not all, the s preadsheet f unctions fo llow s this pattern: functionName (input,[optional parameters]) Input is the input lis t for the func tion . This can be a cell r ange r efer ence , a simple list or an ything that results in a lis t of val u es.
Functions and command s 351 AVERAGE Calc ulates the ar ithmetic mean of a r ange of numbers . AVERAGE([input]) F or example , AVERAGE(B7:B23) r eturns the ar ithmeti c mean of the numbers in the r ange B7 to B2 3. Y ou can also specify a block of cells , as in AVERAG(B7:C23) .
352 Functions and commands STAT1 The S T A T1 functi on pro vi des a range of one -var iable statistic s. It can calc ulate all or any of , Σ , Σ ², s, s², σ , σ ², serr , , n, min , q1 , med, q3, and max. STAT1(Input range, [mode], [outlier removal Factor], ["configuration"]) Input range is the data sour ce (such as A1 :D8) .
Functions and command s 353 F or ex ample if you spec ify "h n Σ x ", the fir st column w ill contain r o w headers , the firs t ro w w ill be the number of it ems in the input data , the second the sum o f the items and the third the mean of the data .
354 Functions and commands 7 y= L/( 1 + a* e x p(b* x )) 8y = a * s i n ( b * x +c)+d 9y = c x ^2+b x +a 10 y = d x ^3+c x ^2+ b x +a 11 y = e x ^4+d x ^3+c x ^2+b x +a • Conf igur ation: a str ing whi ch indicate s whic h values y ou want to place in w hich r ow and if y ou want ro w and columns headers.
Functions and command s 355 PredY Retur ns the predi cted Y for a giv en x. PredY(mode, x, parameters) • Mode go vern s the regr essio n model used: 1 y= sl*x+int 2 y= sl*ln(x)+int 3 y= int*exp(sl*x.
356 Functions and commands HypZ1mean The o ne -sample Z - test fo r a mean. HypZ1mean( , n, 0 , , ,mode, [”configuration”]) The i n p ut p a ra m et e rs c a n b e a ra n g e re fe re nc e, a l i st o f ce l l r efer ences , or a simple list o f values .
Functions and command s 357 Mode: Spec ifies w hich alter nat i ve hy pothesis to use: • 1: 1 < 2 • 2: 1 > 2 • 3: 1 ≠ 2 • Configuration: a string that controls what results are shown and the order in which they appear.
358 Functions and commands • Conf igur ation: a s tring that contr ols w hat re sults are show n and the order in whi ch they appear . An empt y str ing "" display s the defa ult: all results , including headers . The options in the confi guration s tring ar e separ ated b y spaces .
Functions and command s 359 • prob: the lo w er-tail pr obability • cZ: The c riti cal Z -value assoc iated w ith the input α -le vel • cp1 : The lo w er cr itical value o f assoc iated .
360 Functions and commands HypT2mean The two -sample T-test for the difference of two means. HypT2mean((x 1 ,x 2 ,s 1 ,s 2 n 1 ,n 2 ,pooled,mode, [”configuration”]) P ooled: Speci.
Functions and command s 361 • h: header cells w ill be cr eated • Z: the cr itical Z -value • zXl: the lo wer bound of the conf idence in terval • zXh: the upper bound of the confidence interval • std: the standar d dev iation Exam ple: ConfZ1mean(0.
362 Functions and commands • zXh: the upper bound of the conf idence interval • zXm: the midpoin t of the confidence inte r val • std: the s tandard de v iation Example: ConfZ1prop(21, 50, 0.95, "") ConfZ2prop The two- sample Normal confidence interval f or the differ ence of two pr oportions .
Functions and command s 363 Exam ple: ConfT1mean(0.461368, 0.2776, 50, 0 .95, "") ConfT2mean The tw o -sample Studen t’s T confi dence interval f or the difference o f t wo means .
364 Functions and commands Do1VStats Do1 -vari able statisti cs. P erforms the same calc ulations as tapping in the Numer ic v iew o f the Statisti cs 1V ar app and stor es the r esults in the appr opriate S tatistic s 1V ar app r esults var iables. Hn must be one of the S tatisti cs 1V ar app S ymbolic v ie w vari ables H1-H5 .
Functions and command s 365 Statistics 2Var app functions The S tatistics 2V a r app has a number of functi ons. Some ar e design ed to calculate summar y statisti cs based on one of the statistical analy ses ( S1-S5 ) de fined in the S ymboli c vi ew of the Statisti cs 2V ar app .
366 Functions and commands SetIndep Set indepe ndent column. S ets the independent column f or one of the statis tical analy ses S1-S5 to one o f the column var iables C0-C9 . SetIndep (Sn,Cn) Example: SetIndep(S1, C2) se ts the In dependent C olumn fiel d fo r t he S1 analy sis to use the data in list C2 .
Functions and command s 367 Exam ple: HypZ1mean(0.461368, 50, 0.5, 0.2887, 0.05, 1) re t u rn s {1, -.9462…, 0.4614, 0.8277…, 1.6448…, 0.5671…} HYPZ2mean The tw o -sample Z -test for means .
368 Functions and commands Mode: Spec ifies w hich alter native h ypothe sis to use: • 1: < 0 • 2: > 0 • 3: ≠ 0 Example: HypZ1prop(21, 50, 0.5, 0.05,1) ret u rn s {1, -1.1313…, 0.42, 0.8710…, 1.6448…, 0.6148…} HypZ2prop The tw o - sample Z -test for pr oportions .
Functions and command s 369 Mode: Spec ifies w hich alter nat i ve hy pothesis to use: • 1: < 0 • 2: > 0 • 3: ≠ 0 Exam ple: HypT1mean(0.461368, 0.2776, 50, 0.5, 0.05, 1) re t u rn s {1, -.9462…, 0.4614, 0.8277…, 1.
370 Functions and commands ConfZ1mean The one-sample Normal confi dence interval for a mean . Re turns a list containing (in or der): • The lo w er criti cal Z -value • The lo wer bound of the conf idence interval • The upper bound of the conf idence inter val ConfZ1mean( ,n, , C) Example: ConfZ1mean(0.
Functions and command s 371 ConfZ2prop The two -sample Normal confidence inter val fo r the difference of two pr oportions. R eturns a list containing (in or der): • The lo w er cr itical Z -value .
372 Functions and commands Finance app functions The F inance app u ses a set o f functions that all r ef erence the same set o f Finance app v aria bles.
Functions and command s 373 CalcIPYR Sol ves for the inte rest r ate per year o f an inv estment or loan. CalcIPYR (NbPmt,PV,PMTV,FV[,PPYR,CPYR, BEG]) Exam ple: CalcIPYR(360, 150000, -948.10, -2.25) ret u rn s 6.50 CalcNbPmt Sol ves for the n umber of pay ments in an inve stment or loan.
374 Functions and commands Linear Solver app functions The L inear Sol ver app has 3 func tions that offe r the user fle xibility in sol ving 2x2 or 3x3 linear sy stems of equatio ns.
Functions and command s 375 AAS Angle- Angle -Side . T ake s as arguments the measur es of two angles and the length o f the side opposite the first angle and r eturns a list containing the le ngth of the side opposit e the second angle, the length of the thir d side, and the measur e of the thir d angle (in that or der).
376 Functions and commands SSS Side-Side-Side T ak es as ar guments the lengths o f the three sides o f a triangle and r eturns the measur es of the angles opposite them , in order . SSS (side,side,side) Example: SSS(3, 4, 5) in degr ee mode retur ns {36.
Functions and command s 377 Quadratic Explorer functions SOLVE Sol ve quadr atic. G iv en the coeffi cie nts of a quadr atic equation ax 2 +b x +c = 0 , re tu r ns t h e re al s o lu t io n s. SOLVE(a, b, c) Exam ple: SOLVE(1,0,-4) ret u rn s {-2, 2} DELTA Discr iminant .
378 Functions and commands Example: With the F uncti on app as the cur ren t app, CHECK(1) ch e cks the F unction app S ymboli c vi ew var iable F1 . The r esult is that F1(X) i s d r a w n i n t h e P l o t v i e w a n d h a s a c o l u m n o f f u n c t i o n value s in the Numer ic v iew o f the F unction app .
Functions and command s 379 descr ibed in “K ey board functi ons” on page 30 9. Those that ar e also on the CA S menu ar e desc ribed in “CAS men u” on page 3 2 4.
380 Functions and commands + Additi on sy mbol. R eturns the sum of tw o numbers, the t erm-by- term sum of tw o lists or two matri ces, or adds two str ings together . − Subtracti on sy mbol. R eturns the di ffer ence of two numbers , or the term-b y- term subtr action o f two lists or two matr ices .
Functions and command s 381 <> Inequality test. R eturns 1 if the inequality is true, and 0 if the inequality is false . = E qualit y s ymbol . Connects tw o members of an equation . == E quality test . Re turns 1 if the left si de and ri ght side ar e equal , and 0 otherw ise .
382 Functions and commands algvar R eturns the matr ix of the s ymbo lic var iable names us ed in an e xpres sion . The list is o rder ed b y the algebra ic ex tensions r equired to build the or iginal ex pressi on. algvar(Expr) Example: algvar(sqrt(x)+y) gi ves AND L ogical And.
Functions and command s 383 basis Gi ven a matr i x, r eturns the basis of the linear su bspace def ined by the set o f vecto rs in the matri x. basis(Matrix)) Exam ple: basis([[1,2,3],[4,5,6],[7,8,9],[10,11,12]]) giv es [[-3,0,3],[0,-3,-6]] black Used in the S ymboli c vie w of the Geometry app .
384 Functions and commands charpoly R eturns the coeff ic ients of the c harac teris tic poly nomial of a matri x. W ith only one ar gument , the vari able used in the poly nomial is x . With a var iable as second ar gument, the poly nomial retur ned is in terms of that vari able.
Functions and command s 385 companion Retur ns the companion matri x of a polynomial . companion(Poly,Var) Exam ple: companion(x^2+5x-7,x) ret u rn s compare C ompares ob jects, and r eturns 1 if type(ar g1 )<type(arg2) or if type(arg1 )=t ype(ar g2) and arg1<ar g2 , and returns 0 otherwise .
386 Functions and commands contains Gi ven a list or v ector and an element, r eturns the inde x of the firs t occurr ence of the element in the li st or v ector; if the element doe s not appear in the list or v ector , retur ns 0.
Functions and command s 387 covariance_ correlation Retur ns a vector containing both the covar iance and the corr elation of th e elements of a list or matri x.
388 Functions and commands delcols Giv en a matri x and an integer n , deletes the n th column f rom the matr ix and r eturns the r esult . If an interval o f t w o integers is used ins tead of a single intege r , delet es all columns in the interval and r eturns the r esult .
Functions and command s 389 egcd Gi ven two pol ynomials, A and B , returns thr ee poly nomials U, V and D suc h that: U(x)*A(x)+V(x)*B(x)=D(x), whe re D(x)=GCD(A(x),B(x)) , the greates t common div isor of poly nomials A and B. The pol ynomials can be pro vided in s ymbolic f orm or as lists of coeffic ients in descending order .
390 Functions and commands evalc Re turns a complex expr ession w ritten in the form real+i*imag . evalc(Expr) Example: evalc ret u r ns evalf Gi ven an e xp r ession and a number of signif icant digits, r eturns the numer ical e valuation o f the expr essio n to the giv en number of signif icant digits.
Functions and command s 391 exponential_ regression Gi ven a set o f points, r eturns a v ector containing the coeff ic ien ts a and b of y=b*a^x , the exp one ntia l which b est fits the se t of points . The poin ts may be the elemen ts in t wo lists or th e ro ws of a matrix.
392 Functions and commands fMax Gi ven an e xpressi on in x , retur ns the value of x for wh ich t h e e xpression has it s maximum value. G iv en an expres sion and a var iable , re turns the value o f that vari able for w hich the e xpressi on has its max imum value .
Functions and command s 393 fsolve Re turns the numer ical soluti on of an equation or a s yst em of equations . With the optional thir d argument y ou can spec if y a guess for the s olution or an interval w ithin whic h it is expec ted that the soluti on will occ ur .
394 Functions and commands gramschmidt Gi ven a basis of a vec tor subspace , and a function that defines a scalar pr oduct on this vector subspace , retur ns a n orthonor mal basis for that f unction . gramschmidt(Vector, Function) Example: gramschmidt ret u rn s green Used in the S y mbolic vi ew of the Geometry app .
Functions and command s 395 head Returns the first element of a given v ector , sequ ence or string . head(Vector) or head(String) or head(Obj1, Obj2,…) Exam ple: head(1,2,3) gi ves 1 Heaviside Retur ns the value o f the Heavisi de functi on for a gi ven r eal number (i .
396 Functions and commands id Re turns a vec tor containing the soluti on to the identity func tion for th e a rg um en t( s) . id(Object1, [Object2,…]) Example: id([1 2], 3, 4) ret u rn s [[1 2] 3 4] identity Giv en an i nte ger n , r eturns the i dentity matri x of dimension n .
Functions and command s 397 iPart Retur ns a real nu mber withou t its frac tional part or a list of real numbers eac h wi thout its fr actional part . iPart(Real) or iPart(List) Exam ple: iPart(4.3) ret u rn s 4 iquorem Retur ns the Euc lidean quoti ent and remainde r of two integer s.
398 Functions and commands length R eturns the length of a list , string or s et of objec ts. length(List) or length(String) or length(Object1, Object2,…) Example: length([1,2,3]) gi ves 3 lgcd Retur ns the greate st common div isor of a set of int egers or poly nomials, contained in a list, a vect or , or just enter ed direc tly as arguments .
Functions and command s 399 list2mat Returns a matr i x of n columns made by splitting a li st into ro w s, each containing n terms. If the number of elements in the list is not di v isible by n , then the matr i x is completed with ze ros .
400 Functions and commands logistic_ regression R eturns y , y', C, y'max, xmax , and R, w here y is a logisti c functi on (the solut ion of y'/y=a*y+b), such that y(x0)=y0 and wher e [y'(x0) ,y'(x0+1 )...] is the best appr ox imation of t he line for med by the elements in th e list L.
Functions and command s 401 Exam ple: matpow([[1,2],[3,4]],n) gi ves [[(sqrt(33)- 3)*((sqrt(33)+5)/2)^n*-6/(-12*sqrt(33))+(- (sqrt(33))-3)*((-(sqrt(33))+5)/2)^n*6/(- 12*sqrt(33)),(sqrt(33)-3)*((sqrt(3.
402 Functions and commands modgcd Uses the modular algor ithm to retu rn the great est common div isor of two pol ynomials. modgcd(Poly1,Poly2) Example: modgcd(x^4-1,(x-1)^2) gi ves x-1 mRow Gi ven an e xpres sion, a matr ix , and an integer n , m ultiplies row n of the matri x by the e xpr ession.
Functions and command s 403 nDeriv Gi ven an expr ession , a varia ble of differentiati on, and a real number h , r eturn s an appro x imate value o f the deri vati ve of the expr essi on, using f’(x)=(f (x+h)–f(x+h))/(2*h) . Witho ut a third ar gument, the v alue of h is set to 0.
404 Functions and commands order_size Re turns the remainder (O term) o f a series e xpansion: limit(x^a*order_si z e(x),x= 0)=0 if a>0. order_size(Expr) pa2b2 T ak es a prime integer n congruent to 1 modulo 4 and re turns [a,b] such that a^2+b^2=n.
Functions and command s 405 plotparam Used in the Geometry app S ymboli c vie w . T akes a comple x expr ession in one v ariab le and an inter val for that vari able as ar guments. Int erpr ets the comple x expr essi on f(t)+i*g(t) as x=f(t) and y=g(t) and plots the parametr ic eq uation ov er the interval specif ied in the second argumen t.
406 Functions and commands pole Gi ven a c irc le and a line , retur ns the point f or whic h the line is polar with r espec t to the cir cle . pole(Crcle,Line) Example: pole(circle(0, 1), line(1+i, 2)) ret u r n s point(1/2,1/2) POLYCOEF Retur ns the coeff ici ents of a pol ynomi al with r oots gi ven in the v ector or list ar gument.
Functions and command s 407 polygonscatterplot Used in the Geometry app S ymbolic v ie w . Gi ve n an n × m matr ix , dra ws and connec ts the points ( xk, yk) , wher e xk is the elem ent in row k and column 1 , and yk is th e element in ro w k a nd colu mn j (with j fixed fo r k =1 to n r ow s) .
408 Functions and commands power_regression Gi ven a set of points def ined by tw o lists, retur ns a vector containing the coeffi ci ents m and b of y = b* x^m , the monomi al whic h best appr ox imates the giv en points .
Functions and command s 409 propfrac Retur ns a fracti on or rati onal fr action A/B simplif ied to Q+r/ B, w here R<B or the degree of R is less than the degr ee of B .
410 Functions and commands quartile3 Giv en a list or vector , returns the third quartile of the elements of the list or v ector . Gi ven a matr ix , r eturns the third q uartile of the columns of the matr ix .
Functions and command s 411 randperm Gi ven a positi ve integer , returns a r andom permutatio n of [0, 1 ,2 ,...,n–1]. randperm(Intg(n)) Exam ple: randperm(4) r eturns a ra ndom permutati on of the elements of the vect or [0 1 2 3] ratnormal Re wr ites an expr ession as an irr educible r ational fr action.
412 Functions and commands reduced_conic T ak es a conic expr ession and r eturns a vec tor with the fo llow ing items: • The or igin of the coni c • The matr i x of a basis in whi ch the conic is.
Functions and command s 413 residue Re turns the re sidue of an e xpr ession at a valu e. residue(Expr, Var, Value) Exam ple: residue(1/z,z,0) ret u rn s 1 restart P urges all the var iables. restart(NULL) resultant Retur ns the result ant (i.e . the deter minant of the S ylv ester matr ix) of tw o poly nomials.
414 Functions and commands rowAdd Gi ven a matr i x and t w o integers , retur ns the matr ix obtained fr om the g iv en matrix after the ro w indicated b y t he second integer is r eplaced by the sum of the r ow s indicated b y the tw o inte gers .
Functions and command s 415 select Gi ven a Boolean e xpressi on in a single varia ble and a list or vector , tests ea ch element in the l ist or vector and returns a list or vec tor containing the elemen ts that satisfy the Boolean.
416 Functions and commands simult Retur ns the solution to a s y stem of linear equatio ns or sev eral s yste ms of linear equatio ns pres ented in matri x for m. In the case of one s yst em of linear equations , takes a matr ix o f coeff ici ents and a column matr ix o f constants, and r eturns the column matr ix of the s olution .
Functions and command s 417 stddevp Retur ns the population standar d dev iation of the elements of a lis t or a list of the population s tandar d de viati ons of the columns o f a matr ix .
418 Functions and commands sylvester R eturns the S yl ves ter matri x of two pol ynomi als. sylvester(Poly1, Poly2, Var) Example: sylvester(x 2 -1,x 3 -1,x) gi ves table Def ines an arr ay w her e the index es ar e string s or real num ber s.
Functions and command s 419 trunc Gi ven a va lue or list of values , as well a s an integer n , r eturns the value o r list truncated t o n decimal places. If n is n ot pr ov ided , it is taken as 0. A ccepts complex n umbers. trunc(Real, Integer) or trunc(List, Integer) Exam ple: trunc(4.
420 Functions and commands vpotential Given a ve ct o r V an d a ve ct o r of va ria bl es, ret u rn s t h e ve ct or U such that c url(U)=V . vpotential(Vector1, Vector2) Example: vpotential([2*x*y+3,x 2 -4*z,-2*y*z],[x,y,z]) returns when Used to intr oduce a conditional statement .
Functions and command s 421 Inserts a template fo r a summation expr essi on. Insert s a minus sign. Insert s a square r oot sign. Insert s a template for an antideri vativ e expr ession. Inequality test . R eturns 1 if the left and r ight side s are not equal and 0 if the y are equal .
422 Functions and commands 3. I n t h e Fun c ti on field, enter the function. eA A >+fA B >A C New f ields appear below y our f unction , one fo r each var iable us ed in def ining it.
Variables 423 22 Va r i a b l e s V ar iables ar e objects that ha ve names and co ntain data. The y are used to stor e data, either for later use or to control settings in the Prime sys tem.
424 Variables y ou ev aluate that re sult (using the EVAL command) , the CAS w ill no w retu rn {2,4,6} . User var iables are e xplicitly c reated by the user . Y ou cr eate user vari ables either in a progr am or b y assignment in Home vi ew . User var iables cr eated in a pr ogram are either declar ed as local or exported as global.
Variables 425 Working with user variables Example 2 : Create a vari able called ME and assign 2 to it. 1. P r e s s H to displa y Home v iew . 2. A s s i g n 2 to ME : Szj AQAcE 3 . A message appears asking if you w ant to cr eate a var iable called ME .
426 Variables Enter ing HAngle:=0 E fo rce s t he s et ti n g to re t ur n to radians . Y ou can see what value has been assigned to a var iable—whether Home, app , or user—by enter ing its name in Home v iew and pr essing E . Y ou can enter the name letter by letter , or choose the v aria ble from the V ar iables menu b y pr essing a .
Variables 427 Qualifying variables Some app v ariable names ar e shar ed by multiple apps. F or ex ample, the F unction app has a v aria ble named Xmin , bu t so too does the P olar app , the P ar ametri c app, the Sequence app , and the Solv e app . Although named identicall y , these vari ables usual ly hold differ ent values.
428 Variables Home variables The Home v ariables ar e accessed by pr essing a and tapping . Category Names Real A to Z and For exa m p l e, 7 .45 A Comp lex Z0 t o Z 9 F or ex ample, 2+3× i Z1 or (2 ,3) Z1 (depending on y our Comple x number settings) List L0 to L9 For exa m p l e, { 1 ,2,3} L 1 .
Variables 429 App variables The app v ariables ar e accessed by pr essing a and tapping . They ar e grou ped below b y app. (Y ou c a n f i n d t h e n g r o u p e d b y v i e w — Sy m b o l i c , N u m e ri c, P l o t, —in “V ari ables and Progr ams” on page 5 5 6.
430 Variables Results variables Extremum C ontains the value from the la st use of the Extremum functi on fr om the menu in the P lot vie w of the F unction app .
Variables 431 Spreadsheet app variables Solve app variables Category Names Numeric ColWidth Row Cell RowHeight Col Modes AAngle AComplex ADigits AFormat Category Names Sym b o l i c E1 E2 E3 E4 E5 E6 .
432 Variables Advanced Graphing app variables Category Names Sym b o l ic V1 V2 V3 V4 V5 V6 V7 V8 V9 V0 Pl o t Axes Cursor GridDots GridLines Labels Recenter Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoo.
Variables 433 Statistics 1Var app variables Category Names R esults [explained below ] NbItem MinVal Q1 MedVal Q3 MaxVal X X2 MeanX sX X serrX Sym b o l i c H1 H2 H3 H4 H5 H1Type H2Type H3.
434 Variables Results NbItem Co ntains the number of data points in the c urr ent 1 - vari ab l e a n alys i s ( H1-H5 ). MinVal Con tains the minimum value o f the data set in the c urr ent 1- v a r i a b l e a n a l y s i s ( H1-H5 ). Q1 Con tains the value of the f irst quartile in the c urr ent 1 - vari ab l e a n alys i s ( H1-H5 ).
Variables 435 Statistics 2Var app variables Category Names Res u l t s [explained below ] NbItem Corr CoefDet sCov Cov XY MeanX X X2 sX X serrX MeanY Y Y2 sY Y serrY Sy.
436 Variables Results NbItem Co ntains the number of data points in the c urr ent 2 - vari ab l e a n alys i s ( S1-S5 ). Corr Contains the cor relati on coeffi cien t from the latest calc ulation of summary statistic s. This v alue is based on the linear f it only , r egardless o f the fit ty pe chos en.
Variables 437 Y Con tains the sum of the dependent v alues (Y ) of the c urre nt 2 -vari able statisti cal analy sis ( S1-S5 ). Y2 Con tains the sum of the squar es of the dependen t values (Y) o f the curr ent 2 -v ariab le statistical analy sis ( S1-S5 ).
438 Variables Results CritScore Con tains the value of the Z - o r t -distr ibution as soc iated w ith the input -v alue CritVal1 Con tains the low er cr itical value of the e xperiment al var iable a ssoc iated w ith the negati ve TestScore va lu e whi ch wa s calculated fr om the input -le vel .
Variables 439 Parametric app variables Category Names Sym b o l i c X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Y5 X6 Y6 X7 Y7 X8 Y8 X9 Y9 X0 Y0 Pl o t Axes Cursor GridDots GridLines Labels Method Recenter Tmin Tmax T.
440 Variables Polar app variables Finance app variables Category Names Sym b o l ic R1 R2 R3 R4 R5 R6 R7 R8 R9 R0 Pl o t min max step Axes Cursor GridDots GridLines Labels Method Recenter .
Variables 441 Linear Solver app variables Triangle Solver app variables Linear Explorer app variables Quadratic Explorer app variables Category Names Numeric LSystem LSolution a Modes AAngle AComplex ADigits AFormat a. Contains a v ector with the last s olution found b y the Linear Solv er app.
442 Variables Trig Explorer app variables Sequence app variables Category Names Modes AAngle AComplex ADigits AFormat Category Names Sym b o l ic U1 U2 U3 U4 U5 U6 U7 U8 U9 U0 Pl o t Axes Cursor GridD.
Units and constants 443 23 Units and constants Units A unit of measur ement—suc h as inch , ohm, or Becquer el—enable s you to giv e a prec ise magnitude to a phy sical quantity . Y ou can attach a unit of measurement to an y number or numer ical r esult .
444 Units and constants Prefixes The Units menu include s an entry that is not a unit category , namely , Prefix . Selecting this opti on display s a palette o f pref i xes . Unit pre fi xes pro vi de a handy wa y of entering large or small numbers . For e xam ple, the speed of li ght is appro x imately 300, 000 m/s.
Units and constants 445 Example Suppose you w ant to a dd 20 centimeters and 5 inches and hav e the result displa yed in centimeters. 1 . If y ou w ant the re sult in cm, ente r the centimeter measurement f irst. 20 SF (Units) Select Length Select cm 2.
446 Units and constants 4. Now con vert the r esult to kilometer s per hour . SF Select Speed Select km/h E Th e re s ul t i s sh own a s 0 . 29 43 k i l o m e t e rs per hour . Unit tools Ther e are a number of tools f or managing and operating on units .
Units and constants 447 UFACTOR Unit factor con version . Conv er ts a measurement using a compound uni t into a measurement expr essed in constituent units. F or e xample , a Coulomb—a measure o f electr ic c harge— is a compound unit der iv ed fr om the SI base units of Am pere and second: 1 C = 1 A * 1 s.
448 Units and constants 3 . Select Physics . 4. Select c: 299792458 . 5 . Sq uare the sp eed of light and e v aluate the expr ession. jE Value or measurement? Y ou can enter just the v alue of a const ant or the constan t and its units (if it has units).
Units and constants 449 List of constants Category Name and s ymbol Math e MAXREAL MINREAL i Chem i str y Avogadro, NA Boltmann, k molar volume, Vm universal gas, R standard temperature, StdT stan.
450 Units and constants.
Lists 451 24 Li s ts A list consists of comma-separ ated real o r complex numbers , expre ssions, or matr ices, all enc losed in brace s. A list may , fo r ex ample, con tain a sequence of r eal numbers such as {1,2,3} . Lists r ep r esent a conv enient wa y to group related objects.
452 Lists 2 . T ap on the name y ou want to assign to the new list ( L1 , L2 , etc.). The li st editor appears. If y ou’r e creating a new lis t rather than changing , make sur e you c hoose a list with out any elements in it. 3 . Enter the values y ou wa nt in the list , pressing E after each one.
Lists 453 The List Editor The L ist Editor is a special en vir onment for enter ing data into lists. T here are tw o way s to open the List E ditor once the List Catalog is op en: • Highli ght the list and tap or • T ap the name of the lis t.
454 Lists To edit a list 1. O p e n t h e L i s t Catalo g. Sp (List) 2 . T ap on the name of the list ( L1 , L1 ,etc.). The L ist Edito r appears. 3 . Tap on the element y ou want to edit . (Al te rna t ively , p ress = or until the element you want to edit is highli ghted.
Lists 455 Select L1( 2) , that is, the second element in the list . 9 Deleting lists To delete a list In the List C atalog, u se the cur sor k ey s to highli ght the list and pre ss C . Y ou ar e prompted to conf irm your dec ision . T ap or press E .
456 Lists 4. When y ou have f ini shed entering the elements, pr ess E . The list is added to Histo r y (w ith any expr essions among the elements evaluated) . To store a list Y ou can stor e a list in a vari able. Y ou can do this befor e the list is added to His tory , or y ou can copy it fr om Histor y .
Lists 457 To send a list Y ou can send lists to another calc ulator or a P C just as you can apps, pr ogr ams, matrice s, and notes . See “Sharing data” on page 44 f or instructions . List functions Li st functi ons are fo und on the Math menu. Y ou can u se them in Home and in progr ams.
458 Lists Menu format By de fault , a List func tion is pr esented on the Math menu using its desc ripti ve name , not its common command name. T hus the sh orth and name CONCAT is pr es ented a s Concat enate and POS is pr esented as Po s i t i o n .
Lists 459 Reverse Cr eates a list by rev ersing the or der of the ele ments in a list . REVERSE( list ) Example: REVERSE({1,2,3}) returns {3,2,1} Concatenate Concatenates two lists into a new list . CONCAT( list1 , list2 ) Example: CONCAT({1,2,3},{4}) ret u r n s {1,2,3,4} .
460 Lists LIST Creat es a new list comp osed of the fi rst differ ences o f a list; that is, the differences between consec utive elements in the list. The ne w list has one less element than the ori gin al list . The differ ences for { x 1 , x 2 , x 3 ,.
Lists 461 Finding statistical values for lists T o f ind statistical values—suc h as the mean, median , max imum, and minimum of a list—yo u creat e a li st , stor e it in a data set and then use the Stat istics 1V ar app .
462 Lists 4. In the Sy mbolic v iew , spec ify the data set whos e statistic s you w ant to find . Y By def ault, H1 w ill use the data in D1 , so not hin g fur th er needs to be done in S ymboli c vi ew . Ho we ver , if the data of inter est w ere in D2 , or any column other than D1 , y ou would hav e to specify the desired data column here .
Matrices 463 25 Ma tr i ce s Y ou can cr eate , edit, and oper ate on matr ices and v ectors in the Home v iew , CAS , or in pr ograms. Y ou can enter matri ces direc tly in Home or CAS , or use the Matr ix Editor . Vectors V ectors are one -di mensional array s.
464 Matri ces Creating and storing matrices The M a trix Ca ta l og contains the reserved matri x var iables M0-M9 , as w ell as any matri x vari ab le s you have cr e a t e d i n H o m e o r C A S vi ew s (or from a pr ogram if they ar e global).
Matrices 465 Working with matrices To open the Matrix Editor T o creat e or ed it a ma trix, go to th e M atrix Cat alo g, an d tap on a matr ix . (Y ou could also use the c ursor k ey s to highlight the matrix and then press .) Th e M atrix E ditor opens.
466 Matri ces To create a m atrix in the Matrix Editor 1 . Open the Matr ix Catalog: St (Matrix) 2 . If y ou want to c reate a vector , pr ess = or unti l the mat ri x you want to use is highlighted, tap , and then pres s E . Co n ti n ue f rom s t ep 4 b e low .
Matrices 467 Matrices in Home view Y ou can enter a nd operate on matri ces directly in Home v iew . The matr ices can be named or unnamed. Enter a v ector or matr ix in Home o r CAS v iew s direc tly in the entr y line. 1. P r e s s S u ([]) to start a vector or matri x.
468 Matri ces entry line or copied it fr om History to the entry line, tap , enter a name fo r it and press E . T he va ria b l e na m e s res er ve d for v ec t or s a nd m a t ric e s a re M0 thr ough M9 . Y ou can alw ay s use a var iable name y ou dev ise to stor e a vector or matr ix .
Matrices 469 To store one element In Home v iew , enter val u e , ta p , and then ent er matri xname ( row , c o l u mn ). F or ex ample , to change the elemen t in the first r o w and second column o.
470 Matri ces Example 1 . Select the f irst matr ix : St (Matrix) T ap M1 or highlight it and pr ess E . 2 . Enter the matri x elements: 1 E 2 E 3 E 4 E 3. S elect the second matr ix : St (Matrix) T ap M2 or highlight it and pr ess E . 4. Enter the matri x elements: 5 E 6 E 7 E 8 E 5 .
Matrices 471 To multiply two matrices T o multipl y the two matri ces that you c reated f or the pre v ious ex ample, pr ess the f ollow ing ke ys: AQ 1 sA Q 2 E To m u l t i p l y a m a t ri x b y a vector , enter the mat ri x fir st, the n the vector .
472 Matri ces This oper ation is not a mathemati cal div ision: it is a left- multiplicati on by the in ve rse of the di visor . M1/M2 is equi valent to M2 –1 * M1 .
Matrices 473 2 . Cr eate the vect or of the thr ee constants in the linear sy stem . 5 E 7 E 1 E 3 . R eturn to the Matri x Cat al og. St The size of M1 should be showing as 3. 4. Select and clear M2 , and re-open the Matri x E ditor: [Press or = to select M2] C E 5 .
474 Matri ces 6 . R eturn to Home vi ew and left-multiply the cons tants vec tor by the in ver se of the coeff ic ients matr ix : HA Q 2 S n s A Q 1 E The r esult is a v ector of the soluti ons: x = 2 , y = 3 and z = –2 . An al terna tive meth od i s to use the RREF function (see page 4 7 6).
Matrices 475 The matr i x commands are desi gned to support progr ams that use matri ces. The matr ix commands are liste d in the Matri x category of the Commands men u in the Progr am Edito r . T hey are als o listed in the Cat alog menu , one of the T oolbo x menu s.
476 Matri ces RREF Red uc e d Row- Eche l on Form. Ch an ge s a re cta n gu l ar matri x to its reduced r ow-ec helon for m. RREF ( matrix ) Exam ple: RREF returns Create Make Creat es a matri x of dimension rows × columns , u sin g exp res s io n to calculate each element .
Matrices 477 Random Giv en t wo in tegers, n and m , and a matri x name, c reate s an n x m m a t r i x t h a t c o n t a i n s r a n d o m i n t e g e r s i n t h e r a n g e − 9 9 through 9 9 w ith a unifor m distributi on and stor es it in the matri x name.
478 Matri ces Vandermonde Retur ns the V andermonde matr ix . Gi ven a v ector [ n1 , n2 … nj ], r eturns a matri x who se fir st ro w is [(n1 ) 0 , (n1 ) 1 , (n1 ) 2 , …,(n1 ) j- 1 ]. T he second r ow is [(n2) 0 , (n2 ) 1 , (n2) 2 , …,(n2) j- 1 ], etc.
Matrices 479 Spectral Norm Spectral No rm of a squar e matri x . SPECNORM ( matrix ) Example: SPECNORM returns 5.46498570422 Spectral Radius Spectr al Radius of a square matr ix . SPECRAD ( matrix ) Example: SPECRAD returns 5.37228132327 Condition Conditi on Number.
480 Matri ces Trace F inds the trace o f a square matri x. T he trace is equal t o the sum of the diagonal elements. (It is al so equal to the sum of the eigenvalues.) TRACE ( matrix ) Exam ple: TRACE returns 5 Advanced Eigenvalues Di s pl ays th e e ig enva l ue s i n vec tor fo rm for matri x .
Matrices 481 Diagonal Gi ven a lis t, r eturns a matr ix w ith the list eleme nts along its diagonal and z er oes else wher e. Gi ven a matr ix , r eturns a vect or of th e elements along it s diagonal. diag (list) or diag (matrix) Example: diag returns Cholesky F or a numeri cal sy mmetri c matrix A, r eturns the matr ix L such that A=L*tr an(L).
482 Matri ces Hessenberg Matri x r eduction to Hess enberg f orm. R eturns [P ,B] such that B=inv(P)*A*P . hessenberg(Mtrx(A)) Exam ple: In CAS view, hessenberg returns Smith Smith normal f orm of a matr ix w ith coeffi cient s i n Z: re turns U,B ,V such that U and V inv er tible in Z , B is diagonal, B[i,i] div ides B[i+1 ,i+ 1], and B=U*A*V .
Matrices 483 Factorize LQ L Q Fa c t o riza t i o n. Fac t o r izes a m × n matri x into thr ee matri ces L, Q, and P , wher e {[L[ m × n low ertrapez o idal ]],[Q[ n × n orthogonal ]], [P[ m × m permutation ]]}and P*A=L*Q . LQ ( matrix ) Example: LQ returns LSQ Lea st Squar es.
484 Matri ces QR Q R Fa c t o riza t i o n. Fa c t o rize s a n m × n matr ix A numer icall y as Q*R , wher e Q is an or thogonal matr ix and R is an upper tr iangular matri x, and retur ns R. R is stor ed in v ar2 and Q=A*inv(R) is stor ed in var1 .
Matrices 485 SVL Singular V alues . Returns a vector co ntaining the singular val u es of matri x . SVL ( matrix ) Example: SVL returns Vector Cross Product C r oss Product of ve cto r 1 wi t h ve c to r2 . CROSS ( vector1 , vector2 ) Example: CROSS returns Dot Product Dot Product of tw o arra ys , matri x1 and matri x2 .
486 Matri ces Max Norm Re turns the l ∞ nor m (the maximum of the a bsolute v alues of the coordinate s) of a vect or . maxnorm(Vect or Mtrx) Exam ple: maxnorm returns 4 Examples Identity M atrix Y ou can cr eate an identity matr ix w ith the IDENMAT functi on.
Matrices 487 whi ch can then be stor ed as a re al matri x in any matr i x vari able. M1 is used in this e xample . Y ou can t hen use the RREF function to change this to reduced-ro w echelon f orm, s toring it in any matr i x vari able. M2 is used in this e xample .
488 Matri ces.
Notes and Info 489 26 Notes and Info The HP Prime has t wo te xt e ditors for entering notes: • The Note E ditor: opens from w ithin the Note Catalo g (w hich is a collecti on of notes independent of apps) . • The Info Editor: opens from the Info view of an app.
490 Notes and Info The Note Editor The Note E ditor is where y ou cr eate a nd edit notes. Y ou can laun ch the Note Editor fr om t he Notes Catalo g, and also fr om within an app . Notes cr eated within an app stay w ith that app ev en if you s end the app to another calc ulator .
Notes and Info 491 2 . Create a new note. 3 . Ente r a name for y our note . In this ex ample , we ’ll call the note MY NOTE . AA MYNOTE 4. W r ite your note , using the editing ke y s an d formatting options desc ribed in the follo w ing sections .
492 Notes and Info Note Editor: buttons and keys The f ollow ing buttons and ke ys ar e available w hile you are adding or editing a note. But ton or Ke y Purpose Opens the te xt formatting menu . See “F ormatting options ” on page 4 9 4. Pr ov ides bold, it alic, underline , full ca ps, supersc ript and subs cript options .
Notes and Info 493 Entering uppercase and lowercase characters The f ollo wing t able below de scr ibes ho w to qui ckly enter upper case and low ercase c haracter s. E Starts a ne w line. SJ (Clear) Erases the e ntire note . a Menu for entering var iable names, and the conten ts of vari ab les.
494 Notes and Info The le ft side of the n otificati on area of the title bar w ill indica te what ca se w ill be applied to the char acter y ou next ent er . Text formatting Y ou can enter te xt in differ ent formats in the Note Editor . Choose a for mat ting option befor e you start entering te xt.
Notes and Info 495 Inserting mathematical expressions Yo u c a n i n s e r t a mathemati cal expr es sion in textbook f ormat into y our note , as show n in the figur e to th e ri ght. The Note E ditor uses the same 2D editor that the Home and CA S vie ws emplo y , ac tiv ated vi a the menu button .
496 Notes and Info To import a note Y ou can import a note fr om th e Note Catalog into an ap p’ s I n fo view a n d vic e ve rs a. Suppos e you w ant to copy a no te named Assignmen ts fr om the Note Cat alog into the Func tion Info v ie w: 1 . Open the Note Catalog.
Programming in HP PPL 497 27 Pr ogramming in HP P P L This c hapter descr ibes the HP Prime Pr ogramming Languag e (HP PPL). In this chapter y ou’ll lear n about: • progr amming commands • wr it.
498 Programming in HP PP L Some built-in commands employ an alte rnativ e sy ntax wher eby f unction arguments do not appear in parenthe ses. Ex amples include RETURN and RANDOM . Program Structure Progr ams can contain an y number of subr outines (each of whi ch is a func tion or procedur e) .
Programming in HP PPL 499 Open the Program Catalog Pre ss Sx ( Pr ogram) to open the Pr ogram Catalog. The P ro gra m Ca t al o g display s a list of pr ogr am names. T he first item in the Progr am Catalog is a built-in entr y that has the same name as the activ e app .
500 Programming in HP PP L Sav e crea te s a c o py o f the selec ted progr am w ith a new name y ou ar e prompted to gi ve . Rena me renames the sele cted prog ram. Sort sor ts the l ist of progr ams . (Sort options are alpha betical and chr onologi cal) .
Programming in HP PPL 501 Creating a new program In the follo w ing few s ections, w e wi ll creat e a simple progr am that counts to thr ee as an introduc tion to using the Progr am editor and its menus. 1 . Open the Pr ogram Catalog and start a new pr ogr am.
502 Programming in HP PP L The Program Editor Until y ou become familiar w ith the HP Prime commands, the easiest wa y to enter command s is to select them from the Catalog men u ( D ) , or fr om the Commands menu in the Pr ogram E ditor ( ) .
Programming in HP PPL 503 Pre ss J to return to the main menu . The commands in this men u are des cr ibed i n “Commands under the Cmds menu ” , beginning on page 5 3 4.
504 Programming in HP PP L 1. T o c o n t i n u e t h e MYPR OGRA M exam p le (wh ich we began on page 5 0 1), use the c urso r k ey s to position the cu rs or wh e re you wa nt t o i n se r t a command or ju st tap on the desired locati on. In this ex ample , you need to positi on the cursor betw een BEGIN and END .
Programming in HP PPL 505 In this example we’ll select a LOOP command from the menu. 3. S e l e c t Loop and then selec t FOR from the sub-menu . Notice that a FOR_FROM_TO_DO _ template is inserted. All you need do is fill in the missing information.
506 Programming in HP PP L 8. Fill in the ar guments of the MSGBOX command, and type a semicolo n at the end of the command ( S+ ). 9 . T ap to chec k the synt ax of your pr ogram . 1 0. When you ar e finished , pres s Sx to return to the Progr am Catalog or H to go to Ho me vie w .
Programming in HP PPL 507 4. T ap thr ee times to step through the FOR loop . Notice that the number show n incr ements by 1 each time . Aft er th e p rog ram terminates, y ou can r esume an y other activ ity with the HP Pr ime. If a progr am has ar guments, when y ou pr ess a sc reen appears pr ompt ing y ou to enter the progr am parameters .
508 Programming in HP PP L 1 . In the Pr ogram Catalog , select MYPR OGRAM. Sx Select MYPROGRAM 2 . T ap . If there is more than one EXPORT function in a file, a list appears for you to choose which function to debug. While debugging a program, the title of the program or intra-pr ogram function appears at the top of the display.
Programming in HP PPL 509 The message box appears. Note that when eac h message box is displayed, yo u still have to dismiss it by tapping or pressi ng E .
510 Programming in HP PP L : Cut the selection. : Copy the sele ction. 4. Select what y ou wan t to copy or c ut (using the optio ns listed immediately abo ve). 5 . T ap or . 6 . R eturn to the Pr ogram Cat alog and open the target progr am. 7 . Mo ve the c ursor to w here y ou want to ins er t the copied or c ut code.
Programming in HP PPL 511 To share a program Y ou can send pr ograms be tween calc ulators j ust as y ou can send apps , notes, matr ices , and lists. See “Shar ing data” on page 44.
512 Programming in HP PP L var iables is gi ven in chapter 2 2, “V ar iables ” , beginning on page 4 2 3.) In a pr ogram y ou can declare v ari ables for use onl y within a partic ular functi on.
Programming in HP PPL 513 Note that EXPORT command fo r the var iable RADIUS appear s befo re the heading of the functi on whe re RADIUS is assi gned. A fter yo u e xec ute this pr ogram , a ne w vari able named RADIUS appears on th e USER GETRADIUS secti on of the V ar iables menu .
514 Programming in HP PP L Program ROLLDIE W e’ll f irst c reate a pr ogr am called ROLLDIE. It simulates the r olling of a single die, r eturning a r andom integer between 1 and whate ver number is passed into the fun ct ion. In the Progr am Catalog c reate a new pr ogram named ROLLDIE .
Programming in HP PPL 515 L2(roll)+1 ▶ L2(roll); END; END; B y omit ting the EXPORT command when a f unction is declar ed , its visibility can be r estr icted to the progr am w ithin whi ch it is def ined.
516 Programming in HP PP L FOR k FROM 1 TO n DO ROLLDIE(sides)+ROLLDIE(sides) ▶ roll; results(roll)+1 ▶ results(roll); END; RETURN results; END; ROLLDIE(N) BEGIN RETURN 1+RANDINT(N-1); END; I n H .
Programming in HP PPL 517 To activate persistent user mode, press SWSW . Notice that U appears in the title bar. The user keyboard will now remain ac tive until yo u press SW again. If y ou ar e in user mode and pres s a k ey that hasn ’t been r e -assigned, the k ey ’s standard oper ation is perfo rmed.
518 Programming in HP PP L Tip A quick way to write a program to re-assign a key is to press Z and select Create user key when you are in the Program Editor. You will then be asked to press the key (or key combination) you want to re-assign. A program template appears, with the internal name of the key (or key combination) ad ded automatically.
Programming in HP PPL 519 n K_Div K S_Div KA_Di v KS A_Div . K_Dot K S_Dot KA_Dot KS A_Dot K_Dow n KS _Down KA_Do wn KS A_Dow n E K_Enter KS_Enter KA_Enter KS A_Enter H K_Home KS _Home KA_Home KS A_H.
520 Programming in HP PP L App programs An app is a unif ied collection of v ie ws, pr ograms , notes, and asso ciat ed data. Cr eating an app progr am allo ws y ou to re define the app ’s v iew s and ho w a user w ill interact with those v ie ws.
Programming in HP PPL 521 Using dedicated program functions Ther e ar e nine dedicated pr ogram func tion names, as sho wn in the table below . These functions ar e called when the cor res ponding ke y s show n in the table ar e pre ssed .
522 Programming in HP PP L Customizing an app When an app is acti ve , its assoc iated progr am appears as the f irst item in the Pr ogram Cata log. It is w ithin this progr am that y ou put functions to c reate a c ustom app . A usef ul procedur e for c ustomizing an app is illustr ated below : 1 .
Programming in HP PPL 523 1 . I n t he App lica tion Lib r ray , s e l ec t th e Statisti cs 1V ar app but don ’t open it. I Select Statistics 1Var . 2. Ta p . 3 . Enter a name f or the new a pp (such as DiceSimulation .) 4. T ap twi ce. The new app appears in the Application Libr ary.
524 Programming in HP PP L Thes e vie ws w ill be activated b y pressing M and P , but the func tion Plot() in our app progr am will actuall y launc h the latter vi ew after doing s ome config urati on. Befor e entering th e fo llow ing progr am, pr ess S I to open the Info edit or and enter the te xt show n in the figur e.
Programming in HP PPL 525 FOR k FROM 1 TO ROLLS DO roll:=ROLLDIE(SIDES)+ROLLDIE (SIDES); D2(roll-1):= D2(roll-1)+1; END; Xmin:= -0.1; Xmax:= MAX(D1)+1; Ymin:= − 0.
526 Programming in HP PP L BEGIN Xmin:=-0.1; Xmax:= MAX(D1)+1; Ymin:= − 0.1; Ymax:= MAX(D2)+1; STARTVIEW(1,1); END; Symb() BEGIN SetSample(H1,D1); SetFreq(H1,D2); H1Type:=1; STARTVIEW(0,1); END; The ROLLMANY() r outine is an adaptation of the progr am pres ented earlier in this chapter .
Programming in HP PPL 527 2. P r e s s V to see the cu stom app menu . Her e y ou can r eset the app ( Start ), se t the number of sides of the dice , the number of r olls, and execu te a s im u la t io n. 3. S e l e c t Set Rolls and enter 1 00. 4. Select Set Sides and enter 6 .
528 Programming in HP PP L Commands under the Tmplt menu Block The bloc k commands determine the beginning and end of a sub-ro utine or function . Ther e is also a Return command to r ecall results fr om sub-r outines or functio ns.
Programming in HP PPL 529 CASE Syn t a x : CASE IF test1 THEN commands1 END; IF t est2 THEN commands2 END; … [ DEFAULT commands ] END ; Eval u at es test1 . If true, e xec utes commands1 and e nds the CASE . Otherwise , ev aluates test2 . If true, e xec utes commands2 and ends the CASE .
530 Programming in HP PP L Example 1 : This pr ogram deter mines whic h integer from 2 to N has the gr eatest number of f actors . EXPORT MAXFACTORS(N) BEGIN LOCAL cur,max,k,result; 1 ▶ max;1 ▶ result; FOR k FROM 2 TO N DO SIZE(CAS.
Programming in HP PPL 531 RECT(); xincr := (Xmax - Xmin)/318; yincr := (Ymax - Ymin)/218; FOR X FROM Xmin TO Xmax STEP xincr DO FOR Y FROM Ymin TO Ymax STEP yincr DO color := RGB(X^3 MOD 255,Y^3 MOD 255, TAN(0.
532 Programming in HP PP L END; d+1 ▶ d; END; RETURN sum==n; END; The f ollo wing pr ogram dis play s all the perfect numbe rs up to 1 000: EXPORT PERFECTNUMS() BEGIN LOCAL k; FOR k FROM 2 TO 10.
Programming in HP PPL 533 Variable The se commands enable y ou to contr ol the v isibility of a user -defined variable . LOCAL Loc a l. Syn t a x : LOCAL va r1 , var2 ,…v arn; Mak es the vari ables va r1 , var2 , etc . local to the progr am in whi ch the y are fo und.
534 Programming in HP PP L Commands under the Cmds menu Strings A str ing is a sequence of char acter s enclosed in double quotes (""). T o put a double quote in a string, u se two consec utiv e double quotes. The char acter starts an escape sequence , and the character(s) immedi ately follo w ing are inte rpreted s pecia lly .
Programming in HP PPL 535 STRING Syn t a x : STRING ( obj ect ); Ret u r ns a s t ri ng re p re se n ta t io n of objec t . Th e res u l t va rie s depending on the t ype of obj ect . Examples: INSTRING Syn t a x : INSTRING ( str1 ,str2 ) R eturns the index o f the firs t occurr ence of str2 in st r1 .
536 Programming in HP PP L MID Syn t a x : MID ( str ,pos, [ n ]) Extr acts n cha rac te rs from st ri ng str st artin g at i ndex pos . n is optio nal, if not s pecif ied, extr acts all the r emainder of the str ing.
Programming in HP PPL 537 coordinates using the Cartesian plane def ined in th e cur rent app by the var iables Xmin, Xmax , Ymin, and Ymax . The r emaining thirteen wor k with pi xel coordinates w here the pix el 0,0 is the top left pi xel of the GROB , and 320, 240 is the bottom ri ght.
538 Programming in HP PP L Pixels and Cartesian ARC_P ARC Syn t a x ; ARC ( G, x, y , r [ , a1 , a2 , c ]) ARC_P ( G, x, y , r [ , a1 , a2 , c ]) Dra ws an arc or c ir cle on G , center ed on point x, y , wi th rad i u s r and color c starti ng at angle a1 and ending on angle a2 .
Programming in HP PPL 539 sx2 , sy2 ar e optional and if not spec ified w ill be the bottom r ight of the sr cGRB . sx1 , sy1 ar e optional and if not spec ifi ed will be the to p left of sr cGRB . dx1 , dy1 are optional and if n ot spec ified w ill be the top left of tr gtGRB .
540 Programming in HP PP L GROBW_P GROBW Syn t a x : GROBW ( G ) GROBW_P ( G ) Retu rns the wi dth of G . G can be any of the gr aphics v ariables and is opti onal. The d ef aul t i s G0 . INVERT_P INVERT Syn t a x : INVERT ( [ G, x1 , y1 , x2 , y2 ]) INVERT_P ( [ G, x1, y1, x2, y2 ]) Exec ute s a re vers e video o f the selected r egion .
Programming in HP PPL 541 PIXON_P PIXON Sy n t a x : PIXON( [ G ] , x, y [ ,color ]) PIXON_P( [ G ], x, y [ ,color ]) Sets the color o f the pi xel G wit h co o rd in a te s x, y to color . G can be any of the gr aphics var iables and is optional. The d efa ul t i s G0 , the cur rent gr aphic .
542 Programming in HP PP L EXPORT BOX() BEGIN RECT(); RECT_P(40,90,#0 00000); WAIT; END; The pr ogr am below als o uses the RECT_P command . In this case , the pair of arguments 320 and 240 corr espond to x2 and y2 . The pr ogram pr oduces ar e rectangle with a black edge and a red f ill.
Programming in HP PPL 543 TEXTOUT_P TEXTOUT Syn t a x : TEXTOUT ( text [ , G ] , x , y [ ,font , c1 , width , c2 ]) TEXTOUT_P ( text [ , G ] , x , y [ ,font , c1 , widt h, c2 ]) Dra ws te xt usin g color c1 on graphic G at position x, y usin g fo nt .
544 Programming in HP PP L TEXTOUT_P(K ,35,0,2,#FFFFFF, 100,#333399); TEXTOUT_P(A ,90,30,2,#000000,100, #99CC33); sign*- 1 ▶ sign; K+1 ▶ K; UNTIL 0; END; END; The pr ogr am ex ecu tes until the use r press es O to terminate .
Programming in HP PPL 545 EDITMAT Sy n t a x : EDITMAT ( name ) Starts the Matr ix E ditor and displa ys the spec ifi ed matri x. If used in pr ogramming , retur ns to the progr am when user pre sses . Even though this command r eturns the matri x that wa s edited, EDITMAT cannot be used as an argumen t in other matri x commands.
546 Programming in HP PP L App Functions The se commands allow you to la unch an y HP app, br ing up an y vie w of the c urre nt app , and change the options in the Vi ew menu . STARTAPP Syn t a x : STARTAPP( "name" ) Starts the app w ith name .
Programming in HP PPL 547 Y ou can also launch v ie ws that are not spec ifi c to an app by sp e ci f yi n g a va l u e fo r n that is less than 0: Home Screen:-1 Home Settings:-2 Memory Manager:-3 Ap.
548 Programming in HP PP L BITSL Syn t a x : BITSL(int1 [,int2]) Bitwise Shift Left . T akes o ne or t wo int egers as input and r eturns the r esult of shifting the b its in the firs t integer to the left by the number places indicated b y the second integer .
Programming in HP PPL 549 GETBITS Sy n t a x: GETBITS(#integer) R eturns the number o f bits used b y integer , e xpres sed in the default base . Example: GETBITS(#22122) retu rn s #20h or 32 R → B Syn t a x : R → B(integer) Con verts a dec imal integer (base 1 0) to an integer in the defa ult base.
550 Programming in HP PP L Retur ns true (not z er o) if the user selects an objec t, otherwis e retur n false (0). Exam ple: CHOOSE (N,"PickHero", "Euler","Gauss ",".
Programming in HP PPL 551 INPUT Syn t a x : INPUT(var [,"title", "label", "help", reset]); Opens a dialog bo x wi th the title text title , with one fi eld named label , display ing help at the bottom and usin g th e reset val ue if S J is pres sed.
552 Programming in HP PP L ISKEYDOWN Syn t a x : ISKEYDOWN ( key _ id ); Retu rns true (non- z ero) if the k ey w hose key_ id is pro vi ded is c urrentl y pres sed, and false (0) if it is not .
Programming in HP PPL 553 PRINT Syn t a x : PRINT ( ex p ress i on or str ing ); Pr ints the re sult of ex p re ss i o n or string to the terminal. The ter minal is a progr am text output v iew ing mec h anism whi ch is display ed only w hen PRINT commands are e xecuted .
554 Programming in HP PP L More %CHANGE Syn t a x : %CHANGE(x,y) The pe rcent age change in going f ro m x to y . Exam ple: %CHANGE(20,50) ret u rn s 1 50. %TOTAL Syn t a x : %TOTAL(x,y) The p erc en ta g e of x that is y . Exam ple: %TOTAL(20,50) ret u rn s 250.
Programming in HP PPL 555 second list . The plus operator between them adds the two elements until th ere are no mor e pa irs. W ith t wo lists, the numbers appended to & can have two di gits; in .
556 Programming in HP PP L TYPE Syn t a x : T Y PE ( o bj e c t ) Retu rns the type of the obj ect: 0: Real 1: I n t e g e r 2: St ri n g 3: Comple x 4: Mat rix 5: Err or 6: Lis t 8: F unction 9: Un i t 1 4. ?: cas objec t. T he fracti onal part is the cas type .
Programming in HP PPL 557 var iables r epresent the def initions and settings you mak e whe n wo rk i ng wi t h ap ps i n t era ct ive ly . A s you wo rk thr ough an app , the app functi ons may stor e resu lts in app var iables as w ell.
558 Programming in HP PP L App variables Not all ap p var iables a re us ed i n ev er y app. S1F it, for e x a m p l e , i s o n l y u s e d i n t h e S t a t i s t i c s 2 Va r a p p .
Programming in HP PPL 559 GridLines T urns the back gr ound line grid in P lot Vi ew on or off . In Plo t Se tu p view , ch e ck ( o r u n ch eck ) GRID LINES . In a progr am, type: 0 GridLines —to turn the grid lines on (default). 1 GridLines —to turn the grid lines off.
560 Programming in HP PP L Nmin/Nma x Sequence Def ines the minimum and maximum v alues for the independe nt var iable . Appe ars as the N RNG fie l d s i n t h e Plo t Se t u p vi ew . I n Plo t Se tu p vi ew , e nt er va lu e s f or N Rng . In a pr ogra m, type : Nmin Nmax whe re Recenter Recenters at the cur sor when z ooming.
Programming in HP PPL 561 step Polar Sets the s tep siz e f or the independent var iable . In Plo t Se tu p vi ew , e nte r a va l ue fo r Step . In a progr am, type: step whe re Tmin/Tmax Parametric Sets the minim um and max imum independent v aria ble values .
562 Programming in HP PP L Ymin/Ymax Sets the minim um and maximum v ertical value s of the plot scr een. In Plot Se tup vie w , enter the values for Y Rng . In a pr ogra m, type : Ymin Ymax whe re Xzoom Sets the hor i z ontal z oom facto r . In P lot Vie w , pres s then .
Programming in HP PPL 563 E0...E9 Solve Cont ains an equation or expr ession . In Sy mbolic v iew , sele ct on e of E0 through E9 and enter an e xpressi on or equation. The independent variable is selected by highlighting it in Numer ic vi ew . In a progr am, type (f or ex ample) : X+Y*X-2=Y ▶ E1 F0.
564 Programming in HP PP L Method Inference Determines whether the Infer ence app is set to calculate hy p o t h e s i s t e s t re s u l t s o r c o n fi d e n c e i n t e r v a l s . I n Sy m b o l i c vi ew , make a selecti on for Method . In a pr ogra m, type : 0 Method —for Hypothesis Test 1 Method —for Confidence Interval R0.
Programming in HP PPL 565 Type Inference Determines the type of hypothe si s test or confidence interval. Depends upon the value of the v ariable Method . F rom S y mbolic V iew , mak e a selectio n for Type . Or , in a progr am, stor e the constant number fr om the list below into the v ariable T ype .
566 Programming in HP PP L Numeric view variables C0...C9 Statistics 2Var Contain lis ts of numerical data . In Numeric v ie w , ente r numeri cal data in C0 through C9 . In a pr ogra m, type : LIST Cn wher e , 1 , 2 , 3 ... 9 and LIST i s e i t h e r a l i s t o r t h e name of a list .
Programming in HP PPL 567 NumYStart Advanced Graphing Sets the s tarting value for the Y - va lues in a table in Numeric v iew . F rom Numer ic Setup v ie w , enter a v alue for NUMYSTART .
568 Programming in HP PP L NumXZoom Advanced Graphing Sets the z oom fa ctor fo r the valu es in the X column in the Numeri c vie w . F ro m Numeri c Setup v ie w , type in a value f or NUMXZOOM . In a pr ogra m, type : NumXZoom whe re NumYZoom Advanced Graphing Sets the z o om f actor f or the values in the Y column in the Numeri c vie w .
Programming in HP PPL 569 Mean 1 Sets the v alue of the mean of a sample f or a 1 -mean h ypothesis test or co nfidence interval. F or a 2 - mean test or interval , sets the va lue of the mean of the f irst sample . F rom Numer ic v iew , set the v alue of or .
570 Programming in HP PP L P ooled Determine whether or not the samp les are pooled for tests or intervals using the Student ’s T-distributi on invol ving two means. F r om the Numeric v ie w , set the value of Pooled . In a pr ogra m, type : 0 Pooled —for not pooled (default).
Programming in HP PPL 571 x 1 Sets the n umber of successe s for a one -pr oportion h y p o t h e s i s t e s t o r c o n f i d e n c e i n t e r v a l . F o r a t e s t o r i n t e r v a l inv olv ing the differ ence of two pr oportions , sets the number of successes of the first samp le.
572 Programming in HP PP L IPYR Intere st per year . Sets th e annual interes t rate for a cash flo w . Fr om the Numeric v iew o f the F inance app, enter a val u e fo r I%YR . In a pr ogra m, type : IPYR whe re NbPmt Number of pay ments. Sets the number of pay ments for a cash flo w .
Programming in HP PPL 573 GSize Group si z e. Sets the siz e of each gr oup for the amorti zati on table . Fr om the Numer ic v iew of the Finance app , enter a value f or Group Size. In a progr am, type: GSize Linear Solver app variables The f ollo wing v aria bles are u sed by the L inear Sol ver app .
574 Programming in HP PP L SideC The le ngth of Side c . Sets the length of the side opposite the angle C. F r om the T r iangle Sol ver Numer ic v ie w , en ter a positi ve va lue for c. In a pr ogra m, type : SideC whe re AngleA T he measure of angle A.
Programming in HP PPL 575 RECT Cor responds to the status of in the Numeric v ie w of the T r iangl e Solv er app. Determines w hether a general tri angle solv er or a right tr iangle sol ver is used .
576 Programming in HP PP L HComplex Sets the comple x number mode fo r the Home vie w . In Home Setti ngs , che ck o r u nche ck t he Comple x fiel d. Or , in a progr am, ty pe : 0 HComplex —for OFF. 1 HComplex —for ON. Date Contains the sy stem date.
Programming in HP PPL 577 Entry Contains an integer that indi cates the entr y mode . In Home Settings , select an option f or Entry . In a p ro g ram, e n te r: 0 Entry —for Textbook 1 Entry —for Algebraic 2 Entry —for RPN Integer Base R eturns or sets the integer base .
578 Programming in HP PP L Symbolic Setup variables The f ollo wing var iables ar e fou nd in the S ymboli c setup o f an app . The y can be used to o verw rite the v alue of the co rresp o nd in g vari ab le i n Home Settings . AAngle Sets the angle mode .
Programming in HP PPL 579 AFormat Defines the n umber display f ormat used for n umber display in the Home v ie w and to label axes in the P lot view . F rom S y mbolic setup , choos e Standard , Fi xed , Scientific , or Engineering in the Number For mat fie l d.
580 Programming in HP PP L.
Basic integer arithmetic 581 28 Basic integ er arithmetic The common number bas e used in contempor ar y mathematics is base 1 0. By de fault , all calc ulations perfor med by the HP Prime ar e carr ied out in base 1 0, and all r esults are displa yed in base 1 0.
582 Basic integer arithmetic repr esents 2 28 10 . In this case, the bas e marker h in dicates that the number is to interpreted as a he xadec im al number: E4 16 .
Basic integer arithmetic 583 Note that if y ou change the def ault base , an y calcula tion in history that invo lves in teger ar ithmetic for whi ch y ou did not expli citly add a base mark er w ill be r esispla yed in the new bas e.
584 Basic integer arithmetic Examples of integer arithmetic T h e o p e r a n d s i n i n t e g e r a r i t h m e t i c c a n b e o f t h e s a m e b a s e o r o f mix ed bases.
Basic integer arithmetic 585 Integer manipulation The r esult of integer arithmeti c can be further analyz ed, and manipulated, b y vi ew ing it in the Edit Integer di alog . 1 . In Home v ie w , u se the curs or ke ys t o select the re sult of inte re st .
586 Basic integer arithmetic : returns the one’s complement (that is, each bit in the specified wordsize is inverted: a 0 i s replaced by 1 and a 1 by 0. The new integer represented appears in the Out field (and in the hex and decimal fields below it).
Glossary 587 Appendix A Glossary app A sma ll app lica tion, desig ned for t he study of one or more r ela ted topics or to solv e problems of a partic ular t ype .
588 Glossary command An operati on for use in pr ograms . Commands can s tore r esults in var iables, but do not display r esults. ex pres sion A number , var iable , or algebr aic expr essi on (numbers plus f unctions) that produces a v alue. functi on An operation , possibly with ar guments, that r etur ns a result .
Glossary 589 matr ix A two-dimensiona l arra y of r eal or complex numbers enclosed b y square brac kets . Matrices can be cr eated and manipulated b y the Matri x E ditor and stor ed in the Matri x Catalog . V ect ors are als o handled by the Matri x Catalog and Ed itor .
590 Glossary.
Troubleshooting 591 Appendix B T roubleshooting Calculator not responding If the calc ulator does no t res pond, y ou should f irst try to re se t it. T his is much lik e res tar ting a PC . It cancels cer tain operati ons, r estor es cer tain conditions, and c lears tempor ary memor y locations.
592 Troubleshooting Operating limits Opera ting tempe rature: 0 to 45 C (3 2 to 1 1 3 F) . Sto rage t emper atur e: –20 to 6 5 C (– 4 to 1 4 9 F) . Opera ting and storag e humi dity : 90% rel a tive humidity at 40 C ( 1 04 F) max imum.
Troubleshooting 593 S yntax er ror The func tion or command yo u enter ed does not inc lude the proper arguments or order of arguments . The delimiters (paren theses, comma s, peri ods, and semi -col ons) must a lso b e corr ect . Look u p the functi on name in the inde x to find its proper s yntax .
594 Troubleshooting.
Product regulatory information 595 Appendix C Pr oduc t regulatory inform ation Federal Communications Commission notice This equipment has been t ested and found to comply w ith the li mits for a Class B digital dev ice, pursuant to P ar t 1 5 of the FC C Rules .
596 Produ ct regulato ry information Dec larat ion of Confo rmit y for p roduc ts M arked wi th F CC Logo, United States Only This devi ce c omplies with P art 1 5 of th e FCC Rules.
Product regulatory information 597 European Union Regulatory Notice Pr oducts bearing the CE marking co mply w ith the follo w- ing EU Dir ecti ves: • Lo w V oltage Dir ectiv e 2006/95/E C • EMC D.
598 Produ ct regulato ry information Japanese Notice Korean Class Notice Disposal of Wast e Equipment by Users in Private Household in the European Union This sy mbol on the product or on its pack aging indicates that this product must not be disposed o f with y our other household wa ste.
Product regulatory information 599 Chemical Substances HP is committed to pr ov iding our cu stomers w ith informa- tion about the c hemical substances in our pr oducts as needed to comply with legal requirements such as REA CH ( Re gulation EC No 1 90 7/2006 of the Eur opean P a rli ament and the Counc il) .
600 Produ ct regulato ry information.
Index 601 Index A adapter 12 adaptive graphing 99 Advanced Graphing app 69, 125–134 Plot Gallery 134 trace options 129 variables, summary of 432 algebra func tions 324–325 algebraic en try 32, 36,.
602 Index buttons command 20 menu 20 See also menu buttons C cables 45 calcula tions CAS 54, 324–347 confidence intervals 253 financial 287–294 geometric 150 in Home view 36, 309–323 statistical.
Index 603 decimal mark 33 decimal zoom 90, 93, 102 default settings, restoring 21, 87, 100, 106 define your o wn fit 232 degree symbol 21 deleting apps 72 characters 21 lists 455 matrices 464 notes 49.
604 Index keyboard 309–312 Linear Expl orer 376 Linear Solver 374 number 313–314 plot 346–347 polynomial 339–345 probability 317–322 rewrite 332–337 solve 330–332 Solve app 349 spreadshe.
Index 605 Inference app 69, 239–257 confidence interv als 253–257 functions 366–371 hypothesis tests 245–2 52 importing statistics 243 variables Numeric 568 Results 438 summary of 437 Info, So.
606 Index matrix calculations 463 negating elemen ts 47 2 raised to a p ower 471 reduced-row e chelon 486 singular value decompositio n 485 storing 464, 468, 469 swap row 545 transposing 486 variables.
Index 607 physics constants 449 pinch 17 plot box-and-wh isker 220 cobweb 281 color of 85 defined in Geometry a pp 160 functions 346–347 line 220 one-variable sta tistics 219 pareto 221 stairsteps 2.
608 Index Sequence app 70 , 281–286 graph types 281 variables 442 settings 30, 428 CAS 30, 55 sharing data 44 shift keys 22 shortcut palettes 20 shortcuts in Geometry 147 in menus 28 Solve app 70, 2.
Index 609 T tables, custom 103 template key 24 templates 20 test mode See exam mode text 23 textbook entry 32, 33, 36, 47 theme 34 time 16, 34 time-value-of-mo ney problems 287 title bar 14 Toolbox me.
610 Index views definition of 589 in apps 73 Numeric 77 Numeric Setup 78 Plot 75 Plot Setup 76 Symbolic 73 Symbolic Setup 74 Views menu 91, 521 W wireless network 34 wordsize 58 3 Z Z-Intervals 253–.
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