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Annuity

An engineer retires with $650,000 available for
investment. She invests the money in a portfolio which is
expected to have an average return of 5% per annum.
She wants to have the account pay a monthly income to
her and asks the accountant to assume that the income
must last for 20 years. What income can be withdrawn?

The

PV

for this problem is negative because,

from the point of view of the engineer, the
money flow is outward from her to the
investment portfolio. The value of the regular
payment, which has been solved for on the
right, is positive as it is being paid from the
portfolio to her. We also assume that the future value

FV

is to be zero since

the income is only to last for 20 years. On this basis the monthly annuity can
be $4289.71

Loan calculations

You wish to purchase a car by taking out a loan. The
current interest rate is 6.5% and you can afford to make
monthly payments of $300. You want to take out the loan
over a period of 6 years and to still owe $10,000 at the
end of that period (you expect an investment to mature at
that time to pay the final amount). How much can you
borrow?

In this case, from your point of view, the
payments and the

FV

final residual are

outgoing (negative) since they are made to the
bank. We have pressed

to find the

PV

and this is the amount that can be borrowed. It
will be positive since it is paid to you. In this
case it is clear that you can afford to borrow $24,624.29.

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Summary of Contents for 39G

Page 1: ...hp 39g graphing calculator Mastering the hp 39g A guide for teachers students and other users of the hp 39g hp 39g hp 40g Edition 1 1 HP part number F2224 90010 Printed Date 2005 10 11 ...

Page 2: ...M keys 27 Intro to the VIEWS menu 28 The VARS key 28 The SETUP views 30 The MODES view 30 Numeric formats 31 The ANS key 32 The negative key 33 The CHARS key 33 The DEL and CLEAR keys 34 Angle and Numeric settings 35 Memory Management 37 The MEMORY MANAGER view 37 Downloaded aplets memory 38 The GRAPHICS MANAGER 39 The LIBRARY MANAGER 39 Fractions on the hp 39g 40 Pitfalls to watch for 42 The HOME...

Page 3: ...g 62 The FCN menu 63 Root 63 Intersection 64 Slope 64 Signed area 65 Definite integrals 65 Tracing the integral in PLOT 66 Areas between and under curves 67 Extremum 68 Tips Tricks Function 69 Finding a suitable set of axes 69 Composite functions 71 Using functions in the HOME view 72 Differentiating 73 Circular functions 74 Trig functions 76 Retaining calculated values 77 The NUM view revisited 7...

Page 4: ...106 θStep and smoothness 106 Changing the default for θStep 106 Circular circles 106 The Sequence Aplet 107 Recursive or non recursive 107 First second general terms 107 Convenient screen keys provided 108 Tips Tricks Sequences Series 110 Defining a generalized GP and the sum to n terms 110 Solving sequence problems 110 Modeling loans 112 The Solve Aplet 113 Equations vs expressions 113 Entering t...

Page 5: ... model 134 Multiple data sets 134 Choosing from available fit models 135 The User Defined model 135 Connected data 136 Two Variable Statistics 137 Showing the line of best fit 138 Predicting using PREDY 140 Predicting using the PLOT view 140 RelErr as a measure of non linear fit 141 Tips Tricks Bivariate Data 143 New columns as functions of old 143 Using values from in calculations 143 Obtaining c...

Page 6: ...e matrix 174 The dot product 175 Using Lists on the hp 39g 176 The list variables 176 Operations on lists 176 Statistical columns as lists 176 List functions 177 Editing a list 177 Operations on elements 177 Using the Notepad Catalog 178 Aplet notes vs independent notes 178 Independent Notes and the Notepad Catalog 179 Transferring notes using IR 180 Editing software 180 Software 181 For the hp 38...

Page 7: ...ownloaded aplets from the calculator 207 Saving notes aplets and sketches via the Connectivity Kit 208 Capturing screens using the Connectivity Kit 210 Editing Notes with the Aplet Development Kit 211 Programming the hp 39g 212 The design process 212 An overview 212 Choosing the parent aplet 212 Naming conventions 213 Planning the VIEWS menu 214 The SETVIEWS command 214 Special entries in the SETV...

Page 8: ...1 DISPXY 241 DISPTIME 241 GETKEY 241 INPUT 242 MSGBOX 242 PROMPT 242 WAIT 242 The MATH menu functions 243 The Real group of functions 246 CEILING 246 DEG RAD 246 FLOOR 246 FNROOT 247 FRAC 247 HMS 248 HMS 248 INT 249 MANT 249 MAX 249 MIN 250 MOD 250 250 CHANGE 251 TOTAL 251 RAD DEG 251 ROUND 252 SIGN 252 TRUNCATE 253 XPON 253 The Stat Two group of functions 254 PREDY 254 PREDX 254 The Symbolic grou...

Page 9: ...group of functions 265 CONCAT 265 LIST 266 MAKELIST 266 πLIST 267 POS 267 SIZE 268 ΣLIST 268 REVERSE 268 SORT 268 The Loop group of functions 269 ITERATE 269 RECURSE 270 Σ SUMMATION 270 The Matrix group of functions 271 COLNORM 271 COND 271 CROSS 271 DET 272 DOT 272 EIGENVAL 272 EIGENVV 272 IDENTMAT 272 INVERSE 273 LQ 273 LSQ 274 LU 274 MAKEMAT 274 QR 274 RANK 274 ROWNORM 274 RREF 274 SCHUR 275 SI...

Page 10: ...ions 288 Method 1 Graphing the lines 288 Second method using a matrix 288 Third method using the 3x3 Solver aplet 289 Expanding polynomials 290 Exponential growth 291 Solution of matrix equations 293 Inconsistent systems of equations 294 Using the RREF function 294 Finding complex roots 295 Analyzing vector motion and collisions 296 Circular Motion and the Dot Product 297 Inference testing using t...

Page 11: ...EXAMPLES CONTAINED HEREIN ARE PROVIDED AS IS AND ARE SUBJECT TO CHANGE WITHOUT NOTICE HEWLETT PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY NON INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE HEWLETT PACKARD CO SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTI...

Page 12: ...these machines For those concerned with the impact of a graphical calculator on the fundamentals of mathematics it should be recalled that the same fears were held for scientific calculators when they were introduced earlier History has shown that these fears were generally groundless Students are learning topics in high school that their parents did not cover until university years In particular ...

Page 13: ...read the Tips and Tricks sections which follow many of the chapters Early High School Typical topics covered include Solving linear equations graphing linear equations and possibly simple quadratics examining number patterns multiplying polynomials factoring simple polynomials calculations involving powers 2 3 x x square roots cube roots order of operations positives and negatives scientific notat...

Page 14: ...mentioned for high school students Read the suggestions on how to deal with graphs whose shape you don t know in advance Learn how to use the Parametric aplet Your teacher might best advise on which portions of the Statistics aplet will be relevant to you In the MATH menu also learn about functions CEILING ABS and FLOOR POLYCOEF and POLYEVAL Read the section covering the Matrices catalog and the f...

Page 15: ...ifferent contexts The bar at the bottom of the screen labels them Check this bar for special functions in any given context The SYMB key nearly always takes you to a view in which you can enter equations The PLOT key displays the graph view for any given environment HOME is where you will do most of your calculations It is shared by all the aplets and oversees them all The NUM key gives you a tabu...

Page 16: ...ions Notice how the meanings of the row of blank screen keys under the screen changes in different views The SYMB key in this case it is set to graph the function 3 2 7 6 y x x x The PLOT key used to graph the function The NUM key showing a tabular view of the function The APLET key is used to choose which aplet is active There are 10 aplets provided with the calculator and more can be downloaded ...

Page 17: ...e left of the key and below right you will see two additional meanings assigned via the SHIFT and ALPHA keys All references to keys whether they need the SHIFT key or not are written in this typeface KEY The SHIFT key The SHIFT key gives you the second function for each key In the case of the COS key the second function is ACOS sometimes referred to as arc cos or cos 1 or inverse cos Most keys hav...

Page 18: ...e now changed function Press the one under Pop up menus short cuts Sometimes pressing a key pops up a menu on the screen as you just saw You use the up down arrow keys to move the highlight through the menu and make choices by pressing the ENTER key Choices that are listed in a menu will usually be written using italics As an example I might say to press and choose Chronologically The manual you a...

Page 19: ...he divide key and the symbol from the multiply key More information on memories and detailed information on the HOME view in general is given on pages 45 The calculator also comes with a large number of mathematical functions that are very useful They can all be obtained via menus through the MATH key Try pressing the MATH key now and you should find your screen looks like the screen shot on the r...

Page 20: ... same effect by using ALPHA to type in the word letter by letter Some people prefer to do it that way Now type in 4 D 18 3 and press ENTER As you can see the effect was to round off the answer of 4 666666 to 3 decimal places There are shortcuts for obtaining things from the MATH menu that are covered later see page 47 ...

Page 21: ...rm There are ten standard aplets available via the APLET key More can be created by you or obtained via the Internet see pages 212 200 The Function aplet see page 51 Provides f x style graphs calculus functions etc It will not only graph but find intercepts intersections areas and turning points The Inference aplet see page 150 Allows the investigation of inferential statistics via hypothesis test...

Page 22: ...122 132 Handles descriptive statistics really well Data entry is easy as is editing It analyzes univariate and bivariate data drawing scatter graphs histograms and box whisker graphs The Trig Explorer aplet see page 167 This is a teaching aplet allowing the student to investigate the properties of sine and cosine graphs The Function aplet is probably the easiest to understand and also the one you ...

Page 23: ...f your normal requirements in mathematics However one of the great strengths of the hp 39g is its ability to download additional aplets from other calculators from a PC or Mac and from the Internet See page 200 A cable and software were provided with your hp 39g which you can use to connect your PC or Mac to your calculator and then download aplets from the computer to the calculator or to save yo...

Page 24: ...emistry There are a number of web sites which offer aplets The Hewlett Packard site is found at http www hp com calculators follow the links to graphical calculators and then to the library of aplets In addition to this you should check the site called The HP HOME view which can be found at http www hphomeview com contains not only aplets and games but also a huge amount of detailed information on...

Page 25: ...t i is s t th he e H HO OM ME E v vi ie ew w This is the HOME base for the calculator All other aplets can be accessed from it and affect it to varying degrees and all mathematical functions are available in this view Learn to use this view as efficiently as possible since a great deal of work will be done here We will explore the HOME view in the following order 1 Exploring the Keyboard 2 Angle a...

Page 26: ... at the bottom of the screen A common abbreviation used for these keys is SK1 or SK2 etc for screen key 1 In the PLOT view shown above some of the screen keys are labeled such as the key When you press this the row of screen keys labels appear or disappear To see another view where all the keys are in use change to the APLET view Calculator Tip Develop the habit of checking the screen to see if an...

Page 27: ...se settings to change in HOME too See page 35 for more details on this In addition to the standard ten covered in great detail in the chapters following many more aplets are available from the Internet written by other programmers Once these are downloaded into your calculator they can also be accessed via the APLET key For more detail on this type of aplet see the brief summary later in this sect...

Page 28: ...menu taken from an aplet designed to analyze and graph Time Series data The next important key is the HOME key It allows you to change into the HOME view from wherever you are Above it is the MODES key accessed by pressing SHIFT first Far more detailed information on these two views follows later The VARS key The VARS key is used mainly by programmers to access all the different variables stored b...

Page 29: ...in light blue above the key The hp 39g gets twice the action from each key by having this second function The second function is accessed via the SHIFT key on the left side of the calculator Although this book will sometimes tell you explicitly to press this key in most cases it will be assumed that you are intelligent enough to work out for yourself when it is necessary to press it The ALPHA key ...

Page 30: ...nd Using the Notepad Catalog on pages 184 178 Briefly any aplet except for the Quad Trig Explorer aplets has a note and a sketch associated with it which are usually blank unless you have added to them The main use for them comes with aplets downloaded from the Internet Instructions for using the aplet are sometimes included with the aplet in note form and sometimes as an accompanying sketch The M...

Page 31: ...c notation ensures that any results are displayed in scientific notation Of course the calculator s idea of scientific notation may not be the same as yours Since the calculator has no way of displaying powers as superscripts a result of 4 3 203 10 has to be displayed as 3 203E4 The alternative of Engineering notation is very similar to Scientific except that powers are always displayed as multipl...

Page 32: ...comma will use a full stop instead For example ROUND 3 456 2 will become ROUND 3 456 2 Moving back to our tour of the keyboard the next key is the ENTER key This is used as an all purpose I ve finished do your thing signal to the calculator In situations where you would normally press the key on most calculators press the ENTER key instead The ANS key Above the ENTER key is the ANS key This can be...

Page 33: ...for the Ans 2 is that a subtract cannot start a sentence in mathematics while a negative sign can Since the subtract can t come first the calculator decides that you must have intended to subtract from the previous answer Hence the sudden appearance of an Ans This occurs at other times too One of the most common The CHARS key The next important key is the CHARS key above VARS This key is used to a...

Page 34: ...f as a kind of super delete key For example if pressing DEL would erase one function only in the SYMB view then CLEAR will erase the whole set Calculator Tip Another use for the DEL key is to restore factory settings For example if you move back into the MODES screen and change to Degree mode then pressing the DEL key will restore the default of Radians Pressing CLEAR in the MODES view would resto...

Page 35: ...e also not only for the aplet but in the HOME view too For example suppose you have been performing trig calculations in the HOME view with the Function aplet being currently active and have set the angle measure to DEG If you were to now change to the Solve aplet in order to solve an equation then the settings would revert to those of the Solve aplet probably be radians unless you had also change...

Page 36: ...plet agree The problem was that on the hp 38g the default setting for the Function aplet was radians while HOME had a default setting of degrees and its setting was independent of those of the aplet This meant that a calculation such as the one above would give incorrect results and caused considerable confusion to some students It even resulted in users returning their hp 38g to dealers as faulty...

Page 37: ...e hp 39g has over ten times the useable memory of the hp 38g At 232 Kb vs only 23 Kb there are very few users who will come close to filling the hp 39g Depending on size there is enough room for at least fifty aplets or for over 10 000 data points The MEMORY MANAGER view In addition to extra memory the hp 39g supplies a better way to control it through the MEMORY MANAGER view If you press the MEMO...

Page 38: ...y with the parent aplet The memory associated with these programs is not included in that shown for the aplet in the APLET view but will not usually be a large amount Calculator Tip The reason for this naming convention for helper programs is that when you delete the parent aplet in the APLET view the helper programs are not automatically deleted with it You must change to the Program Catalog view...

Page 39: ...AGER and this will almost certainly be empty unless you have games loaded Generally the only aplets which use libraries are those such as games which are written by expert programmers in machine code in order to make them run as fast as possible These games available on the internet are listed in the APLET view along with the normal aplets and when you delete them the associated library is automat...

Page 40: ...onvert to a fraction others such as recurring ones are not so easy Most calculators opt for the easy option of switching to a decimal answer in any mixture of fractions and decimals The makers of the hp 39g took a very different approach Once you select Fraction mode all numbers become fractions including any decimals The first point to remember is that there is no provision for inputting mixed fr...

Page 41: ... fraction it finds in its process of approximation which matches the decimal to that number of significant digits For example a setting in the MODES view of Fraction 1 changes 0 234 to 3 13 which is actually 0 2307692 matching to at least 1 sig fig Fraction 2 changes 0 234 to 7 30 which is actually 0 2333333 matching to at least 2 sig fig Fraction 3 changes 0 234 to 11 47 which is actually 0 23404...

Page 42: ...he user in entering 0 66666 If you want to use this facility to convert decimals to fractions here are some tips if you are converting a recurring decimal to a fraction then make sure you include at least one more digit in the decimal than the setting of Fraction in MODES As you can see in the second screenshot failing to include enough decimal places does not produce the desired result if you are...

Page 43: ...ns Try this for yourself now Type in at least four calculations pressing the ENTER key after each one to tell the calculator to perform the calculation You will now be looking at a screen similar to the one on the right except probably with different calculations If you now press the up arrow key a highlighted bar moves up the screen When you reach the top of the screen the previous calculations w...

Page 44: ...es the whole history This is worth doing regularly since the history uses memory that may be needed for other things even with the immense amount of user memory the hp 39g has You can calculations and results from any number of different lines in building your new expression SHOWing results Next to the key you will see another screen key labeled This key will display an expression the way you woul...

Page 45: ...ones such as storing values into a list see page 176 but 26 is enough for most people Once stored into memory a value can be used in a calculation by typing the letter into the place where you would normally use the value Typing a letter and pressing ENTER will display memory s contents There is an advantage to storing results in memories particularly if they are long decimals or if you re going t...

Page 46: ...wn will of course depend on your settings in the MODES view The reason for the QUOTE X 2 rather than just X 2 is that using X 2 would tell the calculator to use the value currently stored in memory X while QUOTE X 2 tells it to use the symbol The QUOTE function is available through the MATH menu under Symbolic see page 257 This type of work is actually far more easily done in the Function aplet wh...

Page 47: ...is a list of topics Scroll through the topics until you find the one you want then use the right arrow key to move into the list of functions for that topic For example The function ROUND will round off to a specified number of decimal places E g round off 145 25667 to 3 decimal places Press the MATH key right arrow into the Real group of functions Press the R key the 9 key to move to the first of...

Page 48: ...p If you are a user of external aplets then you may find that one will stop working with the message Invalid syntax Edit program There is almost certainly nothing wrong Press try a soft reboot as below then run the aplet again Soft reboot Pressing ON SK3 will perform a soft reboot It is perfectly safe and will not cause any memory loss except that your HOME History will be cleared Hold down the ON...

Page 49: ...ll not only unlock the calculator but retain your data intact Hard reboot with memory wipe To completely wipe the calculator s memory press ON SK1 SK6 Hold down the ON key and while still holding it down press the first and then the last screen keys Release them in the opposite order Don t release SK1 and SK6 together release SK6 then SK1 then ON This method will always cause complete loss of data...

Page 50: ...e entire history Regular clearing will ensure that memory is not gradually eroded 5 The key displays a calculation as you would see it written 6 The MODES view can be used to set the format in which numbers are displayed on the HOME page and to choose the angle measure which is to be used 7 Make sure you understand Fraction mode before using it Remember that the angle and numeric mode settings may...

Page 51: ...g x or f x 2 Choose the aplet The first step for any aplet is to choose it in the APLET LIBRARY Press the APLET key and you will see something similar to the screen on the right Use the arrow keys to move the highlight up or down until the Function aplet is selected Now looking at the list of programmable functions at the bottom of the screen you should see labels of and Press the key under first ...

Page 52: ... are in Let s use that key to produce a graph of the quadratic we dealt with in the earlier section on the HOME view Using the up down arrows move the cursor if necessary to the line F1 X Type in 3 XTθ X 5 XTθ 4 ENTER This will produce the screen shown on the right Notice the check tick mark next to the function F1 X This signifies that this function is to be graphed so that if you had five functi...

Page 53: ...lest way to set the start value and increment is in the NUM SETUP view This will be covered in detail later see page 77 The PLOT view Now try pressing the PLOT key The graph you ll see will not be a terribly useful one see right because the axes will not be set up correctly We ll look next at how to do this One of the easiest ways to set up the axes properly for a function whose shape is not known...

Page 54: ...oesn t choose nice scales such as we would choose going up in 0 2 s or 5 s or 10 s etc so we generally need to tidy up its choice a little If you look at the y axis of the graph you ve just produced you ll see that the axis tick marks are so close together that it looks like a solid line To tidy this up you must change to the PLOT SETUP view If you look above the PLOT SYMB and NUM keys you will se...

Page 55: ...m of the screen you will see Res short for Resolution If you highlight it and press the key you will see that you have a choice of Faster or More Detail More Detail should be selected If you choose Faster then every second dot is plotted instead of every dot This is quicker but may make some graphs appear less smooth particularly graphs with steep gradients There are two pages to this view see the...

Page 56: ...n the order that they are defined This is obviously a bit slower Connect The second option Connect controls whether the separate dots that make up a graph are connected with lines or left as dots vs Axes The third option Axes controls whether axes are drawn The fourth Inv Cross controls the appearance of the cursor that is moved by the arrow keys It is best if you try this one yourself to see the ...

Page 57: ... ar r The MENU toggle If you look at the screen key list at the bottom of the screen you will see only a single entry labeled Press the key under it and your screen will change to look like the one above right Press it again and the screen will clear completely Once more and you are back to the original appearance Try pressing it a few times to get the feel for its behavior This is what is known a...

Page 58: ...play to that shown right Pressing up or down arrow moves from function to function The order used is not related graph but solely to the order that they are defined in the SYMB view If it is turned off then the cursor is free to move anywhere on the screen Try this and then turn it on again Defn Press the key labeled short for Definition You will find that the equation is now listed at the bottom ...

Page 59: ...ll jump to values which are not on the current screen or which would be inaccessible for the current scale For example we can jump to the value x 100 and see the X Y coordinate displayed with the cursor positioned at the far right side of the screen If the left arrow is now pressed tracing will resume from the right edge of the screen in this case at one pixel point back from x 4 Calculator Tip Th...

Page 60: ...examination of the VIEWS menu on page 92 Center This redraws the graph with proportionally the same scale for each axis but re centered around the current position of the cursor If you already have a nice scale this will preserve it while perhaps showing a more interesting section of graph In Out These two options zoom in or out by adjusting the scales by the factor shown The default factor is 4x4...

Page 61: ... opposite corner of a box the box will appear on the screen Pressing expands the box to fill the screen You ll notice that the scale has been disrupted so that the labels are no longer very helpful PLOT SETUP would give better end points for the axes or let you switch off the labels option Rather than doing that however scroll down the menu to a new option of UnZoom This option puts the screen bac...

Page 62: ...ing in or out with the current position of the cursor as its center Changing the x factor is reflected in the menu as you can see in the second screen snapshot Square This option changes the vertical scale to proportionally match the horizontal scale so that circles will appear circular rather than elliptical Auto Scale Decimal Integer and Trig These four options are duplicates of those found on t...

Page 63: ... leave the highlight on Root as shown and press ENTER or then the cursor will jump to the nearest root or x intercept for the function it is on starting its search at the current position Try it now Notice the message at the bottom of the screen giving the value of the root that was found To find the other root you need to move the cursor so that it is closer to the other root than to the present ...

Page 64: ...dinate is stored in the memory X If you immediately change to the HOME view and type X and hit ENTER then you can retrieve and use this value See Tips and Tricks Function on page 83 for more detail and examples Slope This gives the numerical value of the derivative at the point of the cursor for the current function Calculator Tip If the value at which you wish to find the slope is not accessible ...

Page 65: ...ose a starting point Press the key enter the value 2 and press or ENTER The starting value will then be 2 so press again or ENTER to accept it Another menu will appear asking you to indicate what area you wish to calculate In this case there are only two choices between F1 X and the X axis or between F1 X and F2 X If we had defined more functions in the SYMB view then this menu would be longer In ...

Page 66: ...rea instead of just Area 2ndpoint 1st point 1 F X dx Tracing the integral in PLOT Rather than using the key an alternative method is to use the tracing facility The advantage of this is that the area is shown visually as you go by shading as can be seen right The disadvantage of this is that you can only trace to values which are permitted in the scale you are using As soon as you use the shading ...

Page 67: ...ou reach the end point you are looking for press the key and the area will be calculated as before This is shown right To remove the shading press PLOT again Calculator Tip Note that common sense tells us that the answer is almost certainly 3 75 rather than 3 75000000002 The small error is simply due to accumulated rounding error in the internal methods used by the calculator For example an answer...

Page 68: ...ty of the left hand maximum turning point as shown right Press and choose Extremum from the menu You should find that the cursor will jump to the position of the maximum Calculator Tip If your graph has asymptotes then make sure that the cursor is positioned on the side of the asymptote containing the extremum before initiating the process The internal algorithm used does not cope well with interv...

Page 69: ...lpful Try changing to NUM SETUP and setting the value of NumStep to 1 or even 5 or 10 Now scroll through the NUM view and look at what is happening to the F X values Look for two things Firstly where is the function most active For what domain on the x axis is it changing fastest This is likely to be the domain you are most interested in Secondly what is the range What sort of values will you need...

Page 70: ...h very well Place the cursor so that it is in the center of the area you are most interested in Use the menu to adjust the view You may choose first to change the zoom factors to something other than 4x4 and to ensure that Recenter is ed The advantage of doing it this way is that if you zoom in or out by a factor of 2 or 4 or 5 the cursor jumps will stay at relatively nice values allowing you to t...

Page 71: ...of these in turn and the key pressed then the substitution is performed The result is shown in the upper right hand snapshot and the F4 X function is shown right after pressing SHOW Notice that the calculator is smart enough to realize in F3 X that 2 1 x is the same as 1 x although not unfortunately smart enough to keep track of the implications for the domain that F3 X should be defined only for ...

Page 72: ... also hide the domain For example if 2 1 F X X and 2 F X X then 3 1 2 F X F F X will show the correct domain of 0 x in the NUM view Pressing will destroy this Using functions in the HOME view Once functions have been defined in the SYMB view of the Function aplet they can be reused in the HOME view and indeed in any other aplet For example suppose you needed to find some exact points x 0 1 2 and 3...

Page 73: ...ME view you may not receive the result you expect If you try this yourself your result will probably not be the same as that shown The reason for this is that the result you see is the derivative of 2 x x evaluated at whatever value of x happens to be currently in memory This can be seen more clearly if we store a specific value into the memory X beforehand In the example shown right the answer of...

Page 74: ...2x f x but at least it is numerically correct Calculator Tip Doing your differentiation in the Function aplet is much easier and offers the additional advantage of being able to graph the two functions Circular functions There are two issues that influence the graphing of circular functions both related to the scale chosen The first one illustrated on the right causes circles to be ellipses if you...

Page 75: ...h 2 2 9 x y using two slightly different scales You can see that the second example has missing pieces Let s look at the circle 2 2 9 x y as an example This circle only exists from 3 to 3 on the x axis and is undefined outside this domain In order to graph it on the hp 39g you have to rearrange it into two equations of F1 X 9 X2 for the top half F2 X 9 X2 for the bottom half If you enter these equ...

Page 76: ...ill tend to give nice pixel points If your circle is not centered on the origin then just check tick the box in the Set Zoom Factors box to Recenter That will allow you to turn off TRACE move the cursor closer to the point where you d like the centre of screen to be and then ZOOM Trig functions If graphing a trig function using radian measure then you should choose a scale which will cause pixel v...

Page 77: ...es The first and simplest is via the value stored in memory X If you move from PLOT to the HOME view and type X using ALPHA then the value it will contain will be the last position of the cursor If you just found a root or an intersection then this will be the value displayed The second way is via the reserved words of Root Extremum Area Slope and Isect Typing any of these reserved words in any si...

Page 78: ...this setting the NUM view will be empty waiting for you to enter your own values for X Typing in the values of for example 3 ENTER 2 ENTER 5 ENTER will give In this situation the function values are being calculated as you input the X values This can be quite useful if you are wanting to evaluate the behavior of a function at selected points ZOOM If you now use the NUM SETUP view to switch to Auto...

Page 79: ...econd option of Out causes the opposite effect changing the step size upwards by whatever the Zoom Factor is set to The Decimal option restores the default settings It changes from whatever is showing back to the step size of 0 1 The Integer option on the other hand changes the scale so the step size is 1 The Trig option changes the scale so that the step size is 24 π exactly This will obviously b...

Page 80: ...and b are the limits of integration and function is defined in terms of X Let s look first at the definite integral The screen left shows 2 2 1 1 x dx 3 3333 followed by ln2 0 x e dx 1 It may help you to remember the syntax of the differentiation and integration functions if you realize that they are filled in with values in exactly the same way that they are spoken E g 2 2 1 1 x dx is read as the...

Page 81: ...3 only for convenience of viewing All that is now necessary is to read S1 S1 3 3 as 3 3 x x or as it should be read as 3 3 x x c ii If done in the HOME view then S1 must again be used as the variable of integration i e 2 1 x dx is entered as 1 S1 X2 1 X This is shown right together with the results of highlighting the answer and pressing The calculator assumes that X itself may be a function of so...

Page 82: ...ere if we were doing this with the aim of finding an indefinite integral On the other hand we all know that the answer should have a constant of integration so perhaps this extra constant will help you to remember the c In addition to this there are strict limits to what the hp 39g can integrate For example if you try to evaluate 2 sin cos x x dx using the calculator it will not be able to do it E...

Page 83: ...RS and you will see a list of the HOME variables If you press SK2 labeled not the APLET button on the keyboard then the display changes to show the variables specific to whatever aplet you are currently using Those shown right are for the Function aplet and the group of Plot FCN variables is shown If you look at the screen shot you will see that the tag is currently selected showing as and this me...

Page 84: ...ing 2 and the two intersections The shortcut here is to use Intersection to find the first intersection storing the results into memory variable A We then do the same thing for the second intersection storing the result into B We can now calculate the area in the HOME view using 1 2 f f for the first and 2 1 f f for the second Use to duplicate the first integral and edit it to adjust the functions...

Page 85: ...s F1 X X 3 X 2 F2 X X2 2 X 2 AND X 1 F3 X 3 X X 1 Note AND can be found on the key The reason why this works is that the X 2 and the X 2 AND X 1 expressions are evaluated as being either true which for computers has a value of 1 or false which has a value of 0 By dividing by the domain expression we are effectively dividing by 1 inside the range no effect or dividing by zero outside the domain mak...

Page 86: ...apart To zoom out instead of in simply double the values producing dots that are 0 2 apart Similarly if you want to center the graph around a particular value then just add that value to the range values The example right is centered around x 1 by adding 1 to 3 25 and 3 25 A time when nice scales are more important is when you use the Plot Table option in the VIEWS menu If you use the default axes...

Page 87: ... X 1 as X2 X 1 but will not understand F X X X 1 When used in either Function or Solve it will result in the error message of Invalid User Function Similarly if you want to use the sum to n terms formula for a GP in the Solve aplet and enter it as S A 1 R N 1 R then you will see a similar message until you change it to read S A 1 R 1 R The reason for this apparent error is that all of the built in...

Page 88: ...on for this is that the value of ex passes the limit of the capacity of the calculator 10500 and so the top and bottom of the fraction become equal both at a value of 10500 instead of the true situation of the bottom being roughly twice the top This is most likely to happen with limits involving power functions as they will overflow for smaller values of x A related effect happens when investigati...

Page 89: ...hat for that range of numbers the expression 1 1 X X is equivalent mathematically on the HP to 1 00000000003 X This produces a short section of an exponential graph which only looks linear because you don t see enough of it Eventually the calculator reaches a value on the x axis which is large enough that it rounds off to a smaller number than 1 00000000003 which is 1 00000000002 This produces the...

Page 90: ...n formula with X taking the role of h and A being the point of evaluation Change to the NUM SETUP view and change the NumType to Build Your Own By entering successively smaller values for X you can now investigate the limit as h tends towards zero To investigate the gradient at a different point simply change back to the HOME view enter a new value into A and then return to the NUM view The disadv...

Page 91: ...of 3 2 3 3 f x x x We will use the POLYROOT function and store the results into M1 The advantage of this is that you can now view the roots by changing to the Matrix Catalog and pressing See page 170 for more detailed information on matrices In addition to this you can access the roots in the HOME view as shown Calculator Tip This trick is particularly helpful if you are working with complex roots...

Page 92: ...anges according to which aplet you are currently using The Function aplet contents are covered here but the others differ in only small ways However aplets downloaded from the Internet will usually have a radically different VIEWS menus created by the person who wrote the program for the aplet See page 214 for more information on this process if you intend to program the calculator The VIEWS key p...

Page 93: ...s always the active one with results of actions shown on the right We can now use the left graph again to zoom in on another section of interest or alternatively press the key under the label This switches the right hand graph onto the left screen Using or the FCN menu you can then find or examine points of interest Alternatively you can zoom in again using another Box zoom Any of the normal tools...

Page 94: ...4 F X X X X This shown on the right using an XRng of 8 to 8 Changing to Plot Table gives the result shown left As you can see the scale has been preserved unchanged although without labels The table on the right also uses a sensible scale of 0 25 because of the choice of an x axis scale of 8 to 8 Choice of scale in the Plot Table view is discussed in detail in the Tips and Tricks Nice Scales immed...

Page 95: ... is Overlay Plot This option can be used to add another graph over the top of an existing one without the screen being blanked first as it usually is As an example if you have already graphed functions F1 X through to F6 X and then add another one in the SYMB view then you don t really want to have to wait while all the earlier ones are redrawn If you un the earlier graphs and then use Overlay Plo...

Page 96: ... If there are other graphs and they don t fit the scale then they will not benefit As you can see in the example shown right the quadratic shows well but the second graph a cubic shows only an ascending section Zooming out would be an option at this stage as would un ing the quadratic in the hopes that Auto Scaling the cubic might give better results unlikely 3 The resulting y scale is often not a...

Page 97: ...al result of this is rather horrible The final option of Trig is designed for graphing trig functions It sets the scale so each pixel is 24 π This means that if you were graphing 1 2sin F X X then 24 presses of the left or right arrows would move you through exactly π and the value would be exactly 2 instead of a horrible decimal If you zoom in or out from this the jumps will still stay relatively...

Page 98: ... below uses zoom factors of 2x2 with Recenter ed Calculator Tip In the graphs above the cursor is at x π The coordinates at the bottom of the screen should show F1 X 0 but doesn t due to the fact that the value of π stored internally is not and of course cannot be exact The rounding of π in the 13th decimal place means that the resulting trig values will be wrong in the 11th to 15th decimal place ...

Page 99: ...EWS button so that it displays in place of the normal menu Curve Areas This aplet allows the user to find approximations to the area under a curve by finding either the lower rectangular area the upper rectangular area or the trapezoidal area The user can choose the end points of the interval the type of calculation and the number of rectangles to be used The rectangles are drawn on the screen A w...

Page 100: ...t step is to choose it in the Aplet Library Press the APLET key highlight Parametric and press If you wish to ensure that you see the same thing as the examples following then press the button before pressing As with the Function aplet this aplet begins in the SYMB view by allowing you to enter functions but the functions are paired Each function consists of a function in T for X and another for Y...

Page 101: ... at all not how much is displayed of the total picture For example gives a graph of As you can see above changing the T range from 0 2 t π to 0 5 t gives a graph that appears only partially drawn What constitutes fully drawn depends of course on the function used TStep controls smoothness The value of the parameter TStep controls the jump between successive values of T when evaluating the function...

Page 102: ...ays be careful that the angle measure chosen in MODES is correct The default for all aplets is radian measure As usual the NUM view gives a tabular view of the function In this case there are three columns since X1 and Y1 both derive from T As with the Function aplet it is possible to change the starting point and step size of the table and also to change it into a Build Your Own type of table see...

Page 103: ...g graphs are available through this aplet Three quick examples are given below Example 1 Try exploring variants of the graph of 3sin3 2sin4 x t t y t t Example 2 Try varying the values of a and b in the equations 1 cos cos 1 1 sin sin 1 a x t a b t b t b a y t a b t b t b Hint The example shown uses a 4 b 2 5 and has axes set with TRng of 0 to 31 5 step 2 XRng of 21 66 to 21 66 and YRng of 12 to 9...

Page 104: ...erested in the first 2 seconds only so I ll also restrict TRng to 0 to 2 5 Using Y T T for this TRng means the y values will also range from 0 to 2 5 Maximizing visibility of this range of values is the reason for setting YRng to be 0 5 to 3 in PLOT SETUP The range for the x axis is chosen from the values shown in the NUM view The value of TStep is carefully chosen so that when the motion plots th...

Page 105: ...to see the ships path appear As with the previous example the value of TStep is chosen to allow visible motion As the graph appears it can be seen that the ships do not collide even though the final plot may make it appear that they do To find the distance between the two ships at any time t you can enter the equation F1 X 2 2 1 2 1 2 X X X X Y X Y X into the Function aplet Note that the active va...

Page 106: ...ues of θRange and for θStep are critical in controlling the appearance of the graph The values set for θRange control how much of the graph is drawn while the values for XRange and YRange only control how much of the graph is displayed on the screen once drawn θStep controls how smooth the graph is as did TStep in the Parametric aplet The default values for θRange are 0 2 θ π and the default value...

Page 107: ... view when you enter formulas The Sequence aplet uses the terminology U N rather than the other commonly used Tn for its definitions in order to avoid having to use subscripts which would not show up well on the screen All functions of this type are assumed to be defined for the positive integers only for N 1 2 3 4 First second general terms Each definition has three entries U1 1 U1 2 and U1 N see...

Page 108: ...er than having to type all of this we can use the buttons provided pressing then then then then This is a very convenient feature and worth remembering The result There is no mark next to the definition yet since the sequence is defined recursively and no values have yet been given for U2 1 and U2 2 Type in a value of 1 for both of these and then press the NUM button to switch to the NUM view As y...

Page 109: ...ou will find that the values for those terms of each sequence will appear in the U1 and U2 columns almost immediately In case you didn t realize the reason for the larger text is that I have used the button Due to the type of problems one is usually trying to solve with sequences the NUM view rather than the PLOT view is often more useful in this aplet but let s have a look at the PLOT view anyway...

Page 110: ...eference to U1 in the definition of U2 Once U2 is defined in this way you can change both U1 U2 by simply storing new values into A and R Solving sequence problems Questions like What term is the first to be greater than 10 000 or When does Sn first exceed 10 000 can be answered in the NUM view Simply move into the N column make an inspired guess as to the term you require and type it in The table...

Page 111: ...h to the Numeric view to find with some experimenting that U1 46 is the first to exceed one million It is also possible to answer these questions in the Solve aplet For example if we use the Sequence aplet to define U1 N 2 N 1 as before then we can change to the Solve aplet and enter into E1 the equation U1 N 10000 change to the NUM view and press and obtain an answer of 14 29 This means of course...

Page 112: ...rest of 5 5 p a starting Jan 1 1995 with a quarterly repayment rate of 175 Set up U1 and U2 as shown above You can now follow the progress of the loan with U1 containing time and U2 the amount owing at the start of each time period showing it is repaid during the first quarter of 2023 ...

Page 113: ...3 1 6 5 0 y x v u ad b a c d x x are all equations An expression on the other hand does not contain an sign It can be evaluated or rearranged but not solved When you enter an expression into the Solve aplet it internally puts an 0 onto the end so as to convert it into an equation which can be solved eg 2 2 4 1 1 6 5 x b c x x are all expressions Entering the equation Let s start by looking at the ...

Page 114: ...t values are showing on your screen will depend on what happens to be in the memories V U A and D at the time Pressing SHIFT CLEAR will zero all values Move the highlight to V and enter the value 27 78 then to U and enter 16 67 and finally to D and enter 100 Now move the highlight back to A the value you re trying to find and press the button You should find that you obtain the answer to our probl...

Page 115: ...enter the known values remembering that 1 liter 1000cm3 Position the highlight over R enter a positive value as your estimate and press to find the solution shown right of 8 57cm The equation is a quadratic in R which means two solutions are possible If you enter an initial estimate of 10 you will obtain the negative solution which is physically invalid in this case Example 2 If 3 2 2 5 2 f x x x ...

Page 116: ...iew Transferring approximate solutions We require values where the two curves intersect Using the arrow keys move the cursor near to the first intersection point I found see right that 1 6 seemed to be a good approximation Now change back to the NUM view and you will find that this approximation has been carried back as the initial estimate Press to find the true value Repeat the process of obtain...

Page 117: ...ated integrations as the calculator searches for better solutions Example 4 Let X be a random variable representing the heights of basketball players If X is normally distributed with 184 5 µ and 2 105 σ then find the height which cuts off the tallest 5 of players The MATH function for the normal distribution is UTPN see page 282 which gives the upper tailed probability In the Solve aplet set E1 t...

Page 118: ...d the reason for this lies in how Solve interprets your equation When you select B by highlighting it the calculator substitutes the supplied values into all other variables except B and graphs the left and right sides of the equation as two separate graphs This may not always be obvious because the substitution may produce graphs which aren t visible on the default scale In the graph above you ca...

Page 119: ...there is an immediate change in the PLOT view to reflect this Change back to the NUM view and restore the variables to the original values this time leaving the highlight on C Since the active variable is now C substitution of all other values means that 2 5 A B C B becomes 0 4 0 5 C In this case both sides are linear and this is shown in the PLOT view Notice that the axis label is now C This woul...

Page 120: ...messages These are Extremum it found a minimum but could not reach zero Try solving the equation 2 2 4 0 x and you will see this The smallest value that 2 2 4 0 x can have is 4 at x 2 so the answer supplied will be very close to this such as 2 000000001 or 1 999999999 The problem is that unless you check you may not realize that this is not actually a valid solution Calculator Tip It is critical t...

Page 121: ...is going to be more than one solution to a problem then the PLOT view can help you to obtain estimates For example 1 2 2 x x When you plot this you can see that the solutions are near 2 and 1 5 If we now switch to the NUM view we can use these as initial guesses This will give solutions of 2 56 and 1 56 In this case the problem shown will graph easily on the default PLOT view but this will not alw...

Page 122: ...i vs Bi variate data The hp 39g treats univariate and bivariate data quite differently and those differences are reflected in the SYMB and PLOT views Because of this the Statistics chapter has been split into two and univariate data will be dealt with first On the screen you will see a key labeled either or Pressing the key under this label changes from univariate to bivariate and back Make sure t...

Page 123: ...of the notes Press to stop the sort The key behaves normally and vs we have already discussed The last key labeled is the really useful one The STATS key Making sure the highlight is in column C1 press the key and you will see the screen shown right If you use the down arrow you can scroll down and see the rest of the screen below right NOTE If you get an error message instead of summary statistic...

Page 124: ...econd column in the SYMB view The default setup is to only recognize column 1 Registering columns as in use Change into the SYMB view and edit yours so that it looks like the one on the right You must make sure that H2 is ed because only checked columns will show in the view Note that a screen key is provided to give you the letter C without having to use the ALPHA key The stats are now available ...

Page 125: ...he one 7 15 right Make sure 8 9 only H3 is checked The reason for the last instruction is that only one histogram can be drawn at a time and if more than one data set is checked only the first one is drawn Auto scale Now use VIEWS Auto Scale to plot the graph You will hopefully find that it looks like the one on the right The Auto Scale function is always very effective in the Statistics aplet and...

Page 126: ...left right arrows move within the graph As an aside pressing the key produces the normal tools of and They all behave in the normal manner The tool can be quite useful by displaying at the bottom of the screen information on which columns make up each graph if you lose track Looking again at the screen shot of the first page of PLOT SETUP near the top of the previous page you will see that there a...

Page 127: ...ped data HWidth One final note concerns grouped data We saw earlier how to deal with data displayed in a frequency table but did not deal with the case where the data was also grouped into intervals or classes For example suppose we want to analyze the set of grouped data in the table on the right The hp 39g provides some limited methods to deal with data of this form Summary statistics can be obt...

Page 128: ...s can be fixed by using the setting HWidth This variable controls the width of the columns with the initial starting value and end value set by HRng The PLOT SETUP views shown above will produce the graph shown below ...

Page 129: ...uld look the same as the one we produced earlier using the HOME view and the command would give exactly the same results The advantage of this is that it takes much less memory if both columns need not be stored Simulating Dice Many of the most common experiments in probability involve the repeated rolling of dice This can be simulated quite easily in the Statistics aplet using the MATH menu funct...

Page 130: ...s This can also be done using the MATH menu function MAKELIST See previous page for syntax Covered in more detail on page 266 Example 1 Simulate 100 observations on a U 0 1 r v to be stored in C2 In the HOME view type MAKELIST RANDOM X 1 100 1 C2 Note 1 The symbol is one of the screen keys in the HOME view appearing as and read as store 2 The X is only a dummy variable here to count off the values...

Page 131: ... 2 LN 1 RANDOM 1 50 1 C2 As an illustration the result of this particular simulation is shown graphically on the right Its mean turned out to be 2 067 3 decimal places Yours will be different of course after all that s the point of using random numbers Calculator Tip The RANDOM function is not truly random any more than it is on any computer You can however make it as random as possible by using t...

Page 132: ...ow going to look at bivariate paired data On the screen in the NUM view of the Statistics aplet you will see a key labeled as either or Pressing the key under this label changes from univariate to bivariate and back Make sure the key is showing before proceeding Clearing data If your NUM view already has some data in it press CLEAR above DEL and choose All columns The DEL key is used to delete ind...

Page 133: ...nts As you can see it is very similar to the other PLOT SETUP screens that we have encountered with the main difference consisting of the list of settings for S1MARK S2MARK etc These are the markings that are to be used in plotting the points allowing you to choose different markings for different data sets if you are graphing multiple data sets Set your PLOT SETUP screen so that it looks like the...

Page 134: ...LPHA key Specifying the fit model Although we bypassed it in the previous example part of the procedure in dealing with bivariate data is to specify the relationships between columns before plotting This is done via the SYMB view as it is for univariate data Multiple data sets The S1 S2 refer to data sets 1 2 This allows you to display more than one set of bivariate data by specifying the columns ...

Page 135: ...alculated automatically pre store a value of zero into it If the value is known you can store a positive real value into memory L prior to the curve fit 2 If you calculate a line of best fit and want to remove the resulting equation from the SYMB display and return to the m X b display then just position the highlight on the relevant Fit line and press the DEL key When you do this the will be remo...

Page 136: ...e curve we have deduced fits the data quite well How well is a matter for your judgment aided by the RelErr variable see page 141 Connected data One of the settings on the second page of the PLOT SETUP screen can be useful for some types of data For example one of the common tasks in many mathematical courses is the analysis of time series data Unlike most bivariate data time series values are usu...

Page 137: ...rast is illustrated below Two Variable Statistics As with univariate statistics summary statistics are available through the key in the NUM view see right Pressing this key changes to a screen which lists the following MEANX ΣX ΣX 2 MEANY ΣY ΣY 2 ΣXY SCOV PCOV CORR and RELERR See page 141 for information on RelErr Let s use the set of data shown in the table on the right to go through the analysis...

Page 138: ...ake sure that your data set is defined and ed in the SYMB SETUP view before you try to obtain these results Results are only given for data sets that are defined and ed Showing the line of best fit If you now press the PLOT key you will see the graph shown right If there is no line of best fit on yours press the key to get the list of programmable functions along the bottom of the screen and then ...

Page 139: ...eys to scroll the equation left or right if it extends off the screen A caveat Calculator Tip One of the most common mistakes people make is to press instead of Always use when you want to display the entire equation An explanation is given below It is very important that you display the equation in the SYMB view by pressing instead of Although pressing displays the equation in a form which can be...

Page 140: ...its fit curve then pressing up arrow will change the focus of the values at the bottom of the screen from the data points to the PREDY values In the screen snapshots shown right the focus changes from data point 3 2 2 to the PREDY value for x 2 of 2 806 If there is more than one data set and fit lines graphed then the up arrow will move progressively from one to another and finally back to the fir...

Page 141: ...retation placed on it is that the closer it is to zero the better the model fits the data This value is available for any of the data models including the user defined model Alternatively when data is non linear in nature you can transform the data mathematically so that it is linear Let s illustrate this briefly with exponential data As you can see I chose a very simple rule for the data 2x y If ...

Page 142: ...o using RelErr is to graph column C1 against ln C2 which also straightens the data Linearizing will cause problems if some of the data points are outside the domain of the function you use such as negative values in a log function On the other hand you have far more control if you are able to choose the exact function For example if you had a set of data which was derived from cooling temperatures...

Page 143: ...s the mean and standard deviation for use in further calculations With most simpler calculators these values are found by pressing keys rather than reading from a screen so doing a calculation like multiply the mean by 3 5 is not hard The values shown on the screen can also be retrieved for use on the hp 39g relatively easily For example the set of data below contains a suspected outlier erroneous...

Page 144: ...t see right of univariate summary statistics If you highlight one and press ENTER then the variable name will be pasted into the HOME view for use People often find it easier to simply type them Calculator Tip The values of the mean and standard deviation retrieved are those of the last set calculated If you have more than one set of data in the NUM view then firstly un all except the one you want...

Page 145: ...as been displayed the coefficients are not available or worse might belong to another data set If the line of best fit is y m X b see the SYMB screen then the calculations shown below and right will give the slope and y intercept 0 0 and 1 0 1 0 PREDY m b b PREDY PREDY m b m b m b b m Finding Fit Coefficients Linear m X b b PREDY 0 m PREDY 1 PREDY 0 Logarithmic m LN X b b PREDY 1 m PREDY e PREDY 1...

Page 146: ...st fit unlike the correlation changes as the independent and dependent variables swap roles and can t be simply reversed in this way The formula for the slope b in the line of best fit y a bx is given by the formula 2 xy x S b S While the value of xy S will not change if the roles of independent and dependent columns are reversed the value of 2 x S on the bottom means that this formula will give a...

Page 147: ... you could use the expressions MAKELIST X X 1 20 1 C1 and C1 C3 to shortcut the process replacing 20 with whatever is needed Make sure that the option is selected The result should look like this Now position the highlight on column C2 and press the key In the SORT SETUP screen shown below right enter C1 as the Dependent column This will have the effect of pairing columns C1 and C2 and then sortin...

Page 148: ...r to calculate the fit equation Finally change back to the SYMB view and see the equation pressing if necessary eg 2 A population of bacteria is known to follow a growth pattern governed by the equation 0 0 kt N N e t It is observed that at t 3 hours there are 100 colonies of bacteria and also that at t 10 hours there are 10 000 colonies i Find the values of 0 N and of k ii Predict the number of b...

Page 149: ...w and use the PREDY function or use the facilities in the PLOT view Result 268 269 colonies iii Find t so that 0 2 N N The value of 0 N is the y intercept of the line of best fit These values from the curve of best fit are not directly accessible but can be retrieved using the PREDY function see page 145 This is shown in the screen shown right Store the results into memories A and K This saves hav...

Page 150: ...Using the Chi2 test at a 5 level of confidence indicate whether the coins may be biased Number of heads 0 1 2 3 4 Frequency 32 112 158 90 8 We would expect that for an un biased set of coins the distribution would be binomial Our hypotheses are H0 The number of heads is binomially distributed n 4 p 0 5 HA The number of heads is not binomially distributed n 4 p 0 5 Begin by entering the data into t...

Page 151: ...that the observed values do not follow this binomial distribution and hence that the coin is probably biased This does not say that it is not binomially distributed just not with those parameters As can be seen from this example the Statistics and Solve aplets can be used for simple problems particularly in cases where working is required to be shown For more complex problems the Inference aplet p...

Page 152: ...nce you have chosen the aplet you need to nominate the column from which to import the data The default is column C1 which is what we want in this case but you can press the key to select from a list of any other columns which contain data When you have the correct column press Enter the population mean µ0 50 and check that the test level is correct at 0 05 5 If you now change to the NUM view you ...

Page 153: ...f this rejection being incorrect The alternate hypothesis that the mean is not 50 should be accepted Of course in this case despite some boxes containing less than 50 matches the actual mean seems to be above 50 so we can hardly condemn the company for putting more matches in the boxes than they need to Confidence interval T Int 1 µ In the previous example we found that the evidence of our sample ...

Page 154: ...the two groups To distinguish between the two groups of eleven which were caged together to minimize other influences the heads of the chicks were stained red and purple respectively with a harmless vegetable dye The individual weights were recorded in the table to the right From the means at the bottom of the table it appears that supplement A produces a higher mean weight The farmer wishes to kn...

Page 155: ...dard deviation will be obtained if the data is pooled so ensure that this option is ed The NUM view shows the critical values We can see that the probability of obtaining a test student t value of 3 38 is 0 0015 and this is well below the permitted test level of 1 The PLOT view also shows that the vertical line representing the value of 1 2 x x or x is well into the region of rejection indicated b...

Page 156: ...acher believes that this data shows that his students are scoring significantly better and wishes to test this at a level of 5 Test results 57 72 42 50 55 58 59 38 45 53 77 57 52 69 50 55 59 68 62 63 53 56 Enter the data into column C1 of the Statistics aplet Changing to the Inference aplet we choose a Hypothesis test using Z test 1 µ since we know the population standard deviation The hypotheses ...

Page 157: ...ion of rejection marked by the R From the evidence the teacher must reject the alternate hypothesis and conclude that it is not possible to say at the 5 level of significance that his class has averaged significantly higher than the standardized population from which the test was drawn He should re think his proposed paper or his new teaching method Alternatively from the diagram in the PLOT view ...

Page 158: ...her column C1 or C2 but not from both at once What s needed of course is a way to expand the paired frequency table columns into a single column listing all values The program shown below will do this for you It is set up to take a frequency table defined in columns C8 and C9 and convert them into a single column stored in column C0 The program uses columns 8 9 10 because there is seldom data in t...

Page 159: ...mn s mean and standard deviation into the Inference aplet After you have used the column you will probably also want to delete columns C8 C9 and C0 to save space Bear in mind that if you use this program to create a column containing hundreds or even thousands of values then the program will take a long time to complete It might be easier to use the Statistics aplet to calculate the required mean ...

Page 160: ...xplanation for those who need it as does any high school or college textbook When you the aplet you will see the initial view shown right Pressing SYMB NUM or PLOT will make no difference to this aplet as it is quite limited and only has the one view consisting of two related pages Parameters There are a number of parameters or variables which must be either supplied or solved for These are N The ...

Page 161: ...s This can be illustrated simply via the following example Always bear this principle in mind when deciding how to plan your setup of the aplet Straightforward compound interest Invest 1000 into a bank account paying 6 5 per annum for 5 years Interest is calculated monthly and credited to the account at the end of each month What is the investment worth at the end of the period Looked at from the ...

Page 162: ...so assume that the future value FV is to be zero since the income is only to last for 20 years On this basis the monthly annuity can be 4289 71 Loan calculations You wish to purchase a car by taking out a loan The current interest rate is 6 5 and you can afford to make monthly payments of 300 You want to take out the loan over a period of 6 years and to still owe 10 000 at the end of that period y...

Page 163: ...e to the amortization screen The initial appearance is as shown As can be seen the default number of payments to amortize over is 12 Pressing the button will amortized the loan over the first year As can be seen right 2 369 77 has been paid off the principal leaving a balance of 17 630 23 Of the payments made 1 230 23 went towards the payment of interest Pressing the button will transfer the balan...

Page 164: ...opening view Choosing the level The first choice made by the user should be the The default level is that of Y a X h 2 v which allows the student to change all parameters at once By having the student choose the levels of Y aX2 Y x h 2 or Y X2 v the teacher can confine the study to the effects of only one coefficient at a time if desired GRAPH mode The default state for the aplet is to be in mode ...

Page 165: ...k to the graph SYMB mode In mode the student can change the coefficients directly and see the changes reflected in the graph For example on the screen shown below the v coefficient is highlighted and can be changed using the and keys The size of the changes to h and v is controlled by the key and the same range of values is available for the values of a as in mode You can move from one coefficient...

Page 166: ... another by pressing or In mode you must use the arrow keys to change the parameters a h and v until they match the graph shown The accuracy of your answer can be checked by pressing the key labeled which appears as soon as you begin to change the values The number of attempts is monitored and displayed An incorrect answer is shown as an animated graph on the screen when you press flashing repeate...

Page 167: ...en rather than the usual PLOT SYMB and NUM views If the aplet has been used before then it may be necessary to press the screen key to go back to the opening view shown SIN vs COS The or key can be used to toggle between the sin y x curve and the cos y x curve The or key can be used to toggle between radian measure and degree measure The markings on the horizontal axis adjust accordingly see right...

Page 168: ...o the location of the control point when control is set to the graph translates left and right the c coefficient or up down the d coefficient when control is set to the graph dilates parallel to the y axis the a coefficient or parallel to the x axis the b coefficient Unlike the SYMB mode where the b coefficient goes up or down in steps of 0 1 the increments in PLOT mode are not regular but are cho...

Page 169: ...nged using the key labeled to either 9 π or 4 π When in mode the increments are 20o 30o or 45o with 30o being the default The ranges of values available for the four coefficients are shown below Coeff Range a 3 to 3 b 0 2 to 5 c 4π to 4π d 3 to 3 If you go to HP s website you can download a worksheet for use with your class It takes the student through the process of deducing the effects of each o...

Page 170: ...matrices of real vectors complex numbers and complex vectors The key pops up the menu shown on the right replacing the highlighted matrix with any empty one of the new type that you specify Press SHIFT CLEAR to delete all Generally only the default type real is required and apart from small exceptions only those will be covered as the behavior is not significantly different for others Matrices lik...

Page 171: ...reen shot right If you now press the down arrow key on the keyboard the highlight will move back to the first element in the second row Enter the numbers 4 5 and 6 and you will find that the calculator automatically drops down to row three without the need to use the down arrow key again since it now knows how many columns the matrix is to contain Finish your matrix so that it looks like the one s...

Page 172: ... matrices in the section at the back of the book Solving a system of equations Eg 1 Solve the system of equations Solution The system of equations can be represented as the system of matrices this system can be algebraically rearranged to where the inverse matrix is which gives a final answer of 2 3 1 x y z Mathematically what we have done is 2 3 6 3 12 3 4 13 x y z x y z x y z 2 3 1 6 1 3 1 12 3 ...

Page 173: ... 39g and store the result into M3 a 1 1 2 M M b 2 1 M M c INVERSE M1 M2 The best of these is probably a because it doesn t involve fetching the INVERSE function from the MATH menu and unlike b reminds you that the operation is really left multiplication by the inverse rather than division an operation which is not strictly speaking defined for matrices but is allowed for convenience on the hp 39g ...

Page 174: ...y to display the answer The fact that the determinant is incorporated into the inverse makes whole numbers unlikely A better way is often to write the answer as a fraction 1 det A multiplied by a matrix of whole numbers If we multiply the inverse by the determinant then we can usually remove the fractions i e with M2 being Thus we can finally write 13 17 1 1 5 6 2 7 6 10 1 A An alternative to this...

Page 175: ...duct and magnitude respectively when fed with vectors The hp 39g writes vectors as row matrices For example 3 4 a would be written as 3 4 The calculations are shown in the two screen shots on the right Remember to change into degree mode first The list of matrix functions available through the MATH menu is covered starting on page 271 Not all functions are covered since many of them go far beyond ...

Page 176: ...ny of the normal mathematical functions also work on lists of numbers by performing the operation on each individual element Lists on the hp 39g can contain more than simply numbers For example the return value for some matrix functions is a list where each element is a matrix Elements of a list can be matrices lists and other things Statistical columns as lists The column variables C1 C2 C9 C0 in...

Page 177: ...osition shown then a zero is inserted before the 4 with all the elements below shifted down one position You can then type your new number Having entered the editing screen you may be wondering how to exit since no key is apparently provided for this Simply press SHIFT LIST again to return to the catalog level or press HOME if you ve finished altogether Operations on elements Changing of individua...

Page 178: ...the APLET key Thus an instruction to press NOTE refers to the aplet Note In addition to this there is a Notepad Catalog containing independent notes which is available via a key labeled NOTEPAD found above the 0 key Thus an instruction to press NOTEPAD refers to the Notepad Catalog not to the aplet Note Notes attached to aplets are explained in the chapter Using Copying Creating Aplets on page 189...

Page 179: ...ample is shown right of a sketch from one of the aplets available from HP s web site called Periodic This can be viewed via the SKETCH key above the MATH key Sketches can have multiple pages and are covered on page 184 I In nd de ep pe en nd de en nt t N No ot te es s a an nd d t th he e N No ot te ep pa ad d C Ca at ta al lo og g Most users are far more concerned with the Notepad Catalog Notes he...

Page 180: ... you begin to become more familiar with the positions on the keyboard where the various letters of the alphabet can be found your typing speed will improve but it will never remotely compare to typing on a keyboard Editing software If you want to prepare anything more than small Notes then software is available to allow you to edit Notes on a computer See page 211 For the hp 38g and hp 39g it is n...

Page 181: ...ort More information on both of these programs is given on pages 204 211 For the hp 39g At the time of writing the hp 39g had only just been released and new software was in the process of being developed The hp 39g is supplied with a cable that lets it link to the USB port on a PC or a Mac The software being developed should run on any platform including Unix and will allow the transfer of object...

Page 182: ...en up by the indication of how much memory is used When you press ENTER after typing in the name you will see a blank screen waiting for you to begin typing in your Note Locking ALPHA mode Before we begin a word about making your typing easier The normal method to enter an alphabetical character is to use the ALPHA key Lowercase letters are obtained by pressing SHIFT first The ALPHA key can be hel...

Page 183: ...ndo a mistake by reverting to a previously saved version You may wish to now try transferring your Note to a friend s calculator over the infra red link using the and keys Corrupting notes An occasional problem users encounter is finding that the Notes they have saved onto a computer are corrupted when they try to read them back This is almost invariably caused by trying to open read print or othe...

Page 184: ...o do anything at all complex This is not meant as a criticism of the calculator It does an extremely good job at what it was designed for working with numbers but it was never designed to compete with a computer drawing package Adding text to a sketch When you first enter the Sketch page on your hp 39g you will see the view at the top right There are four screen keys available The key allows you t...

Page 185: ...ll cursor cross in the middle of the screen can be moved around using the arrow keys If you press the screen key labeled then a trail will be drawn as you move the cursor Notice the small dot next to the showing that it is engaged Pressing the key turns the cursor into an eraser and automatically disengages as well Pressing the same key again disengages both keys and leaves the cursor free to move...

Page 186: ... G2 G9 G0 called GROBs which is short for graphics objects When you press the message you see on the right will appear asking which GROB to use Storing to a GROB Once you have chosen a GROB in which to store the screen capture you will need to specify the corners of the rectangle to be captured Once an image is captured it is possible to paste the captured screen portion into the a Sketch page usi...

Page 187: ...through the sketches animating them If you can program then you can even automate the animation quite simply Capturing the PLOT screen To capture a PLOT screen just arrange the PLOT display so that it shows the features you wish to capture For example if you don t want the screen menu showing make sure it is set up that way before you proceed When ready press and hold down the ON key then press th...

Page 188: ...lt make the whole process worthwhile If you re intending to do this to produce a set of cheat notes for your next test or exam you would do better to spend the time studying Calculator Tip The screen capture facility demonstrated here can be used to capture any screen as a GROB not just a PLOT screen Pressing ON PLOT at any time will store an image of the current screen into G0 See page 210 ...

Page 189: ...r hp 39g users or from a PC or Mac onto which they have been copied Once aplets have been copied from the Internet onto a PC or Mac the software and cable provided with your hp 39g can be used to download the aplets to the hp 39g Calculator Tip Aplets which were written for the hp 38g or stored from an hp 38g are not compatible with the hp 39g hp 40g or hp 39g On the other hand aplets are freely i...

Page 190: ...the aplet concerned You can make as many copies of any of the standard aplets as you wish with the only limit being the calculator s memory Let s look at each of the two scenarios in turn Copying and adding to the Function aplet In the first case what the student needs to do is to make a copy of the Function aplet to hold his homework the functions he had already set up and then do the unexpected ...

Page 191: ...f 20 numbers NUM view set to univariate stats SYMB view set up for five Box and Whisker graphs axes set up to display all five sets See page 122 for information on the Statistics aplet The next stage is to move to the APLET view and this modified Statistics aplet under a new name say Related Sets If desirable you might also the original Statistics aplet at the same time ready for next use This sav...

Page 192: ...view the Solve aplet and it under the new name of Triangles Now it and enter the formulas shown right The character can be found in the second page of the CHARS view Change into the MODES view and set the angle mode to Degrees unless you want to use another mode Use this to solve problems in right triangles The Prob Distributions aplet In the APLET view the Solve aplet and it under the new name of...

Page 193: ...t 25 terms then a normal approximation will be much faster than using this formula Solve works by repeated iterations converging on the correct value and this will be quite slow if the summation has many terms Equations E3 and E4 can be used for calculations involving individual and cumulative Poisson probabilities where M is the mean The formula in E5 is a generic formula for problems such as the...

Page 194: ...use P is already in use in the formula as the probability of an individual success ii You might choose to split this into two aplets one for the Discrete probability functions and one for the Continuous ones The Transformer aplet This aplet is based on the Parametric aplet and allows students to investigate geometric transformations using 2x2 matrices In the APLET view the Parametric aplet and it ...

Page 195: ...ou might choose simply to suggest that they confine their investigations initially to placing numbers only on the diagonals It is a good idea to challenge them to record their matrices on the board as they discovered them A highly able class will find nearly all relevant matrices within 20 to 30 minutes So how does this aplet work The formulas in the SYMB view form the key to the process by allowi...

Page 196: ...en become corrupted during the transfer and need to be re entered This is not a problem for two reasons Firstly the transfer would require sending not only the aplet but the matrices too by the time this is done it would probably have been faster to have the class set it up themselves Secondly if the class is not to regard this as magic then they need to understand how the aplet works This is best...

Page 197: ...ter This link is exactly like the remote control of a VCR and allows two calculators to talk to each other In the interests of security in tests and exams the distance over which they can talk is limited to about 8 10cm If you look at the keyboard side of the calculator near the hp 39g label above the screen you ll find a small white triangle This marks the position of the infra red port so you ca...

Page 198: ... in Europe it is supplied with a cable which allows you to use the physical port next to the infra red window to send aplets from one hp 40g to another The Disk drive option The second alternative is there for transmitting aplets to and from a PC or Mac via the Connectivity Kit or to a special HP disk drive built for the HP38 39 40G family called the Drive 95 The Drive 95 was released at the same ...

Page 199: ...er programs associated with it For example almost all the aplets available from the Hewlett Packard web site come with sets of up to 6 or 7 programs to do the work and without which they are totally useless As an example the screen shown right contains a number of programs which belong to an aplet called Coin Tossing which can be downloaded from the web site The HP HOME view at http www hphomeview...

Page 200: ...et via the NOTE SKETCH keys will be transferred with the aplet D Do ow wn nl lo oa ad di in ng g a ap pl le et ts s f fr ro om m t th he e I In nt te er rn ne et t Aplets are available to do many tasks such as exploring graphs bivariate and time series analysis as well as many tasks called for in Physics and Chemistry The number of web sites with aplets is increasing with time Finding aplets The H...

Page 201: ...ator Tip It is absolutely critical that you decompress each aplet into a separate directory Each aplet has two files HP39DIR 000 HP39DIR CUR which always have the same name Decompressing two zip files containing aplets into the same directory overwrites the first one s files with the second The aplet itself will not be harmed by this but the effect is to render it invisible to the calculator since...

Page 202: ... pages 204 It allows users to transfer aplets and all other HP objects such as notes from calculator to PC via the serial port Its purpose is purely communication it does not let you edit them in any way However there is also a free piece of software called the Aplet Development Kit available over the internet from HP s web site http www hp com calculators or The HP HOME view at http www hphomevie...

Page 203: ...rred to a PC it can be edited using the same ADK software as is used for the hp 38g hp 39g and hp 40g The only drawback with this is that the ADK will only run on Windows machines It may well be that by the time you are reading this there will be new editing software specifically for the hp 39g and running on other platforms Check the Hewlett Packard website for information on this Information can...

Page 204: ...will be unable to plug in the cable since it requires a COM port If this is the case then you will need to buy a USB to Serial adaptor Unfortunately these often cost more than the cable but it will solve the problem If you are using the software on a school network then you may need to talk to the network administrator Some school networks lock out ports for security reasons Discuss your problem w...

Page 205: ...sion of the aplet instead of the hp 39g hp 39g version It is normally only received if the directory is empty or if one or more files are damaged Tell it and investigate If all has gone well you should find that you are looking at another pop up menu which lists the aplet you are trying to download together with the word Other If all you see is the word Other then it may mean that you haven t deco...

Page 206: ...mentation with an aplet then you should read it It often contains information which is needed for the efficient use of the aplet It may also have one or more student worksheets which can be copied and used in a classroom Don t forget that these programmed aplets have helper programs that are automatically loaded into the Program Catalog When you delete the aplet these are not automatically deleted...

Page 207: ... gradually be used up As an example of this look at the aplet called Coin Tossing shown in the APLET view right Looking at the list of programs shown in the Program Catalog view you will see a set of programs which all begin with the letters COIN The convention encouraged by Hewlett Packard is to name the programs so that it is fairly obvious which ones belong to which aplet hence the COIN code fo...

Page 208: ... directory box by typing at the end of it When you do this the middle icon left will activate Clicking on it will create the new directory In the example shown right I have created a directory called MyFunction to hold a copy of the Function aplet which I have also called MyFunction although it s certainly not important that they have the same name I now need to change into the view which shows th...

Page 209: ...process You will then see a series of messages on the computer and on the calculator telling you that files are being transmitted At the end of the process your aplet or program note etc will have been saved You can re use this directory later to save any other objects from the calculator Next time you use it you will not see the message asking if you want to Initialize directory as the two specia...

Page 210: ...and releasing the 1 key then ON When you do the image appears on the computer The images to the right and above show the screen capture process on the two different pieces of software See page 203 Once the image is captured the Options menu on the HPGComm software package allows you to perform simple tasks such as putting a border around the image and rotating or resizing the image The File menu w...

Page 211: ... Here we will look only at using it to edit Notes Similar software will probably become available for the Macintosh computers but was not available at the time of writing Since the aplets are the same for the hp 39g hp 40g and hp 39g the can all be edited by the ADK The only difference for the hp 39g is that the software used to get it onto the computer is different See page 203 If you have downlo...

Page 212: ... the VIEWS menu means that their final appearance and behavior can be very different to the aplet they derive from Essentially the process involves the following stages Choose the parent aplet Analyze the expected behavior and design the VIEWS menu Write the helper programs and attach them to the aplet using the SETVIEWS function Add supporting documentation Choosing the parent aplet The first sta...

Page 213: ...your new aplet This copy will form the core of your new aplet Decide also what prefix to use for the programs you will associate with your new aplet The prefix needs to be recognizably linked to the name of the aplet so that the user can know which programs to delete when they want to clear the programs out after deleting the aplet from the APLET view after use For example an aplet called Linear L...

Page 214: ... the user back into the NUM view showing the result Some of the choices drop back into the PLOT view to see the data displayed Sometimes choices trigger further menus For example the last option of Graphs runs a program which pops up another menu shown right The reason for this method is generally simply to avoid overcrowding the main menu Another example of an aplet is shown right It is called Ta...

Page 215: ...14 Program Catalog 4 Plot Setup 15 Views menu item 1 Plot Detail in Func 5 Symbolic Setup 16 Views menu item 2 Plot Table in Func 6 Numeric Setup 17 Views menu item 3 Overlay Plot in Func 7 Views menu 18 Views menu item 4 Auto Scale in Func 8 Aplet Note view 19 Views menu item 5 Decimal in Func 9 Aplet Sketch view 20 Views menu item 6 Integer in Func 10 Aplet Catalog 21 Views menu item 7 Trig in F...

Page 216: ...which is called by another program which is in the menu Another example of this is the NAME SV program itself It needs to be included in the list in this fashion since we don t want it to appear on the VIEWS menu but it is usually kept and transmitted with the aplet Strictly this is not necessary since once it has done its job it would normally never need to be run again iii If you include an entr...

Page 217: ...xample will use the SETVIEWS command to design a very simple and totally useless aplet which will illustrate a few of the concepts useful in programming the hp 39g We ll call it the Message aplet and create it as a descendant of the Function aplet Change into the APLET view move the highlight to the Function aplet and it Now save it under the new name of Message and then this new aplet You will fi...

Page 218: ... having a default value of 20 MSG FN MSG S The command GROB in the program left stands for Graphic Object and creates a GROB from the F1 X expression stored in the SYMB view storing it in the graphic memory G1 using the font specified 0 1 2 or 3 The reason for doing it this way is to use proper mathematical layout like SHOW does The DISPLAY command then shows it on screen The SETVIEWS command is d...

Page 219: ...ssage at any time then you may have to and the program When you do this the aplet will run the program MSG S which will display a MSGBOX The line in the SETVIEWS command controlling this was Start MSG S 7 Since the triple ends with a view number of 7 this means that after the program terminates when you press the VIEWS menu will display again If you choose the option Message 1 then this will cause...

Page 220: ... window is still displaying in the background To stop this happening you could have included in MSG IN a line of ERASE which is a command to erase the display screen Try editing the program inserting this line before the MSGBOX line and running it again The option of Message 2 displays the same message as we saw before but presented in a different way The DISP command divides the display screen up...

Page 221: ...ROB G1 F1 QUOTE X 0 converts the expression F1 X into a Graphic Object GROB The number at the end which changes with each repetition controls the font used to display the function The line DISPLAY G1 displays this GROB on the screen and the FREEZE command freezes the display until a key is pressed Finally the LINE and BOX commands commands are used to draw an oblique line across the screen and a b...

Page 222: ...r the aplet Transformer are given below TRANSF SV TRANSF S TRANSF PLOT This program sets up the VIEWS menu to call each of the other programs It need only be run once at the creation of the aplet but is attached via the final line so that it will be sent with all the others if the aplet is transmitted The new user does not have to re run it it will never normally be run again This program sets up ...

Page 223: ...alid size The number of columns is then extracted and used to reset the value of Tmax The new image matrix is also recalculated The indenting used is not required and is there simply to make the program easier to read This program puts up a message instructing the user and then allows them to edit the transformation matrix in M1 The size of the matrix is checked to ensure it is 2x2 with the DO UNT...

Page 224: ...hp 39g Aplets created by one version are not compatible with the other version s calculators Look for the ADK on The HP HOME view at http www hphomeview com Example aplet 3 Run the Aplet Development Kit and use the File New command to see the box shown right Enter Transformer and nominate the parent aplet to be the Parametric aplet in the box provided When you press the OK button the aplet will be...

Page 225: ...ers and no spaces This applies to directories also so if you use Transformer for your directory then you may find it appears in the ADK s directory view as TRANSF 1 which is the Windows short version Save the program under any name I used EDITMAT PRG Make sure you are in the directory you created before you click on Save If you click again on the first view in the View List window you will find th...

Page 226: ...his has absolutely no effect on the running of the aplet When you finish click on the Done button and the files HP38DIR CUR and HP38DIR 000 will be created Exit from the ADK and the aplet is finished and ready to be transferred Example aplet 4 The final example is a very useful aplet called Linr Explorer The name would be better as Linear Explorer but names of more than 14 characters will not disp...

Page 227: ...command to display the menu planner and press Insert three times Our VIEWS menu will be as shown below The first entry should have a Prompt of Plot axes an Object Name of LINEXPL AX and a Next View of 1 Plot view The full code for each of the programs is given on the next page and other settings are shown below and right ...

Page 228: ...variable G is being used here as a flag Before the Explore option can be used we must be sure that the axes have been plotted and this will be done by checking the value of G Zero will mean unready and one will mean ready When the Plot axes option is run the value of G will be set to 1 and this will be checked before allowing the user to run the Explore option By setting it to zero in the program ...

Page 229: ... G is then set to 1 so that the next program can tell that the axes are ready to use The function is also re entered in case the user has changed the SYMB view Users have a habit of changing things so try to allow for this in your programs The next program below illustrates a very important technique where a copy of the PLOT view is stored in the aplet s sketch view and then retrieved and modified...

Page 230: ...two messages which tell them what to do The next section begins the code which performs the work in the aplet The first line assigns initial values to the variables M gradient and C y intercept The DO UNTIL loop which follows partly in the next section of code loops through the code within it until the ENTER key is pressed Within the loop the previously stored SKETCH view is transferred from stora...

Page 231: ...ISPXY x pos y pos font object Suppose M 2 C 3 Then the command will display the text y 2x 3 using font 1 small at the top Ymax left Xmin of the screen The next line places a label on the y axis offset slightly to mark the y intercept A check is then done to see if an x intercept exists and if it does a label is placed to mark it Any labels off the edge of the screen will be ignored Finally the lin...

Page 232: ...uld like to further enhance this aplet then try the following change the order of the code so that the labels are drawn after the line thus ensuring that the text is never obscured by the line add a new variable D to allow the size of the increment to change Set an initial value of D of 0 5 at the same point as the values of M and C Then change the lines above so that D is added subtracted instead...

Page 233: ...ally quite useful if you UNCHECK 0 then all equations are unchecked instead of only equation 0 Unfortunately the same is not true for the CHECK command As they say in the trade It s not a bug it s a feature SELECT name This is used to set the active aplet if necessary If the name has spaces in it then it must be enclosed in quotes This is not usually required as the program will normally be called...

Page 234: ...s the need for nested IF commands but is only worth it if you have more than two or three nested IFs Note that colons are not required for the ENDs which terminate the internal IF clauses IFFERR statements THEN statements ELSE statements END This can be used to error trap programs where there is a possibility of something going wrong which would normally crash the program such as evaluating a func...

Page 235: ...the name has spaces in it then it must be enclosed in quotes STOP This command can be used to abort execution of a program Control resumes in the HOME view T Th he e D Dr ra aw wi in ng g c co om mm ma an nd ds s ARC x center y center radius start angle end angle This command draws an arc on the screen It uses the current values in the PLOT SETUP view as the screen coordinates and the settings in ...

Page 236: ... view PIXON x y and PIXOFF x y This command turns a pixel point on or off at the specified point The coordinates are relative to the current settings in the PLOT SETUP view TLINE x1 y1 x2 y2 This command is the same as LINE except that the line drawn reverses the current set unset value of all pixels It can be used to erase previously drawn lines One of the aplets on The HP HOME view at http www h...

Page 237: ...t register as an error but all sort of strange things happen DO statements UNTIL test clause END This loop executes the statements within it until the test clause evaluates as true It must execute at least once The example right checks for a positive integer from the INPUT statement To be even more user friendly you could let the user know what they had done wrong by adding another few lines of co...

Page 238: ...n edit or input a matrix with an key at the bottom When the user presses execution resumes after the EDITMAT statement REDIM matrix var size This command is very useful if the size of a matrix is not known in advance The user might be prompted to input the size and then these values used to resize it Note that the dimensions must be supplied as a list variable The SIZE command can also be used in ...

Page 239: ...rinter PRHISTORY This command whether issued in the HOME view or in a program will send the entire contents of the History to the infra red printer PRVAR variable This command whether issued in the HOME view or in a program will send the value of the variable to the infra red printer This can be used to capture and send images of graphs without need for programming as follows set up the graph or i...

Page 240: ... C I use 440 2 12 9 to find the frequency of C as 261 6 cycles sec We can use this to form a standard header for any program we want to use to play music The header shown right in the rounded box sets up the scale of C major The code which then follows plays the first two bars of the tune Strangers in the Night In this header the duration of a note T is set to 0 5 seconds It is easy to change the ...

Page 241: ... object result contained in expression at the screen position specified using the font specified An extensive example can be found in the chapter Programming the hp 39g on page 226 DISPTIME This command pops up a box displaying the calculator s internal time and date These can be set by storing values to the variables Time and Date Suppose the current time is 3 46 29 pm on the 1st of December 1998...

Page 242: ...ession you specify If you want a newline character then just enclose a pressing of the ENTER key within the quotes PROMPT variable This is a short form of the INPUT statement for those that don t require such precision of control over appearance The default value is the current value of the variable WAIT duration This command pauses execution for the specified number of seconds Calculator Tip This...

Page 243: ...t functions allowing manipulation and creation of lists of numbers including columns of stats data Loop iterative functions Matrix a rich collection of functions to manipulate matrices Polynom another rich collection this time to manipulate polynomials Prob functions used in probability calculations Some of these functions have little application at school level and will not be covered here Others...

Page 244: ...up begins with a P and there is only one page of them there is no difference between the methods Move the highlight down to POLYFORM and then press the ENTER key Your HOME view should now look like this You will notice that the first bracket has already been inserted for you Complete the expression POLYFORM X 2 5 3X 1 2 X using Xy key to get and then press the ENTER key You will find that the expr...

Page 245: ...rminology that will be used in this section of the manual is argument The arguments of a function are the pieces of information it is expecting you to feed it before it will give you an answer These might be numbers variable names lists matrices or algebraic expressions The calculator will not guess what you mean If you don t feed it the information it requires then it will simply give you an erro...

Page 246: ...deg This function converts degrees to radians Eg DEG RAD 30 0 5235 DEG RAD 180 3 1415926 See also RAD DEG HMS HMS FLOOR num This function is the same as the CEILING function except that it always rounds down Eg FLOOR 3 75 3 FLOOR 45 01 45 Note FLOOR 2 56 3 not 2 The FLOOR function is the same as the mathematical function greatest integer which is studied in many mathematical courses If you want to...

Page 247: ...an initial guess If there is only one answer then any guess will do but if more than one solution is possible then more care needs to be taken with your guess to ensure that it is in the neighborhood of your desired solution Eg a Solve 2 3 5 0 x x Use FNROOT X2 3X 5 X 2 b Solve 3 5 1 3 4 d d Use FNROOT D 3 5 3D 4 1 D 0 As with Solve if your expression involves more than one variable then whatever ...

Page 248: ...function together with HMS can also be used to deal with time Eg What time will it be 1 hr 34 min and 15 sec after 3 min past 6 pm Type HMS 18 03 HMS 1 3415 Ans 37 min 15 sec past 7 pm see right See also HMS RAD DEG DEG RAD HMS num This function works in the same way as the HMS function but in the opposite direction It converts decimal degrees or time to degrees or hours minutes and seconds The fo...

Page 249: ...otation It would be used with the XPON function which returns the power part of the number in scientific notation Eg Change 487 23 into scientific notation to get 2 4 8723 10 MANT 487 23 4 8723 XPON 487 23 2 Change 0 0005087 into scientific notation to get 4 5 087 10 MANT 0 0005087 5 087 XPON 0 0005087 4 See also XPON MAX num1 num2 This function returns the larger of two values entered This is not...

Page 250: ...ay that this function gives you the remainder when one number is divided by another It is considered to be an mathematical operator in the same way that a plus minus times or divide sign is Because of this it does not need its arguments placed in brackets as most of the other functions in the MATH menu do Eg 43 5 48 43 MOD 5 3 35 MOD 7 0 14 MOD 5 1 function To find x of y use the function X Y Eg 1...

Page 251: ... I sell a toy for 5 95 that normally sells for 6 50 What is the discount as a percentage Use CHANGE 6 50 5 95 See also TOTAL TOTAL To find out what percentage X is of Y use the function TOTAL Y X Note the reversed order Eg What percentage is a score of 53 out of 81 on a test Use TOTAL 81 53 What percentage is 124 of 112 Use TOTAL 112 124 See also CHANGE RAD DEG rad This function converts radians t...

Page 252: ...ficant figures s f To do this simply put a negative sign on the second argument Round 32345 to the nearest thousand Use ROUND 32345 2 32000 Round 3405 63475 to 6 s f Use ROUND 3405 63475 6 3405 63 See also INT FLOOR CEILING TRUNCATE FRAC SIGN num Another function designed more for programmers returning a value of 1 0 or 1 depending on whether the number supplied is positive zero or negative Eg SIG...

Page 253: ...al part when transformed into scientific notation of the number you feed it It would be used with the XPON function which returns the power part of the number when in scientific notation Eg Change 487 23 into scientific notation to get 2 4 8723 10 MANT 487 23 4 8723 XPON 487 23 2 Change 0 0005087 into scientific notation to get 4 5 087 10 MANT 0 0005087 5 087 XPON 0 0005087 4 This function could b...

Page 254: ... set has been graphed in the PLOT view and that the FIT screen key has been used to plot the line of best fit for the pair of columns If these conditions are satisfied then the function PREDY 3 5 will produce a predicted y dependent value for the x indep value of 3 5 Calculator Tip The line of best fit used in the function PREDY is whichever one was last plotted It is up to you to ensure that this...

Page 255: ...ther variable To do this the formula must be rewritten so that it is an expression which equals zero The ISOLATE function then rearranges the formula in terms of that variable Eg 1 Rewrite the formula 2 1 2 d at in t Firstly rewrite as 2 1 0 2 d at Use ISOLATE D AT2 2 T The result needs interpretation as the answer should be 2D T A Firstly the T is missing and secondly the symbol S1 stands for the...

Page 256: ...n the other hand if X were one of the constants say X 6 and A were the variable then the expression 2 4 AX B would become 2 6 5 4 A or 36 1 A which is linear Thus LINEAR would return 1 The main use for this is going to be when a programmer does not know in advance what function the user is going to type in QUAD expression var name This function uses the quadratic formula 2 4 2 b b ac x a to give b...

Page 257: ...pressed on the hp 39g in the form a b representing a bi Thus the answer to the second quadratic shown above would represent 2 112 6 with the 112 written as a complex number See also FNROOT LINEAR QUOTE var name Intended for use mainly by programmers Programmers sometimes want to store a function such as X2 4 into one of F1 X F9 X using It turns out that if you use F1 X2 4 then it won t be entered ...

Page 258: ...bol and then the values of all the variables in the expression Any not supplied will be evaluated using the value currently stored in that memory This is again a function which is of more use to programmers since this is probably more flexibly handled in the Solve aplet Eg 1 Evaluate b c a d where b 6 c 2 and d 8 Use B C D B 6 C 2 D 8 Answer 0 5 Eg 2 Using the formula 2 1 2 d at find the distance ...

Page 259: ... ic c g gr ro ou up ps s o of f f fu un nc ct ti io on ns s These two groups of functions cover the Trigonometry functions plus others which are less commonly used and which have consequently not been given their own keys on the face of the calculator Use them in the same way as the normal SIN COS and TAN functions COT SEC etc In the Trig group of functions you will find Function Inverse function ...

Page 260: ...OG key It is another function giving greater accuracy than the one it replaces This greater accuracy would never be required in a school setting EXPM1 num This function is designed to be more accurate when anti logging very small values close to zero It gives the value not of x e but of 1 x e EXPM1 exp minus 1 You may wonder how this is an advantage since you must then add 1 to obtain the correct ...

Page 261: ...e discussed in detail in the chapter dealing with the Function aplet see pages 65 to 83 The functions are the integrate or function the differentiate or function and the TAYLOR function discussed below Briefly a Taylor polynomial allows you to approximate the graph and hence values of a complicated function via a simpler polynomial function For example SIN X can be approximated by taking terms fro...

Page 262: ... ordered pair As soon as you press ENTER the calculator immediately converts the a bi form into an ordered pair The History retains the original in case you need to it later for re use The exception is when you enter a complex number in rcis form using the angle sign on the keyboard When you do this the calculator converts to a more explicit rcis format as shown right Try it Complex numbers can be...

Page 263: ...omplex number a bi it returns the magnitude of the complex number 2 2 a b SIGN real or complex This function is part of the Real group but is very useful with complex numbers and so is also covered here If given a vector complex number a b SIGN will return another vector complex number which is a unit vector in the direction of a b i e SIGN A B returns 2 2 2 2 a b a b a b This is very useful not j...

Page 264: ...d avoids this CONJ complex This function returns the complex conjugate Eg If 2 3 z i then find the complex conjugate z Answer see right 2 3 z i See also IM ARG RE IM complex RE complex These functions return the imaginary and real parts of the complex number supplied See also CONJ ARG RE Note As mentioned earlier a very useful function can be found on the keyboard as the SHIFT function for subtrac...

Page 265: ...e not overflowed the capacity of the calculator The other three π i and e are far more easily obtained via the keyboard The first π is available via a key on the face of the calculator above the 3 key The other two i e are easily obtained as lowercase letters via the ALPHA key pressing SHIFT first to get lowercase T Th he e L Li is st t g gr ro ou up p o of f f fu un nc ct ti io on ns s CONCAT lis...

Page 266: ...increment where expression is the mathematical rule used to generate the numbers variable name is the variable that is to be used in the expression any other letters will be taken constants start is the first value that variable name is be given end is the largest value that variable name is to take and increment is the amount that variable name should be incremented by Eg 1 MAKELIST X2 X 1 10 2 L...

Page 267: ... which immediately follows the chapter on Univariate Statistics See page 130 πLIST list This function returns the product of all the elements of a list Eg LIST 2 3 5 would return a value of 30 POS list num This function conducts a search of a list It returns the position in the list of the first occurrence of the number you specify see example right It is of more use to programmers who will not kn...

Page 268: ...l be when you eventually run the program If the object is a matrix then the return value is a two element list as rows columns ΣLIST list This function returns the sum of all the elements of a list Eg LIST 2 3 5 would return a value of 10 REVERSE list This function reverses the order of elements in a list Eg REVERSE 2 4 1 7 10 would return 10 7 1 4 2 SORT list This function returns a list that is ...

Page 269: ...ified number of times starting with a supplied initial value an using the answer to the previous evaluation as the value for the variable in the next evaluation Eg ITERATE X2 1 X 2 5 gives an answer of 15745023 This answer is obtained as follows initial value X 2 first iteration 2 1 x 3 new value X 3 second iteration 2 1 x 8 new value X 8 third iteration 2 1 x 63 new value X 63 fourth iteration 2 ...

Page 270: ...MATION This function also available on the keyboard offers a way of calculating the results of summation notation problems The syntax of the function is ordered in the same way as one reads a summation expression see the examples below Eg 1 5 2 1 i i which expands to 2 2 2 2 2 1 2 3 4 5 giving an answer of 55 can be evaluated using I 1 5 I2 Eg 2 6 1 i i x where 1 2 3 4 5 6 2 10 13 11 20 2 x x x x ...

Page 271: ...f the functions will be covered only by the comment See User s manual A detailed set of examples for the more commonly used functions is given in the chapter titled Using Matrices on the hp 39g See page 170 COLNORM See User s manual COND See User s manual CROSS vector vector This function finds the cross product of two vectors Vectors for this function are written as single row matrices For exampl...

Page 272: ...or vector This function returns the dot product of two vectors Vectors for this function are written as single row matrices For example 3 3 4 or 4 a would be written as 3 4 See page 175 for a worked example EIGENVAL See User s manual EIGENVV See User s manual IDENTMAT size This function creates an n x n square matrix which is an identity matrix For example IDENTMAT 4 would produce a 4x4 identity m...

Page 273: ...ut then evaluate DET matrix first record the fraction and then evaluate DET matrix INVERSE matrix to obtain the non fractional matrix i e 1 2 3 5 3 1 4 5 4 2 2 A A Remember that the inverse matrix is not just the matrix but the fraction times the matrix See also RREF DET LQ matrix This function takes an mxn matrix factors it and returns a list containing three matrices which are in order an mxn lo...

Page 274: ...nted matrix of size n by n 1 and transforms it into reduced row echelon form with the final column containing the solution Eg The system of equations 2 3 14 2 3 4 2 2 14 x y z x y z x y z is written as the augmented matrix 1 2 3 14 2 1 1 3 4 2 2 14 which is then stored as a 3x4 real matrix M1 We now use the function RREF to change this to reduced row echelon form and store it as M2 ...

Page 275: ... suppose we use the system of equations below in which the third equation is a linear combination of the first two but the constant is not consistent with this ie no solution If we solve this in the same way as before the matrix which results is The final line of 0 0 0 1 indicates no solution See also INVERSE DET SCHUR See User s manual SIZE See User s manual SPECNORM See User s manual SPECRAD See...

Page 276: ...276 TRACE See User s manual TRN matrix This function returns the transpose of an n x m matrix For example if 2 3 1 1 2 0 4 M then TRN M1 would return 2 1 0 3 2 4 ...

Page 277: ...ots 2 3 and 1 The screen shot below shows POLYCOEF correctly giving the coefficients as 1 0 7 and 6 for a final polynomial of 3 7 6 f x x x POLYEVAL coeff1 coeff2 value This function evaluates a polynomial with specified coefficients at the point specified The coefficients must be in square brackets followed by the value of x not in brackets ie 3 7 6 f x x x has value 12 at x 3 Note If evaluating ...

Page 278: ... be scrolled right and left to see the missing terms Eg 2 Expand 4 3 2 a b This function contains two variables A and B which must be expanded separately The first expansion treating A as the variable is done using the expression POLYFORM 3A 2B 4 A As you can see if you examine the view after pressing the expansion of the expression in terms of A has been done but the terms involving B are not ful...

Page 279: ... whose coefficients are specified The coefficients must be input as a vector in square brackets Eg Using our earlier function of 3 2 3 1 7 6 f x x x x x x we can enter the coefficients as 1 0 7 6 As you can see in the screen shot the roots of 2 3 and 1 have been correctly found ...

Page 280: ...choosing 2 men and 3 women for a committee of 5 people from a pool of 6 men and 5 women 6 5 2 3 11 5 p 0 3247 Note The reason for the single COMB 6 2 above the main calculation is to save time Rather than using the MATH menu for every entry of the COMB function you can enter it once and then it repeatedly changing the parameters The function The factorial function finds the number of possible perm...

Page 281: ... The final adding of 5 gives the correct range The RANDSEED command It is important to realize that these are not truly random numbers Inside the calculator is a mathematical procedure an algorithm which uses a seed number to produce them Unfortunately taken straight out of the box two hp 39g s will produce exactly the same sequence of random numbers This can be a problem in that for example a cla...

Page 282: ... exam score of 65 and a standard deviation of 14 What two scores will cut off the top and bottom 10 of students i e Find 0 x such that 0 0 1 P x x Using the Solve aplet right we can reverse the normal direction of the UTPN function Enter the expression to be solved for into the SYMB view as shown above then switch to the numeric view Enter a guess of 0 8 80 and then press The second value can be f...

Page 283: ...his is the Upper Tailed Chi Squared probability function It returns the probability that a 2 χ distribution with the supplied number of degrees of freedom is greater than the value supplied See pages 150 299 for an example of this function s use UTPF numerator denominator value This is the Upper Tailed Snedecor s F probability function It returns the probability that a Snedecor s F distribution wi...

Page 284: ...tom view The advantage of doing it this way is that the answer is given in the same form that you would see it if you used the Quadratic formula Just the result edit and square the decimal part to find the value of the discriminant The S1 is the calculator s version of the sign Just the result and remove the S1 to obtain the positive solution replacing the with a to obtain the other This method is...

Page 285: ...ction Since this is a quadratic it can be done with the QUAD formula mentioned in example 1 since it is capable of giving complex results This is shown right rounded to 4 dec pts It s up to you of course to realize that 0 1 7321 is 3i but if you don t recognize it then just that portion and square it The S1 means Method 2 Using POLYROOT An alternative method is to use the POLYROOT function and sto...

Page 286: ...ROOT function to find the roots This function is in the MATH menu in the Polynom group The results show that the x intercepts are 1 0 2 0 and 3 0 The y intercept is found by evaluating F1 0 in the HOME view giving the point 0 6 Step 3 Switching to the PLOT view via VIEWS Decimal you will find that the function does not display as well as it could Since it is the y axis that is not displaying enoug...

Page 287: ...ind and store the x coordinate of the second turning point into memory B Step 5 The PLOT view shows that part of the area we require for part iv is negative so we need to know the x intercept between the two turning points Fortunately we know from Step 2 that it is the point 2 0 If we did not know this already then we could use the menu again retrieving this time from the VAR menu the variable cal...

Page 288: ...t Switch to the PLOT view and use the Intersection tool to find the point of intersection It is worth noting that although the point of intersection is on the screen here this is not necessary The Intersection tool will work even if neither line is visible on the currently set axes Second method using a matrix Step 1 Rewrite 2 3 7 4 2 x y x y as 2 3 7 1 4 2 x y This means that 1 2 3 7 1 4 2 x y St...

Page 289: ...sed to solve the second 3x3 system of equations Third method using the 3x3 Solver aplet This method uses an aplet which is available from the internet called the Simult 3x3 It allows easy solution of 2x2 and 3x3 systems of linear equations in a format which is more user friendly than the use of matrices for student who are not familiar with them ...

Page 290: ...t Result 4 3 2 16 96 216 216 81 x x x x ii Use POLYFORM 3A 2B 5 B to expand the polynomial as a function of B Then use the polynomial function again ing the result from the first expansion and expanding this time as a function of A The key can then be used to view it using the left and right arrows to scroll the screen left and right Result 5 4 3 2 2 3 4 5 243 810 1080 720 240 32 a a b a b a b ab ...

Page 291: ...p 1 Start up the Statistics aplet set it to and enter the data given Change to the SYMB SETUP view and specify an Exponential line of best fit for the data Step 2 Change to the PLOT SETUP view and adjust it so that it will display the data This is not really needed since the line of best fit is what we need and it will be calculated even if the data doesn t show YTick is set to 1000 incidentally N...

Page 292: ...into memory A and k into memory K so that it is un necessary to re type them See page 145 for instructions on finding the parameters from the exponential fit curve Step 2 Switch to the Solve aplet and enter the equation to be solved Changing into the NUM view you should find the values of A and K already defined so move the highlight to T and press Result Doubling time is 1 0536 hours ...

Page 293: ...wer using the function IDENMAT 2 to produce a 2x2 identity matrix and making sure to store the result into M3 In this case the result is a horrible decimal The fractional equivalent can be found by setting the MODES view to Decimal 6 and then re evaluating as shown right From this it can be seen that the common denominator seems to be 26 so multiplying M3 by 26 will give a final result of 1 22 5 7...

Page 294: ...h matrices which are singular a Entering the augmented matrix of coefficients into M1 see above we then use the RREF function storing the result into M2 This result can be examined via the Matrix Catalog It can be seen that the result is a diagonal of 1s with the result given in the final column Here x 1 y 2 z 3 b Since the coefficients are similar we can edit the augmented matrix in M1 and then r...

Page 295: ... as a b In this case the roots are integers so there is no need to store it into a matrix Coefficients must be in square brackets separated by commas ii The method is to solve the complex polynomial 5 32 0 z setting the other coefficients to zeros This is shown in the second POLYROOT calculation in the screen shot right In this case the results are unlikely to be integers so we store them into M1 ...

Page 296: ...ds and in the axes range chosen This can always be adjusted if my guess is wrong The reason for choosing 15 on the YRng is to ensure that the x axis is visible on the screen Notice in the second screen that Simult must be checked if the plot is to be a good illustration of the ship s movements If you ve done this correctly then you will see the ship s movements on the plot view Careful examination...

Page 297: ...aically that its path is circular The first step is to graph the particle s path We go into the Parametric aplet and enter the rule into the first equation X1 Y1 After setting TRng to 0 to 6 and then using VIEWS Auto Scale we get a result which is does not look like a circle but this may be due to distortion through not using a square screen If we inspect the PLOT SETUP view we can see that the se...

Page 298: ...tor too Use X2 Y2 to hold the velocity and X3 Y3 to hold the acceleration pressing after each one to perform the differentiation Now we go to the Function aplet and enter the formula for the required dot product as X2 X X3 X Y2 X Y3 X If we now switch to the NUM view we can see that this function is evaluating to zero for t 0 1 2 3 Of course this is not the same as a proper algebraic proof but you...

Page 299: ...n grades awarded and years at school They are independent HA There is a relationship If H0 is true then the expected frequencies should be those in the table on the right Enter the observed and expected frequencies into columns C1 and C2 of the Statistics aplet In the HOME view perform the calculation shown right This calculates the individual 2 χ values ready for summing as per the formula 2 2 O ...

Page 300: ... a 3 x 2 contingency table the number of degrees of freedom are 2 To find the critical 2 0 05 χ value we enter values of 2 for D the degrees of freedom and 0 05 the probability and then move the highlight to V the value and press As it turns out the required critical value is 5 99 and so we would accept the null hypothesis and conclude no relationship ...

Page 301: ...ts calculators Into this aplet enter the functions shown and set the axes as shown The choice of x axis means that each pixel is 0 02 apart This aplet can now be sent to each student s calculator at the end of a lesson using the infra red link Accompanying questions should address the issues below and students should be required to either hand in a short written response or contribute to a verbal ...

Page 302: ...e PLOT view in an effort to find the hole They won t of course but you can laugh watching them and then discuss why they didn t a good way to introduce the idea of limits However there is a trick to this If you use the default axes of 6 5 to 6 5 then there will be a hole see right because x 2 falls on a pixel point and so since it is undefined the calculator leaves it out For this to work you need...

Page 303: ...of 0 25 Obviously discussion will now center on why 2 f x x is not the same as f x x and why 1 2 f f x is not the same as 2 1 f f x for x 0 G Gr ra ad di ie en nt t a at t a a P Po oi in nt t This is best introduced using an aplet called Chords downloaded from The HP HOME View web site at http www hphomeview com but you can also use the Function aplet In the Function aplet enter the function being...

Page 304: ... a graph allowing the user to move it along the curve with the gradient displayed at the top left of the screen There are two worksheets included in the documentation which is bundled with this aplet which will take the student through the process of developing a gradient function If it is not desirable to use this aplet then the Statistics aplet can be used to help with the process of finding gra...

Page 305: ...duce a rule O Op pt ti im mi iz za at ti io on n A method which I find to be efficient in introducing the idea of optimization is via the maximization of the volume of an open topped box If we start with a sheet of card which is 15cm by 11cm then we can form a box by removing squares from the corners and folding up the sides I find that it is quite helpful for the students to actually make such a ...

Page 306: ...ur rv ve e F Fa am mi il li ie es s One of the concepts which students find quite difficult to come to grips with is that of sketching a field of slopes from a derivative function and from this sketching a family of curves An aplet from The HP HOME View web site at http www hphomeview com called Slope Fields will assist with this process In this aplet the user enters the derivative function into F...

Page 307: ...h is commonly taught as part of any calculus course is rectilinear motion This can be enhanced by using the Parametric aplet to graphically illustrate the motion of a particle If this is set up properly then it can be a very helpful teaching aid as the graph will slow down and speed up as it appears illustrating the velocity and acceleration of the particle See page 104 for a fully worked example ...

Page 308: ...ed Inside the domain it has no effect Note The word AND is available from the keyboard above the sign S Se eq qu ue en nc ce es s a an nd d S Se er ri ie es s Through the Sequence aplet the hp 39g provides very flexible tools for the investigation of sequences These can easily be adapted to investigate series as well Information and worked examples of using the hp 39g for evaluation of sequences a...

Page 309: ...e basic function into F1 X For example you might enter F1 X X2 You can then enter transformations into the other functions Some examples together with the resulting graphs are shown right This process will also work with piecewise defined functions which are often the type that are used in examination questions There are also two aplets which can aid greatly in this process called Quad Explorer an...

Page 310: ... calculators or on the Help page of The HP HOME view http www hphomeview com What is a CAS Although you may not have thought about it consciously you are probably aware that most calculators do not operate with algebra in the same way that a human does Generally speaking solutions on computers and calculators are found using numeric means This is often done by using successive approximations each ...

Page 311: ...oesn t use algebra However the CAS or Computer Algebra System on the hp 40g does use algebra As you can see in the screen shots to the right the CAS on the hp 40g is perfectly capable of giving you the algebraically correct answer and it does it by following the same rules that you do The CAS on the hp 40g is based on a program called Erable originally written by Bernard Parisse for the HP49G whic...

Page 312: ... calculator s chip is able to detect which model it is in and activate or de activate the CAS accordingly The hp 39g released in 2004 is an upgraded model of the hp 39g the differences being vastly greater speed and the extra Finance aplet If you own an hp 39g and you are wondering if you can fool it into believing that it is an hp 40g and thereby activate the CAS then please don t try it If you d...

Page 313: ...CAS by pressing SHIFT SYMB Entering and editing an expression When entering an expression the main point to remember is that evaluations and appending of operations are always done to the currently highlighted element This is most easily seen with an example In the HOME view press and then follow the sequence of keys below i Press 2 XTθ 3 Xy 4 In this case you will notice that the power of 4 was p...

Page 314: ...ighlight at that point encompasses everything at or below node B In this case this is the expression 2 X Pressing down arrow at that point moved down the tree The default is to move to the left most node D This meant that the 2 was highlighted and so when you pressed Xy 3 it was the expression that was cubed At that point the tree now appears as shown right with the CAS in typing editing mode on n...

Page 315: ...ht will jump horizontally to node A highlighting the entire numerator Pressing down arrow four times moves down through the tree from A to P to B to D to F To access and change the power of 2 press up arrow twice to move up to node B then press right arrow to move from node B to node O If you now press and 3 you will find that this is added to the power with brackets applied as required Try redraw...

Page 316: ...ect is basically to remove nodes of the tree The first node deleted is the one furthest right in the currently highlighted section For example if the highlight was as shown in the screen above then the current focus would be on node B in the tree shown right Successively pressing DEL would begin at node E deleting first the node s contents then the operation multiply which connected it to the tree...

Page 317: ...they will be satisfactory Cursor mode Cursor mode can be used to select portions of an expression by drawing a box around it From the menu select Cursor mode Use the arrow keys to move a cursor around on the screen As you do so it places a box around different parts of the expression that are selectable Press ENTER to select that section The CAS HOME History The CAS has its own history which is es...

Page 318: ... In this case we might wish to also paste the result into the Function aplet This can be done by using to retrieve the expression enclosing it in single quotes from the CHARS view and then storing it into F1 X or whichever is desired The reverse process is also possible using PUSH but it is more limited in that you must use the symbolic variable S1 When you then press you will find that seemingly ...

Page 319: ...r graphing results there is an even easier method simply press PLOT Suppose that we have a result in the CAS editor as shown right Pressing the PLOT button will result in the menu shown in the second screen If you choose the Function aplet then you will be asked to nominate a destination All you need then do is exit the CAS and enter the Function aplet ...

Page 320: ... not be intermediate steps displayed between those shown Notice the lack of a c indefinite constant in the integration result Here this is because we are using the definite integral see page 81 and the page following A better alternative is to use the INTVX function as shown below even though it still does not add the c See the page after this for information on using functions in the CAS Calculat...

Page 321: ...them as the expression is entered In this method the order is to choose the function and then to fill in the parameters required The second is to apply a function to all or part of an expression that has resulted from a previous calculation E g 1 Using LIMIT Find 2 7 2 35 lim 7 x x x x The sequence of keys for this is scroll to LIMIT ENTER XTθ X2 2 XTθ 35 XTθ 7 7 ENTER Find 2 1 lim 2 x x The seque...

Page 322: ...calculation or result can be retrieved in this way just as it can in the normal HOME history iv Factorization While the required expression is highlighted fetch the COLLECT function from the menu by pressing SK2 ENTER ENTER Note Remember that the extent of the highlight plays a very important role Firstly the brackets for the inserted COLLECT function will enclose whatever portion of the expressio...

Page 323: ...s a second parameter which allows you to define the variable to be solved for Changing to complex mode in the CFG menu will find the other two imaginary solutions E g 4 Solving simultaneous equations Solve the following system of equations 3 1 x y x y In the CAS enter LINSOLVE X Y 3 AND X Y 1 X AND Y Note that when entering the two equations you must highlight the first one before pressing AND obt...

Page 324: ...324 The LINSOLVE function can also be used to solve problems of the form below Solve the system of equations The command is LINSOLVE 2 X K Y 1 AND Q 3 X Y 5 X AND Y and it produces the results shown ...

Page 325: ... this to get the first expression in terms of a and b As can be seen above the initial integration gives an equation involving a fraction This can be simplified by multiplying both sides by 6 highlighting the entire equation first Notice that when the final simplification is equal to zero the calculator does not bother to include the 0 The second probability tells us that 2 1 5 27 f x dx and this ...

Page 326: ...rror has been caused by not having the whole expression highlighted before pressing AND Press DEL to remove the AND then do it properly The other equation is still available from the CAS History To fetch it press HOME and highlight the equation Pressing will echo it to the point of the cursor Note that if any portion of the expression in the editor is highlighted when you perform an then it will b...

Page 327: ...o the VARS view you will find that it is now a defined variable Although we used X as our variable here there is no reason for this We could just as easily have defined it as 2 2 1 K f K You can now call this function by simply typing for example F 5 We can now test to see if this is a prime number by using the ISPRIME function from the MATH menu This is found in the Integer section as shown right...

Page 328: ... to jump to the first function beginning with N The help screen can be a little crowded as you can see to the right but generally contains an extremely useful summary An example is always given and pressing will cause this example to be pasted into the editing screen There will often be up to three cross references to other functions Pressing or will take you to the help screens for these function...

Page 329: ...ations are carried out in Z 13Z p 13 and You are working in Rigorous mode that is using absolute values Below the title bar you can see the first section of a series of alternatives which let you manipulate the configuration Most alternatives are toggles having only two values For example choosing Complex and pressing ENTER will cause the menu to momentarily disappear and then re display with the ...

Page 330: ...e relevant information in the manual and or the information in Renée de Graeve s book mentioned in the introduction to this appendix on page 310 T Ti ip ps s T Tr ri ic ck ks s C CA AS S 1 In CAS angles are always expressed in radians When you are the calculator HOME screen you can use the MODES view to change this default but this does not affect the CAS 2 Step by step mode is quite useful for st...

Page 331: ...sult in x 2 x 2 whereas COLLECT X2 4 will result in X2 4 back again On the other hand the FACTOR function will factorize over the irrational and complex sets too Entering FACTOR X2 2 will result in the expression 2 2 x i x i 7 The infinity symbol can be found in the Constants section of the MATH menu but can also be obtained by pressing SHIFT 0 Pressing first will produce while pressing twice will...

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