HP 40gs

Graphing Calculator
This ideal classroom graphing tool uses Computer Algebra System (CAS), familiar algebraic entry-system logic and displays answers in symbolic, numeric, and graphing views. Create and store Aplets with 2.25MB total memory**.
Enhanced classroom power Math and science students will benefit from algebraic entry-system logic and easy-to-use interactive tools. Perform complex arithmetic and calculus functions with Computer Algebra System (CAS) Improve problem solving and learning opportunities with symbolic, numeric and graphic views Easily create and use Aplets to assist in learning Review and work with your data using interactive history, notes and sketch capabilities Complex problem solver Complex problem solving is easier on a large, dynamic split screen with adjustable contrast and 2.25MB of total memory**. Easy readability on dynamic split screen with adjustable contrast Get outstanding performance and ample storage with 2.25MB of total memory (2MB Flash + 256KB RAM)** Tackle tough problems with over 750 built-in functions plus powerful HP solvers and applications Use a built-in library of 29 constants and easy metric unit conversions for math and science Designed to be efficient Access online applications and share data through a variety of connectivity options. Improve accuracy with HP click-style keys. Download and share data with PCs and other devices using USB and serial ports Reduce keying errors and improve accuracy with unique HP click-and-rotate keys Increase protection and improve portability using slide-on hard cover Get added flexibility using on-screen dynamic menu options HP quality and support Have confidence that every time you turn on your HP calculator, every calculation you make, results in dependable, worry-free performance and accurate results. Rely on HP quality and award-wining support online and by phone Get the most from your calculator, visit www.hp.com/calculators for downloads, tutorials and more

Specifications

The HP 40gs Graphing Calculator includes all the features of the HP 9G plus: Computer Algebra System (CAS) Symbolic, numeric and graphic views Linear equation solver and triangle solver 2.25MB total memory (2MB Flash ROM + 256KB RAM)** Enhanced connectivity with serial port, USB Adjustable contrast for greater readability Built-in constant library Slide-on hard cover included
HP Part Number CPU Display size Display Type Connectivity Contrast Entry-system logic Built-in functions Menus, prompts, etc. Internal precision Memory Keyboard Power Power off memory protection Auto power off Size (L x W x D) Enclosure material Key top material Weight What's in the box Warranty Subject suitability Permitted for use on
F2225AA 75Mhz ARMx 64 pixels (7 lines x 33 characters + 2 line header + 1 line menu) LCD USB and serial ports for connectivity to PCs, other HP 40gs calculators and peripherals Adjustable Algebraic Over 750 Yes 15 digits 2.25MB total memory (2MB Flash + 256KB RAM)** Alphanumeric AAA x 4 + CR2032 Yes 5 minutes 18.7 x 9.4 x 3.1 cm (7.4 x 3.7 x 1.2 inches) Plastic Plastic Approximately 249 g (8.8 oz)
Calculator, slide-on protective cover, batteries, user manual, USB cable, unit-tounit cable and CD with connectivity software, Aplets and advanced user manual
1-year warranty (may vary by region) General mathematics, Algebra, Trigonometry, Statistics, Geometry, Biology, Chemistry, Physics, Earth Sciences SAT Reasoning and SAT Subject TestsTM in Math 1 & 2, ACT, PSAT/NMSQT, AP Chemistry/Physics, AP Calculus/Statistics, PLAN, EXPLORE*
2007 Hewlett-Packard Development Company, L.P. The information contained herein is subject to change without notice. The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services. Nothing herein should be construed as constituting an additional warranty. HP shall not be liable for technical or editorial errors or omissions contained herein. *ACT, PLAN and EXPLORE are registered trademarks of ACT, Inc., which was not involved in the production of and does not endorse this product. For more information, go to www.act.org. AP Calculus requires a graphing calculator. Any scientific or graphing calculator (Excludes models with QWERTY (i.e. typewriter) keyboards, electronic writing pads, and pen-input/stylus-driven devices) is permitted for the following College Board tests: AP Chemistry, AP Physics, AP Statistics (a graphing calculator with statistical capabilities is expected), PSAT/NMSQT, SAT Reasoning and SAT Subject Tests in Mathematics Level 1 and Level 2. For more information, go to www.collegeboard.com. Policies are subject to change. AP and SAT are registered trademarks of the College Board. PSAT/NMSQT is a registered trademark of both the College Board and National Merit Scholarship Corporation which were not involved in the production of and do not endorse this product. **Flash ROM memory is for system upgrades only and is not available to the user.

To learn more, visit www.hp.com/calculators

4AA1-0863ENUC, June 2007

7 THE HOME VIEW

In addition to the aplets, there is also the HOME view, which can best be thought of as a scratch pad for all the others. This is accessed via the HOME key and is the view in which you will do your routine calculations such as working out 5% of $85, or finding 35. The HOME view is the view that you will most often use, so we will explore that view first.

What is the HOME view?

This is the HOME base for the calculator. All other aplets can be accessed from it and can affect it to varying degrees. All mathematical functions are available in this view. You should 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:
Exploring the Keyboard Angle and numeric settings Memory management Fractions on the hp 39gs & hp 40gs The HOME History Storing and retrieving memories Referring to other aplets from the HOME view An introduction to the MATH menu Resetting the calculator

Exploring the keyboard

The first step in efficient use of the calculator is to familiarize yourself with the mathematical functions available on the keyboard. If we examine them row by row, you will see that they tend to fall into two categories - those which are specific to the use of aplets, and those which are commonly used in mathematical calculations. The screen keys The first row of blank keys are context defined. The reason they have no label is that their meaning is redefined in different situations - they are the screen keys. The current meaning of each key is listed in the row of boxes at the bottom of the screen.
A common abbreviation used for these keys is SK1 or SK2 etc (for screen key 1 ). In the PLOT view shown right, some of the screen keys key. When you press this key the are labeled, such as the row of screen keys labels in the PLOT view appear or disappear. To see another view where all the keys are in use, change to the APLET view.

The VIEWS key pops up a menu from which you can choose various options. Part of the VIEWS menu for the Function aplet is shown right. See page 85 for more detailed information. A summary only is given below.
Essentially the VIEWS menu is provided for two purposes Intro to the VIEWS menu Firstly, within the standard aplets (Function, Sequence, Solve etc.) it provides a list of special views available to enhance the PLOT view.
For example the standard PLOT screen provides a standard graph covering the whole screen, but the VIEWS menu lets you use a split screen such as shown right. Information on the VIEWS menu is given in the chapter dealing with the Function aplet.
In its second role, the VIEWS key also has a critical purpose when using aplets which have been downloaded from the Internet. When a programmed aplet is created for the hp 39gs or hp 40gs, a menu is provided by the programmer to let you control and use it. During the programming this menu is tied to the VIEWS key, replacing the menu normally found on the key.
For example, the snapshot shown right is of a VIEWS menu taken from an aplet designed to analyze and graph Time Series data.
The next important key is the HOME key. It allows you to change into the HOME view from wherever you are. Above it is the MODES key, accessed by pressing SHIFT first. More detailed information on these two views follows later.
The VARS key The VARS key is used, mainly by programmers, as a compact way to access all the different variables stored by the calculator including aplet environment variables.
Shown right are two views of the VARS screen, the first from the HOME list showing the graphic variables (memories) G1, G2. and the next from the APLET list showing some of the variables in the set controlling PLOT.
The VARS key is not generally used much, and you may not have followed this explanation. This is not important as it is a key that is very rarely used by the average user. A few uses for the average user are detailed in the Function aplets Expert User section on page 62.
The MATH key next to VARS is far more important and provides access to a huge library of mathematical functions. The more common functions have keys of their own, but there is a limit to the number of keys that one can put on a calculator before it takes too long to find the key required. Hence the MATH key.
The MATH menu lists all those functions that would not fit onto the keyboard plus some which also appear on the keyboard. Shown in the screen snapshot right is a small selection of the total list. For a listing of almost all the functions, with examples of their use, see the chapter entitled The MATH Menus on page 165.
As is usual with all calculators, most of the keys have another function above the key. The hp 39gs and hp 40gs get 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.

You may have noticed that all the results so far have been improper fractions. For example the first calculation shown right gives the answer as 22/15 rather than 1 7. The fraction setting of Mixed Fraction is 15 essentially the same but answers are given as mixed fractions instead of improper fractions, as shown.
If you want to use the Fraction setting to convert decimals to fractions, here are some tips
if 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 right, failing to include enough decimal places does not produce the desired result.
if you are converting an exact decimal to a fraction, then set a Fraction n value of at least one more than the number of decimal places in the value entered. Both examples in the third screen shot to the right were done at Fraction 6.
Not understanding the significance of the setting of Fraction can produce some unfortunate effects. For example, at Fraction 2, the value of 123.456 becomes 123, with the 0.456 dropped entirely. An example of this is shown right. If you use a setting of only Fraction 2 to perform the calculation shown, you will find to your amazement that 1/3 + 4/5 = 8/7 , whereas using Fraction 6 gives the correct answer.
The reason for this error is that the 1/3 and 4/5 were converted to decimals and added to give
1.133333. This was converted back to a fraction using Fraction 2 to give 8/7 (1.1428.).
This may seem odd but it does match sufficiently closely in Fraction 2 to be accepted.
Generally it is not a good idea to go below the default setting of
Fraction 4. In fact, a Fraction 6 setting tends to be more reliable.
Fraction in the MODES view.
A new feature of the hp 39gs and hp 40gs is the setting of Mixed
The results of this new setting can be seen in the image to the right. Using the setting of Mixed Fraction the result is 4+1/7 ( 4
the answer of 29/7 is obtained using the old Fraction setting.

1 ) whereas 7

Calculator Tip If you scroll back through the History and re-use a result such as the 4+1/7 shown above then dont forget to put brackets around it to ensure that no order of operations errors occur.

The HOME History

The HOME page maintains a record of all your calculations called the History. You can re-use any of the calculations or their results in subsequent calculations.
Try this for yourself now. Type in at least four calculations of any kind, 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).

Calculator Tip If you are a user of external aplets then you may occasionally find that an aplet that has been working perfectly will unexpectedly 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 (Keyboard) 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 key and, while still holding it down, press the third screen key from the left. The calculator will very briefly display a boot screen and then redisplay the HOME view, with the Function aplet as the active one. If you find that the calculator locks up so completely that the keyboard will not respond then a method of reset is provided below which is independent of the keyboard. This shouldnt happen but it is important to know how to deal with it in case it happened during a test or an exam.
Soft reboot (Hardware) Thi s method is provided in case the calculator is locked up to the point that the keyboard no longer responds. On the back of the calculator is a small hole. Poke a paper clip or a pin into this hole and press gently on the switch inside. This briefly interrupts the power supply and, to the calculator, is exactly equivalent to a soft reboot as outlined in the previous section. Normally it should not only unlock the calculator but retain your data intact. However, it must be pointed out that a problem so severe that it has locked up the keyboard may be so bad that it has corrupted the memory anyway. If so then you may find that you see the Memory Clear message when it reboots. If you find that it keeps locking up repeatedly then you should perform a hard reboot as described in the next section. If you have important data on the calculator then you might try to save it to a PC before doing this since a hard reboot will wipe all user memory.
Hard reboot (with loss of memory) To completely reset the calculators memory back to factory settings press ON+SK1+SK6. (SK1=screen key 1) When doing this, dont press them all at once; 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 is deliberately made complex so that it wont happen by accident! This type of reset will always cause complete loss of data. If you find that the screen fills with garbage, or if the calculators in-built diagnostic routine starts to run, then it is just that you have not released them in the right order. Simply try again.

Problems when evaluating limits In evaluating limits to infinity using substitution, problems can be encountered if values are used which are too large.

ex x 2e x + 6

It is possible to gain an idea of the value of this limit by entering the function F1(X)=e^X/(2*e^X+6) into the Function aplet, changing to the NUM view and then trying increasingly large values. As you can see (right) the limit appears to be 0.5, which is correct. It is not the intention here to pretend that this is any sort of thorough mathematical justification but it does provide you with an indication of whether or not you are on the right track.
However, if you continue to use larger values then the limit appears to change to 1 (see right). This is obviously not correct, so why is it happening?
The reason for this is that the calculated value of ex very quickly passes the upper limit of the capacity of the calculator, which is 10500. When this happens 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 size of the top. This error is most likely to happen with limits involving power functions as they will overflow for smaller values of x. The hp 40gs can instead evaluate limits algebraically using the CAS (see page 324). An example is shown right to illustrate the results.
A related effect happens when investigating the behavior of the commonly used
1 calculus limit of lim 1 + . One of the common tasks given to students in introductory calculus classes is n n
to evaluate this expression for increasing values of n to see that it tends towards e. This can easily be done in the Function aplet using the NUM view but there is a trap in store for the unwary!
Begin as follows: 1. Entering the function into the SYMB view as F1(X)=(1+1/X)^X 2. Change to the NUM SETUP view and choose Build Your Own

in the NumType field.

3. Now change to the NUM view enter increasingly large values

for X.

The convergence towards e can also be seen graphically in the PLOT view but is very slow to reach high accuracy.
The trap mentioned earlier lies in the fact that the slow convergence will mean that people will often try to graph this function for very large values of X. The first graph on the right shows the graph of this function for the domain of 0 to 100. The second graph shows how instability develops in the domain 0 to 1E11 ( 11011 ).

This is a very convenient feature, and worth remembering.
mark next to the definition yet, since the sequence is There is no 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 you can see in the screenshot right, the NUM view shows the actual values in the sequence as a table. If you move the highlight into the U1 button and see the sequence and U2 columns, you can press the rule. You can experiment for yourself and see the result of pressing the button is also button (see next page for an example). The available as usual, but it is easier to use other methods.
The NUM SETUP view offers more useful features. Change to that view now and change the NumStep value to 10. If you then swap back to the NUM view you will see (as right) that the sequence jumps in steps of 10. In case you dont realize 2.1475E9 is computer speak for 109.
Now go back to the NUM SETUP view and change the Automatic setting to Build Your Own by moving the highlight to it and pressing the. Switch back to the NUM view and enter the + key or by using values 1, 10, 50 and 100 into the N column.
You will find that the values for those terms of each sequence will appear in the U1 and U2 columns almost immediately. In case you didnt realize, the reason for the larger text is that the button has been pressed.
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. Two types of plots are available, the default being Stairstep.
Change to the PLOT SETUP view and ensure that the setup view is the same as that shown in the two screens above right. Then change to the PLOT view and you should see a graph similar to the one shown below right. The second type of graph is the Cobweb.
15 THE EXPERT: SEQUENCES & SERIES
Defining a generalized GP and the sum to n terms for it. If we define our GP using memory variables then it becomes far more flexible.
The advantage of this method is that you now need only change the values of A and R in the HOME view to change the sequence.

PREDY (0) = m *0 + b

and PREDY (1) PREDY (0) = (m *1 + b) (m

*0 + b) = m + b b

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)
- b*EXP(m*X) b = PREDY(0)
m = LN(PREDY(1)/PREDY(0))

- b*X^m b = PREDY(1)

m = LN(PREDY(e)/PREDY(1))
a = (PREDY(2)-2*PREDY(1)+PREDY(0))/2 b = (PREDY(2)+4*PREDY(1)-3*PREDY(0))/2 c = PREDY(0)
a 1 PREDY (0) b = 1 PREDY (1) c 1 PREDY (2)

Exponential

Quadratic

- a*X^2+b*X+c

- a*X^3+b*X^2+cX+d
a 0 b = 1 c 8 d 27 1 PREDY (0) PREDY (1) 1 PREDY (2) 1 1 PREDY (3)

Exponent

- b*EXP(m*X)

b = PREDY(0)

m = PREDY(1)/PREDY(0)

Trigonometric

- a*SIN(b*X+c)+d
There is no easy way to retrieve the coefficients in the trigonometric equation. The simplest way is to firstly transfer it to the Function aplet by entering F1(X)=PREDY(X) into the Function aplet, highlighting it and then pressing. If you now change to the HOME view and type F1(QUOTE(X)) then the equation will it and edit out any coefficients you want. Clearly this is not appear in the HOME view. You can then ideal. It would be simpler to write them down and re-type them when required!
Correct interpretation of the PREDX function The PREDX function in the MATH menu is not really a way of predicting x values despite its name. Algebraically it simply reverses the line of best fit. For example, the equation Y = X +earlier would use

X = (Y 1.1662) 0.8199

to predict the X values.
Whether this is mathematically correct depends on how you interpret the PREDX function. If, as HP intended, you interpret it to mean give me an x value which, if used in the PREDY function, would give me this y value, then it is correct. However, it should not be interpreted to mean predict an x value based on this y value as most people might. The reason for not using the second interpretation is that the results it gives would then be incorrect. The line of best fit (unlike the correlation) changes as the independent and dependent variables swap roles and cant be simply algebraically reversed in this way. It should not be thought that the hp 39gs & hp40gs are unusual in this odd interpretation. Most calculators equivalent of the PREDX function behave in the same manner.

Using Stats to find equations from point data eg. 1 Find the equation of the quadratic which passes through the points (1,5), (3,15) and (-5,71).
mode and enter the data. Now In the Statistics aplet, choose change to the SYMB SETUP view and choose the Quadratic data model. Clearly this process will only work for those equations which are available as data models but that does offer quite a few choices (see page 126).
Change to the PLOT view using the VIEWS Auto Scale option and key. Dont worry that the scale is not good because we press the dont care about the graph. It only needs to be drawn in order 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 N = N 0 e
; t 0. It is observed that at t = 3 hours, there are 100
colonies of bacteria and also that at t = 10 hours there are colonies. i. Find the values of N 0 and of k. ii. Predict the number of bacteria colonies after 15 hours. iii. How long does it take for the number of colonies to double?

i. Find N 0 and k.

and enter the Start up the Statistics aplet, set it to data given. Change to the SYMB SETUP view and specify an Exponential model for the data.
Either use the VIEWS Auto Scale option, or 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 doesnt show.
Now change to the PLOT view and press draws.

. Wait while the line

Change to the SYMB view, move the highlight to the equation of the. Rounded to 4 decimal places, this regression line and press gives an equation of N = e06579 t.
Predict N for t = 15 hours.
Change to the HOME view and use the PREDY function or use the
facilities in the PLOT view.

Result: colonies.

Find t so that N = 2N 0.
The value of N 0 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 135). This is shown in the screen shown right. Store the results into memories A and K. This saves having screen. to re-type them from the
Now 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 (that was why we stored the curve values into the. appropriate memories), so move the highlight to T and press Result: Doubling time is 1.0536 hours.
An alternative to this would be to only retrieve the value of N 0 and store it into A. The Solve equation could then be PREDY(T)=2*A and the result would be the same.

In the PLOT view, we can see visually that the vertical line representing the sample mean is not within the region 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 it seems that his mean is not far from being significant. Perhaps he simply needs to collect more data in the hopes that this may back up his view. The result he has obtained is, after all, only a probability and further investigation may give a different view.
23 THE EXPERT: CHI2 TESTS & FREQUENCY TABLES
We will start with a small digression to look at a simple inferential problem which can be solved using only the Statistics and Solve aplets. Using the Chi2 test on a frequency table Four coins are tossed 400 times and the number of heads noted for each toss.
The results are shown below. Using the Chi2 test at a 5% level of confidence,
indicate whether the coins may be biased.
Number of heads Frequency
We would expect that for an un-biased set of coins the distribution would be binomial. Our hypotheses are: H0: HA: The number of heads is binomially distributed (n=4 & p=0.5)
The number of heads is not binomially distributed (n=4 & p=0.5)
Begin by entering the data into the first two columns of the Statistics aplet (right).
We now need to calculate the expected values based on our null hypothesis. The expected values are based on the assumption that the results are binomially distributed with n=4 and p=0.5. We can do this in the HOME view using the calculation shown right button. (and below), inserting the results into column C3 using the
400*COMB(4,C1)*.5^C1*.5^(4-C1) C3
We can now calculate the X2 value as the sum of the values in column C4 using the LIST function. The calculations are shown right, placing the individual values into column C4 for inspection if required and then finding the sum of the column. The values can be seen by changing to the NUM view.
In the MATH menu, Probability section (see page 208), there is a function called UTPC (Upper-Tailed Probability Chi-squared) which will give the critical X2 probability for a supplied number of degrees of freedom and a value. In this case we would like the value for a given probability so we will enter the formula into the Solve aplet.

(<num>,<num>,<expression>,<var_name>) This function will return the definite integral of the expression when integrated with respect to the variable specified. Any other variables in the expression will be regarded as constants with values taken from the current memory values. Symbolic integration can be done in two ways. Firstly by replacing one of the limits of integration with a symbolic variable S1 (S1S5). Secondly, and more conveniently, by doing it in the Function aplet (see pages 59 to 75).
<var_name>(<expression>) This function will differentiate the expression with respect to the variable specified. This can be done in two ways. When done in the HOME view the result is numeric because the derivative is evaluated for the current value of the variable in memory. For example, if X currently has the value of 3 then the result is as shown right. When done in the Function aplet, or using a symbolic variable (S1S5), the result is the algebraic derivative (see pages 59 to 75).
TAYLOR(<expression>,<var_name>,<num>) Briefly, a Taylor polynomial allows you to approximate a complicated function via a simpler polynomial function. The <expression> supplied is approximated with respect to <var_name> by terms of a polynomial up to <num> power. The screen shot on the right shows the calculator deriving the Taylor polynomial for sin(x) up to the 7th power. The SIN(X) function can be approximated by taking terms from the polynomial:

sin( x) = x = x

x3 3! 1 6

x5040 x 7

In this example, the result is shown twice. The first is calculated with MODES set to Standard, the second with MODES set to Fraction 4. The second screen shot shows the fractional polynomial in more detail after highlighting it and pressing.
The Complex group of functions
Complex numbers on the hp 39gs & hp 40gs can be entered in either of two ways. Firstly, in the same way as they are commonly written in mathematical workings: a + bi. Secondly, as an ordered pair: (a,b).

Solving simultaneous equations.
Solve the systems of equations below: (i)

2 x 3 y = 7 x + 4y = 2

2x y = 4
3x + 2 y z = 10.5 x 3 y + z = 10.5
Method 1 - Graphing the lines Because the first set of equations is a 2x2 system it can be graphed in the Function aplet. To do this it is necessary to re-arrange the functions into the form y = and store them into F1(X) and F2(X) in the SYMB view of the Function aplet. 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 Intersection tool will work even here, this is not necessary. The if neither line is visible on the currently set axes.
Method 2 - Using a matrix

Step 1.

Rewrite
2x 3 y = 7 x 7 as = x + 4y = 4 y 2
x 7 This means that = 2 y
Step 2. Switch into the Matrix Catalog (SHIFT MATRIX). Position. Enter the matrix shown the highlight on M1 and press right.
Press SHIFT MATRIX to change back to the catalog view and

will

create M2 as shown below right. Note that setting make it easier to enter M2.
Step 3. Change into the HOME view and enter the calculation M1-1*M2. The result is the (x,y) coordinate of the solution displayed as a matrix.
A similar method can be used to solve the second 3x3 system of equations. The matrix M1 and the result are shown right.
Method 3 - Using the Linear Solver aplet This method uses an aplet called the Linear Solver which was added into the new hp 39gs and hp 40gs. For earlier models there is a similar aplet available from the internet called the Simult 3x3 aplet.
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. The disadvantage is that it shows no working.
Note: If your simultaneous linear equations have algebraic coefficients then you will not be able to use any of the above methods because they will all substitute the current value for the coefficients rather than assuming they are symbolic. If you are fortunate enough to own an hp 40gs rather than an hp 39gs then you can use the CAS for this. See page 346 for an example.

Expanding polynomials

Expand the expressions below.

(i) (ii)

( 2x + 3) ( 3a 2b )
Use POLYFORM((2X+3)^4,X) to expand the polynomial. key to examine the result. Use the Result: 16x + 96 x + 216x + 216x + 81
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 key can then be this time as a function of A. The used to view it, using the left and right arrows to scroll the screen left and right.

Erasing, copying, cutting and pasting When you press the DEL button in the CAS editor the effect 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 nodes contents then the operation (multiply) which connected it to the tree. Try it and see.

R A P ^ Q E B

This process is best seen with experimentation. My experience has been that if you are simply wishing to edit a small portion of the expression then the best method may be to use the Edit Expr. command in the menu. The tree structure used by the editor means that although it is usually very easy to add new operations and expressions within an existing one, it can sometimes be frustratingly difficult.

D ^ F G X

If you want to delete the entire expression then the simplest method is to press HOME, exit the CAS and then re-enter it with a blank screen. Alternatively you can highlight part or all of the expression and then press SHIFT ALPHA CLEAR. The highlighted section will be cleared.
Cutting and pasting of all or part of an expression can be easily done menu. This provides access to commands of Cut, using the Copy and Paste which behave in exactly the same manner as they do in any word processor.
Simply highlight the relevant portion of the expression first and then either cut or copy it. Then move to the new position and paste it. As you can imagine from the tree structure the results of a paste can sometimes be unexpected but generally they will be satisfactory.
The CAS HOME History The CAS has its own history which is essentially similar in its behavior to the normal HOME History. If you press SYMB while in the CAS then you will see something similar to the view on the right, with all previous calculations and results recorded.
if the memory is not As with the normal History it is worth deleting the contents regularly by pressing to be gradually used up. Alternatively you can access the Memory Manager (see page 30) and clear the CAS History there.

will take

It is strongly suggested that you spend some valuable time going carefully through this collection of help pages. They will give you an excellent feel for the capabilities of the CAS.

Configuring the CAS

In most of the examples which precede this section it was assumed that the CAS was in its default settings. Two versions of the configuration screen are shown to the right.
These screens can be accessed within the CAS in a number of ways:
To ensure that the CAS is in default mode, enter the CAS and press SHIFT MODES. Now press SHIFT CLEAR. This will restore default settings.
Configuration of the CAS can be done in a number of ways and only an overview will be given here. One method is via the configuration line (CFG) at the top of each menu. The line shown right of CFG R= X S means that the calculator is set to exact-real mode, that X is the current variable, and you are working in Step by step mode.
If you select this option of the menu then you will see the further menu shown to the right. At the top of this menu is more information about the current configuration. The example to the right means that

R= STEP

X 13 ||
You are in exact-real mode Step by step mode is selected Polynomials are written with their terms in descending order by exponent X is the current variable Modular calculations are carried out in Z/13Z (p = 13) 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 new setting of Real. Pressing ENTER again will revert back to Complex. It is important to realize that the entry shown in the menu is the one that is NOT in use! For example, if it shows Complex then you are in Real mode and vice versa. Using the menu you can choose:
Quit config Complex Approx Direct

1 + x + x

Sloppy Num. factor

Cmplx vars

English Default cfg
(when youre finished making changes)

(or Real)

(or Exact)
(or Step by Step see following page)
(or x + x +1 ; governs how polynomials will display)
(or Rigorous, if you want to work in absolute values)

(or Symb factor)

(or Real vars if you want all symbolic variables to be assumed real)