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Sharp el-9950, Manual

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198

Chapter 10: The SOLVER Feature

Newton&bisection method

 is a technique of finding approximate 

solutions to a math problem via calculus, when conventional 
algebraic techniques just cannot work. If the Equation method 
fails, the calculator will automatically switch to Newton&bisection 
method.

Example

Solve “X

2

 

+

 4X 

–

 2 = 0”.

1.  Enter SOLVER by pressing 

@

 

'

. If you have items 

left on the screen, clear the entries by pressing the 

C

 key 

several times.

2.  Enter “X

2

 

+

 4X 

–

 2”. When 

the expression is entered as 
a non-equation format, then 
“=0” is automatically assumed 
at the end. When done, press 

E

.

3.  The next screen indicates the 

variable “X” and its previously 
set value. This value will be 
assumed as the starting point 
of the calculation segments, 
and the Newton&bisection 
SOLVER will find the closest approximation to the starting point. 
Enter “0”, and press 

E

.

4.  Now, press 

@

 

h

 

to execute the SOLVER. 
Since this cannot be solved 
using the Equation method, 
the calculator automatically 
switches analysis to 
Newton&bisection method.

5.  The next window confirms the 

starting point of the analysis 
(set to “X = 0” from step #3), 
and the size of each step 
(default is set to “0.001”). 
Press 

@

 

h

.

Newton&
bisection 
method

Summary of Contents for el-9950

Page 1: ......

Page 2: ...equential or otherwise from the use of this material SHARP strongly recommends that separate permanent written records be kept of all important data Data may be lost or altered in virtually any electronic memory product under certain circumstances Therefore SHARP assumes no responsibility for data lost or otherwise rendered unusable whether as a result of improper use repairs defects battery repla...

Page 3: ...0 Cursor Basics 20 Editing Entries 22 Second Function Key 23 ALPHA Key 24 Math Function Keys 25 MATH STAT and PRGM Menu Keys 27 SETUP Menu 28 SETUP Menu Items 29 Calculations Using MATH Menu Items 32 Precedence of Calculations 45 Error Messages 46 Resetting the Calculator 47 1 Using the reset switch 47 2 Selecting the RESET within the OPTION menu 48 Chapter 3 Manual Calculations 49 1 Try it 49 2 T...

Page 4: ...g a Window 92 11 Tables 93 12 The DRAW Function 96 13 Other Useful Graphing Features 111 Split screen 111 Substitution feature 113 Chapter 5 SLIDE SHOW Feature 116 1 Try it 116 2 The SLIDE SHOW menu 119 Chapter 6 Matrix Features 121 1 Try it 121 2 Entering and Viewing a Matrix 123 Editing keys and functions 124 3 Normal Matrix Operations 125 4 Special Matrix Operations 126 Calculations using OPE m...

Page 5: ...w to edit the list 146 Chapter 8 Statistics Regression Calculations 147 1 Try it 147 2 Statistics Features 151 1 STAT menus 151 2 Statistical evaluations available under the C CALC menu 152 3 Graphing the statistical data 155 1 Graph Types 155 2 Specifying statistical graph and graph functions 159 3 Statistical plotting on off function 159 4 Trace function of statistical graphs 160 4 Data list ope...

Page 6: ...parison operands 207 5 Programming commands 208 A PRGM menu P A 208 B BRNCH menu P B 209 C SCRN menu P C 210 D I O menu P D 210 E SETUP menu P E 210 F FORMAT menu P F 212 G S_PLOT menu P G 213 6 Flow control tools 214 7 Other menus convenient for programming 216 H COPY menu P H 216 VARS menu 217 8 Debugging 219 9 Preinstalled program 220 Calculating the area between equations for a given interval ...

Page 7: ... Error Messages 235 5 Error Conditions Relating to Specific Tasks 237 1 Financial 237 2 Error conditions during financial calculations 239 3 Distribution function 239 6 Calculation Range 241 1 Arithmetic calculation 241 2 Function calculation 241 3 Complex number calculation 246 7 List of Menu Sub menu Items 247 ...

Page 8: ... and avoid exposing it to excessively humid or dusty environments Since this product is not waterproof do not use it or store it where fluids for example water can splash onto it Raindrops water spray juice coffee steam perspiration etc will also cause malfunction Clean with a soft dry cloth Do not use solvents Avoid using a rough cloth or anything else that may cause scratches Do not use a sharp ...

Page 9: ...ation sheet from the memory backup battery 4 Place the battery cover back and make sure that the notch is snapped on 5 After a few seconds press O and you will see the following message on the display PRESS CL KEY TO CLEAR ALL DATA PRESS ON KEY TO CANCEL 6 Make sure to press C to reset the calculator s memory The memory will be initialized and ALL DATA CLEARED will be displayed Press any key to se...

Page 10: ...ay contrast may vary with the ambient temperature and or remaining battery power you may want to adjust the contrast accordingly Here s how 1 Press then p 2 Adjust the contrast by using the and keys increases the contrast Hold down the key decreases the contrast 3 When done press C to exit the mode Press o to turn the calculator off Automatic power off function The calculator is automatically turn...

Page 11: ...10 Chapter 1 Getting Started To open the cover When in use When not in use Using the Hard Cover ...

Page 12: ...11 Chapter 1 Getting Started Part Names and Functions Main Unit 1 Display screen 2 Power ON OFF key 5 Cursor keys 3 Key operation keys 4 Graphing keys ...

Page 13: ...g mode ALPHA LOCK 4 Graphing keys These keys specify settings for the graphing related mode Y Opens the formula input screen for drawing graphs G Draws a graph based on the formulas programmed in the Y window t Opens a Table based on the formulas programmed in Y W Sets the display ranges for the graph screen Z Changes the display range of the graph screen U Places the cursor pointer on the graph f...

Page 14: ...sets the calculator settings such as LCD contrast and memory usage n key Obtains the screen for the slide show l key Accesses list features key Creates your own slide shows key Sets the statistical plotting Keyboard Basic Operation keys E Used when executing calculations or specifying commands C q Clear Quit key B Backspace delete key D Delete key i Toggle input mode between insert and overwrite i...

Page 15: ...erts hexadecimal decimal octal and binary numbers or solves systems of linear equations finds roots for quadratic and cubic equations m Enter menu for matrix functions Enter screen and menu for Solver features z Enter the menu for calculator specific variables g Enter menu for financial solver and functions Scientific Calculation keys See each chapter for details ...

Page 16: ... key in green press A first then press the key When in Menu selection screen however you do not have to press A to access the characters Press C to cancel If you want enter alphabetical letters green sequentially use Press A to return to the normal mode In this manual alphanumeric characters to be entered are indicated as they are without using the key symbols Use of the key symbol indicates that ...

Page 17: ...oons butter Based on these values solve the following problems using the calculator Question If you make 60 doughnuts according to the above recipe how many cups of warm milk are required At first you may calculate how many cups of warm milk are required for 1 doughnut 3 4 18 As for the ordinary calculator the answer is 0 041666666 But how much is 0 04166666 of a cup of warm milk Quick Run through...

Page 18: ...f the previous calculation press b and you do not have to reenter the value 6 Press b or directly multiplication Ans is displayed ANS is a calculator specific variable which indicates the answer of calculations just before When you enter addition subtraction multiplication division it is not required to press b 7 Press 60 8 Press E Answer 1 2 2 cups of warm milk are required for making 60 doughnut...

Page 19: ...0 9 decimal point key and negative number key _ to enter numbers into the calculator To clear the screen entry press C In the examples and descriptions in this manual a point is used to provide a Display decimal point to coincide with the display of the computer Example Type 10 23456789 onto the Calculation screen 1 Enter the Calculation screen then clear the screen entry C 2 Enter numbers with th...

Page 20: ...h negative values Press _ before entering the value Note Do not use the key to specify a negative value Doing so will result in an error Example Type 9460 827513 into the Calculation screen C _ 9460 827513 Note can be used to enter a value in scientific notation Example 6 3 108 4 9 107 C 6 3 8 4 9 7 Entering a negative value ...

Page 21: ...59 2 Example Obtain the answer to 9 7 5 3 C 9 7 5 3 E Note The multiplication sign as the one in the above example can be abbreviated if it proceeds a math function a parenthesis or a variable Please note that the precedence of calculations may be changed see page 45 And the multiplication sign after a parenthesis cannot be abbreviated For examples Abbreviating 1 2 3 to 1 2 3 will result in an err...

Page 22: ...ure 4 Press to move the cursor out of the area then enter at the cursor 5 Press _ again Notice that the cursor is automatically placed so that you can specify the depth of this root figure Type 3 and 8 6 Press E to obtain the answer Mode Symbol Remarks Normal mode The appearance of the cursor pointer may vary according to the mode or When A is pressed position The major shapes and the definitions ...

Page 23: ...SOR B key erases one BEFORE THE CURSOR Use C to clear the entire entry line When the editing mode is set to one line insert mode needs to be manually specified Press and release then i to set the insert mode Press i again to return to the overwrite mode The C key clears all screen entries in the Calculation screen as well as clearing error messages It also clears a single line equation in the Y sc...

Page 24: ... and its functions refer to the section Second Function Key of this chapter Second Function Key Use to call up the calculator s extended key functions math functions and figures All functions associated with are color coded orange and are printed above each key Example Enter 2π on the screen 1 Press C to clear the screen then enter 2 by pressing 2 2 Press When the key is released the cursor on the...

Page 25: ... N will be entered as a variable Call up the figure and equation names from within the second functions and various menus instead If a colon is used data may continue to be entered in more than one term Example Enter 2 A on the screen 1 Press C to clear the screen Enter 2 by pressing 2 2 To enter A press A the cursor pattern changes to A _ upon releasing the key 3 Press A to call A at the cursor A...

Page 26: ...he cursor Enters an arctangent function at the cursor l Enters a logarithm function at the cursor 0 Enters 10 to the xth power then sets the cursor at the x I Enters a natural logarithm function at the cursor Enters e constant to the power of x then sets the cursor at the x y Enters 2 at the cursor to raise a number to the second power x Enters 1 at the cursor to raise a number to the negative fir...

Page 27: ...s Examples 2 d 3 4 d 2 3 4 Enters a comma at the cursor Enters a root figure at the cursor R Stores a number or a formula into a variable r Recalls an item stored in a variable X Enters a variable x θ T or n The variable is automatically determined according to the calculator s coordinate setup x for rectangular θ for polar T for parametric n for sequential z Brings up the VARS menu See Chapter 6 ...

Page 28: ...e the and keys to move the cursor up and down the menu As you scroll you will see the corresponding sub menu contents shown on the right side of the screen change 3 Set the cursor at B NUM Menu items can also be selected by using shortcut keys A through H in this example simply press B to select B NUM There is no need to use A for this operation 4 Press a shortcut key 2 to select 2 round The scree...

Page 29: ...exit the SETUP menu press C Example Display the calculation result of 10002 in scientific notation 1 Press then Within the SETUP menu press C then 3 to select 3 Sci under the C FSE menu Tips Using the arrow keys move the cursor down to the C FSE position press E and then move the cursor down to the 3 Sci position Press E to select the sub menu item 2 The display goes back to the SETUP menu s initi...

Page 30: ...n decimal form with a floating decimal point default The SETUP in TAB does not have any effect on this setting default If the value of the mantissa does not fit within the range 0 000000001 to 9999999999 the display changes to scientific notation The display mode can be changed according to the purpose of the calculation Fix Answers are given in decimal form The decimal point can be set in the TAB...

Page 31: ...ntial graph coordinates ANSWER Sets the answer preference to various number formats Decimal Real Answers will be given in decimal form default Mixed Real Answers will be given in mixed fractions whenever appropriate Improp Real Answers will be given in improper fractions whenever appropriate e g 1 2 2 x yi Complex Answers will be given in complex rectangular form r Complex Answers will be given in...

Page 32: ...stored in the SOLVER window Resetting to the default settings p E 1 will also clear the above data Expression of up to 114 bytes can be entered in the Equation edit mode If the expression exceeds the screen width it is horizon tally extended Expression of up to 160 bytes can be entered in One line edit mode if the expression exceed the screen width it goes to the next line SIMPLE Sets the preferen...

Page 33: ...ite number of digits beyond the decimal point Note Please use Degree DEG for angle values and not GRAD because this is used to represent Grads where one turn comprises 400 Grads A CALC Contains sub menu tools for advanced calculations 01 log2 log2 value Enters a base 2 logarithm log2 02 2X 2value Raises 2 to a power Sets the cursor to exponent 03 fmin fmin equation lower limit of x upper limit of ...

Page 34: ... 0 7 E 07 dx Enters a differential dx in an integration expression 08 expression initial value end value increment Returns the cumulative sum of a given expression from an initial value to an end value in the specified increment value if not specified default increment is 1 09 sec sec value Enters a secant function to be used in a trigonometric expression 10 csc csc value Enters a cosecant cosec f...

Page 35: ...e hyperbolic cosine 20 tanh 1 tanh 1 value Enters an inverse hyperbolic tangent B NUM Use the sub menu items below to convert a value 1 abs abs value Returns an absolute value A real number a list matrix variable or equation can be used as values Example Find an absolute value of 40 5 M B 1 _ 4 0 5 E 2 round round value digit number of decimals Returns the rounded value of the term in parentheses ...

Page 36: ...xample Discard the integer part of 32 01 0 01 M B 4 3 2 0 1 E 5 int int value Rounds down a decimal number to the closest integer Example Round down 34 56 to the nearest whole number 34 M B 5 3 4 5 6 E 6 min min list Finds and returns the minimum value within a list of numbers To define a list of more than two numbers group the numbers with brackets and with each element separated by a comma Examp...

Page 37: ...d 36 M B 9 1 6 3 6 E C PROB 1random random number of trial Returns a random decimal number between 0 and 1 uniform distributed Example Make a list with three random numbers Note Set the FSE to Fix and TAB to 0 M C 1 100 M C 1 100 M C 1 100 E 2 rndInt rndInt minimum value maximum value number of trial Returns a specified number of random integers between a minimum and a maximum value Example Produc...

Page 38: ...s will generate different numbers every time Therefore the table values of the random functions will be different every time When in case of random based graphing calculations the tracing values and other parameters of the graph will not match the graph s visual representation 5 nPr Returns the total number of different arrangements permutations for selecting r items out of n items nPr n n r Examp...

Page 39: ...ure angles was introduced to the world by Hipparchus 555 514 B C and Ptolemy 2nd cent A D about 5000 years later We still use these ancient systems today and this calculator supports both formats 1 deg Takes a number in sexagesimal form and converts it into a decimal number To enter a number in sexagesimal form use items in the ANGLE sub menu described as described in Chapter 3 Example Convert 34 ...

Page 40: ...ersion formulas x rcosθ y rsinθ 3 xy r xy r x coordinate y coordinate Returns polar coordinate radius value from X Y rectangular coordinates 4 xy θ xy θ x coordinate y coordinate Returns polar coordinate θ value from X Y rectangular coordinates The following ranges are used to find θ Degree mode 0 θ 180 Radian mode 0 θ 2π Gradient mode 0 θ 200 5 rθ x rθ x r coordinate θ coordinate Returns rectangu...

Page 41: ...er in radians Example Type 2 radian 2 M E 4 5 g Enters an g symbol to enter a number in gradients F INEQ Use the equality inequality figures to compare two values These sub item tools return 1 true or 0 false 1 Tests whether a preceding value and a following value are equal 2 Tests whether a preceding value and a following value are not equal 3 Tests whether a preceding value is larger than a foll...

Page 42: ...or B 1 1 1 0 A xor B 0 1 1 0 A xnor B 1 0 0 1 A notA 1 0 0 1 The following examples show the answer screen when executing a boolean operation for AND OR XOR XNOR between 1100 and 1010 in binary mode Compare the results binary to the above table 1 Press V A E to enter the binary octal and hexadecimal calculation mode 2 Press to select the binary mode 1 and value A and value B Enters an AND logic fi...

Page 43: ...10 E H COMPLX In order to use the sub menu items within the COMPLX menu the calculator must be set up to handle complex numbers Otherwise the result will be a data type error Refer to the section SETUP Menu Items in chapter 2 for changing verifying the calculator s setup to enable complex number answers in either rectangular or polar coordinates 1 conj conj complex number Returns the complex conju...

Page 44: ...i and returns the θ Calculations using complex numbers To calculate using complex numbers select the sub menu item 4 x yi or 5 r in the F ANSWER of the SETUP menu items The initial screen for the complex number calculation mode is the same as for the real number mode Complex numbers can be noted using either 4 x yi rectangular coordinates or 5 r polar coordinates Example Calculate 3 4i 4 6i Note I...

Page 45: ... number calculations The following function keys are available for complex number calculations without the limits existing in the real number calculations y x l I 0 a _ The following MATH menu functions are also available for complex number calculations abs round ipart fpart int ...

Page 46: ...a value and a stored variable constant with abbreviated 2π 2A etc 6 Single calculation functions where the numerical value occurs after the function sin cos tan sin 1 cos 1 tan 1 log 10x ln ex abs int ipart fpart not neg etc 7 Multiplications between a number and a function in 6 3cos20 etc cos20 is evaluated first 8 Permutations and combinations nPr nCr 9 10 11 and 12 or xor xnor 13 Equalities and...

Page 47: ...8 24 6 2 E 0 25 48 24 6 2 Error Messages The calculator will display an error message when a given command is handled incorrectly or when instructions cannot be handled correctly such that the task cannot be processed further Various types of error messages are given to inform users the types of situations to be remedied For example performing the following key strokes 5 E will result in an error ...

Page 48: ...battery cover located on the back of the calculator 2 Place the battery cover back until the notch is snapped on 3 Wait a few seconds and press O The verification window will appear on the screen 4 Press C to clear all the stored data Press O to cancel resetting After C is pressed the calculator s memory will be initialized Press any key to display the calculation screen Note If the above verifica...

Page 49: ...le in the OPTION menu press E to select E RESET the RESET sub menu items should appear on the right side of the screen 3 The first item 1 default set will initialize only the SETUP and FORMAT settings while the second item 2 All memory will erase all memory contents and settings To reset the memory select 2 All memory by pressing 2 The verification window will appear 4 Press the C key to clear all...

Page 50: ...r the period of one day you also rotate around the globe at a certain speed Knowing the facts above can you figure out how fast you are traveling in miles per hour Since distance traveled average speed time taken the following equation can be formed to find out the circumference of the earth x miles x 7 5 186282 Then x 186282 7 5 Since you know the earth turns around once a day which means in 24 h...

Page 51: ...ble is a symbol under which you can store a numerical value We will use variable A to store the circumference of the earth Press R to set the store mode Press A A then E to store the answer To call up the stored answer press A A E again Note While checking the stored values you may see 0 this means that no value is stored in the variable 4 Now since the value you have stored under A is the distanc...

Page 52: ...rent setup will be displayed Make sure that the top line is indicated as Deg i e degrees If not then the angle system will need to be changed Press B to select B DRG then press 1 to select 1 Deg 3 Now let s work on the actual calculation part Press the key to enter the Calculation screen and press C to clear any screen entries 2 Try it The Mendocino Tree a coast redwood growing in Montgomery Woods...

Page 53: ...and you may answer okay But what if an incomplete sentence is thrown such as how are You ll wonder how are what it just doesn t make sense A math expression needs to be complete as well 1 2 4x 2sinx cosx form valid expressions while 1 and cos do not If an expression is not complete the calculator will display an error message upon pressing the E key Enters a sign for addition Example Calculate 12 ...

Page 54: ...is b It is followed by a variable or a mathematical constant π e etc c It is followed by a scientific function such as sin log etc _ Sets a negative value Example Calculate 12 4 _ 1 2 4 E Note Do not use the key to enter a negative value use the _ key instead Enters an open parenthesis Use with as a pair or the calcula tion will result in an error Enters a closing parenthesis a parenthesis left op...

Page 55: ...s function keys to simplify various calculation tasks s Enters a sine function to be used in a trigonometric calculation Example Calculate sine π 2 s b 2 E c Enters a cosine function to be used in a trigonometric calculation Example Calculate cosine π 3 c b 3 E Enters a tangent function to be used in a trigonometric calculation Example Calculate tangent π 4 b 4 E s Enters an arcsine function to be...

Page 56: ...ression Example Calculate arctangent 1 1 E Note Expressions with inverse trigonometric functions evaluate in the following ranges θ sin 1 x θ tan 1 x θ cos 1 x Deg 0 θ 90 Deg 0 θ 180 Rad 0 θ π 2 Rad 0 θ π Grad 0 θ 100 Grad 0 θ 200 l Enters a log function for a logarithmic calculation Example Calculate log 100 l 1 0 0 E 0 Enters a base of 10 setting the cursor at the exponent Example Calculate 5 10...

Page 57: ...r Example Obtain the answer to 122 144 12 y E Note When no base number is entered the base number area will be left blank and just the exponent appear C y 1 2 E x Enters x 1 and returns an inverse by raising a value to the 1 power The inverse of 5 for example is 1 5 Example Raise 12 to the 1 power 0 083333333 1 2 x E Note When no base number is entered x 1 will be entered with x left blank C x 1 2...

Page 58: ... be a natural number A variable can not be used Equation or use of parenthesis such as 1 2 2 3 or 5 2 3 causes syntax error When a numerator or a denominator is negative the calculator will cause error b Enters a fraction setting the preceding number as its numerator If the calculator is set to one line mode then will be entered instead For example 2 5 indicates 2 5 Example Calculate 2 5 3 4 2 b 5...

Page 59: ...e 23 2 82 press 2 a 3 a 2 E _ Enters a Example Bring 4 to the 5th root 1 319507911 5 _ 4 E Note When no depth of power is entered a is entered with both number areas left blank C _ 5 4 E Enters a square root symbol Example Obtain the square root of 64 8 6 4 E Enters a comma at the cursor A comma is required in some of the MATH functions Sets the following value as θ assuming the preceding value is...

Page 60: ...polar T for parametric n for sequential z Accesses the VARS menu Enter braces to group numbers as a list b Recalls the previous answer Use this key to incorporate the answer to the previous calculation into an expression Example Perform 3 3 3 3 E Subtract the value of the previous answer from 10 1 0 b E Note b can be considered as a variable its value is automatically set when E is pressed If b is...

Page 61: ...ode in the SETUP menu all the numerical and graph equations stored in the temporary memory are cleared and cannot be recalled Enters pi Pi is a mathematical constant representing the ratio of the circumference of a circle to its diameter Example Enter 2π 6 283185307 2 E j Calls up the CATALOG menu From the CATALOG menu you can directly access various functions in the menus Functions are listed in ...

Page 62: ...will not affect the ANSWER settings in the SET UP menu If a decimal number is not rational fraction conversion will not function and display the answer in decimal format Only a value that can be converted to a fraction is displayed in a fraction form Only a rational number within 10 digits can be simplified if Manual is selected in the SETUP menu item H SIMPLE Default setting is Auto for simplifyi...

Page 63: ...gers to simulate a coin flip 0 head or 1 tail The size of the list i e how many times the virtual coin is thrown can be specified The same as rndInt 0 1 number of times Example Make the calculator flip a virtual coin 4 times rndCoin 4 E rndDice Returns specified number of random integers 1 to 6 to simulate rolling dice The size of the list i e how many times the die is thrown can be specified The ...

Page 64: ...E Simp E Simplified by 2 the lowest common factor of 12 an 6 Simp E Simplified by 3 the lowest common factor of 6 and 3 Specifying a common factor Simplify the fraction using the specified common factor Example 1 b 12 5 b 12 E Simp 6 E Manually specify 6 the Greatest Common Factor of 12 and 6 to simplify the fraction Note If the wrong number is specified for a common factor an error will occur Sim...

Page 65: ...e Get 25 of 1234 1 2 3 4 2 5 E Percentage must be a positive value equal to or less than 100 Note The CATALOG commands and the equivalent keys Equivalent key CATALOG command b a 2 y 1 x R C M C nCr P M C nPr d Sequen and Simul features can also be accessible from the CATALOG menu ...

Page 66: ...variable 3 Pressing E will store the list in the LIST variable Note that this procedure will overwrite the list previously stored in the LIST variable Refer to Chapter 7 LIST Features to learn more about how LIST variables can be utilized 6 TOOL Menu The TOOL menu contains items to help calculating in different number systems as well as to help solve both linear and polynomial equation Press V to ...

Page 67: ...ange the calculator will also return an error Decimals can be used for DEC mode only cannot be used in the other modes If you convert decimal values to binary octal or hexadecimal number the decimal part is discarded and only the integer part is converted When numerical values of binary octal and hexadecimal modes are negative the display is switched to complements of 2 B SYSTEM With this tool lin...

Page 68: ...sired 2 In the next screen an equation ax2 bx c 0 is displayed with an entry area for the known values a b and c 3 Enter the values as shown in the screen to the right Pressing E at each entry will store the value and sets the cursor at the next entry area 4 When done press h to execute the calculation The results i e the x intersects will be displayed 5 To enter a different set of numbers for a b...

Page 69: ...te crossing point can be found 2 The exact crossing point can be found with the TABLE function There are two taxi cab companies in your city Tomato Cab and Orange Cab with different fare systems The Tomato Cab charges 2 00 Euro upon entering the taxi cab and 1 80 Euro for each mile the taxi travels The Orange Cab on the other hand charges 3 50 Euro plus 1 20 Euro per mile This means that taking th...

Page 70: ... Use the X key to enter the x representing the distance in miles 4 When the equation line is complete press E The first equation is now stored and the cursor automatically jumps to the second line where the second equation can be entered 5 At the second line press C to clear any entries then enter 3 5 1 2X to represent the Orange Cab s fare system When done entering the equation press E The two eq...

Page 71: ...o find the values per graph increment When the traveling distance is 2 miles the Tomato Cab charges 30 cents less overall than the Orange Cab but it costs 30 cents more at 3 miles To make the X increment smaller press y 9 When the Table setting window appears move the cursor down to TBLStep type 5 and press E Now the Y values will be sampled at every 0 5 mile 10 Press t to show the table again It ...

Page 72: ...h CONCEPT 1 Grasp the idea of sequential equations 2 Use the graph tracing function to obtain approximate values You have just opened your own bank account with an initial deposit amount of 2000 Euro Suppose your monthly income is 3000 Euro and you will spend 60 percent of what you have in the account every month how much will your balance be after one year How much will you have in the account 6 ...

Page 73: ...enter u and press X for n Press E when done entering Note Press C to clear the previous entry Using a capitalized U or N here will result in an error upon pressing the G key 5 On the second entry row u nMin enter 2000 then press E The figure is automatically enclosed by braces 6 The v and the w entry sets will not be necessary in this case so press C to clear then press E to move one row down Repe...

Page 74: ... value X value since the graph is set to Time format increases and the Y value the balance of your account will change Find the Y value when the n value is 6 after 6 months as well as the value when n 12 after 12 months 1 year You can obtain the value directly from the CALC menu 1 Press k and select 1 VALUE n will appear on the bottom line of the screen 2 Enter the n value of 6 and press E 3 Follo...

Page 75: ...d in the Graph equation window only the vertical Y and horizontal X axis will be displayed upon pressing the G key t Displays the graph values in a table The default sample increment value of the graph s X axis is 1 See 11 Tables on page 93 W Displays the graph window setup The setup values the minimum maximum X Y values and X Y axis scale can be changed manually 1 While the graph is displayed on ...

Page 76: ... for the graph appearance on zooming in out The menu items with each function and the sub menu items are described below A ZOOM 1 Auto According to the WINDOW setup the graph will be zoomed in by adjusting the Ymin the minimum Y value and Ymax the maximum Y value according to the Xmin the minimum X value and Xmax the maximum X value When this item is selected the graph will automatically be redraw...

Page 77: ...h will be magnified two times Refer to the B FACTOR segment of this section for more information 4 Out The graph image will be zoomed out according to the B FACTOR setup under the ZOOM menu 5 Default The graph will be displayed with default graph setting Xmin 10 Xmax 10 Xscl 1 Ymin 10 Ymax 10 Yscl 1 6 Square Set the same scale for X and Y axes The Y axis scale is adjusted to the current X axis sca...

Page 78: ... E after entering a value will switch the cursor position to Y_Fact Enter the required zooming factor and press E 4 To go back to the ZOOM menu press the Z key C POWER 1 x2 Use this zooming tool when the equation contains a form of x2 2 x 1 Use this zooming tool when the equation contains a form of x 1 3 x Use this tool to zoom correctly when the equation contains a form of x D EXP 1 10X Use this ...

Page 79: ...when the equation contains an inverse hyperbolic sine function 5 cosh 1 X Use this when the equation contains an inverse hyperbolic cosine function 6 tanh 1 X Use this when the equation contains an inverse hyperbolic tangent function G STO Under this menu item there is one tool that enables the storing of graph window settings 1 StoWin By selecting this sub menu item the current graph window setup...

Page 80: ... present X Y coordinates 2 Trace the graph using the or keys The key decreases the value of x while the key increases it 3 Pressing the U key again will redraw the graph with the cursor at the center of the screen If the cursor is moved beyond the range of the screen pressing the U key will redraw the screen centered around the cursor 4 When done press the C key to escape the tracing function If m...

Page 81: ...2 to select 2 Param Be sure that the other settings are as shown on the right To exit the SETUP menu press C 3 Press Y to go to the Graph Equation Entry window 4 Enter 16cos t for X1T Press E when done entering 5 Enter 9sin t for Y1T Press E when done entering Note The right side variable is automatically set to T When the X key is pressed within the Graph Equation Entry window it will enter the v...

Page 82: ...s elevation angle θ Example Draw a graph r 16cos θ sin θ 1 Press The SETUP menu appears 2 Press E to select E COORD then press 3 to select 3 Polar Be sure that the other settings are as shown on the right To exit the SETUP menu press C 3 Press Y The Graph Equation Entry window will appear 4 At the first entry row R1 enter 16cos θ sin θ Press E 5 Press G to draw the graph Press Z then press 6 to se...

Page 83: ... Using the sequence 1 2 4 8 16 32 as an example this means u n 2 n explicit representation u n 2 u n 1 recursive representation In f G TYPE five different settings are pos sible for drawing sequences The default setting is Time If the expected graph is not drawn or the error message Invalid appears this may be caused by an incorrect setting for TYPE For base n Time The values of n are plotted alon...

Page 84: ... G TYPE 2 Time 3 By pressing Y you now enter the input window for sequence equations The cursor is placed on the first line u n pressing C will delete existing entries and the cursor will be moved to the right side of the equation 4 Input 2 n Use the X key to input n And input 1 for u nMin 5 Select Z A 1 for the automatic zoom function in order to set suitable window settings automatically 6 Using...

Page 85: ... uv 2 Press Y and input the equation 2 0 9 n 1 in the v n line And input 1 for v nMin 3 Select Z A 1 for the automatic zoom function in order to set suitable window settings automatically Using U you can now read concrete values of both sequences If a third sequence equation is input in w this can be compared with the first sequence using TYPE setting 4 uw and using setting 5 vw with the second se...

Page 86: ...ss f G 1 to select Web 2 Press Y and input the equation in the u n line Because this is a recursive representation a value for u nMin must be input 3 If the lower four lines still contain entries move the cursor down and delete them using C 4 Select Z A 1 for the automatic zoom function in order to set suitable window settings automatically Using U you can now read concrete values of the sequence ...

Page 87: ...et to Polar If not this will need to be changed accordingly Also make sure the angle unit B DRG is set to Rad Otherwise the graph will not be drawn correctly Press f press F to select F CURSOR and 2 to select 2 PolarCoord 2 Press Y to verify the previously entered polar graph equation then press G to draw the graph Adjust the view by using Z menu items 3 Press k 4 Press 1 to select 1 Value The gra...

Page 88: ...tsct With this tool the intersection s of two or more graphs can be found where the flashing cursor will be placed When the intersection is found then the X Y coordinates of the intersection will be displayed at the bottom of the screen If there is more than one intersection the next intersection s can be found by selecting the tool again Note If there is only one graph equation entered there will...

Page 89: ...laces the flashing cursor at that position If there is more than one Y_zero the next Y_zero can be found by selecting the tool again Note If the graph has no Y_zero an error message will be displayed 6 Y_Incpt Finds an Y intercept of the given graph and places the flashing cursor at that position Note If the graph has no Y intercept an error message will be displayed Note The result may be differe...

Page 90: ...raph equation Y1 x2 5 2 Press k 8 3 Move the cursor to the point of lower and press E The line is drawn between the point of lower and X axis 4 Move the cursor to the point of upper and press E The calculation result is displayed and shaded on the graph Note In the step 3 and 4 it is also possible to input the X value and press E ...

Page 91: ... are displayed on the graph screen in the trace mode etc To not display the equations on the graph select 2 OFF by pressing 2 at this menu item C Y The numeric derivative dx dy can be displayed on the graph screen in the trace mode etc To activate this function select 1 ON by pressing 1 at this menu item D AXIS The graph axis can be set invisible with this menu item To hide the X Y axis of the gra...

Page 92: ...e G TYPE menu will not appear in the other modes 1 Web A web graph plot mode where x u n 1 and y u n 2 Time Time graph plot mode where x n and y u n v n w n default 3 uv A uv mode where x u n and y v n 4 uw A uw mode where x u n and y w n 5 vw A vw mode where x v n and y w n Note u n v n and w n indicate the n th term of the se quences ...

Page 93: ...metric coordinate system Tmin Tmax Minimum and maximum values for T respectively Tscale Cursor pointer step value for tracing Others Same as rectangular coordinate system Polar coordinate system θmin θmax Minimum and maximum angle for θ respectively θstep Cursor pointer step value for tracing Others Same as rectangular coordinate system Sequential coordinate system nMin nMax Minimum and maximum va...

Page 94: ...table The variable X is always displayed in the left end column The 10 digit value in the column where the cursor is currently located is displayed on the bottom line of the screen Move the cursor using Non input equation numbers and equations invalid for graphing will not be displayed in the above table Parametric coordinate system The variable T is displayed in the left end column The columns X1...

Page 95: ...digit value in the column where the cursor is currently located is displayed on the bottom line of the screen The cursor can be moved using Non input equation numbers and equations invalid for graphing will not be displayed in the above table Setting a table To display the table press t Table setting allows you set how to input data for a table Press y to enter the table setting screen The cursor ...

Page 96: ...X Y2 X2 and Y3 X2 3 1 Press y and _ 5 E 1 E 2 Press t If the cursor is on the top or bottom line of the table or can still be used The table contents will move to become visible in the display area Example Create a table in the User mode under the above conditions 1 Press y and E 0 E 1 E 2 Press t Blank table will appear 3 Press 2 E _ 3 E to enter X values An automatically created table in the Use...

Page 97: ...B POINT menu item A DRAW The tools in this menu add lines circles additional graphs and text on the graph screen The tools below can be accessed from the GRAPH window or any other windows such as the Graph Equation Entry window and Calculation screen Most of these tools such as Line can be entered directly onto a graph from the cursor point 01 ClrDraw Clears all items on the graph window EXCEPT fo...

Page 98: ...to end at 8 8 2 Enter 1 2 8 8 right after the Line object then close the expression with 3 Press E The GRAPH window will appear with the specified line drawn on the graph Note If you enter 0 for the 5th element of Line function e g Line 1 2 8 8 0 and press E you can clear the specified line 02 Line Draws a line according to the given X Y coordinates of a start end point Note This tool can be used ...

Page 99: ... 3 Move the flashing cursor on the screen to set the starting point of the line Note The pixel increment can be set within the ZOOM menu While A ZOOM is selected choose 7 Dec to set each pixel size to 0 1 0 1 or 8 Int to set to 1 1 4 When the starting point is set press E to anchor the location 5 Move the cursor to indicate the end point of the line When set press E to finalize the line drawing 6 ...

Page 100: ...to move the flashing cursor to the appropriate position 3 Press E to draw the line H_Line y value Draws a horizontal line y value on the graph window Example Draw a horizontal line of y 5 1 Press d A 0 3 and enter the value 5 03 H_line Draws a horizontal line on the graph window From the Calculation screen From the GRAPH window ...

Page 101: ...he graph window From the Calculation screen V_Line x value Draws a vertical line x value on the graph window Example Draw a horizontal line of x 3 1 Press d A 0 4 and enter the value 3 V_Line Example Draw a vertical line manually 1 Press d A 0 4 2 Use the cursor navigation keys to move the flashing cursor to the appropriate position 3 Press E to draw the line 05 T_line Draws a tangential line at t...

Page 102: ... to specify a function equation from Y0 to Y9 if stored N_ line Y1 1 T_line Example Draw a tangential line by manually specifying the point 1 Select T_Line 2 Use to move the flashing cursor on the targeted graph line Use to select a graph to draw the tangential line 3 When the point is set at the tangent point press E It is also possible to input the x value and press E Note The equation of the ta...

Page 103: ...ation may include a margin of error 07 Draw Draw equation Draws an additional graph based on a given expression Example Draw the graph of y 3x2 4x 2 1 Select Draw 2 Enter 3x2 4x 2 on the line 3 Press E Note This tool can be used with rectangular coordinate graphs only 08 Shade Shade equation1 equation2 lower value upper value Draws two graphs and shades the area between the two If the x range is s...

Page 104: ... screen Circle x coordinate of center y coordinate of center radius Example Draw a circle with center at 2 3 and of radius 7 1 Select Circle 2 Enter 2 3 7 on the line 3 Press E Note Before drawing a circle press Z A 6 to set the X Y coordinates to square Example Shade the area enclosed by y 1 4 x2 8 and y x within the range of 2 x 3 Before starting operation Select ClrDraw to clear the graphs prev...

Page 105: ...he circle is drawn at the location 11 Text Text column row strings Enters a text string at a given coordinate Text column row variable Draw the value of A Z θ Example Draw HELLO on the graph at column 2 row 1 Text 2 1 HELLO Note Use M E 3 to enter double quotes Column and row definitions for text input Refer to the following diagram to specify the coordinates where you wish to start writing the te...

Page 106: ...iven coordinate Deletes the point when it is displayed and draws the point when it is not displayed Note Lines points and curves drawn by the Draw menu are handled as pictures Therefore they cannot be traced Graphs drawn by the Draw menu are automatically cleared if any screen settings are changed To save the graph use the StoPict menu B POINT Utilize these tools to manage point drawing and deleti...

Page 107: ...ocation indicated by column and row 7 PxlTST PxlTST column row Returns 1 if a pixel point is present at a given screen location indicated by column and row Returns 0 if no pixel point exists 4 PxlON PxlON column row Draws a pixel point at a given screen location indicated by column and row The column and row definitions are as follows Column 0 to 132 Row 0 to 64 0 0 126 0 0 62 126 62 column 132 Th...

Page 108: ... mode is selected in this example Use the cursor keys to select the required line type and press E C ON OFF Sets the visibility status of a given graph number 0 9 1 DrawON DrawON equation number 1 or DrawON Sets the specified graphs visible If no argument is given then all graphs will be set visible 2 DrawOFF DrawOFF equation number 1 or DrawOFF Sets the specified graphs invisible If no argument i...

Page 109: ...ber 0 9 Saves the graph data Example Store the current graph data in location 1 Note The lines graphs and pixels drawn with the A DRAW tools will not be saved here use StoPict under F PICT instead 2 RclGD RclGD number 0 9 Recalls the saved graph data Example Call back the previously stored graph data from location 1 Note Attempting to call back graph data from an empty location will result in an e...

Page 110: ...e graph equations will not be saved or recalled with these tools 1 StoPict StoPict number 0 9 Saves the pixel data Example Store the current graph including the drawings in location 1 2 RclPict RclPict number 0 9 Recalls the saved pixel data Example Call back the previously stored graph data from location 1 ...

Page 111: ... appropriate position 5 Press z E 6 Press 1 to select Y1 7 When the value is set press the G key The graph will be redrawn 8 Let s add another inequation so that the area where the two inequality overlap can be shaded Press the Y key and enter another simple graph equation such as X 4 for Y2 9 Now return to the SHADE menu by pressing d and G Press 1 to select 1 SET 10 Within the Set shade window a...

Page 112: ...while showing the X Y values in a table on the right The cursor is positioned on the table and can be scrolled up down using the or keys Graph and table Graph and equation When are pressed on the graph screen the graph and table are displayed on the same screen When are pressed on the equation input screen the graph and equation are displayed on the same screen ...

Page 113: ...or The table or equation on the right of the screen is also changed accordingly The table on the split screen does not relate to the table settings on the full screen table The table on the split screen is displayed in units of trace movement amount based on the cursor pointer position on the graph screen When the full screen table is displayed by pressing t a different table may appear on the scr...

Page 114: ...f numeric value sets can be substituted while referring to the graph drawing screen This clearly shows the changes in the graph depending on numeric values For example the graph for Y1 AX3 BX2 CX2 D is drawn by substituting numeric values for variables A B C and D of the equation 22 kinds of variables characters A to Z except for R T X and Y can be used for the substitution feature Up to seven var...

Page 115: ...raph for Y1 2X2 is drawn Since B and C have no values they are ignored At this time the graph for Y2 is also drawn Y2 also uses variable A which is used in Y1 Therefore the drawing of the graph for Y2 is also valid If you need to draw only the graph for Y2 it is necessary to change variables characters or make the graph drawing for Y1 invalid 3 Press 1 E 1 is input to B The graph is changed from Y...

Page 116: ...s sharp Move the cursor accordingly and substitute other numeric values for variables to view how the graph changes The trace function cannot be used in the substitution feature When U is pressed the full screen graph will appear 2 Press h to return to the equation display screen The equation is written based on the last numeric values input on the substitution feature screen Once h have been pres...

Page 117: ...red To enter the SLIDE SHOW press To exit the SLIDE SHOW feature press 1 Try it Make a SLIDE SHOW named CUBIC to explain how to draw the graph of a factor base cubic function and explain how to solve cubic equations using factors Use the following cubic function as a sample y x 3 x 1 x 2 Create a new SLIDE SHOW 1 Set up a SLIDE SHOW file Press to enter the SLIDE SHOW menu 2 Press C E to select C N...

Page 118: ...e SLIDE SHOW 7 Press G Note You cannot capture an image while drawing If the cursor flashes at the up per right corner of the screen the calculator is busy processing tasks The SLIDE SHOW fea ture cannot capture images during this period A captured image cannot be recaptured 8 After the graph is drawn press n The image will be stored on page 2 of the SLIDE SHOW CUBIC 9 Press to split the screen be...

Page 119: ...B to select B PLAY A list of saved SLIDE SHOW projects will be shown 2 Select the one you want to play back either by using the shortcut key strokes or by moving the cursor Select the item and press E The first page of the SLIDE SHOW will appear The number appearing at the upper right of the screen is the slide number 3 Use the key or E to display the next image press the key to show the previous ...

Page 120: ... to store screen images D SELECT Enables you to select a SLIDE SHOW file to be edited and display its name in the A CURR window E EDIT Enables you to move delete captured images or change the file name of the current SLIDE SHOW Note If no SLIDE SHOW file is stored selecting any of the following sub menu items will result in an error 1 MOVE With this sub menu tool a selected screen image can be mov...

Page 121: ...d image captured in the SLIDE SHOW 1 While in the SLIDE SHOW menu press E to select E EDIT then press 2 to select the 2 DEL sub menu item 2 With the and cursor keys select the image you wish to delete 3 Press E to remove the selected image from the SLIDE SHOW file 3 RENAME Use this sub menu tool to rename the SLIDE SHOW 1 In the SLIDE SHOW menu press E to select E EDIT then press 3 to select the 3...

Page 122: ...y You can solve the above system of linear equations by using a matrix CONCEPT 1 Enter the coefficients as elements in a matrix 2 Use the rrowEF function to obtain the reduced row echelon form Three sheaves of the first class crop two of the second and one of the third are sold for 39 dollars Two of the first three of the second and one of the third for 34 dollars And one of the first two of the s...

Page 123: ...irst row of 3x 2y z 39 The cursor will automatically position itself at the beginning of the second row 5 Press 2 E 3 E 1 E 3 4 E to enter the second row of 2x 3y z 34 6 Press 1 E 2 E 3 E 2 6 E to enter the third row of x 2y 3z 26 7 Press to return to the calculation screen Matrix A is now set 1 Press m to enter the MATRIX menu 2 Press B to select B EDIT and then 1 to select 1 mat A PROCEDURE Sele...

Page 124: ...n be defined Define dimensions 2 Enter the row dimension number and press E Cursor moves to the column dimension 3 Enter the column dimension number and press E The matrix will be displayed with null values See below It is not required to press E when the dimension number is 2 digits Up to 5 rows by 3 columns of elements can be displayed on the screen Press to scroll the matrix Use row and column ...

Page 125: ...ta input Note Elements in Matrix can be specified using the NAME menu of the MATRIX menu such as mat A 1 1 Editing keys and functions Move the cursor within the current row or scroll horizontally Move the cursor within the current column or scroll vertically On the top row moves the cursor to the dimensions field E ENTER the number in the cursor position and move the cursor to the next position C ...

Page 126: ... row dimension of the second matrix Example 1 Press C 2 Press m A 1 m A 2 3 Press E To add or subtract matrices the dimensions must be the same Example 1 Press C 2 Press m A 1 m A 2 3 Press E 3 Normal Matrix Operations Many functions can be used for calculations of matrices and scalars Examples of each calculation are as follows Matrix Matrix Matrix Matrix Matrix Matrix Square of Matrix ...

Page 127: ...tor has three Matrix calculation menus OPE MATH and Examples of each calculation are as follows Calculations using OPE menus 01 dim dim matrix name Returns the dimensions of the specified matrix Example Check the dimensions of mat A Newly define or change the dimensions to 2 3 for Mat C 02 fill fill value matrix name Fills each element with a specified value Example Enter the value 5 into all the ...

Page 128: ...atrices must have the same number of rows Example Create a new matrix with matrix A augmented by matrix B 05 identity identity dimension value Returns the identity matrix with specified value of rows and columns Example Create the identity matrix of 3 rows 3 columns 06 rnd_mat rnd_mat number of row number of column Returns a random matrix with specified values of rows and columns Example Create a ...

Page 129: ... Add the 2nd row data to the first row of matrix E e1j e1j e2j 09 row_mult row_mult multiplied number matrix name row number Returns the scalar multiplication of elements in a specified row Example 3 each element of 1st row of mat E e1j 3 e1j 10 row_m p row_m p multiplied number matrix name row number row number Returns the scalar multiplication of elements in a specified row and adds result to el...

Page 130: ... list name 1 list name n Example Make List 1 and List 2 by using the 1st and 2nd columns of matrix E respectively mat list matrix name column number list name Example Make List 3 by using the 3rd column of matrix E 12 list mat list mat list 1 list n matrix name Creates a matrix using specified lists This function is the same as list mat in the List OPE menu Note The list items must be prepared pri...

Page 131: ...ns transposed to rows and the rows transposed to columns Example Transpose rows and columns of matrix B 3 rowEF rowEF matrix name Returns the row Echelon Form of the specified matrix The number of columns must be greater than or equal to the number of rows Example Give the row echelon form of matrix B 4 rrowEF rrowEF matrix name Returns the reduced row Echelon Form of the specified matrix The numb...

Page 132: ...r expression for each element Separate each element with commas 4 Press m 2 to indicate the end of the first row 5 Repeat above steps 2 to 4 to enter all the rows 6 Press m 2 to indicate the end of the matrix 7 Press E The matrix will be displayed Using a Matrix in an expression To use a matrix in an expression you can do any of the followings Select a matrix from the m NAME menu Enter the matrix ...

Page 133: ...roximately 0 75 seconds to react to a situation before actually applying the brakes Once the brake pedal is depressed it takes additional time for the car to come to a complete stop Here is the equation used to compute total stopping distance on dry level concrete The reaction time distance in feet 1 1 times the speed in miles per hour The braking distance 0 06 times the speed squared y 1 1 v 0 06...

Page 134: ... y and press E 6 Press 1 1 1 0 06 1 y 7 Press E 8 List 87 140 205 282 371 472 will appear So the solutions are Car speed Stopping distance 30 miles hour 87 feet 40 miles hour 140 feet 50 miles hour 205 feet 60 miles hour 282 feet 70 miles hour 371 feet 80 miles hour 472 feet Store the list in L1 4 Press R 1 5 Press E to store the list in L1 Enter the equation using L1 ...

Page 135: ...sible Both lists must contain the same number of elements The following examples use the L1 and L2 values stored in the previous section 2 Creating a list A list is a series of values enclosed by braces and is treated as a single value in calculations or an equations The calculator has 6 storage areas for lists from L1 to L6 You can edit or access lists by pressing 1 to 6 numeric keys from 1 to 6 ...

Page 136: ... results extend beyond the display to the right Use to scroll left or right respectively Calculate 10 L1 and store the results in L3 1 Press 10 1 R 3 E Calculate the sine of L3 Calculate L1 L2 3 Press 1 2 E Change the 3rd element of L1 to 3 4 Press _ 3 R 1 3 A 1 E Append the new value 7 to L1 as the 5th element Calculate the root of L2 6 Press 2 E ...

Page 137: ...ing order 2 sortD sortD list name Sorts lists in descending order Example Sort the above list L1 in descending order Note sortA list name 1 list name 2 If two or more lists are entered separated by commas a sort is performed on the first list as a key and the following lists are sorted in the order corresponding to the elements in first list key list Example Store lists 2 7 4 and 3 4 1 in L1 and L...

Page 138: ...ed number Example Set the dimension of list L6 to 4 All the elements are initially 0 This operation overwrites the existing list dimensions The existing values within the new dimensions remain as they are 4 fill fill value list Enter the specified value for all the items in the specified list The dimension of the list must be set beforehand Example Set the dimension of list L6 to 4 and substitute ...

Page 139: ...nd all odd numbers from 1 to 21 the 3rd all even numbers from 0 to 10 If increment is omitted the default value 1 is used 6 cumul cumul list Sequentially cumulates each item in the list li l1 l2 li where li is the i th item of the list Example Set the list L1 to 4 2 7 and obtain the cumulated list L1 Cumulate the above result 7 df_list df_list list Returns a new list using the difference between a...

Page 140: ...ied matrix name Example Make a matrix mat A using list L1 as the first column and list L2 as the second column The dimensions of the two lists must be the same Complex numbers cannot be used with this function This function is the same as list mat of the OPE menu in the MATRIX function 0 mat list mat list matrix name list name 1 list name n mat list matrix name column number list name Makes lists ...

Page 141: ...inimum value of the list L1 2 max max list Returns the maximum value in the list Example Calculate the maximum value of the specified list L2 Note min list 1 list 2 max list 1 list 2 If two lists are specified in parenthesis separated by a comma then a list consisting of minimum or maximum values is returned 3 mean mean list frequency list Returns the mean value of items in the specified list Exam...

Page 142: ...ange of items in the list to sum sum L1 1 2 means sum the 1st to 2nd items of the list L1 sum L1 2 means sum all items from the second to the last of the list L1 6 prod prod list start number end number Returns the multiplication of items in the specified list Example Calculate the multiplication of items in the list L1 You can specify the range of items in the list to multiply prod L1 1 2 means m...

Page 143: ...f the specified list items Example Calculate the variance using the list items of list L2 9 P_stdDv P_stdDv list frequency list Returns the population standard deviation of the specified list items Example Calculate the population standard deviation using the list items of list L2 Standard deviation and variance Standard deviation s Variance Population standard deviation σ where n number of list i...

Page 144: ...e1 list name2 Calculate the cross product vector product of two lists Example Calculate the cross product of L1 and L2 Note Calculation range up to 3 dimensional vector The dimensions of the vectors have to be identical 2 DotPro DotPro list name1 list name2 Calculate the dot product Example Calculate the dot product of L1 and L2 Note Calculation range up to 9 dimensional vector The dimensions of t...

Page 145: ...L6 to enter the equation 1 Set the lists L1 to L3 as follows 3 2 L1 5 3 L2 2 4 L3 and then 2 Enter the equation as follows Y1 L1x2 L2x L3 6 Using L_DATA functions The calculator can store up to 10 list groups in memory L_DATA 0 to L_DATA 9 You may store or recall any one of these list groups Each list group can contain up to 6 lists 1 StoLD StoLD natural number 0 9 Stores the current group of list...

Page 146: ...ts of the lists Though the STAT menu was originally designed for Statistics function calculations the List Table is very useful for entering or editing list items How to enter the list 1 Press S A E The list table will appear The first column indicates the order number of each list and the 2nd column corresponds to the list L1 the 3rd to the L2 and so on 2 Move the cursor to the target cell and en...

Page 147: ...new value and press E The new value will be stored in the target cell The display on the bottom line relates to the cell where the cursor pointer is located Though any number can be entered in a cell the bottom line of the screen can display up to a maximum of 10 digits excluding exponents and the cell can display up to a maximum of 8 digits including exponents ...

Page 148: ...5 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Sunday 98 72 55 3 6 24 15 30 59 72 55 43 21 10 150 151 135 108 204 253 232 251 75 30 Monday 32 8 12 2 4 19 32 72 95 91 123 201 184 108 95 72 45 38 75 111 153 90 84 35 The following statistical and regression features are available Statistical calculations such as means and standard deviations Graphing statistical data Plotting regression c...

Page 149: ...will appear in position L2 1 and the cursor will move to the second row 10 Input 72 for hour 02 and press E Continue the procedure to the end of the data 11 Press to move the cursor to the top line of L3 12 Input 32 for hour 01 and press E 13 Continue the procedure to the end of the data 1 Press or to move the cursor pointer to the target cell 2 Input the correct number and press E Now we can plot...

Page 150: ...ress to move the cursor to the next line ListX 7 The default list name for ListX is L1 If another list name is set press 1 to enter L1 8 L1 is set to be used for x axis items 9 Press to move the cursor to the next line Freq 10 Press 2 to enter L2 11 Press to move the cursor to the next line GRAPH 12 The graph format defaults to histogram so if that is what is required this does not need to be chan...

Page 151: ... menu will appear 2 Enter the values as shown in the diagram to the right Ymax is determined by the maximum access number 253 at 20 00 on Sunday 3 Press G You can compare up to 3 statistical data by setting PLOT2 PLOT3 to on 1 Press A E and move the cursor to GRAPH 2 Press again 3 Press B and 1 broken line with circle dots 4 Press G The histogram is now changed to a broken line graph 5 Press q to ...

Page 152: ... mode and displays a list table B OPE Calculation menu for operations such as ascending or descending sort C CALC Obtains statistical values D REG Calculates regression curves E TEST Statistical hypothesis tests F DISTRI Distribution menu items Use a list table to enter the statistical data press S to access Up to 999 elements can be used for each list though the amount of data able to be entered ...

Page 153: ...e x n Sample number xmin Smallest value of sample x Q1 First quartile of sample x Med Median of sample x Q3 Third quartile of sample x xmax Largest value of sample x 2_Stats 2 variable x y statistical calculations The following values are added to the 1 variable statistic calculations y _ Mean of sample y sy Standard deviation of sample y σy Population standard deviation of sample y Σy Sum of samp...

Page 154: ... on the top line of the screen followed by the cursor 3 Press 2 to enter L2 and press E All the statistical values will be displayed on the screen 4 Press or to scroll the screen 5 Press S to display the statistics menu 6 Press C and then 1 1_Stats will be displayed on the bottom line of the screen followed by the cursor 7 Press 3 to enter L3 and press E Hours 01 02 03 04 05 06 07 08 09 10 11 12 1...

Page 155: ...ress E All the statistical values will be displayed on the screen 4 Press or to scroll the screen ANOVA The ANOVA feature performs an analysis of variance to compare up to six population means 1 Press C and S to display the statistics menu 2 Press C and then 3 ANOVA _ will display on the top line of the screen 3 Press 2 3 4 Press E The answer will appear on the screen Each character represents the...

Page 156: ...iagram and XY line Broken line plot normal probability plot modified box plot scatter diagram and XY line can use 3 different types of points circle cross and square Statistical graph types overview chart PLOT1 PLOT2 PLOT3 POINT POINT POINT Histogram Broken line plot Normal probability plot Normal distribution plot Box plot Modified box plot Pie chart Scatter diagram XY line 1 Graph Types A bar gr...

Page 157: ... of the standardized normal distribution with the statistical data x on the X axis or Y axis If the points plot almost linearly it indicates that the data is of normal distribution The distance between the dots is set by the Xscl The Xscl can be changed between 1 and 64 Use the Window Setting Menu to change the figure See page 74 You cannot set the frequency in the Normal probability plot The stat...

Page 158: ...lue xmin of the sample x B The tip of extension which is defined by Q3 Q1 x 1 5 C The first quartile Q1 D Median Med of the sample x E The third quartile Q3 F The tip of extension which is defined by Q3 Q1 x 1 5 G The maximum value xmax of the sample x Statistical data on the outside of the extension are indicated by points selectable from circle cross or square The length of the extension from th...

Page 159: ...g cursor depend on the Window settings The values are stored in variables A to H As all the displayed values are rounded down in the percentage display mode the total percentage may not be 100 A two dimensional plot graph using two samples x y Two sets of statistical data are required for the scatter diagram Three types of points are selectable from circle cross and square Two statistical data lis...

Page 160: ...ple x of the statistical graph 4 Press 1 1 SET 5 Enter the appropriate value for Lower limit and press E 6 Enter the appropriate value for Upper limit and press E 7 Press D D Limit and press 2 2 LimON E to display a line that indicates the mean value of sample x as well as the upper and lower limit lines 8 Press D 3 3 LimOFF and E not to display the lines Upper and lower limit values are displayed...

Page 161: ...pointer will appear on the top left corner of the first bar If you press or the cursor pointer sequentially jumps between top left corners of the bars X and Y values are displayed at the bottom line of the screen Use or to change between graphs to trace After pressing U the cursor pointer will appear on the Med value of sample x If you press or the cursor pointer sequentially jumps among specific ...

Page 162: ... the sortD menu item in List functions See page 136 for details 3 SetList SetList list name 1 list name 2 Changes the list order as specified Example To change the order of lists in order of L2 L3 L1 Press E to execute Each list must be separated by a comma If only a single list name is specified the specified list moves to the left end of the table After changing the list order execute SetList wi...

Page 163: ...sion line linear regression Formula y ax b Parameters a b r r2 03 Rg_ax Rg_ax list name for x list name for y frequency list equation name to store Finds the regression line linear regression Formula y ax Parameters a r2 04 Rg_a bx Rg_a bx list name for x list name for y frequency list equation name to store Finds the regression line linear regression Formula y a bx Parameters a b r r2 05 Rg_x2 Rg...

Page 164: ...tore Finds the regression curve using the natural logarithm natural logarithm regression Formula y a b ln x Parameters a b r r2 09 Rg_log Rg_log list name for x list name for y frequency list equation name to store Finds the regression curve using the common logarithm common logarithm regression Formula y a b log x Parameters a b r r2 10 Rg_abx Rg_abx list name for x list name for y frequency list...

Page 165: ...tic list name for x list name for y frequency list equation name to store Finds the regression curve using the logistic function logistic regression Formula y c 1 ae bx Parameters a b c 15 Rg_sin Rg_sin iterations list name for x list name for y frequency list period equation name to store Finds the regression curve using the sine function The calculator will fit a sine curve for unequal and equal...

Page 166: ... estimated value of y for a given value of x by applying the function determined by the regression formula Example Using above data find the estimated value for y given x 80 100 1 Press 80 100 S D 1 7 E 16 x and 17 y will be valid after executing a regression calculation excluding 2nd 3rd 4th degree polynomial logistic and sine regressions The following table shows the relationship between the tim...

Page 167: ... in an optimum range since window setting values of the graph plotting screen are automatically set using the list data 1 Press C S D 0 5 05 Rg_x2 2 Press 1 2 z A E A 1 If you enter Y1 as the last variable the obtained formula will automatically be set to the formula Y1 3 Press E The regression formula and parameters will be displayed on the screen 4 Press G The calculator will draw the scatter di...

Page 168: ... operation resid cannot be graphed when specified independently 6 Statistical Hypothesis Testing The calculator performs hypothesis tests on statistical data 1 Press S E E TEST The statistics test menu will appear 2 There are 17 options in the statistics test menu Press to navigate between pages and press or to scroll the window 3 Press the appropriate number to access a specific test The statisti...

Page 169: ... 01 χ 2 test 05 TtestLinreg 10 Ztest1prop 11Ztest2prop 14 Zint1prop and 15 Zint2prop To clear the contents entered in Freq move the cursor to the list name then press D E 01 χ 2 test Uses the sample data from a two dimensional table represented by a matrix Example If mat A 3 2 5 4 6 1 3 8 2 3 5 1 execute the χ 2 test and store the obtaining results in mat B 1 Press S E 0 1 2 Enter mat A as the Obs...

Page 170: ... to select σ1 σ2 4 Enter the values into the parameter fields 5 6 E 20 E 6 2 E 50 E 5 Press h to execute the test F Statistics p Probability 03 Ttest1samp Tests the hypothesis of population mean µ Example Test the population mean µ0 65 with the sample data of 65 6 62 8 66 0 64 5 65 1 65 3 63 8 64 2 63 5 64 4 from a given population alternate hypothesis of µ µ0 1 Enter the above statistical data in...

Page 171: ...pty 04 Ttest2samp Tests two sample means µ1 and µ2 Example Test the following two samples List 1 2 37 2 51 2 43 2 28 2 46 2 55 2 49 List 2 2 63 2 71 2 56 2 61 2 55 2 68 2 42 2 48 2 51 2 65 1 Enter the above data into lists L1 and L2 respectively 2 Press S E 0 4 The parameter input screen will appear 3 Enter the appropriate value into each field If no Freq specification data is input an initial Fre...

Page 172: ...lists X and Y into lists L1 and L2 respectively 2 Press S E 0 5 The parameter input screen will appear 3 Enter the appropriate value into each field Equation items may not be required If a linear regression calculation has been executed using the data and the function equation has been stored in Y0 to Y9 input that equation number for the equation items 4 Press h Answers are displayed on the scree...

Page 173: ...3 Enter the C level value of 0 99 4 Set the List to L1 and press E 5 Press h Answers are displayed on the screen where sx indicates the sample standard deviation If you enter a value from 1 to 100 for the C level it will be changed to the input mode In the numerical value input mode n is a positive integer 07 Tint2samp Finds the confidence interval for the difference of two sample means µ1 and µ2 ...

Page 174: ...l of confidence is 99 In the numerical value input mode n1 n2 are positive integers 08 Ztest1samp Tests the hypothesis of population mean µ Example The average weight of a newly developed product is known to be 53 4 g and standard deviation σ is 4 5 Judge the validity when the average weight of 20 units is 52 4 g x Set the input method to value input mode 1 Press S E 1 7 E 2 Press S E 0 8 The para...

Page 175: ... Answers will be displayed on the screen where z indicates the test statistic and p indicates the p value of the test 09 Ztest2samp Tests the equality of two sample means µ1 and µ2 Example Test µ1 µ2 where x _ 1 77 3 σ1 3 4 n1 30 and x _ 2 75 2 σ2 2 8 n2 20 Set the input method to value input mode 1 Press S E 1 7 E 2 Press S E 0 9 The parameter input screen will appear 3 Enter the appropriate valu...

Page 176: ...The test will be conducted using hypothesis prop P0 x is the number of successes observed and n is the number of trials where n is a positive integer 2 Enter the appropriate value into each field 3 Press h p Success probability obtained from the sample data 11 Ztest2prop Executes a comparative test for two success probabilities P1 P2 Example Test the equality of P1 and P2 given the sample data n1 ...

Page 177: ...rd deviation σ is 4 5 Given the average weight of 20 units is 53 4 g x find the confidence interval of the data where the level of confidence C level is 0 95 Set the input method to value input mode 1 Press S E 1 7 E 2 Press S E 1 2 The parameter input screen will appear 3 Enter the appropriate value into each field 4 Press h Answers will be displayed on the screen where the numerical value within...

Page 178: ...ppropriate value into each field 4 Press h Answers will be displayed on the screen where the numeric value within indicates the confidence interval of µ1 and µ2 at a confidence level of 90 n1 and n2 are positive integers 14 Zint1prop Finds the confidence interval of the success probability of a population from the success probability obtained from sample data collected from a population Example A ...

Page 179: ...cess probability obtained from the two sets of sample data collected from two different populations Example Find the confidence interval of the success probability P1 P2 at a confidence level of 0 9 for the two sets of sample data n1 50 x1 16 and n2 20 x2 5 1 Press S E 1 5 The parameter input screen will appear 2 Enter the appropriate value into each field 3 Press h 4 Answers will be displayed on ...

Page 180: ...01 pdfnorm pdfnorm value mean standard deviation Finds the probability density of the specified value x for the normal distribution N µ σ2 A list cannot be used When mean µ and standard deviation σ are omitted µ 0 and σ 1 are applied Example Find the nominal distribution probability density for x 65 when the normal distribution of the test score averages is 60 with a standard deviation of 6 02 cdf...

Page 181: ... pdfT pdfT value degree of freedom Finds the probability density of a specified value x for the T distribution with n degrees of freedom A list cannot be used Limitations Degree of freedom 140 Degrees of freedom is a positive real number If decimal values are used for the degrees of freedom the calculator uses the closest integer of the given degree of freedom An error may occur when an extremely ...

Page 182: ...of freedom Finds the probability density of a specified value x for the χ 2 distribution with n degrees of freedom A list cannot be used Limitations Degree of freedom 141 Degree of freedom is a positive real number Example Find the probability density of χ 2 distribution with 15 degrees of freedom when x 6 5 07 cdfχ2 cdfχ2 lower limit upper limit degree of freedom Finds the χ 2 distribution probab...

Page 183: ...m Example Find the probability density for the F distribution generated with degrees of freedom 15 and 10 when x 3 09 cdfF cdfF lower limit upper limit degree of freedom of numerator degree of freedom of denominator Finds the F distribution probability of a specified range x for the F distribution with two independent degrees of freedom m and n A list cannot be used Limitations Degree of freedom 6...

Page 184: ...al distribution A list cannot be used except for success numbers When the success number is not specified the calculation is executed by entering values from 0 to the trial number and displays the list Example Find the probability of range up to x 7 for the F distribution generated with degrees of freedom 15 and 10 When using function terms please note that values for the number of trials and for ...

Page 185: ...ty density of a specified value x for the geometric distribution Limitations Success probability is 0 p 1 Example Find the probability density of a geometric distribution of success at the 26th time with success probability of 5 6 15 cdfgeo cdfgeo success probability value Finds the probability of a specified range of x for the geometric distribution Limitations Success probability is 0 p 1 Exampl...

Page 186: ... for a price of 300 000 The down payment is 100 000 Calculate the monthly payments for a 30 year loan at an annual interest rate of 5 for the remaining 200 000 A horizontal line indicates a time flow left to right divided into even sections months in this case Each section indicates a compound period and the total number of sections indicates the total number of periods for payment 1 Draw the foll...

Page 187: ...nt due at the beginning of the period In this case payment is due at the end of the period 3 Determine the inflow and outflow and place the present value PV 200 000 on the diagram We can consider the present value PV as a loan and thus inflow revenue from the customer s point of view So place the PV at the top left end of the diagram We also can consider the principal interest total Future value a...

Page 188: ...ss 12 for P Y number of payments per year and press E The payment due time is set to the end of period Payment due settings Number of payment periods Interest Present value principal sum Payment or received amount Future value principal interest total Number of payments per year Cumulative interest per year Setting the payment due time 5 Press g 6 Press C C PERIOD 7 Press 1 1 PmtEnd and press E Pa...

Page 189: ...t decimal point format set TAB to 2 and FSE to FIX Answer You have to pay 1 073 64 per month for 30 years Simple interest and compound interest There are two ways to calculate interest simple and compound In the FINANCE mode the calculator can execute compound interest calculations Example of depositing 10 000 in a bank for 3 years at an annual interest rate of 3 Period Simple interest Compound in...

Page 190: ...M SOLVER screen will appear with the cursor flashing on N 3 Press three times to move the cursor to PMT 4 Press _ 800 and E Be sure to enter the minus sign to indicate payment 5 Move the cursor to PV 6 Press h 7 PV will change to 149025 29 This indicates that the total amount over 30 years will be 149 025 29 if the maximum monthly payment is limited to 800 Cash flow PV 300 000 down payment FV 0 N ...

Page 191: ... Compare the principal interest total when accumulating an interest of 2 18 monthly on 100 for 5 years with payment due at the beginning of the period and at the end of the period 1 Payment due at the beginning of the period 1 Press g C 2 and press E 2 Press g A E Payment due is now set to the beginning of the period 3 Enter the values 4 Move the cursor to FV and press h 2 Payment due at the end o...

Page 192: ... FV Future value principal interest total P Y Number of payments per year C Y Cumulative interest per year The contents calculated on the calculation screen do not affect the variable values in the TVM SOLVER 01 slv_pmt solv_pmt N I PV FV P Y C Y Calculates monthly payment PMT 02 slv_I slv_I N PV PMT FV P Y C Y Calculates annual interest 03 slv_PV slv_PV N I PMT FV P Y C Y Calculates present value...

Page 193: ...n 07 Irr Irr initial investment list of following collected investment frequency list assumed revenue rate Calculates the investment revenue rate where the net present value is 0 Example If the investment for the sales plan in the previous example is 28 000 how much is the investment revenue rate 12 42 is obtained as the answer thus the investment revenue rate for the above condition is 12 42 In t...

Page 194: ...emaining 200 000 08 Bal Bal number of payments decimal place to round Calculates loan balance Calculate the loan balance after 15 years 180 months 09 ΣPrn ΣPrn initial number of payments end number of payments decimal place to round Calculates the principal amount of the total payments Compare the principal amount of the total payments after 5 1 to 60 months and 10 years 61 to 120 months 10 ΣInt Σ...

Page 195: ... Eff nominal interest rate number of settlements Converts nominal interest rate to effective interest rate Example If the annual nominal interest rate is 8 how much is the effective interest rate for monthly compound interest How much is it over half a year 13 days days start month day year end month day year days day month year day month year Calculates the number of days between dates entered wi...

Page 196: ... menu will appear 3 Select the appropriate variable to use The variables in the VARS sub menu are the same as those of the TVM SOLVER feature 1 Press g D 1 E 2 Press g D 2 E 3 Press g D 3 E Each variable of the TVM SOLVER can be recalled and then reentered Reenter 400 for N instead of 360 1 Press 400 R 2 Press g D 1 E How to recall the content of N How to recall the content of I How to recall the ...

Page 197: ...ithin the SOLVER feature will also change the global value of A 1 Three Analysis Methods Equation Newton bisection and Graphic To switch your preferred analysis style 1 Go into the SOLVER menu by pressing within the SOLVER window The SOLVER menu appears with four menu items 2 While A METHOD item is selected on the left select your preferred method by pressing 1 2 or 3 Note When you enter an equati...

Page 198: ...n this window this simply indicates the value of C was previously set to 57 4 Enter 4 for variable A and 5 for variable B Press 4 E 5 E 5 When the two known values have been specified make sure that the cursor is at the value yet to be determined in this case the value of C 6 Press h to execute the SOLVER The value of C will be obtained After the solution has been found press C to return to the va...

Page 199: ...ed as a non equation format then 0 is automatically assumed at the end When done press E 3 The next screen indicates the variable X and its previously set value This value will be assumed as the starting point of the calculation segments and the Newton bisection SOLVER will find the closest approximation to the starting point Enter 0 and press E 4 Now press h to execute the SOLVER Since this canno...

Page 200: ...k to step 3 Enter the value of X then press h to execute the SOLVER again When the next window appears try entering smaller step value 0 00001 for example 8 Press E to register the step value change then h Although the value of X appears to be unchanged the margin of error will have become small enough 0 in this example to be as close to zero as possible Note As you may well know there may be more...

Page 201: ...e as 0 and press E The right side value of the equation is now set Note Unlike in the Newton bisection method the X value will not be assumed as the starting point for the Graphic method 4 Before proceeding further you will need to set the SOLVER to the Graphic method Press to call up the SOLVER menu and press A for A METHOD then 3 for 3 Graphic The Graphic method is now set 5 Press h to proceed 6...

Page 202: ...he analysis as well as the graphical representation of the equation Note that while the cursor flashes at the upper right corners of the screen the calculator is busy processing tasks 8 When the processing is complete you will get the first value of X the smallest with a flashing star on the graph at the crossing point To obtain the next X value press k Note To enlarge a part of graph after the so...

Page 203: ... can be entered To enter numbers press A The equation name should consist of 8 characters numbers or less 4 When done press E The screen goes back to the SOLVER function screen Saved SOLVER expressions can also be renamed 1 Go to the SOLVER menu by pressing and press D to select the D RENAME sub menu 2 A list of saved equation names appears in the sub menu Select the equation name you wish to chan...

Page 204: ...quation is called back Note Any changes unsaved prior to recalling will be lost Also be aware that any changes to the recalled equation will not be retained unless saved manually Functions of the SOLVER feature Functions of the SOLVER feature are as follows ab c a b x2 x 1 ab a log ln log2 10x ex 2x sin cos tan sin 1 cos 1 tan 1 sinh cosh tanh sinh 1 cosh 1 tanh 1 sec csc cot sec 1 csc 1 cot 1 int...

Page 205: ...ers cannot be used in programming 1 Try it Display a message HELLO WORLD on the display 1 Press P The program menu screen will appear A EXEC Executes the selected program B EDIT Opens a stored program file C NEW Creates a new program file D V_INDX Show variables which are used in the programs 2 Press C E A new program window will open 3 Input the program name HELLO on the top line of the screen Up...

Page 206: ...habetic lock mode 11 Type HELLO WORLD Up to 160 alphanumeric characters can be input per line Strings of up to 158 characters maximum can be entered per line excluding commands because each command is regarded as a single character When a line exceeds the width of the screen the display will shift to the left 12 Press E The cursor will move to the next line and the data input will be stored Store ...

Page 207: ...r characters Press to use an ALPHA LOCK mode to input a series of alphabetical characters In general only a single command can be input per line After pressing E or the line will be stored in memory Otherwise it is not stored Be sure to store the all lines by pressing E or before quitting editing pressing q Blank lines are ignored during execution You can include blank lines to gain better readabi...

Page 208: ...rmula MX B Index of variables in the programs Programs can overwrite variables that you are using e g in the calculation screen Here you can check for which variable names this is the case Press P D and then select the program title The index of variables which are used in the selected program is displayed The subjects of the index are as follows A Z θ L1 L6 mat A mat J Press or to display the pre...

Page 209: ... the SET UP menu settings Character strings displayed by the print command will break at the edge of the screen 2 command strings Characters enclosed by double quote marks are considered to be strings The closing double quote can be omitted when it would appear at the end of a line 3 Input Input prompt strings variable Enables the user to input a value list etc for the specified variable during ex...

Page 210: ...to the end of the line These lines are ignored at execution Comments should be entered as notes for future reference though it should be noted that they do occupy some memory space 6 End End Indicates the end of a program End is not necessary at the last line of the program 7 Key Key variable If a numeric key or one of the cursor keys is pressed the variable is set to the corresponding numeric val...

Page 211: ...text screen 4 DispG DispG Displays the graph screen D I O menu P D This menu is used to send or receive data from externally connected devices 1 Get Get variable Receives data from externally connected devices 2 Send Send variable Sends data to externally connected devices E SETUP menu P E SETUP menu commands are used to set the various settings used in graphing and calculations 01 Rect Rect Sets ...

Page 212: ...s the graph coordinates as the axes of sequence graphs u n is set to the X axis and w n is set to the Y axis 08 vw vw Sets the graph coordinates as the axes of sequence graphs v n is set to the X axis and w n is set to the Y axis 09 Deg Deg 10 Rad Rad 11 Grad Grad Sets the angle mode to degree radian and gradient respectively 12 FloatPt FloatPt 13 Fix Fix 14 Sci Sci 15 Eng Eng 16 Tab Tab integer 0...

Page 213: ...N Sets the derived function Y to be displayed on the graph screen 06 Y OFF Y OFF Sets the derived function Y to not be displayed on the graph screen 07 AxisON AxisON Sets the specified axis to be displayed on the graph screen 08 AxisOFF AxisOFF Sets the specified axis to not be displayed on the graph screen 09 GridON GridON Sets the grid lines to be displayed on the graph screen 10 GridOFF GridOFF...

Page 214: ...list name Y list name frequency list Press to specify a graph type 4 PlotON PlotON number Sets drawing of the specified statistical graph to on If no number is specified this command turns on all of the statistical graphs 5 PlotOFF PlotOFF number Sets drawing of the specified statistical graph to off If no number is specified this command turns off all of the statistical graphs 6 LimON LimON This ...

Page 215: ...the same program Up to 10 characters can be used for a Label name Up to 50 Labels can be used in a single program 02 Goto Goto label name To shift the program execution to a label 03 If If conditional statements Goto label name or If conditional statements Then commands or multiple statements Else commands or multiple statements EndIf Multiple statements mean a group of statement lines separated b...

Page 216: ...highly recommended that Label and Goto statements are not used in For loop structures While conditional statements commands or multiple statements WEnd While and WEnd statements must be placed at the beginning of the line Multiple While loops can be nested to within the memory capacity Conditional statements are evaluated before entering the While clause It is highly recommended that Label and Got...

Page 217: ...xt line after the Gosub statement Up to 10 subroutines can be nested 7 Other menus convenient for programming H COPY menu P H You can copy and paste line by line using the COPY menu commands 1 Move the cursor to the line that you wish to copy 2 Press P H 3 Select 1 StoLine and press E The selected line will be stored in the memory 4 Move the cursor to the line where you wish to paste the stored li...

Page 218: ...ta9 and G_Data0 F PICTUR Specifies picture data Pict1 to Pict9 and Pict0 G TABLE Specifies table setting values Table Start Table Step Table List H STAT Specifies statistics functions x _ Σx y _ regression expressions points and statistical verification functions The commands and functions in the VARS menu can be displayed on the screen Current setting data can also be reset The results of arithme...

Page 219: ...ax 5 R z E 5 E 1 Yscl 1 R z E 6 E Operation to input a function equation for example x2 2 to the graphic equation Y1 is also made using R in the same manner as described above X2 2 Y1 P A 2 X y 2 P A 2 R z A E A 1 Note Function equations cannot be assigned in the graphic equations such as Y1 if the EDITOR mode under SET UP is set to Equation Switch the EDITOR to One line mode prior to assigning su...

Page 220: ...t the program to debug If any bugs are present error messages will appear The following example indicates that the same label name has been used two or more times 2 Press or to display the line where the error exists and correct the mistake Execution can be interrupted by pressing O Use this command if the program enters an infinite loop Press or to display the program source with the cursor on th...

Page 221: ...he second equation if need 4 Input a lower value while LOWER is displayed then press E 5 Input an upper value while UPPER is displayed then press E The calculation result is displayed with highlighted graph 6 Press E to display the calculation result without the graph Errors and calculation ranges If ERROR is displayed instead of a calculation result press E then enter the numeric values again If ...

Page 222: ...variables below Therefore please note that some numbers are stored in these variables if you execute the program Program name Variable Storage location of the calculation result integral A B C D E M S T C Note This program will not be deleted by resetting the calculator To delete a program please refer to Deleting an entire program on page 206 in this operation manual Note that the program will be...

Page 223: ...een contrast 1 Press p The screen contrast setting window will appear 2 Press to darken or to lighten the screen 2 Checking the memory usage The memory usage window enables you to check how much memory you have used If the memory is nearly full delete files or reset the calculator to operate safely 1 Press p 2 Press B The memory check window will appear The remaining number of bytes of user memory...

Page 224: ...amount of memory bytes used by matrices Graph Eqn The amount of memory bytes used by graph equations Solver Eqn The amount of memory bytes used by solver equations Program The amount of memory bytes used by program files Picture The amount of memory bytes used by graph pictures G_Data The amount of memory bytes used by stored graph data L_Data The amount of memory bytes used by stored list data Sl...

Page 225: ...ample Displayed items may vary according to data input and use Press pC0todeletethememoriespreviouslyentered 4 Linking to another EL 9950 or PC The optional products CE 451L and CE LK4 are not available in some regions Using the optional CE 451L or CE LK4 the EL 9950 can be linked to another EL 9950 To transfer data press p D to open the Link option window Press 1 to send data and press 2 to recei...

Page 226: ...s a list of all the stored list files 03 Matirx Displays a list of all the stored matrix files 04 Graph Eqn Displays a list of all the stored graph equations 05 Solver Eqn Displays a list of all the stored solver equations 06 Program Displays a list of all the stored program files 07 G_Data Displays a list of all the stored graph data files 08 L_Data Displays a list of all the stored list data fil...

Page 227: ...on Y2 to the other calculator 1 Prepare the receiving calculator by pressing p D 2 2 Press p D 1 on the sending calculator The send menu will appear 3 Press 0 1 A list of all the data stored will be are displayed and the cursor positioned on the top line You can also select 02 List for L1 03 Matrix for mat A and mat B and 04 Graph Eqn for Y2 for example and send the data category by category 4 Mov...

Page 228: ...ulator is required Just connect the cable and press the power on key and the entire operation can be controlled from the PC CE LK4 can also be utilized to update the calculator s software 5 Reset function If a problem occurs after replacing batteries or the calculator does not function correctly use the RESET option 1 Press p E 2 Press 1 to return the calculator s SETUP and FORMAT settings to the ...

Page 229: ...utions for handling batteries Fluid from a leaking battery accidentally entering an eye could result in serious injury Should this occur wash with clean water and immediately consult a doctor Should fluid from a leaking battery come into contact with your skin or clothes immediately wash with clean water If the product is not to be used for some time to avoid damage to the unit from leaking batter...

Page 230: ... the unit operation batteries are removed otherwise all the calculator s stored memory will be lost 4 Replace the battery compartment cover 5 After a few seconds press O The following message will appear If the message does not appear repeat the procedures from step 2 6 Press O Do not press C This will clear all the data Once every 5 years the lithium battery will need to be replaced The lithium b...

Page 231: ... lithium battery cover and fasten the screw 6 Replace the battery compartment cover wait a few seconds and then press O The following message will appear 7 Press O Do not press C This will clear all the data 1 Perform procedures 1 and 2 as shown above Do not remove the unit operation batteries 2 Remove the screw and the lithium battery cover as shown ...

Page 232: ...he display Press p then press A to enter A CTRST the screen contrast can be adjusted by using the or the key The calculator won t take the minus sign calculation results in a syntax error To set a negative value use the _ key instead of the key The calculation results are very different from what is usually expected The angle unit and other configurations may be incorrectly set Check the configura...

Page 233: ... not work then press then O to tell the running application to quit If everything fails then the calculator s memory may need to be reset Resetting the calculator s memory will clear all the stored information such as programs lists and variables To reset the unit s memory open and close the battery compartment cover wait a few seconds and then press O to open the verification window To prevent da...

Page 234: ...calculation coordinate conversion binary octal decimal hexadecimal calculation Boolean operation matrix calculation complex number calculation complex function calculation statistic calculation regression calculation statistic authorization calculation financial calculation etc Input method Manual key entry Graphic features Rectangular polar parametric sequence coordinate graph Graph range specifi...

Page 235: ...pply Operation 6 V DC AAA manganese battery R03 4 Memory backup 3 V DC Lithium battery CR2032 1 Automatic power off Approx 10 minutes Operating temperature range 0 C to 40 C 32 F to 104 F Battery life Operation battery set approx 150 hours with 5 minutes of continual use and 55 minutes in the display state for every hour at a temperature of approx 20 C 68 F Memory backup approx 5 years at a temper...

Page 236: ...used in Solver features Domain Argument definition outside of domain Increment Increment error found Irr Calc More than two inflection points for Irr calculation Stat Med Med Med law statistic error found No Argument Argument missing Not pair dx and dx are not used in a pair Not pair Brackets are not used in a pair Not pair Parentheses are not used in a pair Not pair Braces are not used in a pair ...

Page 237: ...g to the WEnd command Without Then Then is missing corresponding to the If command Without EndIf EndIf is missing corresponding to the If command Without If If is missing corresponding to the EndIf command I O device Communication error found among devices Wrong Mode Wrong communication mode set Memory over Memory is full cannot store data as requested System error System error found user memory s...

Page 238: ...S 1 Pmt_Begin S 0 Pmt_End C Y 1 1 I 100 C Y P Y 1 I calculation 1 If PMT 0 r 1 1 n PV FV 2 If PMT 0 f r PV 1 r s PMT 1 1 r n r FV 1 r n r 0 f r PV PMT n FV r 0 calculate the following for r solved in 1 and 2 I 100 C Y r 1 P Y C Y 1 2 PV calculation 1 If r 0 r 1 PV 1 r s 1 1 r n r PMT FV 1 r n 2 If r 0 PV n PMT FV 3 If r 1 Error ...

Page 239: ...s PMT 1 r n FV 2 If r 0 FV n PMT PV 3 If r 1 Error 4 PMT calculation 1 If r 0 r 1 1 1 r n r PMT 1 r s PV FV 1 r n 2 If r 0 PMT PV FV n 3 If r 1 Error 5 N calculation 1 If r 0 r 1 log 1 r log N 1 r 1 r s PMT FV 1 r 1 r s PMT PV 2 If r 0 N FV PV PMT 3 If r 1 Error ...

Page 240: ...egin mode PV PMT 0 and FV 0 PV PMT 0 and FV 0 If PMT 0 Pmt_End mode PV 0 and FV PMT 0 PV 0 and FV PMT 0 Pmt_Begin mode PV PMT 0 and FV 0 PV PMT 0 and FV 0 If PMT 0 PV FV 0 FV N PMT PV 0 or FV N PMT PV 0 Irr calculation all cash flows have the same sign 3 Distribution function 1 pdfnorm 1 f x exp x µ 2 2σ2 2πσ 2 pdfT f x πdf df 2 x2 df df 1 2 df 1 2 Γ Γ 1 Calculation result Xreg Calculation result ...

Page 241: ... c 1 P x c n c p c 1 1 p c 0 1 n 1 6 pdfpoi f x e µ µx x x 0 1 2 7 pdfgeo f x p 1 p x 1 df Degree of freedom m Degree of freedom of numerator n Degree of freedom of denominator n Trial number integers greater than 0 p Success probability 0 p 1 c Success number x First successful trial number However Γ s 0 xs 1 e x dx However Γ s 0 xs 1 e x dx ...

Page 242: ...n error increases in continuous calculations due to accumulation of each calculation error This is the same for ab b n ex In etc where continuous calculations are performed internally Additionally a calculation error will accumulate and become larger in the vicinity of inflection points and singular points of functions for example calculating sinh X or tanh X at X 0 Function Calculation range Note...

Page 243: ...092 1 10100 x 100 x 1 10100 x 1 1050 0 x 1 10100 0 5 n 69 5 When a 0 1 10100 b log a 100 When a 0 0 b 1 10100 When a 0 b is an integer or 1 b is an odd number b 0 However 1 10100 b log a 100 When b 0 1 10100 1 a log b 100 a 0 When b 0 0 a 1 10100 When b 0 a is an odd number or 1 a is an integer a 0 However 1 10100 1 a log b 100 0 r n 9999999999 When r _ n 2 _ r 1 n _ n r 10100 When _ n 2 r _ r n n...

Page 244: ...1111111111 0 x 0111111111111111 Octal 4000000000 x 7777777777 0 x 3777777777 Hexadecimal FDABF41C01 x FFFFFFFFFF 0 x 2540BE3FF x 1 10100 x 1 10100 y 1 10100 x2 y2 1 10100 y x 1 10100 r 1 10100 Binary 1000000000000000 x 1111111111111111 0 x 0111111111111111 Octal 4000000000 x 7777777777 0 x 3777777777 Hexadecimal FDABF41C01 x FFFFFFFFFF 0 x 2540BE3FE Binary 1000000000000001 x 1111111111111111 0 x 0...

Page 245: ...d 4th degree polynomials x 1 1050 y 1 1050 Σx 1 10100 Σx 2 1 10100 Σy 1 10100 Σy 2 1 10100 Σxy 1 10100 n 1 10100 n 0 n 1 Σx 1 1050 0 Σx 2 n Σx2 n 1 1 10100 n 0 Σx 1 1050 0 Σx 2 n Σx2 n 1 10100 n 0 Σx 1 1050 Σy 1 1050 0 Σx2 Σx 2 n Σy2 Σy 2 n 1 10100 Σxy ΣxΣy n 1 10100 1 10100 n 0 Σx 1 1050 Σx Σy 1 10100 0 Σx2 Σx 2 n 1 10100 Σxy ΣxΣy n 1 10100 1 10100 ...

Page 246: ... bx _ 1 10100 y _ bx _ 1 10100 bx 1 10100 a bx 1 10100 y a 1 10100 y a b 1 10100 0 x 1010 0 x 1010 x 10100 x 1010 Error is returned when the number of elements exceeds 1000 Error is returned when specifying columns or rows that exceed 100 mat An n 255 Same as above Same as b for other A number with 10 or less decimal places or the 1010 th or above decimal places are 0 ...

Page 247: ...ion error may occur and increase due to inner continuous calculations Function Calculation range Notes 1 x yi x yi 2 In x yi log x yi x yi e x yi 10 x yi x yi a bi x yi 0 x 1050 y 1050 x 1050 y 1050 xy 5 1099 x 1050 y 1050 y x 10100 x 230 y 230 x 100 y 100 x 1050 y 1050 a 10100 b 10100 ...

Page 248: ...n lower limit of x upper limit of x A 0 4 32 d dx d dx equation value of x tolerance A 0 5 32 equation lower limit upper limit tolerance dx A 0 6 33 dx equation lower limit upper limit tolerance dx A 0 7 33 expression initial value end value increment A 0 8 33 sec sec value A 0 9 33 csc csc value A 1 0 33 cot cot value A 1 1 33 sec 1 sec 1 value A 1 2 33 csc 1 csc 1 value A 1 3 34 cot 1 cot 1 valu...

Page 249: ...an standard deviation number of trial C 3 37 nPr nCr rndNorm value A nPr value B C 5 value A nCr value B C 6 value C 7 38 M M M M CONV deg value deg D 1 38 dms value dms D 2 38 xy r xy r x coordinate y coordinate D 3 39 xy θ xy θ x coordinate y coordinate D 4 39 rθ x rθ x r coordinate θ coordinate D 5 39 rθ y rθ y r coordinate θ coordinate D 6 39 M M M M ANGLE value value value E 1 40 value value ...

Page 250: ...lue A xor value B G 4 42 xnor value A xnor value B G 5 42 M M M M COMPLEX conj conj complex number H 1 42 real real complex number H 2 42 image image complex number H 3 43 abs abs complex number H 4 43 arg arg complex number H 5 43 M M M M in the N base calculation mode LOGIC and value A and value B A 1 41 or value A or value B A 2 41 not not value A 3 41 neg neg value A 4 42 xor value A xor value...

Page 251: ...min value A value B or min list B 1 140 max max value A value B or max list B 2 140 mean mean list frequency list B 3 140 median median list frequency list B 4 141 sum sum list start number end number B 5 141 prod prod list start number end number B 6 141 stdDv stdDv list frequency list B 7 142 varian P_stdDv varian list frequency list B 8 B 9 142 142 l l l l l l l l L_DATA StoLD StoLD natural num...

Page 252: ... to store D 0 1 162 Rg_ax b list name for x list name for y frequency list equation name to store D 0 3 162 Rg_ax b Rg_ax list name for x list name for y frequency list equation name to store D 0 2 162 Rg_a bx Rg_a bx list name for x list name for y frequency list equation name to store D 0 4 162 Rg_x2 Rg_x2 list name for x list name for y frequency list equation name to store D 0 5 162 Rg_x3 Rg_x...

Page 253: ...tion name to store D 1 5 164 x value or list x D 1 6 165 y value or list y D 1 7 165 S S S S TEST χ2 test No arguments E 0 1 168 Ftest2samp No arguments E 0 2 169 Ttest1samp No arguments E 0 3 169 Ttest2samp No arguments E 0 4 170 TtestLinreg No arguments E 0 5 171 Tint1samp No arguments E 0 6 172 Tint2samp No arguments E 0 7 172 Ztest1samp No arguments E 0 8 173 Ztest2samp No arguments E 0 9 174 ...

Page 254: ... 0 9 182 pdfbin pdfbin number of trial success probability success numbers F 1 0 183 cdfbin cdfbin number of trial success probability success numbers F 1 1 183 pdfpoi pdfpoi mean value F 1 2 183 cdfpoi cdfpoi mean value F 1 3 184 pdfgeo pdfgeo success probability value F 1 4 184 cdfgeo cdfgeo success probability value F 1 5 184 Functions Commands Syntax Keystrokes Page PLOT1 PLOT2 PLOT3 LIMIT ON ...

Page 255: ...ts F 1 158 Pie No arguments F 2 158 Scattr No arguments G 1 158 Scattr No arguments G 2 158 Scattr No arguments G 3 158 xyLine No arguments H 1 158 xyLine No arguments H 2 158 xyLine No arguments H 3 158 Functions Commands Syntax Keystrokes Page d d d d DRAW ClrDraw No arguments A 0 96 Line Line x coordinate of start point y coordinate of start point x coordinate of end point y coordinate of end p...

Page 256: ...HG PxlCHG column row B 6 106 PxlTST PxlTST column row B 7 106 d d d d ON OFF LINE G_DATA PICT SHADE DrawON DrawON equation number 1 equation number 2 C 1 107 DrawOFF DrawOFF equation number 1 equation number 2 C 2 107 LINE No arguments D E 107 StoGD StoGD number E 1 108 RclGD RclGD number E 2 108 StoPict StoPict number F 1 109 RclPict RclPict number F 2 109 SET No arguments G 1 110 INITIAL No argu...

Page 257: ...ts A 9 76 Z Z Z Z FACTOR POWER FACTOR No arguments B E 77 x2 Zm_x2 No arguments C 1 77 x 1 Zm_x 1 No arguments C 2 77 Zm_ No arguments C 3 77 Z Z Z Z EXP 10x Zm_10x No arguments D 1 77 ex Zm_ex No arguments D 2 77 log x Zm_log No arguments D 3 77 ln x Zm_ln No arguments D 4 77 Z Z Z Z TRIG sin x Zm_sin No arguments E 1 77 cos x Zm_cos No arguments E 2 78 tan x Zm_tan No arguments E 3 78 Functions ...

Page 258: ...o arguments F 4 78 cosh 1 x Zm_cosh 1 No arguments F 5 78 tanh 1 x Zm_tanh 1 No arguments F 6 78 StoWin No arguments G 1 78 RclWin No arguments H 1 78 PreWin No arguments H 2 79 Functions Commands Syntax Keystrokes Page k k k k CALC Value Value x A 1 87 Intsct No arguments A 2 87 Minimum No arguments A 3 87 Maximum No arguments A 4 88 Y_zero No arguments A 5 88 Y_Incpt No arguments A 6 88 Inflec N...

Page 259: ...4 NEW V_INDX No arguments C No arguments D E 204 204 P P P P in the Prgramming mode PRGM Print Print variable Print character strings A 1 208 characters A 2 208 Input Input prompt strings variable A 3 208 Wait Wait natural number A 4 209 Rem Rem comments A 5 209 End No arguments A 6 209 Key Key variable A 7 209 P P P P in the Prgramming mode BRNCH Label Label label name B 0 1 214 Goto Goto label n...

Page 260: ... 210 Send Send variable D 2 210 P P P P in the Prgramming mode SETUP Rect No arguments E 0 1 210 Param No arguments E 0 2 210 Polar No arguments E 0 3 210 Web No arguments E 0 4 211 Time No arguments E 0 5 211 uv No arguments E 0 6 211 uw No arguments E 0 7 211 vw No arguments E 0 8 211 Deg No arguments E 0 9 211 Rad No arguments E 1 0 211 Grad No arguments E 1 1 211 FloatPt No arguments E 1 2 211...

Page 261: ...212 GridON No arguments F 0 9 212 GridOFF No arguments F 1 0 212 Connect No arguments F 1 1 212 Dot No arguments F 1 2 212 Sequen No arguments F 1 3 212 Simul No arguments F 1 4 212 P P P P in the Prgramming mode S_PLOT Plt1 Plt1 graph type X list name Y list name frequency list G 1 213 Plt2 Plt2 graph type X list name Y list name frequency list G 2 213 Plt3 Plt3 graph type X list name Y list name...

Page 262: ...7 131 mat H row column A 8 131 mat I row column A 9 131 mat J row column A 0 131 m m m m EDIT mat A No arguments B 1 123 mat B No arguments B 2 123 mat C No arguments B 3 123 mat D No arguments B 4 123 mat E No arguments B 5 123 mat F No arguments B 6 123 mat G No arguments B 7 123 mat H No arguments B 8 123 mat I No arguments B 9 123 mat J No arguments B 0 123 m m m m OPE dim dim matrix name C 0 ...

Page 263: ...column number list name C 1 1 129 list mat list mat list 1 list n matrix name C 1 2 129 m m m m MATH det det matrix name D 1 130 trans trans matrix name D 2 130 rowEF rowEF matrix name D 3 130 rrowEF rrowEF matrix name D 4 130 No arguments E 1 131 No arguments E 2 131 Functions Commands Syntax Keystrokes Page g g g g SOLVER CALC SOLVER TVM SOLVER screen appears A E 187 slv_pmt slv_pmt N I PV FV P ...

Page 264: ...1 194 Eff Eff nominal interest rate number of settlements B 1 2 194 days days start month day year end month day year days day month year day month year B 1 3 194 g g g g PERIOD PmtEnd No arguments C 1 190 PmtBegin No arguments C 2 190 g g g g VARS N No arguments D 1 195 I No arguments D 2 195 PV No arguments D 3 195 PMT No arguments D 4 195 FV No arguments D 5 195 P Y No arguments D 6 195 C Y No ...

Page 265: ...Functions Commands Syntax Keystrokes Page in the Solver mode METHOD EQTN SAVE RENAME Equation No arguments A 1 196 Newton Bisect No arguments A 2 198 Graphic No arguments A 3 200 EQTN No arguments B 203 SAVE No arguments C E 202 RENAME No arguments D 202 Functions Commands Syntax Keystrokes Page ...

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