EL-9900 ® 02JGK(TINSE0511EH01) PRINTED IN CHINA/IMPRIMÉ EN CHINE/IMPRESO EN CHINA GRAPHING CALCULATOR SHARP CORPORATION ® MODEL EL-9900 GRAPHING CALCULATOR OPERATION MANUAL
In the U.S.A. Declaration of Conformity Graphing Calculator: EL-9900 This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions: (1) This device may not cause harmful interference, and (2) this device must accept any interference received, including interference that may cause undesired operation.
Introduction This graphing calculator can handle many types of mathematical formulas and expressions for you. It is powerful enough to process very complex formulas used in rocket science, but yet so compact that it fits in your coat pocket.
Introduction Reversible Keyboard This calculator comes equipped with a reversible keyboard. Reverse the keyboard to select Basic Mode or Advanced Mode. Basic Mode A green background color keyboard with basic mathematical functions. This mode is suitable for learning mathematics in lower grades.
Introduction Advanced Mode (Default mode) A blue background color keyboard with advanced mathematical functions. This mode is suitable for learning or studying mathematics in higher grades.
Contents Caring for Your Calculator ............................................................................................... 1 Chapter 1 Getting Started ..............................................................................................................2 Before Use ...................................................................................................................... 2 Using the Hard Cover .......................................................................................
Contents Chapter 4 Basic Graphing Features — Basic Keyboard ......................................................... 50 1. Try it! ........................................................................................................................50 2. Explanations of Various Graphing Keys ................................................................. 52 3. Other Useful Graphing Features ............................................................................. 58 Substitution feature ..........
Contents Chapter 9 List Features ............................................................................................................ 131 1. Try it! ..................................................................................................................... 131 2. Creating a list ....................................................................................................... 133 3. Normal List Operations ...............................................................................
Contents Chapter 13 Programming Features ........................................................................................... 202 1. Try it! ..................................................................................................................... 202 2. Programming Hints ...............................................................................................204 3. Variables ............................................................................................................
Contents 3. Complex number calculation ........................................................................ 245 7. CATALOG Feature ................................................................................................246 8. List of Menu/Sub-menu Items .............................................................................. 247 1. MATH menus ................................................................................................. 247 2. LIST menus ................................
Caring for Your Calculator Caring for Your Calculator • Do not carry the calculator around in your back pocket, as it may break when you sit down. The display is made of glass and is particularly fragile. • Keep the calculator away from extreme heat such as on a car dashboard or near a heater, 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.
Chapter 1 Getting Started Before Use Inserting batteries resetting the memory 1. Open the battery cover located on the back of the calculator. Pull down the notch, then lift the battery cover up to remove it. 2. Insert the batteries, as indicated. Make sure that the batteries are inserted in the correct directions. 3. Pull off the insulation sheet from the memory backup battery. 4. Place the battery cover back, and make sure that the notch is snapped on. 5.
Chapter 1: Getting Started Adjusting display contrast Since the display 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 -: decreases the contrast 3. When done, press C to exit the mode. Turning the calculator OFF Press @ o to turn the calculator off.
Chapter 1: Getting Started Part Names and Functions Main Unit 1 Display screen 2 Power ON/ OFF key 4 Graphing keys 5 Cursor keys 3 Key operation keys 4
Chapter 1: Getting Started 1 Display screen: Displays up to 132 pixels wide by 64 pixels tall of graphs and texts. 2 Power ON/OFF key: Turns calculator ON. To turn off the calculator, press @, then o. 3 Key operation keys: These keys are used to change the key functions. @: Changes the cursor to “2”, and the next keystroke enters the function or mode printed above each key in yellow. A: Changes the cursor to “A”, and the next keystroke enters the alphabetical letter printed above each key in purple.
Chapter 1: Getting Started 5 Cursor keys: Enables you to move the cursor (appears as _, ■, etc. on the screen) in four directions. Use these keys also to select items in the menu. Reset switch (in the battery compartment): Used when replacing batteries or clear the calculator memory. # key: Returns calculator to calculation screen. p key: Sets or resets the calculator settings, such as LCD contrast and memory usage. n key: Obtains the screen for the slide show. l key: Accesses list features.
Chapter 1: Getting Started Menu keys (Function of these keys may vary between basic and advanced mode.) M: Enter the Math menu with additional mathematical functions. S: Enter the statistics menu. P: Enter the programming menu. z: Enter the menu for calculator specific variables. Advanced Mode specific keys V: Converts hexadecimal, decimal, octal and binary numbers or solves systems of linear equations, finds roots for quadratic and cubic equations.
Chapter 1: Getting Started Basic Key Operations Since this calculator has more than one function assigned to each key, you will need to follow a few steps to get the function you need. Example x-1 F Operation of y @ x: Specify x-1 A F: Specify character F y: Specify x 2 • Press “as is” to get the function and number printed on each key. • To access secondary function printed above each key in yellow, press @ first, then press the key. Press C to cancel.
Chapter 1: Getting Started Changing the Keyboard This calculator is designed with a reversible keyboard, which by utilizing it will not only change the appearance, but will also change the internal functions and configurations of the calculator as well. To change the keyboard: 1. Press @ o to turn off the calculator’s power. 2. Open the battery compartment cover. Hold the calculator as illustrated. 3. Slide the keyboard eject tab (KEYBOARD EJECT) down. The keyboard will be ejected.
Chapter 1: Getting Started When you reverse the keyboard, the following settings are automatically changed. Basic → Advanced • Simplifying: Auto (Auto at SIMPLE in SETUP menu) Advanced → Basic • Coordinate system: Rectangular coordinates (Rect at COORD in SETUP menu.) • Answer mode: Displays a mixed number if ANSWER is set to complex numbers. • Angle unit: Set to Deg if DRG is set to Grad. • Decimal format: Set to FloatPt if FSE is set to Eng.
Chapter 1: Getting Started Set up the calculator before calculation 1. Press # to enter the calculation screen. Enter fractions 3. Press 3 b 4 '. 2. Press C to clear the display. 4. Press b 18 '. 5. Press E. 1 Now we have found 24 of a cup of warm milk is required per one doughnut, how many cups are required for 60 doughnuts? If you want to use the answer of the previous calculation, press b and you do not have to reenter the value. 6. Press @ b |, or directly | (multiplication).
Chapter 1: Getting Started On the Basic Mode, you can toggle between decimal values, mixed values, and improper fractions using >, /, and <, respectively. 1. Press > E. 2. Press < E. 3. Press / E. Change answer mode from fractions to decimals 1. Press @ ;. 2. Select F ANSWER and press 1. 3. Press C. Now the answer mode is set to the decimal answer mode and 2.5 is displayed.
Chapter 2 Operating the Graphing Calculator Basic / Advanced Keyboard This calculator comes equipped with a reversible keyboard to support two different keyboard configurations: Basic and Advanced keyboard. By reversing the keyboard, the calculator switches its set of functions and behaviors as well as its visual aspect. The Basic keyboard, with its key frame colored in dark green, is designed to be used by students at lower grades of math classes.
Chapter 2: Operating the Graphing Calculator 1. Entering numbers Use the number keys (0 ~ 9), decimal point key (.), and negative number key (_) to enter numbers into the calculator. To clear the screen entry, press C. Number entry Example Type 10.23456789 onto the Calculation screen. 1. Enter the Calculation screen, then clear the screen entry: #C 2. Enter numbers with the number keys and decimal point key, as follows: 10 . 23456789 Note: $ can be used to enter a value in scientific notation.
Chapter 2: Operating the Graphing Calculator 2. Performing standard math calculations By utilizing the + - | and = keys, you can perform the standard arithmetic calculations of addition, subtraction, multiplication, and division. Press E to perform each calculation. Perform an arithmetic calculation Example Obtain the answer to “6 × 5 + 3 – 2”. #C6|5+3 -2E Using parentheses With the ( and ) keys, parentheses (round brackets) can be added to group sections of expressions.
Chapter 2: Operating the Graphing Calculator Example Enter “ 4 65536 × 3 8 ” in the Calculation screen. Jump the cursor to the beginning of the expression (just for this exercise), then press E to calculate. 1. Press #, then C to clear the display. 2. Enter 4 for the root’s depth, then press @ _. The root figure is entered, with the cursor automatically placed below the figure. For detailed instructions of how to use the @ key, refer to “Second Function Key” and “ALPHA Key” in this chapter. 3. Enter 65536.
Chapter 2: Operating the Graphing Calculator Editing Entries Editing modes The calculator has the following two editing modes: equation mode, and one line mode. You can select one from the G EDITOR menu of the SETUP menu. Equation editor One line editor * See page 26 for details. Cursor navigation Use ; ' { } to move the cursor around, and use the D B C keys to edit entries. • D key deletes an entry AT THE CURSOR. • B key erases one BEFORE THE CURSOR. • Use C to clear the entire entry line.
Chapter 2: Operating the Graphing Calculator Example Type 4500000, then remove 500. #C4500000; ;;BB B Tips: You can jump the cursor to the beginning or the end of line by using the @ and ; ' keys. Likewise, press @ } to jump the cursor all the way to the bottom. Press @ { to jump the cursor to the top. To learn about how to use the @ key and its functions, refer to the section “Second Function Key” of this chapter.
Chapter 2: Operating the Graphing Calculator ALPHA Key Use A to enter an alphabet character. With the Basic keyboard, all 26 alphabet characters from “A” up to “Z”, and space can be typed; the Advanced keyboard has all 26 characters accessible, as well as “θ ”, “=”, “ : ”, and space. All functions associated with A are color coded purple, and are printed above each key. Note: Entering one Alphabet character Do not type out math figures (sin, log, etc.), graph equation names (Y1, Y2, etc.
Chapter 2: Operating the Graphing Calculator Math Function Keys Basic keyboard Advanced keyboard Mathematical functions can be called up quickly with the Math Function keys. The Math Function key sets for both the Basic and Advanced Keyboards are designed to suit the needs of calculations at each level.
Chapter 2: Operating the Graphing Calculator c Enters an arc cosine function at the cursor t Enters a tangent function at the cursor t 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” X Enters a variable “x”, “θ”, “T”, or “n”.
Chapter 2: Operating the Graphing Calculator Note: If a number precedes d b a and _, then the number will be set as the first entry of the figure. Else, the first entry is blank and the cursor flashes. Examples 2d3} 4' d ;2'3}4' 22 + Enters a “root” figure at the cursor , Enters “ , ” (a comma) at the cursor R Stores a number or a formula into a variable r Recalls an item stored in a variable z Brings up the VARS menu.
Chapter 2: Operating the Graphing Calculator MATH, STAT, and PRGM Menu Keys By using the M, S, and P keys, you can access many menu items for complex calculation tasks. The appendix “List of Menu/Sub-menu Items” shows the contents of each, with detailed descriptions of each sub-menu item. Note that the contents of menu items differ drastically between the Basic keyboard and the Advanced keyboard.
Chapter 2: Operating the Graphing Calculator 5. Type 3 4 . 5 6 7 , 0 ), and press E. SETUP Menu Use this menu to verify basic configurations, such as to define the calculator’s editing preferences, and scientific and mathematical base units. Checking the calculator’s configuration To check the current configuration of the calculator, press @, then ;. By entering menu items (B DRG through H SIMPLE), various setups can be changed. To exit the SETUP menu, press C.
Chapter 2: Operating the Graphing Calculator 4. Press # C to clear the Calculation screen, type 1 0 0 0 y, then E.
Chapter 2: Operating the Graphing Calculator TAB: COORD: Sets the number of digits beyond the decimal point (0 through 9). The default is “9”. Sets the calculator to various graph coordinate systems. Rect Param Polar Seq ANSWER: Parametric equation coordinates (for Advanced mode only) Polar coordinates (for Advanced mode only) Sequential graph coordinates (for Advanced mode only) Sets the answer preference to various number formats.
Chapter 2: Operating the Graphing Calculator Notes: Immediately after changing the EDITOR, the calculator will return to the calculation screen and the following data will be cleared. • ENTRY memory • Equations stored in the graph equation window (Y) • Equations temporally 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.
Chapter 2: Operating the Graphing Calculator 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 nonequalities (<, ≤, >, ≥, ≠, =, →deg, →dms, etc.) Example The key operation and calculation precedence 5 + 2 | s 30 + 25 | 5 a 3 E 1st 4th 2nd 5th 3rd 6th • If parentheses are used, parenthesized calculations have precedence over any other calculations.
Chapter 2: Operating the Graphing Calculator Resetting the Calculator Use the reset when a malfunction occurs, to delete all data, or to set all mode values to the default settings. The resetting can be done by either pressing the reset switch located in the battery compartment, or by selecting the reset in the OPTION menu. Resetting the calculator’s memory will erase all data stored by the user; proceed with caution. 1. Using the reset switch 1.
Chapter 2: Operating the Graphing Calculator • The message on the right may occasionally appear. In this case, repeat the procedure from step 1 to prevent loss of data. 2. Selecting the RESET within the OPTION menu 1. Press @, then p. The OPTION menu appears. 2. While in the OPTION menu, press E to select E RESET; the RESET submenu items should appear on the right side of the screen. 3.
Chapter 3 Basic Calculations — Basic Keyboard In this chapter, we explore more features of this calculator using the Basic Keyboard. Features such as fraction to decimal conversion and the quotient-remainder key, as well as basic arithmetic calculations, will be covered in this chapter. Note: To try the examples in the chapter, it is required that the Basic Keyboard is already set up by the user. To learn how to set up the Basic Keyboard, read “Changing the Keyboard” in Chapter 1. 1.
Chapter 3: Basic Calculations — Basic Keyboard CONCEPT 1. Enter a math expression, then perform the calculation. 2. Save a number into a variable, then recall the value later. PROCEDURE 1. First, press #, then C to clear any screen entries. 2. Type 186282 = 7.5, then press E. The circumference of the earth is thus obtained. 3. Store the answer in a variable. A variable is a symbol under which you can store a numerical value. We will use variable A to store the circumference of the earth.
Chapter 3: Basic Calculations — Basic Keyboard 2. Arithmetic Keys Performing addition, subtraction, multiplication and division E There are various keys for arithmetic calculations. Use the + - | =, _, ( and ) keys to perform basic arithmetic calculations. Press E to solve an equation. Executes an expression. Example • Calculate 1 + 2. #C1+2E A Note about expressions + An expression is a mathematical statement that may use numbers and/or variables that represent numbers.
Chapter 3: Basic Calculations — Basic Keyboard | Enters a “×” sign for multiplication. Example • Multiply 12 by 34. 12|34E = Enters a “÷” sign for division. Example • Divide 54 by 32. 54=32E When to leave out the “×” sign The multiplication sign can be left out when: a. It is placed in front of an open parenthesis. 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.
Chapter 3: Basic Calculations — Basic Keyboard ( Enters an open parenthesis. Use with “)” as a pair, or the calculation will result in an error. ) Enters a closing parenthesis; a parenthesis left open will result in an error. Example • Calculate (4 + 6) ÷ 5. (4+6)= 5E Note: Functions, such as “round(”, automatically include an open parentheses. Each of these functions needs to be closed with a closing parenthesis. 3.
Chapter 3: Basic Calculations — Basic Keyboard Specifying a common factor Simplify the fraction using the specified common factor. Example 1 b 12 ' + 5 b 12 E Q 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. Q is effective in a fraction calculation mode only (when the ANSWER mode is set to Mixed or Improp in the SETUP menu). / Converts an improper fraction to a mixed number.
Chapter 3: Basic Calculations — Basic Keyboard i Performs an integer division, and returns a quotient and a remainder. Example • Get a quotient and a remainder of 50 ÷ 3. 50 i 3 E * Quotient value is set to Ans memory and remainder is not stored. y Squares the preceding number. 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 d Enters a mixed number.
Chapter 3: Basic Calculations — Basic Keyboard b Enters a fraction, setting the preceding number as its numerator. * If the calculator is set to one-line mode, then “ ¬” will be entered 2 instead. For example, “2 ¬ 5” indicates “ ”. 5 Example 2 3 • Calculate 5 + 4 . 2b5'+b 3'4'E a Enters an exponent, setting the preceding number as its base. Example • Raise 4 to the 5th power. (= 1024) 4a5E Note: When no base value is entered, “ab” will be entered with both number areas left blank.
Chapter 3: Basic Calculations — Basic Keyboard x Second functions Enters an “x”, an unknown variable. Use this key when working with graph equations. Refer to Chapter 4 “Basic Graphing Features” to learn how to use this feature. To access the second function of a key (printed above the keys in yellow), press and release @, then press the key you want to use. % Set the preceding value as a percentage. Example • Get 25% of 1234. 1234|25@ %E * Percentage must be a positive value equal to or less than 100.
Chapter 3: Basic Calculations — Basic Keyboard r Recalls a variable. Example • Set C = 8. 8RACE Recall the value of C. @rACE z {} b Accesses the VARS menu. Refer to chapters 4 and 6 to learn how to use each item in this menu. Enter braces to group numbers as a list. Recalls the previous answer. Use this key to incorporate the answer to the previous calculation into an expression. Example • Perform 3 × 3. 3|3E Subtract the value of the previous answer from “10”.
Chapter 3: Basic Calculations — Basic Keyboard e Recalls the previous entry. This is useful when you want to modify the previous entry, rather than reenter the whole expression over. Example • Calculate 4 × 6. 4|6E Next, calculate 4 × 8. @eB8E Note: Executed expressions are stored in a temporary memory in the executed order. If the temporary memory is full, the oldest data is automatically deleted. Be aware that e may not function on these occasions.
Chapter 3: Basic Calculations — Basic Keyboard 4. Calculations Using MATH Menu Items The MATH menu contains functions used for more elaborate math concepts, such as trigonometry, logarithms, probability, and math unit/format conversions. The MATH menu items may be incorporated into your expressions. Note: A Note about Degrees and Radians The default angle measurement unit while using the calculator’s Basic Keyboard is degrees.
Chapter 3: Basic Calculations — Basic Keyboard 3 tan Enters a tangent function to be used in a trigonometric calculation. Example • Calculate tangent 45°. MA345E 4 log Enters a “log” function for a logarithmic calculation Example • Calculate log 100. MA4100 E 5 10x Enters a base of 10, setting the cursor at the exponent. Example • Calculate 5 × 105. 5|MA55E B NUM Use the NUM sub-menu items when converting between various number systems. 1 abs( abs(value) Returns an absolute value.
Chapter 3: Basic Calculations — Basic Keyboard 2 round( round(value [, digit number of decimals]) Returns the rounded value of the term in parentheses. A rounding point can be specified. * A real number, a list, matrix, variable, or equation can be used as values. Example • Round off 1.2459 to the nearest hundredth. (= 1.25) MB21.2459,2)E 3 ipart ipart value Returns only the integer part of a decimal number. * A real number, a list, matrix, variable, or equation can be used as values.
Chapter 3: Basic Calculations — Basic Keyboard 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. Example • Find the smallest value among 4, 5, and -9. MB6@{4,5,_9 @})E 7 max( max(list) Finds and returns the maximum value within a list of numbers. Example • Find the largest value among 4, 5, and -9.
Chapter 3: Basic Calculations — Basic Keyboard 0 remain natural number remain natural number Returns the remainder of a division. Example • Obtain the remainder when 123 is divided by 5. 123MB05 E C PROB Use the PROB sub-menu items for probability calculations. 1 random random [(number of trial)] Returns a random decimal number between 0 and 1. Example • Make a list with three random numbers. Note: Set the “FSE” to “Fix” and “TAB” to “0”.
Chapter 3: Basic Calculations — Basic Keyboard 3 rndCoin rndCoin [(number of trial)] Returns a specified number of random integers 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. MC3(4 )E 4 rndDice rndDice [(number of trial)] Returns specified number of random integers (1 to 6) to simulate rolling dice.
Chapter 3: Basic Calculations — Basic Keyboard 6 nCr Returns the total number of combinations for selecting “r” item out of “n” items. n Cr = n! r!(n – r)! Example • How many different groups of 7 students can be formed with 15 students? 15MC67 E 7 ! Returns a factorial. Example • Calculate 6 × 5 × 4 × 3 × 2 × 1. 6MC7E D CONV CONV sub-menu items are to be used when converting a number in decimal form (degrees) to a number in sexagesimal form (degrees, minutes, seconds), or vice versa.
Chapter 3: Basic Calculations — Basic Keyboard 2 →dms Takes a number in decimal form (in degrees), and converts it into a sexagesimal number. To enter a number in sexagesimal form, use items in the “ANGLE” sub-menu, described in the next subsection of this Chapter. Example • Show 40.0268 degrees in degrees, minutes, and seconds. 4 0 . 0268 M D 2E E ANGLE The Basic mode has two angle modes: Deg (degree) and Rad (radian).
Chapter 4 Basic Graphing Features — Basic Keyboard This chapter takes the knowledge you have gained in Chapter 3 several steps further. Note: To try the examples in this chapter, it is required that the Basic Keyboard is already set up by the user. To learn how to set up the Basic Keyboard, read “Changing the Keyboard” in Chapter 1. 1. Try it! There are two taxi cab companies in your city, Tomato Cab and Orange Cab, with different fare systems. The Tomato Cab charges $2.
Chapter 4: Basic Graphing Features — Basic Keyboard CONCEPT 1. By using two linear graphs, the approximate crossing point can be found. 2. The exact crossing point can be found with the TABLE function. PROCEDURE 1. Press Y to enter the Graph Equation window. Six equation entry areas appear, from “Y1=” to “Y6=”. Since we need only two equations in this exercise, let’s use “Y1=” and “Y2=”. 2. By default, the cursor should be placed on the right side of the “Y1=” equation, next to the equal sign.
Chapter 4: Basic Graphing Features — Basic Keyboard Graph Basics The graph examples in this exercise are called X-Y graphs. An X-Y graph is quite useful for clearly displaying the relationship between two variables. 7. Let’s take a look at the graph. The vertical axis represents the Y value, while X is represented by the horizontal axis.
Chapter 4: Basic Graphing Features — Basic Keyboard =: The expression can be represented as a graph. =: The expression cannot be drawn as a graph. • Move the cursor pointer to the “=” sign and press E to change between to-draw and not-to-draw. Note: To switch the window back to the calculation screen, simply press the # key. G: Draws a full-screen graph based on the equation(s) entered in the Graph Equation window. To cancel the graph drawing, press O.
Chapter 4: Basic Graphing Features — Basic Keyboard 2 Box A box area can be specified with this sub-menu tool so that the area within the box will be displayed full screen. To select a box area to zoom: 1. While the ZOOM menu item is selected within the ZOOM window, press 2 to select 2 Box. 2. The graph appears on the screen. Use the cursor keys to position the cursor at a corner of the required box area. Press E to mark the point as an anchor. 3.
Chapter 4: Basic Graphing Features — Basic Keyboard B FACTOR Use this menu to set the vertical and horizontal zooming factor. The factor set under this menu directly affects the zoom rate of the 3 In and 4 Out sub-menu tools under the ZOOM menu, as described above. To set the zooming factor, do the following: 1. Within the B FACTOR menu, press E to activate the setup tool. 2. When the “Zoom factor” window appears, the cursor is automatically placed at “X_Fact=”.
Chapter 4: Basic Graphing Features — Basic Keyboard E TRIG 1 sin X Use this when the equation contains a sine function. 2 cos X Use this when the equation contains a cosine function. 3 tan X Use this when the equation contains a tangent function. F STO Under this menu item there is one tool that enables the storing of graph window settings. 1 StoWin Note: By selecting this sub-menu item, the current graph window setup will be stored. The actual graph image will not be stored with this tool.
Chapter 4: Basic Graphing Features — Basic Keyboard U: Press this button to trace the graph drawn on the screen, to obtain the X-Y coordinates: 1. While the graph is displayed, press the U key. The cursor appears, flashing on the graph line, with the 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.
Chapter 4: Basic Graphing Features — Basic Keyboard 4. Now the right boundary of the graph can be set. Enter the required value here (“3”, for example), and press E. Note: The “Xmax=” value cannot be set equal to or smaller than the value of “Xmin”. If so done, the calculator will display an error message upon attempting to redraw the graph, and the graph will not be displayed. 5. The next item “Xscl=” sets the frequency of the X-axis indices. The default value is “1”.
Chapter 4: Basic Graphing Features — Basic Keyboard The following illustration shows these relationships. Y G G @" Y Y @" G @" • The split screen is always in the trace mode. Therefore, the cursor pointer appears on the graph. Accordingly, the coordinate values are displayed reverse in the table and in the equation at which the cursor pointer is located is also displayed reversely. • Using ; or ', move the cursor along the graph. (Values displayed reverse in the table are also changed accordingly.
Chapter 4: Basic Graphing Features — Basic Keyboard k: Calculations can be performed on the entered graph equation(s). Press @ k to access. The following 6 sub-menu tools are available: 1 Value Note: 2 Intsct Note: 3 Minimum Note: 60 With this sub-menu tool, the Y value can be obtained by entering an X value. The flashing graph cursor will then be placed in that position on the graph. If more than one graph equation is set, use the { or } keys to switch to the equation you wish to work with.
Chapter 4: Basic Graphing Features — Basic Keyboard 4 Maximum Note: 5 X_Incpt Note: 6 Y_Incpt d: Finds the maximum of the given graph, and places the flashing cursor at that position. If the given graph has no maximum value, an error message will be displayed. Finds an X-intercept (a crossing point of the graph on the X-axis) of the given graph, and places the flashing cursor at that position. If there is more than one Xintercept, the next X-intercept can be found by selecting the tool again.
Chapter 4: Basic Graphing Features — Basic Keyboard 2. Press @, and d to enter the DRAW menu, then press G to select G SHADE. The SHADE sub-menu appears. 3. Press 1 to select 1 SET. The “Set shade” window appears. 4. Using the cursor keys, move the cursor pointer to the appropriate position. 5. Press @ z A. 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.
Chapter 4: Basic Graphing Features — Basic Keyboard f: The graph appearance can be set and verified under this menu. Press @ f to access. A –––––– Displays the current FORMAT settings.
Chapter 4: Basic Graphing Features — Basic Keyboard • 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 variables (characters) can be used for one equation. (If the equation contains more than seven variables (characters), up to seven characters from the top of the equation are determined as variables and subsequent characters are ignored.
Chapter 4: Basic Graphing Features — Basic Keyboard 2. Press 2 E. (2 is input to A.) The graph 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.
Chapter 5 Advanced Calculations — Advanced Keyboard Note: To try the examples in the chapter, it is required that the Advanced Keyboard is already set up by the user. To learn how to set up the Advanced Keyboard, read “Changing the Keyboard” in Chapter 1. 1. Try it! The Mendocino Tree, a coast redwood growing in Montgomery Woods State Reserve in California, is known to be the tallest living tree in the world.
Chapter 5: Advanced Calculations — Advanced Keyboard PROCEDURE 1. Since the angle of elevation is measured in degrees, the calculator’s angle setting will need to be matched with that. Press @ ; to bring up the SETUP menu. 2. On the right side of the SETUP menu, the current 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.
Chapter 5: Advanced Calculations — Advanced Keyboard s Enters a sine function to be used in a trigonometric expression. c Enters a cosine function to be used in a trigonometric expression. t Enters a tangent function to be used in a trigonometric expression. l Enters a common logarithm function. I Enters a natural logarithm function. Example • Calculate In e4. I @ @ 4 E. y Raises the preceding value to the 2nd power. If no preceding value exists, then the base value will be left blank.
Chapter 5: Advanced Calculations — Advanced Keyboard The following math functions can be accessed with the use of @ key. To learn the basic steps of how to access the second function of each key, refer to the section “Second Function Key” of Chapter 2. s Enters an arcsine function to be used in a trigonometric expression. Example • Calculate arcsine 1. @ s 1 E. c Enters an arccosine function to be used in a trigonometric expression. Example • Calculate arccosine 0.5. @ c 0.5 E.
Chapter 5: Advanced Calculations — Advanced Keyboard x Raises a preceding value to the power of -1. If no value is preceded, then the cursor will be placed at the base. _ Enters an ath root of a base. When a value precedes, then the value will be incorporated as the index number. Otherwise, both entry areas will be left blank. + Enters a square root; sets the cursor at the base entry area. $ Enters π (3.14…).
Chapter 5: Advanced Calculations — Advanced Keyboard 02 2X 2value Raises 2 to a power. Sets the cursor to exponent. 03 fmin( fmin(equation, lower limit of x, upper limit of x) Returns the value of variable x when the equation Y has the minimum value within the specified range of x. 04 fmax( fmax(equation, lower limit of x, upper limit of x) Return the value of variable x when the equation Y has the maximum value within the specified range of x.
Chapter 5: Advanced Calculations — Advanced Keyboard 08 ∑( 72 ∑(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) function to be used in a trigonometric expression.
Chapter 5: Advanced Calculations — Advanced Keyboard B NUM 18 sinh-1 sinh-1 value Enters an inverse hyperbolic sine. 19 cosh-1 cosh-1 value Enters an inverse hyperbolic cosine. 20 tanh-1 tanh-1 value Enters an inverse hyperbolic tangent. Use the sub-menu items below to convert a value. Refer to “Chapter 3: Basic Calculation — Basic Keyboard” to learn how these tools can be used. 1 abs( 2 round( Returns the absolute value of a given number. Returns a rounded value of a given term in parentheses.
Chapter 5: Advanced Calculations — Advanced Keyboard C PROB These sub-menu items are useful for probability calculations. Refer to “Chapter 3: Basic Calculations — Basic Keyboard” for details. A comprehensive list of menu items can be found in the Appendix. 1 random 2 rndInt( Returns a list of random integers, between a minimum and a maximum value. 3 nPr Returns the total number of permutations for selecting “r” items out of “n” items.
Chapter 5: Advanced Calculations — Advanced Keyboard Rectangular to polar coordinate conversion functions Conversion formulas: r = (x2 + y2)1/2, θ = tan-1(y/x) 3 xy→r( xy→r(x coordinate, y coordinate) Returns polar coordinate radius value from X-Y rectangular coordinates. θ( 4 xy→θ xy→θ θ(x coordinate, y coordinate) Returns polar coordinate θ value from X-Y rectangular coordinates. The following ranges are used to find θ.
Chapter 5: Advanced Calculations — Advanced Keyboard E ANGLE F INEQ 76 Use these tools to enter the symbols to specify angle units. 1° Inserts a symbol for “degrees”. 2’ Inserts a symbol for “minutes”. 3” Inserts a symbol for “seconds”. 4r Enters an “r” symbol, to enter a number in radians. 5g Enters an “g” symbol, to enter a number in gradients. Use the equality/inequality figures to compare two values. These sub-item tools return 1 (true) or 0 (false).
Chapter 5: Advanced Calculations — Advanced Keyboard G LOGIC Use the LOGIC sub-menu items to perform boolean operations. In the N-base calculation mode (binary, octal, decimal and hexadecimal), A LOGIC will directly appear when M is pressed.
Chapter 5: Advanced Calculations — Advanced Keyboard 4 neg Note: “4 neg” menu appears only in the N-base calculation (binary, octal, decimal and hexadecimal) mode. 5 xor value A xor value B Enters an ExclusiveOR (xor) logic figure. 1100 M 5 1010 E 6 xnor H COMPLX neg value Enters a “neg” logic figure. M41 E value A xnor value B Enters an ExclusiveNOR (xnor) logic figure.
Chapter 5: Advanced Calculations — Advanced Keyboard 2 real( 3 image( real(complex number) Returns the real part of a complex number (or list of complex numbers). image(complex number) Returns the imaginary part of a complex number (or list of complex numbers). 4 abs( abs(complex number) Returns the absolute value of a complex number (or list of complex numbers). 5 arg( arg(complex number) Takes the coordinates (x + yi), and returns the θ.
Chapter 5: Advanced Calculations — Advanced Keyboard Example • Calculate (3 + 4i) × (4 – 6i) Note: It is possible to input complex numbers (i) in the real number mode, however an error message will return. Functions available for complex 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.
Chapter 5: Advanced Calculations — Advanced Keyboard 5. 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 access the TOOL menu. Press the # key (or @ q) to escape from the menu. A NBASE Calculations can be performed in different number base systems, while simultaneously converting the calculation result into hexadecimal, decimal, octal, and binary systems. 1.
Chapter 5: Advanced Calculations — Advanced Keyboard B SYSTEM With this tool, linear equations containing up to 6 unknown values (i.e., ax + by + cz + du + ev + fw = g) can be solved. 1. Press B to select B SYSTEM, and select the number of unknown values. For example, press 2 if values x and y are unknown. 2. In the next screen, an equation ax + by = c is displayed, with an entry table for the known values — a, b, and c. 3. Enter 2 sets of the known values, as shown in the figure.
Chapter 5: Advanced Calculations — Advanced Keyboard 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, and c, press C to go back to the previous screen. To select a different degree of polynomial, press @ V to go back to the TOOL menu.
Chapter 6 Advanced Graphing Features — Advanced Keyboard In this chapter, some real-life situations are featured. You are encouraged to modify the examples to make your own graph schemes. Note: To try the examples in this chapter, it is required that the Advanced Keyboard is already set up by the user. To learn how to set up the Advanced Keyboard, read “Changing the Keyboard” in Chapter 1.
Chapter 6: Advanced Graphing Features — Advanced Keyboard CONCEPT 1. Grasp the idea of sequential equations. 2. Use the graph tracing function to obtain approximate values. PROCEDURE 1. First, let us set the calculator to the appropriate graphing coordinate mode. Press @ ; to enter the SETUP menu, press E to select E COORD, then press 4 to select 4 Seq, and press C. 2. We will use the “Time” sequential graph type within the FORMAT menu. Press @ f, press G to select G TYPE, and 2 to select 2 TIME. 3.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 7. Press G to draw the graph. 8. If the line is outside of the graph’s range, press Z then 1 to select automatic zoom. This will only display a small portion of the graph, so the graph’s range will need to be changed. 9. Press W. Find nMax= and change the value to 15 (default: 10). Next, find Xmax= and change the value to 15 too (default: 10). 10. Press the G key again. 11. Use the graph trace function by pressing U.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 2. Graphing Parametric Equations A two-dimensional parametric equation assumes that both X and Y are represented by functions in a third variable T. When set in parametric graphing mode, the calculator automatically sets up the Graph Equation Entry screen to take one set of X and Y per each graph, with the equation’s right side variable to be set as “T”. Example • Draw a graph: x(t) = 16cos(t), y(t) = 9sin(t). 1. Press @ ; to enter the SETUP menu.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 3. Polar Graphing Polar coordinates are a different method of specifying a point in two dimensions; the location of the point is described by the distance from the X-Y intersect “r”, and its elevation angle “θ”. r 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.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 4. Graphing Sequences The sequence graph mode can store and simultaneously draw three graph equations u(n), v(n), and w(n). Variables u, v, and w are entered as @ u (or v, w). Use X to enter the natural number n. A sequence is an ordered set of numbers with a defined relationship. The recursive sequential formulas can be described as un = un-1 + d un = un-1 × r and/or where un is the n-th term, d is the common difference, and r is the ratio.
Chapter 6: Advanced Graphing Features — Advanced Keyboard phase-based (uv, uw, or vw) The un values will be plotted against the vn values (uv). (n–1)-based (Web) The un values will be plotted against the un-1 value. Note: • When un–2 is incorporated in to the equation, the u(nMin) requires two values: the minimum, and the second smallest. For example, you will need {0, 1} in the u(nMin) entry row if u(n–1) + u(n–2) is entered as the equation. • When Web is selected, n – 2 cannot be referred to.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 4. Now, go to the Graph Equation Entry window by pressing Y. The cursor is set at the first line u(n); pressing C will clear any previous entry, as well as to put the cursor at the right side of the equation. 5. Enter 2 × 2n-1. Use the X key to enter n. When done, press E. The cursor moves down to the second row. 6. In the entry area u(nMin)=, enter the minimum value of the n, 1, then press E. 7. Press the G key. 8.
Chapter 6: Advanced Graphing Features — Advanced Keyboard The calculator can accept up to three sequential equation entries. We will use the v set, since the u set already has an entry. Move the cursor down to the v(n) entry area, and press C. 4. Enter 2 × 0.9n-1, then press E. The cursor will be set to the fourth entry row v(nMin=). 5. Press C, then enter 1. 6. Press the G key to draw the graph, then zoom the graph so that it be comes visible (Z, 1 Auto). 7. Use the U function to trace the graph.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 3. Press the Y key to go to the Graph Equation Entry window. 4. At the first equation entry row, enter u(n - 1) + 100. When done entering, press E. 5. At the next entry row, make sure that it has the starting value “0”. 6. Bring the cursor down, and clear the rest of the four rows. 7. Press G, then press Z, 1 Auto to view the graph.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 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 graph is drawn back on the screen again, with the θ= prompt visible at the bottom left side of the screen. 5. Enter the θ value at the prompt. Enter π, for example. Be aware that θ cannot be more than 2π (2π radians = 360 degrees). 6.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 6. Format Setting You can set up the Graph screen format from the FORMAT menu. Press @ f to display the Graph format menu. Advanced keyboard specific sub-menus Note: A –––––– G TYPE appears only when the sequence coordinate graph mode is selected. Displays the current FORMAT settings.
Chapter 6: Advanced Graphing Features — Advanced Keyboard F CURSOR The coordinate system that indicates the location selected by the trace or other function can be selected from 1 RectCoord (Rectangular coordinates) or 2 PolarCoord (Polar coordinates) (In the parametric system, the T indication is added.) G TYPE This menu is only active when the sequence coordinate graph mode is selected in the SETUP menu. The G TYPE menu will not appear in the other modes.
Chapter 6: Advanced Graphing Features — Advanced Keyboard D EXP 2ex 4 In X Use this tool when the equation contains a form of “ex”. Use this tool when the equation contains a form of “In x”. E TRIG 4 sin–1 X Use this when the equation contains an arc sine function. 5 cos–1 X Use this when the equation contains an arc cosine function. 6 tan–1 X Use this when the equation contains an arc tangent function. 1 sinh X Use this when the equation contains a hyperbolic sine function.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 8. Setting a Window The W key displays the graph window setup. The display will differ according to the selected coordinate system. See also Chapter 4 “Basic Graphing Features — Basic Keyboard” on pages 57 to 58 for details of rectangular coordinate system settings.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 9. Tables The calculator enables you to illustrate the changes using the equation and graph you have input. It also has tables for showing a list of X and Y values. Each column item can display up to 7 digits, including a sign and/or a decimal point. There are four kinds of tables available corresponding to the coordinate system. Rectangular coordinate system • The variable X is displayed in the left end column.
Chapter 6: Advanced Graphing Features — Advanced Keyboard Polar coordinate system • The variable θ is displayed in the left end column. • The columns θ, R1 to R3 are displayed on the first screen. • Press ; ' to horizontally scroll the table. • The 10-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.
Chapter 6: Advanced Graphing Features — Advanced Keyboard User: Displays a blank table. As you input values for variable columns, table values are automatically calculated by the equation. Thus, although TableStart and TableStep inputs can be made when selecting User, set values will be ignored. • Press ; or ' to switch between Auto and User. • TableStart is a start value of the variable in the table, and TableStep is a step value of the variable. Both are numeric values.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 10. The DRAW Function With the DRAW function, lines, circles, graphs, and pixel points can be added to the graph window. The DRAW menu also contains configuration tools for the ordinary graphs entered in the Graph Equation Entry window: line types, shading, and visibility status of each graph. Press @ d to enter the DRAW menu. Note: A DRAW When entering coordinates, the DRAW function assumes that rectangular coordinates will be entered.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 2 Line( Note: From the Calculation screen Draws a line according to the given X-Y coordinates of a start/end point. This tool can be used with any type of graph. Line(x-coordinate of start point, y-coordinate of start point, x-coordinate of end point, y-coordinate of end point [,0]) Example 1. Select the DRAW menu. Select A DRAW in the menu, then select 2 Line(. “Line(” will appear.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 2. Press A to select A DRAW, then press 2 to select 2 Line(. The GRAPH window reappears, with the coordinate of the cursor showing at the bottom of the screen. Note: To change the cursor coordinate system, use the FORMAT menu. Select F CURSOR, then select the required coordinate system for the cursor. 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.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 3 H_line From the Calculation screen Draws a horizontal line on the graph window. H_Line y-value Draws a horizontal line (y = value) on the graph window. Example • Draw a horizontal line of y = 5. 1. Press @ dA 3 and enter the value 5. From the GRAPH window H_Line Example • Draw a horizontal line manually. 1. Press @ dA 3. 2. Use the cursor navigation keys ({ } ; ') to move the flashing cursor to the appropriate position. 3.
Chapter 6: Advanced Graphing Features — Advanced Keyboard From the GRAPH window V_Line Example • Draw a vertical line manually. 1. Press @ d A 4. 2. Use the cursor navigation keys ({ } ; ') to move the flashing cursor to the appropriate position. 3. Press E to draw the line. 5 T_line( From the Calculation screen Draws a tangental line at the specified point of a graph curve. T_line(equation, x-value) Example • Draw the tangental line of y = x2 at x = 1. 1. Select T_Line(. 2. Enter “x2, 1)” on the line.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 6 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: 7 Shade( This tool can be used with rectangular coordinate graphs only. Shade(equation1, equation2 [, lower value, upper value]) Draws two graphs, and shades the area between the two. If the x range is specified, it shades the area within the specified range.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 8 DrawInv DrawInv equation Draws an inverse of a given graph expression. Example 1 • Draw the inverse graph of y = 4 x2 – 8. 1. Select DrawInv. 1 2. Enter “ 4 x2 – 8” on the line. 3. Press E. Note: 9 Circle( From the Calculation screen It is also possible to specify a function equation from Y0 to Y9 if stored. Draw a circle on the graph screen.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 0 Text( Text(column, row, “strings”) Enters a text string at a given coordinate. 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 text.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 1 PntON( PntON(x-coordinate, y-coordinate) Draws a point at a given coordinate. It takes the X-Y coordinate as an argument. This tool can either be accessed from the GRAPH window or other windows. Entering from the GRAPH window enables a graphic entry, while entering from other windows enables text-based entry. 2 PntOFF( PntOFF(x-coordinate, y-coordinate) Erases a pixel point. It takes the X-Y coordinate as an argument.
Chapter 6: Advanced Graphing Features — Advanced Keyboard 7 PxlTST( C ON/OFF 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. Sets the visibility status of a given graph number (0-9). 1 DrawON 2 DrawOFF DrawON [equation number 1, ....] or DrawON Sets the specified graphs visible. If no argument is given, then all graphs will be set visible. DrawOFF [equation number 1, ....
Chapter 6: Advanced Graphing Features — Advanced Keyboard D LINE Sets the line appearance of each graph. Each graph coordinate mode (i.e., rectangular, polar, etc.) can retain a set of line appearance preferences. Solid line, dotted line, bold line, locus and dots can be selected. 1. Press @ d D to select D LINE, then press E. 2. The next window enables you to select the line types of each graph in the set coordinate mode. (The rectangular coordinate mode is selected in this example.
Chapter 6: Advanced Graphing Features — Advanced Keyboard Note: F PICT Attempting to call back graph data from an empty location will result in an error. Stores and recalls the displayed pixel data for the graph window. The 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.
Chapter 6: Advanced Graphing Features — Advanced Keyboard G SHADE With these sub-menu tools, inequalities, intersections and compliments of multiple graphs can be visualized. 1 SET 2 INITIAL Sets up the shading area for each graph. Refer to “3. Other Useful Graphing Features” in Chapter 4 of this manual to learn how to utilize this tool. Initializes the shading setup, and brings up the shading setup window. 11. Substitution Feature Refer to the page 63 for details.
Chapter 7 SLIDE SHOW Feature The SLIDE SHOW feature is especially incorporated to help students understand math concepts utilizing the calculator’s graphing capabilities. With this feature, the calculator’s screen images can be captured, organized, and stored. The SLIDE SHOW feature is designed to be used with SHARP’s optional overhead projection system, which offers a hassle-free math presentation environment for the entire class. The SLIDE SHOW can be used in both Basic and Advanced mode.
Chapter 7: SLIDE SHOW Feature Capture images 4. Press Y to enter the graph equation mode. 5. Enter (x – 3)(x – 1)(x + 2) at the first equation. 6. Press @ n. The message “STORE SCREEN: 01” will appear. The image will be stored on page 1 of the SLIDE SHOW “CUBIC,” and the screen will automatically return to the previous screen. Each time you press @ n, the screen image will be captured and stored in the SLIDE SHOW. 7. Press G. Note: • You cannot capture an image while drawing.
Chapter 7: SLIDE SHOW Feature Playing back the newly created SLIDE SHOW 1. Press ] to go to the SLIDE SHOW menu. Press 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.
Chapter 7: SLIDE SHOW Feature 6. Go down to the last captured image using the } key. 7. Press E to mark the image. Specify the insertion point 8. Go up to the page 3 using the { key. 9. Press E. The marked image will be inserted at page 3. 2. The SLIDE SHOW menu This section of the chapter summarizes each item in the SLIDE SHOW feature menu. A CURR Displays the name of the currently selected or working SLIDE SHOW. Press @ n to capture an image.
Chapter 7: SLIDE SHOW Feature 1. While in the SLIDE SHOW menu, press E to select E EDIT, then press 1 to select the 1 MOVE sub-menu item. 2. With the { and } cursor keys, select the captured image you wish to move, then press E. 3. Select the position to which you wish to move the previously selected image using the { and } cursor keys. 4. Pressing E will place the selected image at the new location. The selected image will be placed immediately before the current screen.
Chapter 8 Matrix Features Within the Matrix features, up to ten different matrices can be entered. To get to the Matrix features, press @ m. Define and edit the matrices within this mode too. 1. Try it! 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 second and three of the third for 26 dollars.
Chapter 8: Matrix Features PROCEDURE Select a matrix to edit 1. Press @ m to enter the MATRIX menu. 2. Press B to select EDIT and then 1 to select 1 mat A. Define dimensions 3. Press 3 E 4 E to define the dimensions of the matrix (3 rows × 4 columns). Enter the values 4. Press 3 E 2 E 1 E 3 9 E to enter the first 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.
Chapter 8: Matrix Features 10. Press E. The reduced row echelon form of the matrix is displayed. Display Solution 1x + 0y + 0z = x = 9.25 0x + 1y + 0z = y = 4.25 0x + 0y + 1z = z = 2.75 2. Entering and Viewing a Matrix Select a matrix Note: Define dimensions 1. Press @ m, then press B (select EDIT) and select the matrix you want to define. Up to 10 matrices from 1 matA to 0 matJ can be defined. 2. Enter the row dimension number and press E. Cursor moves to the column dimension. 3.
Chapter 8: Matrix Features Enter elements in the matrix 1. Press appropriate number keys to enter numbers at the 1st row and 1st column. The number is displayed at the bottom of the screen. 2. Press E. The cursor moves to the 1st row, 2nd column. 3. Sequentially input the element data. 4. Press # after completion of data input. Editing keys and functions ;' Move the cursor within the current row or scroll horizontally. {} Move the cursor within the current column or scroll vertically.
Chapter 8: Matrix Features 3. Normal Matrix Operations Many calculations can be made between a matrix and a real number or between matrices. Examples of each calculation are as follows: Matrix + Matrix Matrix – Matrix To add or subtract matrices, the dimensions must be the same. Example 1. Press # C. 2. Press @ m A 1+@m A2 3. Press E. Matrix × Matrix To multiply two matrices, the column dimension of the first matrix must match the row dimension of the second matrix. Example 1. Press # C. 2.
Chapter 8: Matrix Features 4. Special Matrix Operations This calculator 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.
Chapter 8: Matrix Features 03 cumul cumul matrix name Returns the cumulative matrix. Example • Obtain the cumulative sum of mat A. cumulative sum of aij = ai1 + ai2 + ...... + aij 04 augment( augment(matrix name, matrix name) Appends the second matrix to the first matrix as new columns. The first and second matrices must have the same number of rows. Example • Create a new matrix with matrix A augmented by matrix B.
Chapter 8: Matrix Features 07 row_swap( row_swap(matrix name, row number, row number) Returns the matrix with specified rows swapped. Example • Swap the 2nd and 3rd rows in the matrix E. e2j = e3j , e3j = e2j 08 row_plus( row_plus(matrix name, row number, row number) Adds the first specified row data to the second specified row data. Example • Add the 2nd row data to the first row of matrix E.
Chapter 8: Matrix Features 11 mat→list( Creates lists with elements from each column in the matrix. If dimensions of columns is greater than the number of lists specified, extra columns are ignored. Also, if it is less than the number of lists specified, extra lists are ignored. mat→list(matrix name, list name 1, ..., list name n) Example • Make List 1 and List 2 by using the 1st and 2nd columns of matrix E, respectively.
Chapter 8: Matrix Features Calculations using MATH menus 1 det det matrix name Returns the determinant of a square matrix. The determinant can only be applied to a matrix which has the same row and column dimensions. Example • Give the determinant of matrix A. 2 trans trans matrix name Returns the matrix with the columns transposed to rows and the rows transposed to columns. Example • Transpose rows and columns of matrix B.
Chapter 8: Matrix Features Use of [ ] menus Using [ ] menus, you can manually enter a matrix on the calculation screen. 1. Press @ m E 1 ( [ ) at the beginning of the matrix. 2. Press @ m 1 ( [ ) to indicate the beginning of the first row. Once you enter the manual matrix entry mode, you can directly enter “or” by selecting 1 or 2. 3. Enter a number or expression for each element. Separate each element with commas. 4. Press @ m 2 ( ] ) to indicate the end of the first row. 5.
Chapter 9 List Features List features can be used in both Advanced and Basic mode. In this chapter, all the procedures are based on the Advanced mode. In the Basic mode, press @ l and select A NAME to access L1 to L6. 1. Try it! By analyzing years of data, we found that it takes the driver of a car approximately 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.
Chapter 9: List Features Store the list in L1 4. Press R @ 1. Enter the equation using L1 6. Press 1.1 | @ 1 + 0.06 | @1y 5. Press E to store the list in L1. 7. Press E. 8. List {87, 140, 205, 282, 371, 472} will appear.
Chapter 9: List Features 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). Using @ l (L_DATA) menus, you can store up to 10 sets (L_DATA 0 to L_DATA 9) of lists (L1 to L6) in a memory and recall any of the stored sets as required.
Chapter 9: List Features Calculate 10 × L1 and store the results in L3 1. Press 10 | @ 1R@3 E. Calculate the sine of L3 2. Press s @ 3 E. “...” shows that results extend beyond the display to the right. Use ;, ' to scroll left or right, respectively. 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 5. Press 7 R @ 1 (5)A/ @ 1 E.
Chapter 9: List Features 4. Special List Operations This calculator has three list calculation menus: OPE, MATH and L_DATA. * In the Basic mode, L1 to L6 (list names) can be accessed from the LIST menu. Calculations using the OPE menu functions 1 sortA( sortA(list name) Sorts lists in ascending order. Example • Store list {2, 7, 4} in L1, and sort L1 in ascending order. 2 sortD( sortD(list name) Sorts lists in descending order. Example • Sort the above list L1 in descending order.
Chapter 9: List Features 3 dim( dim(list) Returns the number of items (dimension) in the list. Example • Display the dimension of list L1. natural number ⇒ dim(list name) Set the number of items (dimension) of specified list to the specified 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.
Chapter 9: List Features 5 seq( seq(equation, start value, end value[, increments]) target list name Makes a list using the specified equation, range (start value and end value) and increments. Example • Fill the list using the equation y = x2 – 8, where x increases from -4 to 4 by increments of 2. * If increment is omitted, the default value 1 is used. 6 cumul cumul list Sequentially cumulates each item in the list (for Advanced mode only). li = l1 + l2 + ...
Chapter 9: List Features 8 augment( augment(list 1, list 2) Returns a list appending the specified lists. Example • Obtain the list appending L1 ({4, 2, 7}) and L2 ({-1, -3, -4}). 9 list→mat( list→mat(list 1, ..., list n, matrix name) Makes a matrix using the specified list as column data, stored under the specified matrix name (for Advanced mode only). 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.
Chapter 9: List Features Calculations using MATH Menus During the following explanations, the values of lists, L1 and L2 will be assumed to be: L1 = {2, 8, -4} L2 = {-3, -4, -1} 1 min( min(list) Returns the minimum value in the list. Example • Calculate the minimum 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.
Chapter 9: List Features 4 median( median(list [, frequency list]) Returns the median value of items in the specified list. Example • Calculate the median value of the list L2. 5 sum( sum(list [, start number, end number]) Returns the sum of items in the specified list. Example • Calculated the sum of the list items of L1. * You can specify the range of items in the list to sum. sum(L1,1,2) means sum the 1st to 2nd items of the list L1.
Chapter 9: List Features 7 stdDv( stdDv(list [, frequency list]) Returns the standard deviation of the specified list items. Example • Calculate the standard deviation using the list items of list L2. 8 varian( varian(list [, frequency list]) Returns the variance of the specified list items. Example • Calculate the variance using the list items of list L2.
Chapter 9: List Features 3. Press G. Two graphs are drawn as shown on the right. In this case, the first one represents the equation y = 3x2 + 5x + 2 and the second y = -2x2 + 3x + 4. You can also use L1 to 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).
Chapter 9: List Features 2 RclLD RclLD natural number (0-9) Recall the stored group of lists for use. Any current list data (not stored in L_DATA) is overwritten. Example 1. Press @ l and select C 2. 2. Enter the number to recall and press E. “Done” will appear and the current lists will be overwritten by the recalled list group. 7. Using List Table to Enter or Edit Lists You can use List Table in the STAT menu to easily access the contents of the lists.
Chapter 9: List Features How to edit the list 1. Press S and select A EDIT, then press E. 2. Use the cursor keys to move the cursor to the target cell. 3. Enter the 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.
Chapter 10 Statistics & Regression Calculations Note: The explanation of this chapter is based on the Advanced Keyboard. The following statistical and regression features are available: • • • • • • • Statistical calculations such as means and standard deviations Graphing statistical data Plotting regression curves Statistical tests Estimation Obtaining coefficients from regressions Distribution functions 1.
Chapter 10: Statistics & Regression Calculations 2. Select A EDIT and press E. The List table will appear. Initially, all elements are blank and the cursor pointer is located at L1-1 (top left). Entering hours (index value) 3. Input 1 for hour. 4. 1 will be displayed at the bottom line of the display. 5. Press E to input the index value. 6. Continue the procedure to input 2 to 24. Entering the data for Sunday 7. Press ' to move the cursor to the top line of L2. 8. Input 98 for hour 01.
Chapter 10: Statistics & Regression Calculations Setting the graph drawing “on” 3. The first line shows if the graph drawing is on or off. Initially, the graph drawing is off. With the cursor pointer at the “on” position, press E to set the graph drawing on. Selecting whether 1variable plotting or 2-variable plotting 4. Press } to move the cursor to the next line (DATA).
Chapter 10: Statistics & Regression Calculations 15. Select 9 Stat and press E. You can directly press 9 at step 13 to select 9 Stat. The histogram will appear on the display. When you draw the graph using the automatic statistics zoom function (9 Stat), the division number is automatically set to Xmax –Xmin (default value: 10). If you wish to show the graph Xscl hour by hour, change the value in the W menu. Set the WINDOW settings 1. Press W. Window (Rect) setting menu will appear. 2.
Chapter 10: Statistics & Regression Calculations 8. Move the cursor to GRAPH and press [. 9. Press B 2 (broken line with cross points). 10. Press G. Now you can compare the difference in web site access counts between Sunday and Monday. Press @ q. 2. Statistics Features 1. STAT menus Press the S key to access the statistical calculation menus. The menus are as follows: A EDIT Provides the entry or edit mode and displays a list table.
Chapter 10: Statistics & Regression Calculations 2.
Chapter 10: Statistics & Regression Calculations The web site access counts example on page 145 will be used again to demonstrate the calculation of statistical values.
Chapter 10: Statistics & Regression Calculations Calculating the previous two-variable statistical values can be performed in a single operation. Use a “ , ” (comma) to separate the two variables. 1. Press # C and S to display the statistics menu. 2. Press C and then 2. 2_Stats will be displayed on the top line of the screen followed by the cursor. 3. Press @ 2 , @ 3 to enter L2 and L3, and press E. All the statistical values will be displayed on the screen. 4. Press } or { to scroll the screen.
Chapter 10: Statistics & Regression Calculations 3. Graphing the statistical data Press [ to access the statistical graphing mode. The calculator can plot statistical data on up to 3 types of graph (PLOT1 to PLOT3) to check the state of distribution. The graph types can be selected from histogram, broken line plot, normal probability plot, normal distribution plot, box plot, modified box plot, pie chart, scatter diagram and XY line.
Chapter 10: Statistics & Regression Calculations Broken line plot (B.L.) A broken line graph for the frequency distribution of sample (x) Three types of points can be selected from circle, cross and square. The broken line is displayed by connecting the upper left points of the bars of the histogram, as the upper left point of each bar represents each class value in the histogram. The calculator can draw both a histogram and a broken line plot at the same time. Normal probability plot (N.P.
Chapter 10: Statistics & Regression Calculations Box plot (Box) A box plot graph of sample (x) A. The minimum value (xmin) of the sample (x) B. The first quartile (Q1) A B C D E C. Median (Med) of the sample (x) D. The third quartile (Q3) E. The maximum value (xmax) of the sample (x) Modified box plot (MBox) A modified box plot graph of sample (x) A. The minimum value (xmin) of the sample (x) B. The tip of extension which is defined by (Q3 – Q1) x 1.5 A B CD E F G C. The first quartile (Q1) D.
Chapter 10: Statistics & Regression Calculations Pie chart (PIE) Pie graph of sample (x) • Maximum number of division is 8. • Calculation range: 0 ≤ x < 10100 • Data can be displayed in two modes: • Value display: 8 digits • Percentage display: Fixed decimal (2 digits decimal) * Pie graphs are drawn in the same order as on the specifying list. * Pie graphs cannot be displayed simultaneously with other graphs and X/Y axis, though lines or dots can be drawn.
Chapter 10: Statistics & Regression Calculations 2. Specifying statistical graph and graph functions • Up to three graphs can be plotted per sample data. Specifying type of statistics graphing 1. Press [. 2. Select from A PLOT1, B PLOT2 or C PLOT3 and press E to set the statistical graphing specifications. Press @ q before step #3. • You may just press A to C to select. • You can overlap 3 plotting graphs (from PLOT1 to PLOT3) on a single screen.
Chapter 10: Statistics & Regression Calculations 3. • To set the all plotting ON: Press 1 (1 PlotON). • To set the all plotting OFF: Press 2 (2 PlotOFF). * You can control the plotting of PLOT1 to PLOT3 separately by pressing 1 ~ 3 after PlotON (or PlotOFF). 4. Press E to set. 4. Trace function of statistical graphs • The trace feature is available in statistical graphing and can be used to trace the curves of graphs with the cursor. Tracing the graph 1. Press U. Histogram How tracing is done 2.
Chapter 10: Statistics & Regression Calculations 4. Data list operations Descending sort, ascending sort, changing the list order and deleting the lists can be done in the Operation menu. Press S B OPE to access the data list operations. 1 sortA( sortA(list) Sorts the list in ascending order. This function is the same as the sortA( menu item in List functions. See page 135 for details. 2 sortD( sortD(list) Sorts the list in descending order.
Chapter 10: Statistics & Regression Calculations 5. Regression Calculations Accessing the 1. Press S D REG. regression menu The Regression menu is displayed. 01 Med_Med Med_Med (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression line using the median-median method. (linear regression) Formula: y = ax + b Parameters: a, b 02 Rg_ax+b Rg_ax+b (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression line.
Chapter 10: Statistics & Regression Calculations 06 Rg_x4 Rg_x4 (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression curve using the fourth degree polynomial. (quartic regression) Formula: y = ax4 + bx3 + cx2 + dx + e Parameters: a, b, c, d, e, R2 07 Rg_ln Rg_ln (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression curve using the natural logarithm.
Chapter 10: Statistics & Regression Calculations 11 Rg_x–1 Rg_x–1 (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression curve using the reciprocal function. (reciprocal regression) Formula: y = a + bx-1 Parameters: a, b, r, r2 12 Rg_axb Rg_axb (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression curve using the power function.
Chapter 10: Statistics & Regression Calculations value or list x’ Finds the estimated value of x for a given value of y by applying the function determined by the regression. 15 x’ Example When the following is entered as statistical data: x y 10 20 20 40 30 60 40 80 50 100 Find estimated value of x given y = 140. 1. Enter the above data into L1 (x) and L2 (y) and execute Rg_ax+b (L1, L2). 2. Press # 140 S D 1 5 E.
Chapter 10: Statistics & Regression Calculations Enter a data in a list table 1. Press S A E. 2. Enter the time into list 1 (L1). 3. Enter the temperature into list 2 (L2). Plotting the data 1. Press [ A E. 2. Press E to turn on the plotting. 3. Press } and ' to select XY of DATA menu and press E. Freq will change to ListY and set L2 to ListY. Selecting the graph type 1. Press } to move the cursor to GRAPH. 2. Press [ G and 2 (2 Scattr+) to set the graph type to scatter and point type to “+”. 3.
Chapter 10: Statistics & Regression Calculations About the residual list • There are residuals between regression curves and actual values. • The residual list stores these residuals automatically. • The resid list can be found in B REGEQN of the STAT VARS menu (@ z H E B 0). • Use the following key operation to recall the residual list from the calculation screen. #C@zHEB0 • Press E to display the residual list on-screen.
Chapter 10: Statistics & Regression Calculations • 16 InputList and 17 InputStats specify the above input methods. 16 InputList: Sets the input mode to the statistic data list method 17 InputStats: Sets the input mode to the value input mode For example, press S E 1 6 E to set to the list input mode. 5. Press @ h to execute the hypothesis test.
Chapter 10: Statistics & Regression Calculations 02 Ftest2samp Two samples data are tested for equality of standard deviation σ1 and σ2. Example Test when population standard deviation σ1 < σ2, n1 = 20, standard deviation sx1 = 5.6, n2 = 50, and standard deviation sx2 = 6.2 Set the input method to value input mode 1. Press # S E 1 7 E. 2. Press S E 0 2. The parameter input screen will appear. 3. Press ' E } to select σ1 < σ2. 4. Enter the values into the parameter fields. 5.6 E 20 E 6.2 E 50 E. 5.
Chapter 10: Statistics & Regression Calculations 3. Press ' E } to select µ < µ0 and press E. 4. Move the cursor pointer to µ0 and input 65 and press E. 5. Set the List to L1 and press E. 6. Press @ h. Answers are displayed on the screen, where t is the t statistic for the test, p is the p value for the test and sx indicates sample standard deviation. • If there is no weight list, the Freq field can remain empty. 04 Ttest2samp Tests two sample means, µ1 and µ2.
Chapter 10: Statistics & Regression Calculations 4. Press @ h. 05 TtestLinreg Tests the significance of the slope for the linear regression and its correlation coefficient ρ. Example The test is for the slope β, and correlation coefficient ρ obtained from statistical data X {65, 56, 78, 86, 92, 71, 68} and Y {95, 59, 88, 78, 75, 68, 80} are not equal to zero (β & ρ ≠ 0.) 1. Input the above lists X and Y into lists L1 and L2, respectively. 2. Press S E 0 5. The parameter input screen will appear. 3.
Chapter 10: Statistics & Regression Calculations 06 Tint1samp Finds the confidence interval for the population mean µ. Example Find the confidence interval for the statistical 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 and the level of confidence is 0.99. 1. Enter the above statistical data into list L1. 2. Press S E 0 6. The parameter input screen will appear. 3. Enter the C-level value of 0.99. 4. Set the List to L1 and press E. 5. Press @ h.
Chapter 10: Statistics & Regression Calculations 1. Enter the above data in to lists L1 and L2. 2. Press S E 0 7. The parameter input screen will appear. 3. Enter the appropriate value in each field. 4. Press @ h. Answers are displayed on the screen, where the numerical value within () indicates the confidence interval for the differences between µ1 and µ2 when the level of confidence is 99%. In the numerical value input mode, “n1”, “n2” are positive integers.
Chapter 10: Statistics & Regression Calculations • µ0 indicates the hypothesis mean, σ indicates the population standard deviation, x indicates the sample mean and n indicates the sample size. (“n” is a positive integer.) 4. Enter the appropriate value in each field. 5. Press @ h. 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 x1 = 77.
Chapter 10: Statistics & Regression Calculations 10 Ztest1prop Tests the success probability P0 of a population. Example A coin was tossed 100 times and landed head side up 42 times. Normally, the probability of head facing up is 0.5. Test to see if the coin is fair. 1. Press S E 1 0. The parameter input screen will appear. • prop is the hypothesis probability. The test will be conducted using hypothesis prop ≠ P0.
Chapter 10: Statistics & Regression Calculations 3. Press @ h. Answers will be displayed on ^ the screen, where P indicates the calculated success rate of the data combined with sample data 1 and 2, ^ ^ and P1 and P2 show the success rates of sample data 1 and 2, respectively. n1 and n2 are positive integers. 12 Zint1samp Finds the confidence interval of a population mean, µ. Example The average weight of a newly developed product is known to be 52.4 g and standard deviation (σ) is 4.5.
Chapter 10: Statistics & Regression Calculations 13 Zint2samp Finds the confidence bound of two sample means µ1 and µ2. Example Find the confidence interval of µ1 and µ2 of sample data with the _ _ confidence level of 0.9, where x1 = 77.3, σ1 = 3.4, n1 = 30 and x2 = _ _ 75.2, σ2 = 2.8, n2 = 20 (x1 and x2 indicate sample means of two data.) Set the input method to value input mode 1. Press # S E 1 7 E. 2. Press S E 1 3. Parameter input screen will appear. 3. Enter the appropriate value into each field. 4.
Chapter 10: Statistics & Regression Calculations 2. Enter the appropriate value into each field. 3. Press @ h. Answers will be displayed on the screen, where the numerical value within () indicates the confidence interval of the success probability at a confidence level of 95%. * n is a positive integer. 15 Zint2prop Finds the confidence interval of the difference (P1-P2) of the success probability obtained from the two sets of sample data collected from two different populations.
Chapter 10: Statistics & Regression Calculations 7. Distribution functions The calculator has distribution features to find statistical calculations. To enter the distribution menu, 1. Press S F (F DISTRI). The distribution menu will appear. 2. There are 15 options in the distribution menu. Press ' to navigate between pages, and press { or } to scroll the window. 3. Press E to select the function. 4. Input the specified values. 5. Press E to solve.
Chapter 10: Statistics & Regression Calculations 03 InvNorm( InvNorm(probability [, mean, standard deviation]) Finds the value of x of a given normal distribution probability. A list cannot be used. * When mean (µ) and standard deviation (σ) are omitted, µ = 0 and σ = 1 are applied. Example Find the value of x for the probability of 0.8 in the above sample. 04 pdfT( pdfT(value, degree of freedom) Finds the probability density of a specified value x for the T distribution with n degrees of freedom.
Chapter 10: Statistics & Regression Calculations 05 cdfT( cdfT(lower limit, upper limit, degree of freedom) Finds the T distribution probability within the specified range of x for the T distribution with n degrees of freedom. A list cannot be used. Limitations: Degree of freedom ≤ 670 • Degrees of freedom is a positive real number. Example Find the probability of range X = 0.5 to 3.2 for T distribution with 9 degrees of freedom.
Chapter 10: Statistics & Regression Calculations 08 pdfF( pdfF(value, degree of freedom of numerator, degree of freedom of denominator) Finds the probability density of a specified value x for the F distribution that possesses two independent degrees of freedom, m and n. A list cannot be used. Limitations: Degree of freedom ≤ 70 • Degree of freedom is a positive real number. • An error may occur when an extremely large number is entered for degrees of freedom.
Chapter 10: Statistics & Regression Calculations 10 pdfbin( pdfbin(trial number, success probability [, success number])) Finds the probability density of a specified value x for the binomial 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. Limitations: Success probability is 0 ≤ p ≤ 1.
Chapter 10: Statistics & Regression Calculations 13 cdfpoi( cdfpoi(mean, value) Finds the probability of a specified range x for a Poisson distribution of mean mu. Example Find the probability within the range up to x = 4. 14 pdfgeo( pdfgeo(success probability, value) Finds the probability density of a specified value x for the geometric distribution. Limitations: Success probability is 0 ≤ p ≤ 1.
Chapter 11 Financial Features The financial calculation features include capabilities for compound interest calculations. Press @ g. The financial menu screen will appear. • Specifies the TVM-SOLVER mode. • Selects a financial calculation function • Specifies payment due (to pay at the beginning or end of period) • Determines individual settings (in TVM-SOLVER mode) 1. Try it! 1 You plan to purchase a house for a price of $300,000. The down payment is $100,000.
Chapter 11: Financial Features • Vertical arrows along the horizontal line indicate the cash flow. An UP arrow indicates inflow (+) and a DOWN arrow indicates outflow (–). • The calculator considers the cash inflow for each period is constant. (Even payment.) 2. Determine the time each payment is due. For deposits and loan payments, the time each payment is due (paid at the beginning or the end of the period) makes for a different cash flow diagram.
Chapter 11: Financial Features Starting the calculation Setting the payment due time 5. Press @ g. 6. Press C (C PERIOD). 7. Press 1 (1 PmtEnd) and press E. Payment due time is now set to the end of the period. Enter the value using the SOLVER function 8. Press @ g. 9. Press A E. 10. The following TVM-SOLVER screen will appear. The payment due time is set to the end of the period. The payment due time is set to the end of period.
Chapter 11: Financial Features 17. Press E. Usually C/Y (cumulative interest per year) is the same value as P/Y. If not, enter the value instead. 18. Press { 3 times to move the cursor to PMT (payment amount). 19. Press @ h. The result will appear as follows. 20. Payment amount per month PMT = -1073.643246 (Negative value indicates payment.) The numerical value input format and display format in the FINANCE mode comply to that of SETUP.
Chapter 11: Financial Features Try it! 2 If the monthly payments in the first example is limit to a fixed $800, how much must be the present value (PV) and the required amount of down payment. ( +) PV = 300,000 – down payment I = 5% FV = 0 Cash flow Time flow (–) Set the TAB and FSE (2 and FIX respectively) 1 2 3 358 359 N = 360 PMT = 800 1. Press @ ; C 2 D 2 TAB is set to 2 and FSE is set to FIX. 2. Press C @ g A and E. The previous TVM-SOLVER screen will appear with the cursor flashing on N. 3.
Chapter 11: Financial Features • So, the required amount of down payment is $300,000 – $149,025.29 = $150,974.71. Using the TVM-SOLVER screen, you can obtain various results by inputting the known variables and then moving the cursor to the unknown variable and pressing @ h. The value where the cursor pointer is placed will be calculated from the known variables. Example Compare the principal interest total when accumulating an interest of 2.
Chapter 11: Financial Features 2. CALC functions Press @ g B to access the CALC functions. The CALC functions 01 to 05 calculate any of the following variables from the other variables. (The same calculations are possible as the SOLVER functions.
Chapter 11: Financial Features 06 Npv ( Npv (Interest rate, initial investment, list of following collected investment [, frequency list]) Calculates the net present value and evaluates the validity of the investment. You can enter unequal cash flows in the list of following collected investment. Example The initial investment is $25,000 planning to achieve the profits each year as shown on the right, Evaluate whether annual revenue of 18% is achieved.
Chapter 11: Financial Features The following CALC functions, 08 Bal, 09 ΣPrn and 10 ΣInt require the values of I%, PV and PMT variables. Enter the values beforehand in the TVMSOLVER function. Example using the 08 and 10 calculations You plan to purchase a house for the price of $300,000. The down payment is $100,000. Calculate the monthly payments for a 30year loan at an annual interest rate of 5% for the remaining $200,000.
Chapter 11: Financial Features Conversion functions 11 →Apr ( →Apr (effective interest rate, number of settlements) Converts effective interest rate to nominal interest rate Example If the effective interest rate is 12.55%, how much is the nominal interest rate for the quarterly compound interest? If the monthly compound interest rate is 10.
Chapter 11: Financial Features 3. VARS Menu The VARS menu consist of a list of the variables used for the TVM-SOLVER functions. • The VARS menu can be used to enter values in the sub-menu within the Finance menu. 1. Press @ g D. 2. The VARS sub-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. How to recall the content of N 1. Press # @ g D 1 E. How to recall the content of I% 2. Press @ g D 2 E.
Chapter 12 The SOLVER Feature The SOLVER feature is one of the calculator’s most powerful and distinctive features, and helps you solve math problems with various analysis methods. Using this feature, problems from linear equations to complex formulas can be solved with ease. To access the SOLVER feature, press @ '; to exit, press #. Note: • The SOLVER feature is not available in the Basic mode. • The SOLVER feature shares variables with other calculator features.
Chapter 12: The SOLVER Feature 1. Enter SOLVER by pressing @ '. The word SOLVER will flash on the screen, indicating that you are now in the SOLVER feature mode. 2. Enter the equation “A = 2B2 + 4C”. Press A A A = 2ABy+4 A C. 3. Press E. The screen above right appears, indicating that there are 3 variables to be assigned. Note: If values were assigned to those variables prior to this operation, then the previously set values will be shown here.
Chapter 12: The SOLVER Feature Newton’s method Newton’s 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’s method. Example Solve “X2 + 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 “X2 + 4X – 2”.
Chapter 12: The SOLVER Feature 6. The following window shows the approximate value of X (0.449489742), the right side value of the equation (assumed as “0”, at step #2), the left side value (which the entered expression results to this value when the value X is entered), and the difference between the left and the right side. 7. Since the L-R difference above indicates a margin of error, try entering smaller steps. Press C to go back to step #3.
Chapter 12: The SOLVER Feature Graphic method The Graphic method is another way of approximating solutions, using graphical representations. This method is particularly useful when finding more than one solution on a graph axis. Example Obtain values for “Y = X3 – 3X2 + 1”, when Y = 0. 1. Press @ ' to enter SOLVER. Clear screen entries by pressing C several times. 2. Enter “Y = X3 – 3X2 + 1” into the initial window, and press E. 3. In the next window, set the Y value as “0”, and press E.
Chapter 12: The SOLVER Feature Note: The analysis will be limited to the range specified; a solution outside of the analysis range will not be detected. If no crossing point is found in the range, then a message “No solution found” will show at the bottom of the screen. 7. Pressing @ h at this point will engage the 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.
Chapter 12: The SOLVER Feature 2. Saving/Renaming Equations for Later Use The expressions you have entered in the SOLVER can be named and stored: 1. Go to the SOLVER menu by pressing @ '. 2. Press C to select the C SAVE menu, and press E. 3. When the next screen appears, ALPHA LOCK mode is automatically set and the cursor is changed to “A”, indicating that alphabet characters can be entered. To enter numbers, press A. The equation name should consist of 8 characters/numbers or less. 4. When done, press E.
Chapter 12: The SOLVER Feature 3. Recalling a Previously Saved Equation To recall a stored SOLVER equation: 1. Go to the SOLVER menu, and press B to select the B EQTN sub-menu. 2. A list of saved equation names appears in the submenu. Select the equation you wish to call back. 3. Press E. The stored equation 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.
Chapter 13 Programming Features The calculator has programming features that enable automatic processing of a series of calculations any number of times. * The Programming features are only supported by the Advanced mode. In the Basic mode, only the execution of programs is available. Almost all the calculation and graphing language can be used in programs as well as the usual control flow statements such as If, For, While and Goto (with Label).
Chapter 13: Programming Features 2. Press C E. A new program window will open. 3. Input the program name (HELLO) on the top line of the screen. Up to 8 characters can be used for the title. 4. Press E. 5. The cursor will move to the program input field just under the title. Starting programming 6. Press P. The program menu will open. The commands and other statements are preinstalled in the calculator. Do not directly type in commands using the Alphabetical mode, select each command from the program menu.
Chapter 13: Programming Features When a line exceeds the width of the screen, the display will shift to the left. Store the program line by line 12. Press E. The cursor will move to the next line and the data input will be stored. Store the program line by line by pressing E, { or }. 13. Press @ q to exit the program edit screen. Execute the program 14. Press P A. A list of stored programs will appear. 15. Press 0 1 to execute the program 01 “HELLO”. 2.
Chapter 13: Programming Features Storing a program line by 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 line Blank lines are ignored during execution. You can include blank lines to gain better readability. Deleting a line Move the cursor to the line you wish to delete and press C.
Chapter 13: Programming Features 3. Variables • Single letters (uppercase letter from A to Z and θ) can be used as variables. • Defined once in one program, a variable is set as a global variable across all other stored programs unless redefined. Hence results calculated in one program can be used by another. • Only value (numbers) can be set as variables. • Strings cannot be set as variables. Setting a variable Use R to input a specific value or the value of formula into the variable.
Chapter 13: Programming Features 5. Programming commands • Print, Input, Wait, Rem, End and other commands can be used in a program. Screen settings, data input/output, graph settings and others can be controlled from a program. • Press P in the program edit mode to input the command. A PRGM menu P A 1 Print Print variable Print “character strings [“] Displays the value of the variable on the screen. The display format may vary according to the SET UP menu settings.
Chapter 13: Programming Features 4 Wait Wait [natural number (1 to 255)] Interrupts execution for the (natural number) of seconds. If no value is specified, interruption continues until any key is pressed. • A symbol will flash at the upper right corner of the screen during the wait. • This command can be used for displaying intermediate results or other information. 5 Rem Rem comments Comments start with Rem and extend to the end of the line. These lines are ignored at execution.
Chapter 13: Programming Features B BRNCH menu P B See 6. Flow control tools on page 214. C SCRN menu P C C SCRN menu commands are used to display or clear the screen. 1 ClrT ClrT Clears the program text screen without affecting the plotted graph. 2 ClrG ClrG Clears the graph screen without affecting the specified graph. After the graph screen is cleared, the specified graph statement is drawn. 3 DispT DispT Displays the program text screen. 4 DispG DispG Displays the graph screen.
Chapter 13: Programming Features E SETUP menu P E SETUP menu commands are used to set the various settings used in graphing and calculations. 01 Rect 02 Param 03 Polar 04 Web Rect Sets the graph coordinates as X and Y coordinates. Param Sets the graph coordinates as parametric coordinates. Polar Sets the graph coordinates as polar coordinates. Web Sets the graph coordinates as axes in sequence graphs. u(n – 1) is set to the X axis and u(n) is set to the Y axis.
Chapter 13: Programming Features 12 FloatPt FloatPt 13 Fix Fix 14 Sci Sci 15 Eng Eng 16 Tab Tab integer (0 to 9) Sets the number display mode to floating point, fixed decimal, scientific and engineering, respectively. 17 Decimal Decimal 18 Mixed Mixed 19 Improp Improp 20 x±yi x±yi 21 r ∠ θ r∠θ Sets the answering mode to the one specified. F FORMAT menu P F F FORMAT menu commands are used to set the graph format.
Chapter 13: Programming Features 07 AxisON 08 AxisOFF 09 GridON AxisOFF Sets the specified axis to not be displayed on the graph screen. GridON Sets the grid lines to be displayed on the graph screen. 10 GridOFF GridOFF Sets the grid lines to not be displayed on the graph screen. 11 Connect Connect Draws a graph with connected lines. 12 Dot 13 Sequen 14 Simul 212 AxisON Sets the specified axis to be displayed on the graph screen. Dot Draws a graph with dots.
Chapter 13: Programming Features G S_PLOT menu P G S_PLOT menu commands are used for statistics plotting. 1 Plt 1( Sets the statistical graph settings for plot 1. 2 Plt 2( Sets the statistical graph settings for plot 2. 3 Plt 3( Sets the statistical graph settings for plot 3. The above menu commands have the same usage as the following: Plt1(graph type, X list name [, Y list name, frequency list]) * Press [ to specify a graph type.
Chapter 13: Programming Features 6. Flow control tools The calculator has the common flow control tools such as Goto - Label loop structures, and If-, For- and While-statement clauses for enhancing a program’s efficiency. It also has the capability for subroutines. It is recommended to use If, For or While statements rather than Goto-Label loop structures. To access the flow control tools, use the P B BRNCH menu. 01 Label Label label name Specifies a branch destination for Goto or Gosub.
Chapter 13: Programming Features 07 For 08 Next For variable, initial value, end value [, increment] commands or multiple statements Next • The increment value can be omitted. The default value is 1. • For and Next statements must be placed at the beginning of the line. • If the comparisons variable > end value (positive) or variable < end value (negative) are satisfied, the program will end the loop and go to the line indicated by the Next command.
Chapter 13: Programming Features 11 Gosub 12 Return Gosub label name ..................... End [Rem start of the subroutine (label name)] Label label name Statements Return Subroutine structures can be used for programming. • The Gosub label name must be the same as the Label starting the subroutine. • A Return statement is necessary at the end of the subroutine. When the Return statement is executed, the calculator executes the next line after the Gosub statement. • Up to 10 subroutines can be nested.
Chapter 13: Programming Features 5. Press P H, select 2 RclLine and press E. The stored line will be inserted at the targeted position. • Please note that only a single line can be stored in the memory. VARS menu • Functions that control the graph screen can be selected from the VARS menu. • Press @ z to display the VARS menu (shown to the right). * There are differences in functions between the Advanced mode and the Basic mode. The following menus and their descriptions are based on the Advanced mode.
Chapter 13: Programming Features • The commands and functions in the VARS menu can be displayed on the screen. Current setting data can also be reset. • The results of arithmetic functions can also be displayed. • The ZOOM command is selected directly from the ZOOM menu. Names of some ZOOM commands change when inserted into programs. These are [A ZOOM], [C POWER], [D EXP], [E TRIG], and [F HYP] of the ZOOM menu. “Zm_” is automatically added to each of these functions when inserted into programs.
Chapter 13: Programming Features Example The following data are included in list L1. L1: 165, 182.5, 173.8, 166.5, 185.3 A one-variable calculation was executed based on this data. After returning to the calculation screen, average values can be viewed by using the following procedure. • Press @ z H E A 0 2 to _ display “x ” on the screen. • Press E to obtain the average value of X as determined in the previous calculation.
Chapter 13: Programming Features When an infinite loop occurs 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 the line where interrupted. * Refer to Appendix “Error Codes and Error Messages” on page 235. * It is highly recommended that goto-Label statements are not used in If, While and For loop structures.
Chapter 13: Programming Features HIST 10 ⇒ dim(L1) Gosub INSCORE Gosub AVGSCORE Plt1(Hist, L1) Zm_Stat Wait End Sequencially input the data in list L1. Label INSCORE 1⇒I Input “ENTER SCORE”, A A ⇒ L1(1) 2⇒I For I, 2, 10 Input “ENTER NEXT”, A A ⇒ L1(I) Next Return Calculate the median of List L1.
Chapter 14 OPTION Menu The calculator is equipped with OPTION menu for adjusting the display contrast, checking memory usage, deleting stored data, transferring data, and resetting the calculator’s memory. Accessing the OPTION Menu Press @ p. The OPTION Menu will appear. A: Adjusts the display contrast B: Checks the memory usage C: Deletes files D: Link command to use with another calculator or PC. E: Resets the calculator 1. Adjusting the screen contrast 1. Press @ p.
Chapter 14: OPTION Menu 3. If you want check the details, press E. The detailed memory usage window will appear. The total remaining memory will appear on the bottom line of the screen. 4. Press } to scroll the window.
Chapter 14: OPTION Menu 3. Deleting files Press @ p C to enter the delete menu. The sub-menu items are the same as those of the Memory Check menu (List, Matrix, Graph Eqn, Solver Eqn, Program, Picture, G_Data, L_Data and Slide). Deletions can be executed entry by entry. To delete the matrix mat C 1. Press @ p C 2. The matrix deletion window will appear with the cursor pointer at the top (mat A). 2. Move the cursor pointer to mat C using { / }. 3. Press E.
Chapter 14: OPTION Menu 2. Press @ p D on both calculators. 3. Press 2 on the receiving machine. The receive mode screen will appear on the display. 4. Press 1 on the sending machine. 5. The send menu will appear on the display. Specify the data to send from the following categories. A SELECT Displays the menu window to send the data specified as follows: 01 ALL Displays a list of all the stored files category by category. 02 List Displays a list of all the stored list files.
Chapter 14: OPTION Menu 6. Select the item to send using { / } and pressing E. A “✱” will be placed by the selected item. 7. Press @ E to send. 8. Transmission begins and a busy message will appear on the displays of the both calculators. • An data in the same memory locations in the receiver will be automatically overwritten. • Up to 10 files can be selected to send at once. Example If you wish to send the list L1, matrices mat A and mat B and graph equation Y2 to the other calculator. 1.
Chapter 14: OPTION Menu Transmission between the EL9900 and PC • The optional kit CE-LK2 (cable and Windows software) is required for calculator to data communication with PC. • Refer to the CE-LK2 operation manual for details. • During communications between calculator and PC, no operation of the calculator is required. Just connect the cable and press the power on key, and the entire operation can be controlled from the PC. 5.
Appendix 1. Replacing Batteries The calculator uses two different kinds of batteries: manganese (AAA) for unit operation, and lithium (CR2032) for memory backup. Compatible battery types Type (use) Manganese battery (for unit operation) Lithium battery (for memory backup) Model AAA Quantity 4 CR2032 1 * To prevent loss of stored data, DO NOT remove both the unit operation and memory backup batteries at the same time.
Appendix Procedures for replacing unit operation batteries When battery power becomes low, a message will show indicating that a new set of batteries are needed. 1. Turn off the calculator’s power (@ o). 2. Turn over the calculator. Locate the battery compartment cover, and open the cover as illustrated. 3. Replace all four AAA batteries as illustrated. 4. Replace the battery compartment cover. 5. Press O. The following message will appear.
Appendix 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. 3. Use a pen to lift the lithium battery out of the battery compartment. 4. Insert the new battery with the PLUS (+) side facing up. 5. Replace the lithium battery cover and fasten the screw. 6. Replace the battery compartment cover and press O. The following message will appear. 7. Press O. Do not press C. This will clear all the data.
Appendix 2. Troubleshooting Guide Refer to the list of possible symptoms, and solutions may be found here. The calculator’s power won’t turn on! • The operation batteries may not be installed, may be exhausted, or may be inserted incorrectly. Check the operation batteries in the battery compartment. • Place the battery cover securely or the calculator will not turn on. The saved calculator configurations are not retained! • Both the lithium battery and the operation batteries may need to be replaced.
Appendix The screen images cannot be stored (SLIDE SHOW) • The available memory may be too small to store the screen image. Select “B MEMCHK” under @ p menu. Select and delete unnecessary items under “C DEL”. There appears to be no functions available for integral/differential calculations! • Make sure that the Advanced mode is selected. The integral/ differential calculation tools can be found in the M menu. • Access CATALOG menu by pressing @ j.
Appendix 3. Specifications Model EL-9900 Product name Graphing Calculator Display 132 x 64 dot matrix liquid crystal display Number of digits: mantissa 10 digits, exponents 2 digits (standard screen); 7 digit display (including negatives, decimals) for table screen, split screen, etc.
Appendix List features Direct data entry/edit to list, calculation function for various lists, and list/matrix conversion. Substitution features Graph drawing, numerical input from split-screen Slide Show features Screen image capture, play function The maximum number of pages to be captured: Approx.
Appendix 4. Error Codes and Error Messages Error Code Error Message Description 01 02 Syntax Calculate 03 Nesting 04 Invalid Matrix definition error or entering an invalid value. 05 Dimension Matrix dimension, or STAT list dimension, inconsistent. 07 08 Invalid DIM Argument Size of list/matrix exceeds calculation range. Inconsistency found in argument of the structured function. 09 Data Type Invalid data type used in calculation. 10 No Sign Change Financial calculation error found.
Appendix Error Code Error Message Description 38 Too many obj More than 30 objects selected. 40 Lbl duplicate Labels with identical name found in program. 41 Lbl undefined Goto/Gosub encountered with no defined label. 42 Lbl over More than 50 labels found in program. 43 Gosub stack Nesting of more than 10 subroutines found. 44 Line too long Line contains more than 160 characters. 45 Can’t return Return used without jumping from subroutine.
Appendix 5. Error Conditions Relating to Specific Tasks 1. Financial * Define constants “r” and “s” as used in the equation below. r= ( I (%) 100 ) ÷ C/Y + 1 C/Y P/Y –1, { SS == 10 (Pmt_Begin) (Pmt_End) } 1. I% calculation 1 If PMT = 0 ( r = - PV FV - 1n ) –1 2 If PMT ≠ 0 -n f (r) = PV + (1 + r × s) × PMT × 1 – (1 + r) + FV (1 + r)-n: (r ≠ 0) r f (r) = PV + PMT × n + FV: (r = 0) calculate the following for r solved in 1 and 2 P/Y I (%) = 100 × C/Y × ((r + 1)C/Y –1) 2.
Appendix 3. FV calculation 1 If r ≠ 0, r > -1 FV = – 1 – (1 + r)-n × PMT r -n (1 + r) PV + (1 + r × s) × 2 If r = 0 FV = -n × PMT – PV 3 If r ≤ -1 Error 4. PMT calculation 1 If r ≠ 0, r > -1 PMT = – PV + FV × (1 + r)-n 1 – (1 + r)-n (1 + r × s) × r 2 If r = 0 PMT = – PV + FV n 3 If r ≤ -1 Error 5.
Appendix 2. Error conditions during financial calculations • r ≤ -1 • N = 0 in PMT calculations • I% = 0 and PMT = 0, or I% ≠ 0 and FV = (1/r) (1 + r × s) × PMT, in N calculations.
Appendix 3 pdfχ2( 1 2 f (χ , df) = 2Γ ( df ) 2 df χ2 2 – 1 (- χ ) e 2 ) 2 2 ( ∞ However: Γ(s) = ∫ 0 xs–1 e-x dx df: Degree of freedom 4 pdfF( f (x) = Γ (m + n) m m –1 2 ( m ) 2 x 2 (1 n m n Γ( ) Γ( ) 2 2 + mx ) n - m 2+ n ∞ However: Γ(s) = ∫ 0 xs–1 e-x dx m: Degree of freedom of numerator n: Degree of freedom of denominator 5 pdfbin( P (x = 0) = (1 – p)n P (x = c + (n – c) p 1) = P (x = c) (c + 1)(1 – p) (c = 0, 1, ...
Appendix 6. Calculation Range 1. Arithmetic calculation The results for dividend, multiplicand and operand are: -1 × 10100 < x ≤ -1 × 10-99, 1 × 10-99 < x ≤ 1 × 10100 or x = 0 (valid within the range of display capability) Note: Calculation results and input values less than 1 × 10-99 are considered equal to 0. 2. Function calculation Calculation accuracy In principle, calculation errors are ±1 of the last digit.
Appendix Function ln x log x ex 10x x- 1 x 2 x n! Calculation range Notes ln x = loge x 1 × 10-99 ≤ x < 1 × 10100 e .=. 2.71828... -1 × 10100 < x ≤ 230.2585092 -1 × 10100 < x < 100 |x| < 1 × 10100 |x| < 1 × 1050 0 ≤ x < 1 × 10100 x≠0 -0.5 ≤ n ≤ 69.5 n is an integer or integer + 0.
Appendix Function →dms →deg xy → r xy → θ Calculation range Notes |x| < 1 × 10100 |x| < 1 × 10100, |y| < 1 × 10100 x2 + y < 1 × 10 y | x | < 1 × 10100 2 r = x2 + y2 100 y θ = tan-1 x x = r cosθ rθ → x rθ → y y = r sinθ |r| < 1 × 10100 Binary: The range of θ is the same as x of sin x and cos x 1000000000000000 ≤ x ≤ 1111111111111111 0 ≤ x ≤ 0111111111111111 not Octal: 4000000000 ≤ x ≤ 7777777777 0 ≤ x ≤ 3777777777 Hexadecimal: FDABF41C01 ≤ x ≤ FFFFFFFFFF 0 ≤ x ≤ 2540BE3FE Binary: 10000000000
Appendix Function _ n≠0 x Calculation range Notes n>1 sx |Σx| < 1 × 1050 (Σx)2 Σx2 – n < 1 × 10100 0≤ n–1 _ Same for y, sy and σy n>0 σx |Σx| < 1 × 1050 (Σx)2 Σx2 – n < 1 × 10100 0≤ n n>0 |Σx| < 1 × 1050 |Σy| < 1 × 1050 r (Σx)2 (Σy)2 ) (Σy2 – n ) <1 n ΣxΣy | < 1 × 10100 n 0 < (Σx2 – |Σxy – × 10100 < 1 × 10100 n>0 |Σx| < 1 × 1050 |(Σx) (Σy)| < 1 × 10100 b (Σx)2 | < 1 × 10100 n ΣxΣy | < 1 × 10100 n 0 < |Σx2 – |Σxy – Regression calculations excluding 2nd, 3rd, and 4th degree polynomials.
Appendix Function Calculation range Notes int÷ 0 ≤ x < 10 remain 0 ≤ x < 1010 % |x| < 10100 → a b/c |x| < 1010 A number with 10 or less decimal places, or the 1010-th or above decimal places are 0. List Error is returned when the number of elements exceeds 1000. This is the same when the result of a list function specifies 1000 or more elements. Matrix Error is returned when specifying columns or rows that exceed 100. 10 → b/c 3.
Appendix 7. CATALOG Feature Press @ j to display the CATALOG menu. You can directly access various features and commands from the CATALOG menu. CATALOG menu lists are different between the Basic mode and the Advanced mode. For example, in Program edit mode of the Advanced mode, you can access the program commands from the CATALOG menu. Please note that you can enter the eular number “e” only from the CATALOG menu.
Appendix 8. List of Menu/Sub-menu Items CATALOG function lets you access almost all the functions and commands. Square brackets indicate that the value or variable is optional. 1.
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page M NUM abs( abs(value) B1 B1 73/43 round( round(value [, digit number of decimals]) B2 B2 73/44 ipart ipart value B3 B3 73/44 fpart fpart value B4 B4 73/44 int int value B5 B5 73/44 min( min(value A, value B) or min(list) B6 B6 73/45 max( max(value A, value B) or max(list) B7 B7 73/45 lcm( lcm(natural number, natural number) B8 B8 73/45 gcd( gcd(natural number, natural number) B9 remai
Appendix Functions Commands g Syntax value g Keystrokes Advanced mode Basic mode Page E5 76 M INEQ = value A = value B F1 76 ≠ value A ≠ value B F2 76 > value A > value B F3 76 ≥ value A ≥ value B F4 76 < value A < value B F5 76 ≤ value A ≤ value B F6 76 value A and value B G1 77 or value A or value B G2 77 not not value G3 77 xor value A xor value B G4 78 xnor value A xnor value B G5 78 M LOGIC and M COMPLEX conj( conj(complex number) H1 78 real( re
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page L2 No arguments A2 132 L3 No arguments A3 132 L4 No arguments A4 132 L5 No arguments A5 132 L6 No arguments A6 132 sortA( sortA(list name [, subordinate list name1, ... , subordinate list name n]) A1 B1 135 sortD( sortD(list name [, subordinate list name1, ...
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page @l{} { No arguments E1 132 } No arguments E2 132 3. STAT menus Functions Commands Syntax Keystrokes Advanced mode Basic mode Page S EDIT/OPE EDIT No arguments AE AE 149 sortA( sortA(list [, subordinate list 1, ... , subordinate list n]) B1 B1 159 sortD( sortD(list [, subordinate list 1, ... , subordinate list n]) B2 B2 159 SetList SetList [list name 1, list name 2, list name 3, ...
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page Rg_abx Rg_abx (list name for x, list name for y [, frequency list] [, equation name to store]) D09 D4 161 Rg_aebx Rg_aebx (list name for x, list name for y [, frequency list] [, equation name to store]) D10 161 Rg_x-1 Rg_x-1 (list name for x, list name for y [, frequency list] [, equation name to store]) D11 D5 162 Rg_axb Rg_axb (list name for x, list name for y [, frequency list] [, equation name to store]) D12
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page cdfnorm( cdfnorm(lower limit, upper limit [,mean, standard deviation]) F02 177 InvNorm( InvNorm(probability [, mean, standard deviation]) F03 178 pdfT( pdfT(value, degree of freedom) F04 178 cdfT( cdfT(lower limit, upper limit, degree of freedom) F05 179 pdfχ2( pdfχ2(value, degree of freedom) F06 179 cdfχ2( cdfχ2(lower limit, upper limit, degree of freedom) F07 179 pdfF( pdfF(value, degree of freedom o
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page Broken + No arguments B2 B2 154 Broken No arguments B3 B3 154 Norm •_X No arguments C1 C1 154 Norm+_X No arguments C2 C2 154 Norm _X No arguments C3 C3 154 Norm •_Y No arguments C4 C4 154 Norm+_Y No arguments C5 C5 154 Norm _Y No arguments C6 C6 154 NormDis No arguments D1 D1 154 Box No arguments E1 E1 155 MBox • No arguments E2 E2 155 MBox+ No arguments E3 E3 155 MBo
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page Draw Draw equation A6 A6 107 Shade( Shade(equation 1, equation 2 [, begin, end]) A7 A7 107 DrawInv DrawInv equation A8 A8 108 Circle( Circle(x-coordinate of center, y-coordinate of center, radius) A9 A9 108 Text( Text(column, row, "character strings") A0 A0 109 @ d POINT PntON( PntON(x-coordinate, y-coordinate) B1 B1 110 PntOFF( PntOFF(x-coordinate, y-coordinate) B2 B2 110 PntCHG( PntCHG(x-co
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page In Zm_In No arguments A3 A3 54 Out Zm_Out No arguments A4 A4 54 Default Zm_Default No arguments A5 A5 54 Square Zm_Square No arguments A6 A6 54 Dec Zm_Dec No arguments A7 A7 54 Int Zm_Int No arguments A8 A8 54 Stat Zm_Stat No arguments A9 A9 54 Z FACTOR/POWER FACTOR No arguments BE BE 55 x2 _ Zm_x2 No arguments C1 C1 55 x-1 Zm_x-1 No arguments C2 C2 55 No arguments C3 C3 55
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page sin-1 x Zm_sin-1 No arguments E4 97 cos-1 x Zm_cos-1 No arguments E5 97 tan-1 x Zm_tan-1 No arguments E6 97 Z HYP/STO/RCL sinh x Zm_sinh No arguments F1 97 cosh x Zm_cosh No arguments F2 97 tanh x Zm_tanh No arguments F3 97 sinh-1 x Zm_sinh-1 No arguments F4 97 cosh-1 x Zm_cosh-1 No arguments F5 97 tanh-1 x Zm_tanh-1 No arguments F6 97 StoWin No arguments G1 F1 56 RclWin No arguments
Appendix 8. SLIDE SHOW menus Functions Commands Syntax Keystrokes Advanced mode Basic mode Page ] CURR/PLAY/NEW/SELECT/EDIT CURR No arguments AE AE 118 PLAY No arguments NEW No arguments B B 118 CE CE 118 SELECT No arguments D D 118 MOVE No arguments E1 E1 118 DEL No arguments E2 E2 119 RENAME No arguments E3 E3 119 9.
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page For variable, start value, end value [, increment] commands Next B07 215 B08 215 B09 215 WEnd While conditional statements commands WEnd B10 215 Gosub Gosub label name B11 216 Return No arguments B12 216 For Next While P (in the Prgramming mode) SCRN ClrT No arguments C1 209 ClrG No arguments C2 209 DispT No arguments C3 209 DispG No arguments C4 209 P (in the Prgramming mode) I/O Get Get v
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page Decimal No arguments E17 211 Mixed No arguments E18 211 Improp No arguments E19 211 x ± yi No arguments E20 211 r∠θ No arguments E21 211 P (in the Prgramming mode) FORMAT RectCursor No arguments F01 211 PolarCursor No arguments F02 211 ExprON No arguments F03 211 ExprOFF No arguments F04 211 Y'ON No arguments F05 211 Y'OFF No arguments F06 211 AxisON No arguments F07 212 AxisOFF
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page P (in the Prgramming mode) COPY StoLine No arguments H1 216 RclLine No arguments H2 217 10.
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page augment(matrix name A, matrix name B) C04 126 identity identity dimension value C05 126 rnd_mat( rnd_mat(number of row, number of column) C06 126 row_swap( row_swap(matrix name, row number, row number) C07 127 row_plus( row_plus(matrix name, row number, row number) C08 127 row_mult( row_mult(multiplied number, matrix name, row number) C09 127 row_m.p.( row_m.p.
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page Irr( Irr(initial investment, list of following collected investment [, frequency list] [, assumed revenue rate]) B07 190 Bal( Bal(number of payments [, decimal place to round]) B08 191 ∑Prn( ∑Prn(initial number of payments, end number of payments [, decimal place to round]) B09 191 ∑Int( ∑Int(initial number of payments, end number of payments [, decimal place to round]) B10 191 →Apr( →Apr(effective interest rat
Appendix Functions Commands Syntax Keystrokes Advanced mode Basic mode Page 6 No arguments B6 82 2 No arguments C2 82 3 No arguments C3 82 13.
Appendix INDEX : (colon) ......................................................... 134, 214 (n-1)-based (Web), sequence ................................ 90 “, PRGM ................................................................ 207 1_Stats, CALC ...................................................... 150 2nd Function key .................................................... 18 2ndF key ......................................................... 5, 8, 18 2x, CALC ...............................................
Appendix CONV ..................................................................... 48 CONV, MATH ..................................................... 74 Conversion ......................................................... 48 Conversion keys, fraction and decimal .............. 36 Conversion, coordinates ........................................ 74 COORD .................................................................. 26 COPY menu, programming .................................. 216 cos ..................
Appendix F H FACTOR, ZOOM .................................................... 55 Factorial .................................................................. 48 Factorial, PROB ................................................. 74 fill(, OPE ....................................................... 125, 136 FINANCE key ........................................................... 7 Financial features ............................................. 183 Fix .......................................................
Appendix K Key, PRGM ........................................................... 208 Keyboard, changing the ........................................... 9 L Label, BRNCH ...................................................... 214 lcm( ......................................................................... 45 lcm(, NUM .......................................................... 73 Least common multiple ...................................... 45 Less than ......................................................
Appendix OPE menu, List .................................................... 135 OPE menu, Matrix ............................................ 125 OPE menu, STAT ............................................. 159 Operand, programming ........................................ 206 OPTION key ............................................................. 6 OPTION Menu ................................................. 222 or, LOGIC ............................................................... 77 Out, ZOOM .....
Appendix RclLD, L_DATA ..................................................... 143 RclPict, PICT ........................................................ 113 RclWin, ZOOM ....................................................... 56 Real part, COMPLX ............................................... 79 real(, COMPLX ................................................... 79 Recall, variable ....................................................... 40 Recalling a equation ........................................
Appendix SLIDE SHOW ....................................................... 115 SLIDE SHOW key ................................................ 6 SLIDE SHOW menu ......................................... 118 slv_FV, CALC ....................................................... 189 slv_I%, CALC ....................................................... 189 slv_N, CALC ......................................................... 189 slv_pmt, CALC .....................................................
Appendix uw, TYPE ................................................................ 96 V Value, CALC ........................................................... 60 Variable, programming ......................................... 206 Variable, store .................................................... 38 varian(, MATH ....................................................... 141 Variance ........................................................... 141 VARS key ....................................................
In Europe: Authorized representative responsible for the European Union Community Market In Canada: Au Canada: This Class B digital apparatus complies with Canadian ICES-003. Cet appareil numérique de la classe B est conforme à la norme NMB003 du Canada. NOTE: FOR NETHERLANDS ONLY For USA only: This product contains a CR Coin Lithium Battery which contains Perchlorate Material – special handling may apply, California residents, See www.dtsc.ca.
EL-9900 ® PRINTED IN CHINA/IMPRIMÉ EN CHINE/IMPRESO EN CHINA 06JGK(TINSE0511EH30) GRAPHING CALCULATOR SHARP CORPORATION ® MODEL EL-9900 GRAPHING CALCULATOR OPERATION MANUAL
