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.
Contents Caring for Your Calculator................................................................................................. 7 Chapter 1 Getting Started...............................................................................................................8 Before Use........................................................................................................................ 8 Using the Hard Cover......................................................................................
Contents Chapter 4 Graphing Features........................................................................................................68 1. Try it!........................................................................................................................... 68 2. Try it!........................................................................................................................... 71 3. Explanations of Various Graphing Keys......................................................
Contents Chapter 7 List Features...............................................................................................................132 1. Try it!......................................................................................................................... 132 2. Creating a list............................................................................................................ 134 3. Normal List Operations........................................................................
Contents Chapter 10 The SOLVER Feature..................................................................................................196 1. Three Analysis Methods: Equation, Newton & bisection, and Graphic..................... 196 2. Saving/Renaming Equations for Later Use............................................................... 202 3. Recalling a Previously Saved Equation.................................................................... 203 Functions of the SOLVER feature.......................
Contents Appendix 1. Replacing Batteries.................................................................................................. 228 2. Troubleshooting Guide.............................................................................................. 231 3. Specifications............................................................................................................ 233 4. Error Codes and Error Messages.............................................................................
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 Note: Adjusting display contrast I f the above message does not appear or malfunction occurs, check the direction of the batteries and close the cover again. If this does not solve the problem, remove the battery cover, and then gently push the RESET switch with the tip of a ball-point pen or a similar object while pressing O simultaneously. And then, follow steps 4 to 6 above.
Chapter 1: Getting Started Using the Hard Cover To open the cover: When in use: When not in use: 10
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 11
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 orange. A: Changes the cursor to “A”, and the next keystroke enters the alphabetical letter printed above each key in green.
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 M: Enter the Math menu with additional mathematical functions. S: Enter the statistics menu. P: Enter the programming menu. V: Converts hexadecimal, decimal, octal and binary numbers or solves systems of linear equations, finds roots for quadratic and cubic equations. m: Enter menu for matrix functions. ': Enter screen and menu for Solver features. z: Enter the menu for calculator specific variables. g: Enter menu for financial solver and functions.
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 F Operation of y @ x : Specify x -1 A F : Specify character F y : Specify x2 • Press “as is” to get the function and number printed on each key. • To access secondary function printed above each key in orange, press @ first, then press the key. Press C to cancel.
Chapter 1: Getting Started Quick Run-through Here are the major ingredients for 18 doughnuts: 1 cup warm water 4 3 cup warm milk 4 1 cup sugar 3 4 cups all-purpose flour 2 eggs 3 tablespoons butter Based on these values, solve the following problems using the calculator.
Chapter 1: Getting Started Enter fractions 3. Press 3 b 4 '. 4. Press b 18 '. 5. Press E. 1 of a cup of warm milk is required per one Now we have found 24 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). “Ans×” is displayed. ANS is a calculator specific variable which indicates the answer of calculations just before.
Chapter 2 Operating the Graphing Calculator Basic Key Operations - Standard Calculation Keys The standard calculation keys, located at the bottom four rows of the keyboard, enable you to access the basic functions of the 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.
Chapter 2: Operating the Graphing Calculator Note: $ can be used to enter a value in scientific notation. Example 6.3 × 108 + 4.9 × 107 # C 6.3 $ 8 + 4.9 $ 7 Entering a negative value Note: The negative number key _ can be used to enter numbers, lists, and functions with negative values. Press _ before entering the value. Do not use the - key to specify a negative value. Doing so will result in an error. Example Type -9460.827513 into the Calculation screen. # C _ 9460.
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 “ 65536 × 3 8 ” in the Calculation screen. Then press E to calculate. 4 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. At this moment, the cursor is still placed under the root figure. 4.
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 31 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. All 26 characters accessible, as well as “θ ”, “=”, “ : ”, and space. All functions associated with A are color coded green, 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.), list names (L1, L2, etc.), or matrix names (mat A, mat B, etc.), etc. with A keys.
Chapter 2: Operating the Graphing Calculator Math Function Keys Mathematical functions can be called up quickly with the Math Function keys.
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' 26 , Enters “ , ” (a comma) at the cursor + Enters a “root” figure at the cursor R Stores a number or a formula into a variable r Recalls an item stored in a variable X Enters a variable “x”, “θ”, “T”, or “n”.
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. Example Round the following number beyond the decimal point: 34.567 1. Press # C, then M. The MATH menu takes over the screen, as shown to the right. MATH menu items are displayed on the left side of the screen. 2.
Chapter 2: Operating the Graphing Calculator 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. Example Display the calculation result of “10002” in scientific notation. 1.
Chapter 2: Operating the Graphing Calculator SETUP Menu Items DRG: For trigonometric calculations and coordinate conversions, various angle units can be selected: Please make sure to use the appropriate angle unit when making trigonometric calculations (e.g. sin, cos). Deg Angle values to be set in degrees. (360°) Rad Angle values to be set in radians (default). (2π) Grad Angle values to be set in gradients.
Chapter 2: Operating the Graphing Calculator COORD: Sets the calculator to various graph coordinate systems. Rect Param Polar Seq ANSWER: Mixed (Real) Improp (Real) x±yi (Complex) 30 Parametric equation coordinates Polar coordinates Sequential graph coordinates Sets the answer preference to various number formats. Decimal (Real) r Rectangular coordinates (default) (Complex) Answers will be given in decimal form (default). Answers will be given in mixed fractions, whenever appropriate.
Chapter 2: Operating the Graphing Calculator EDITOR: Note: Sets the editing style to one of two available formats. Equation Formulas can be entered in a "type it as you see it approach" (default setting). One line Formulas will be displayed on one line. Immediately after changing the EDITOR, the calculator will return to the calculation screen and the following data will be cleared.
Chapter 2: Operating the Graphing Calculator 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. A Note about Degrees and Radians Note: A CALC Please use "Degree" (DEG) for angle values and not GRAD because this is used to represent Grads, where one turn comprises 400 Grads.
Chapter 2: Operating the Graphing Calculator 06 ∫ ∫ equation, lower limit, upper limit [, tolerance] dx Calculates an integral value of equation Y from the lower limit to the upper limit using the specified tolerance (if not specified, default value is 1E–5). Use in conjunction with the 07 dx sub-menu item. • P ress the keys as follows in the Equation edit mode. M A 0 6 2 { 8 ' ( X a 3 ' - 0.5 X y + 6 ) , 0.001 M A 0 7 E 07 dx Enters a differential “dx” in an integration expression.
Chapter 2: Operating the Graphing Calculator 13 csc-1 csc-1 value Enters an inverse cosecant. 14 cot-1 cot-1 value Enters an inverse cotangent. 15 sinh sinh value Enters a hyperbolic sine. 16 cosh cosh value Enters a hyperbolic cosine. 17 tanh tanh value Enters a hyperbolic tangent. 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.
Chapter 2: Operating the Graphing Calculator 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. Example iscard the fraction part of 42.195. (=42) • D MB342.195E 4 fpart fpart value Returns only the fraction part of a decimal number. * A real number, a list, matrix, variable, or equation can be used as values. Example iscard the integer part of 32.01. (=0.01) • D MB432.
Chapter 2: Operating the Graphing Calculator 8 lcm( lcm(natural number, natural number) Returns the least common multiple of two integers. Example • F ind the least common multiple of 12 and 18. MB812,18)E 9 gcd( gcd(natural number, natural number) Returns the greatest common divisor of two integers. Example ind the greatest common • F divisor of 16 and 36. MB916, 36)E C PROB 1random random [(number of trial)] Returns a random decimal number between 0 and 1 (uniform distributed).
Chapter 2: Operating the Graphing Calculator 3 rndNorm( 4 rndBin( rndNorm(mean, standard deviation [,number of trial] ) Returns a random real number from a specified normal distribution. * Number of trial : 1 ≤ n ≤ 999 (n is an integer.) Standard deviation : 0 < s rndBin(number of trial, probability of success [, number of simulations] ) Returns a random real number from a specified binominal distribution.
Chapter 2: Operating the Graphing Calculator 7 ! Returns a factorial. Example • Calculate 6 × 5 × 4 × 3 × 2 × 1. 6MC7E D CONV These tools deal with conversions between different angle units and between rectangular and polar coordinates. Sexagesimal and Degree System The “base 60” sexagesimal system, as well as the minutes-second measurement system, was invented by the Sumerians, who lived in the Mesopotamia area around the fourth millennium B.C.
Chapter 2: Operating the Graphing Calculator Rectangular/polar coordinate conversion This calculator is equipped with rectangular coordinates and polar coordinates conversion capabilities.
Chapter 2: Operating the Graphing Calculator E ANGLE Use these tools to enter the symbols to specify angle units. 1 ° Inserts a degree, and sets the preceding value in degrees. 2 ’ Inserts a minute, and sets the preceding value in minutes. 3 ” Inserts a second, and sets the preceding value in seconds. Example nter 34° 56’ 78”. • E 34ME1 5 6 M 2 ← “E ANGLE” remains selected; 78M3 type the number to enter the symbols. E 4 r Enters an “r”, to enter a number in radians.
Chapter 2: Operating the Graphing Calculator 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 2: Operating the Graphing Calculator 4 neg neg value Enters a “neg” logic figure. M41E 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 Exclusive-OR (xor) logic figure. 1100 M 5 1010 E 6 xnor value A xnor value B Enters an Exclusive-NOR (xnor) logic figure. 1100 M 6 1010 E H COMPLX In order to use the sub-menu items within the COMPLX menu, the calculator must be set up to handle complex numbers.
Chapter 2: Operating the Graphing Calculator 3 image( 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. Calculations using complex numbers To calculate using complex numbers, select the sub-menu item 4 x ± yi or 5 r ANSWER of the SETUP menu items.
Chapter 2: Operating the Graphing Calculator 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 2: Operating the Graphing Calculator Precedence of Calculations When solving a mathematical expression, this calculator internally looks for the following figures and methods (sorted in the order of evaluation): 1) Fractions (1/4, a/b, , etc.
Chapter 2: Operating the Graphing Calculator • About the order of precedence of the multiplications, that the multiplication sign "×" before such as "(", π and a variable is abbreviated, are higher than that of the multiplications that the multiplication sign "×" is not abbreviated. Therefore, if there is a division before a multiplication, the order of calculations may be changed and then the calculation results may be changed.
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 Manual Calculations 1. Try it! The speed of light is known to be 186,282 miles (approximately 300,000 kilometers) per second. That means light can go around the earth 7 and a half times within a second! Suppose you are standing at the equator. While the earth rotates over the period of one day, you also rotate around the globe at a certain speed.
Chapter 3: Manual Calculations 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. Press R to set the “store” mode.
Chapter 3: Manual Calculations 2. 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. You are to find out how tall the tree is by using the following factors: • The distance from you to the bottom of the tree is exactly 505.8 feet, and the tree stands vertically. • T he angle of elevation between the top and the bottom of the tree is 36 degrees If the base length of the right triangle is 505.
Chapter 3: Manual Calculations 4. Press 505.8 | 36. Press E to execute the calculation. 3. 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.
Chapter 3: Manual Calculations | 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.: _ Sets a negative value. Example • Calculate -12 × 4.
Chapter 3: Manual Calculations 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. 4. Calculations Using Various Function Keys Use the calculator’s function keys to simplify various calculation tasks. s Enters a sine function to be used in a trigonometric calculation. Example • Calculate sine π .
Chapter 3: Manual Calculations c Enters an arccosine function to be used in a trigonometric expression. Example • Calculate arccosine 0.5. @ c 0.5 E Enters an arctangent function to be used in a trigonometric expression. Example • Calculate arctangent 1. @ Note: 1E Expressions with inverse trigonometric functions evaluate in the following ranges.
Chapter 3: Manual Calculations I Enters a natural logarithm function. Example • Calculate In e4. I @ @ 4 E. @ Enters the Euler Number e (2.71…) to a power. The cursor will then be placed at the exponent. Example • Obtain a value of e3. @ @ 3 E. 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.
Chapter 3: Manual Calculations Note: When no value is entered prior to this key, the number areas will be left blank. * If the calculator is set to one-line mode, d enters “ ” (integerfraction separator) only. Use d in combination with b as follows. 5 • Enter 4 6 in one-line mode 4d5b6 * Integer part of the mixed number must be a natural number. A variable can not be used. Equation or use of parenthesis, such as (1+2) 2¬3 or (5) 2¬3, causes syntax error.
Chapter 3: Manual Calculations Note: When no base value is entered, “ab” will be entered with both number areas left blank. Ca;4'5E When calculating x to the power of m-th power of n, enter as follows; 2 • Calculate 23 (= 512) 2a3a2E 2 The above calculation is interpreted as 23 = 29. If you wish to calculate (23)2 = 82, press ( 2 a 3 ' ) a 2 E. _ Enters “ a ”. Example • Bring 4 to the 5th root. (= 1.319507911) 5@_4E Note: When no depth of power is entered, “ a number areas left blank.
Chapter 3: Manual Calculations R Stores a number in a variable. Example • Let A = 4, and B = 6. Calculate A + B. 4RAAE 6RABE AA+ABE r Recalls a variable. Example • Set C = 8. 8RACE Recall the value of C. @rACE X Enters a variable “x”, “θ”, “T”, or “n”. The variable is automatically determined according to the calculator’s coordinate setup: “x” for rectangular, “θ” for polar, “T” for parametric, “n” for sequential. z Accesses the VARS menu. {} b Enter braces to group numbers as a list.
Chapter 3: Manual Calculations 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. A maximum of 160 bytes can be stored in the temporary memory.
Chapter 3: Manual Calculations →a b/c Converts an improper fraction to a mixed number. Example 12 • Change 5 to a mixed number. 12 b 5 ' →a b/c E →A.xxx Converts a fraction to a decimal number. Example 12 • Change 5 to a decimal number. 12 b 5 ' →A.xxx E →b/c Converts a mixed number to an improper fraction. Example 2 • Change 2 5 to an improper fraction. 2d2' 5' →b/c E Note: Above three conversions will not affect the ANSWER settings in the SET UP menu.
Chapter 3: Manual Calculations int÷ Executes an integer division and returns its quotient and remainder. Example • Get a quotient and a remainder of 50 ÷ 3. 50 int÷ 3 E * Quotient value is set to Ans memory and remainder is not stored. remain Returns the remainder of a division. Example • Obtain the remainder when 123 is divided by 5. 1 2 3 remain 5 E rndCoin Returns a specified number of random integers to simulate a coin flip: 0 (head) or 1 (tail). The size of the list (i.e.
Chapter 3: Manual Calculations Simp Simplifies a given fraction stored in the ANSWER memory. • S et the ANSWER mode to Mixed(Real) or Improp (Real), and the SIMPLE mode to Manual in the SETUP menu to use this key. Specifying no common factor Simplify the fraction using the lowest common factor other than 1. Example 1 b 12 ' + 5 b 12 E Simp E (Simplified by 2, the lowest common factor of 12 an 6.) Simp E (Simplified by 3, the lowest common factor of 6 and 3.
Chapter 3: Manual Calculations % Set the preceding value as a percentage. Example • Get 25% of 1234. 1 2 3 4 | 2 5 % E * Percentage must be a positive value equal to or less than 100. Note : • The CATALOG commands and the equivalent keys: CATALOG command ¬ Equivalent key ^ a 2 y -1 x b R C M C nCr P M C nPr d • Sequen and Simul features can also be accessible from the CATALOG menu.
Chapter 3: Manual Calculations 5. More Variables: Single Value Variables and LIST Variables Additional single value variables (from A to Z, and θ) may be accessed. In addition, six LIST variables (from L1 to L6) are readily accessible through the second function. To save a list of numbers, follow the procedure below: 1. On the Calculation screen (#), create a list of numbers (“1, 2, 3”, in this example). Separate numbers with a comma (,), and group the numbers with braces ({ and }). 2.
Chapter 3: Manual Calculations 2. Type 1B | 9, for example. When entering the hexadecimal B, simply press the B key; using the A key will call up the variable B instead. 3. When done entering the hexadecimal expression, press E. The calculation result will be displayed in three other number base systems, as well as in hexadecimal format.
Chapter 3: Manual Calculations 4. When done entering the known values, press @ h. The calculation result will be displayed on the next screen. Pressing C will bring back the previous entry screen. 5. To go back to the TOOL menu to perform another calculation, press @ V. C POLY This tool is designed so that quadratic (ax2 + bx + c = 0) or cubic (ax3 + bx2 + cx + d = 0) equation may be solved. 1. Press C to select C POLY, and select the degree. For example, press 2 if a quadratic equation is desired. 2.
Chapter 4 Graphing Features 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 2.00 Euro upon entering the taxi cab, and 1.80 Euro for each mile the taxi travels. The Orange Cab, on the other hand, charges 3.50 Euro plus 1.20 Euro per mile. This means that taking the Tomato Cab will initially cost less than going with the Orange Cab, but will be more expensive as you travel longer distances.
Chapter 4: Graphing Features 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. If this is not so, use the cursor keys to bring the cursor to the “Y1=” line, then press the C key to clear any entries.
Chapter 4: Graphing Features 7. Let’s take a look at the graph. The vertical axis represents the Y value, while X is represented by the horizontal axis. It appears that the two diagonal lines cross at the point where the X value is somewhere between 2 and 3, indicating that Orange Cab costs less than the other, after 3 miles of traveling. 8. Next, press t to find the values per graph increment.
Chapter 4: Graphing Features 2. Try it! You have just opened your own bank account, with an initial deposit amount of 2000 Euro. Suppose your monthly income is 3000 Euro, and you will spend 60 percent of what you have in the account every month, how much will your balance be after one year? How much will you have in the account, 6 months from now? The example can be expressed as a sequential equation, as follows: un = un–1 × (1 – 0.
Chapter 4: Graphing Features PROCEDURE 1. F irst, 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. W e 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. Then press Y. The Graph Equation Entry window will open. 4. E nter a new equation set u(n1) × (1 - 0.6) + 3000 for u(n)=.
Chapter 4: Graphing Features 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. As ' is pressed several times, the n value (=X value, since the graph is set to “Time” format) increases, and the Y value (the balance of your account) will change. Find the Y value when the n value is 6 (after 6 months) as well as the value when n=12 (after 12 months = 1 year).
Chapter 4: Graphing Features 3. Explanations of Various Graphing Keys The explanations in this section are based on the rectangular coordinates (COORD RECT). Y: Displays the Graph Equation window. Up to 10 different equations can be entered. After the graph expression is entered, press E to store the equation. =: 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.
Chapter 4: Graphing Features 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”. If, for example, the value is set to “0.5”, then indices will be displayed on the X-axis at increments of 0.5. Enter the required “Xscl=” value (“0.
Chapter 4: Graphing Features 3. Once the initial anchor is set, move the cursor to a diagonal corner to define the box area. When the required area is squared off, press E. If a mistake is made, the anchor can be removed by pressing the C key. 4. The graph will automatically be redrawn. 3 In 4 Out The graph image will be zoomed out according to the B FACTOR setup under the ZOOM menu.
Chapter 4: Graphing Features 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. W hen the “Zoom factor” window appears, the cursor is automatically placed at “X_ Fact=”. The default zoom factor is 4; enter the required value here.
Chapter 4: Graphing Features 2 cos X Use this when the equation contains a cosine function. 3 tan X Use this when the equation contains a tangent function. 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. F HYP 1 sinh X Use this when the equation contains a hyperbolic sine function.
Chapter 4: Graphing Features 2 PreWin n selecting this sub-menu item, the window setup prior to the O current zoom setup will be recalled, and the graph will be redrawn accordingly. 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.
Chapter 4: Graphing Features 5. 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. 2.
Chapter 4: Graphing Features 6. 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. To exit the SETUP menu, press C. 3. Press Y.
Chapter 4: Graphing Features 7. Graphing Sequences The Setup setting COORD Seq enables you to input and draw up to three explicit or recursive sequence equations u(n), v(n), w(n) . Variables u, v and w are entered as @ 7, @ 8, and @ 9 respectively. Use X to enter the natural number n. A sequence is an ordered, numbered series of numbers. Sequence equations may be recursive or explicit.
Chapter 4: Graphing Features Example 1: Sequence representation when using the Time default setting Draw the sequence u(n) = 2 n First, ensure that the graphic coordinates are set to sequential (See page 72). 1. Use @ f to navigate to the Format menu. 2. Select G (TYPE) 2 (Time). 3. By pressing Y you now enter the input window for sequence equations. The cursor is placed on the first line, u(n); pressing C will delete existing entries and the cursor will be moved to the right side of the equation.
Chapter 4: Graphing Features Example 2: Representation using the uv setting (n-1) Compare 2 × 0.9 with the sequence previously input. n Sequence 2 is still stored in u(n) from the previous example. Now, sequence v(n) is to be defined and the representation type to be changed. 1. Press @ f G 3 to select uv. 2. Press Y and input the (n-1) equation 2 × 0.9 in the v(n) v(nMin). line. And input 1 for 3. Select Z A 1 for the automatic zoom function in order to set suitable window settings automatically.
Chapter 4: Graphing Features Example 3: A representation using the Web TYPE setting View the sequence u(n) = u(n-1) + 100 by comparing the sequence elements u(n) with the predecessor elements u(n-1) . 1. Press @ f G 1 to select Web. 2. Press Y and input the equation in the u(n) line. Because this is a recursive representation, a value for u(nMin) must be input. 3. If the lower four lines still contain entries, move the cursor down and delete them using C. 4.
Chapter 4: Graphing Features 8. The CALC Function The CALC function utilizes the entered graph equation to calculate values. In conjunction with the 4 graph coordinates, it can be called up anywhere. Note however that the CALC function will not do anything if no graph equation has been entered or specified. The following is an example that uses the previously entered polar graph equations above. 1. First, verify the graph coordinate mode by pressing @ ;; check to see if E COORD is set to Polar.
Chapter 4: Graphing Features Specific submenus Note: 1 Value Note: 2 Intsct Note: 3 Minimum Note: When coordinate system is Polar, Param or Seq, only 1 Value is selectable in the CALC menu. 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: Graphing Features 4 Maximum Note: 5 Y_zero Note: 6 Y_Incpt 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. If there are several maximum values, please use this function again. Finds an Y_zero (a intersect point or a contact point of the graph on the X-axis) of the given graph, and places the flashing cursor at that position.
Chapter 4: Graphing Features 8 ∫ dx Calculates the numerical integral of equation and display it on a graph. Example 1. Enter the graph equation. Y1 = – x2+ 5. 2. Press @ k 8. 3. Move the cursor to the point of lower and press E. • The line is drawn between the point of lower and X axis. 4. Move the cursor to the point of upper and press E. • Note: The calculation result is displayed and shaded on the graph. In the step 3 and 4, it is also possible to input the X value and press E.
Chapter 4: Graphing Features 9. Format Setting You can set up the Graph screen format from the FORMAT menu. Press @ f to display the Graph format menu. Specific sub-menus Note: A –––––– G TYPE appears only when the sequence coordinate graph mode is selected. Displays the current FORMAT settings.
Chapter 4: Graphing Features 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. 1 Web A web graph plot mode where x = u(n-1) and y = u(n). 2 Time Time graph plot mode where x = n and y = u(n), v(n), w(n). (default) 3 uv A uv mode where x = u(n) and y = v(n). 4 uw A uw mode where x = u(n) and y = w(n). 5 vw A vw mode where x = v(n) and y = w(n).
Chapter 4: Graphing Features 10. Setting a Window The W key displays the graph window setup. The display will differ according to the selected coordinate system.
Chapter 4: Graphing Features 11. 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. • The columns Y1 to Y3 are displayed on the first screen.
Chapter 4: Graphing Features 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 4: Graphing Features • 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. Example Automatically create a table starting from -5 with a step of 1 in the X-Y coordinate after equations, based on “Y1 = X”, “Y2 = X2”, and “Y3 = -X2 + 3”. 1. Press @ y and } _ 5 E 1 E. 2. Press t. * If the cursor is on the top or bottom line of the table, { or } can still be used.
Chapter 4: Graphing Features 12. 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: When entering coordinates, the DRAW function assumes that rectangular coordinates will be entered.
Chapter 4: Graphing Features 02 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 02 Line(. “Line(” will appear. Suppose you wish to draw a line, starting from an X-Y coordinate (1,2) to end at (8,8). 2.
Chapter 4: Graphing Features 2. Press A to select A DRAW, then press 0 2 to select 02 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 4: Graphing Features 03 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 0 3 and enter the value 5. From the GRAPH window H_Line Example • Draw a horizontal line manually. 1. Press @ dA 0 3. 2. Use the cursor navigation keys ({ } ; ') to move the flashing cursor to the appropriate position. 3. Press E to draw the line.
Chapter 4: Graphing Features 04 V_line From the Calculation screen Draws a vertical line on the graph window V_Line x-value Draws a vertical line (x = value) on the graph window. Example • Draw a horizontal line of x = 3. 1. Press @ d A 0 4 and enter the value 3. From the GRAPH window V_Line Example • Draw a vertical line manually. 1. Press @ d A 0 4. 2. Use the cursor navigation keys ({ } ; ') to move the flashing cursor to the appropriate position. 3. Press E to draw the line.
Chapter 4: Graphing Features From the GRAPH window T_line( Example • Draw a tangential line by manually specifying the point. 1. Select T_Line(. 2. Use ; ' to move the flashing cursor on the targeted graph line. Use { } to select a graph to draw the tangential line. 3. When the point is set at the tangent point, press E. • It is also possible to input the x-value and press E. Note: 06 N_line( From the Calculation screen The equation of the tangent line is displayed temporally.
Chapter 4: Graphing Features From the GRAPH window N_line( Example • Draw a normal line by manually specifying the point. 1. Select N_Line(. 2. Use ; ' to move the flashing cursor on the targeted graph line. Use { } to select a graph to draw the orthogonal line. 3. When the point is set at the point, press E. • It is also possible to input the x-value and press E. Note: 07 Draw The equation of the line is displayed temporally. (The equation may include a margin of error.
Chapter 4: Graphing Features Example • Shade the area enclosed by y = 1 x2 – 8 and y = x 4 within the range of –2 ≤ x ≤ 3. Before starting operation, Select ClrDraw to clear the graphs previously drawn. 1. Select Shade(. 2. Enter “ 1 x2 – 8, x, 4 -2, 3)” on the line. 3. Press E. Note: 09 DrawInv It is also possible to specify a function equation from Y0 to Y9 if stored. DrawInv equation Draws an inverse of a given graph expression. Example • Draw the inverse graph of y = 1 x2 – 8. 1. Select DrawInv.
Chapter 4: Graphing Features From the GRAPH window Circle( Example • Draw a circle manually. 1. Select Circle(. 2. Move the cursor to set the center point of the circle. Press E to set the anchor. 3. Move the cursor to determine the radius length of the circle. 4. When done, press E. The circle is drawn at the location. 11 Text( Text(column, row, “strings”) Enters a text string at a given coordinate. Text(column, row, variable) Draw the value of A-Z, θ.
Chapter 4: Graphing Features Note: Lines, points, and curves drawn by the Draw menu are handled as pictures. Therefore, they cannot be traced. Graphs drawn by the Draw menu are automatically cleared if any screen settings are changed. To save the graph, use the StoPict menu. B POINT Utilize these tools to manage point drawing and deletion on the graph. There are two operation methods. One is to directly move the cursor pointer to the location on the graph screen where you wish to insert the point.
Chapter 4: Graphing Features 4 PxlON( PxlON(column, row) Draws a pixel point at a given screen location indicated by column and row. The column and row definitions are as follows: Column: 0 to 132, Row: 0 to 64. column 132 (0, 0) (126, 0) (0, 62) (126, 62) row 64 106 This area cannot be specified 5 PxlOFF( PxlOFF(column, row) Erases a pixel point at a given screen location indicated by column and row. 6 PxlCHG( PxlCHG(column, row) Changes the status (i.e.
Chapter 4: Graphing Features C ON/OFF 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, ....] or DrawOFF Sets the specified graphs invisible. If no argument is given, then all graphs will be set invisible. Example • Set Y1 and Y2 to visible and Y3 to invisible. 1. Press @ d C 1. 2.
Chapter 4: Graphing Features E G_DATA All graph data, including the graph equations and window settings, can be stored in 10 graph storage areas (1-9, and 0), which can be called up later. 1 StoGD StoGD number (0-9) Saves the graph data. Example • Store the current graph data in location #1. Note: 2 RclGD The lines, graphs and pixels drawn with the A DRAW tools will not be saved here; use StoPict under F PICT instead. RclGD number (0-9) Recalls the saved graph data.
Chapter 4: Graphing Features F PICT 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. Example • Call back the previously stored graph data from location #1.
Chapter 4: Graphing Features G SHADE 1 SET With these sub-menu tools, inequalities, intersections and compliments of multiple graphs can be visualized. Sets up the shading area for each graph. Example 1. Set up a simple graph within the Graph Equation window. Enter “X2” for Y1, for example. 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.
Chapter 4: Graphing Features 13. Other Useful Graphing Features Split screen It splits the display vertically, to show the graph on the left side of the screen while showing the X-Y values in a table on the right. The cursor is positioned on the table, and can be scrolled up/down using the { or } keys. Graph and table Graph and equation • When @ " are pressed on the graph screen, the graph and table are displayed on the same screen.
Chapter 4: Graphing Features 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: Graphing Features Substitution feature • The substitution feature allows you to input an equation using characters and variables, and then substitute numeric values for the characters to draw the graph. • The substitution feature is valid only in the rectangular coordinate system. Using this feature, any number of numeric value sets can be substituted while referring to the graph drawing screen. This clearly shows the changes in the graph depending on numeric values.
Chapter 4: Graphing Features If independent memories A to C contain any numeric values, the graph is drawn based on these values. * If the equation (in this example, Y1) on which the cursor is located contains no variables, the substitution feature screen will not appear. 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.
Chapter 4: Graphing Features Next, change variable A from 2 to 5 and see how the graph changes. Rewrite the equation based on the numeric values input on the substitution feature screen. 1. Press { { 5 E. (The cursor is moved from C to A and 5 is input.) The slope of the graph becomes sharp. * Move the cursor accordingly and substitute other numeric values for variables to view how the graph changes. * The trace function cannot be used in the substitution feature.
Chapter 5 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. To enter the SLIDE SHOW, press ]. To exit the SLIDE SHOW feature, press #. 1. Try it! Make a SLIDE SHOW named “CUBIC” to explain how to draw the graph of a factorbase cubic function and explain how to solve cubic equations using factors.
Chapter 5: 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 5: 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 5: 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 5: 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 6 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 6: Matrix Features PROCEDURE Select a matrix to edit 1. Press @ m to enter the MATRIX menu. 2. Press B to select B 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 6: 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 6: 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. Note: Elements in Matrix can be specified using the NAME menu of the MATRIX menu such as “mat A (1, 1).
Chapter 6: Matrix Features 3. Normal Matrix Operations Many functions can be used for calculations of matrices and scalars. Examples of each calculation are as follows: Matrix + Matrix Matrix – Matrix 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. Press @ m A 1|@m A2 3.
Chapter 6: Matrix Features Inverse of Matrix For the calculation of the inverse of a matrix, please proceed as for the reciprocal of a real number. Example 1. Press # C. 2. Press @ m A 1 @ x E. 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.
Chapter 6: 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 6: 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 6: 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 6: 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 6: 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. 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. Repeat above steps 2 to 4 to enter all the rows. 6. Press @ m 2 ( ] ) to indicate the end of the matrix. 7. Press E.
Chapter 7 List Features 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. Here is the equation used to compute total stopping distance on dry, level concrete: The reaction time distance (in feet) = 1.1 times the speed (in miles per hour); The braking distance = 0.
Chapter 7: List Features Store the list in L1 4. Press R @ 1. 5. Press E to store the list in L1. 6. Press 1.1 | @ Enter the equation using L1 1 + 0.06 | @1y 7. Press E. 8. List {87, 140, 205, 282, 371, 472} will appear.
Chapter 7: 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 7: List Features Calculate 10 × L1 and store the results in L3 1. Press 10 | @ 1 R @ 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 7: List Features 4. Special List Operations This calculator has four list calculation menus: OPE, MATH, L_DATA and VECTOR. 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. Note: sortA(list name 1, list name 2,...
Chapter 7: 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 7: 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. Additional examples • The 1st command displays all number from 0 to 10, the 2nd all odd numbers from 1 to 21, the 3rd all even numbers from 0 to 10. * If increment is omitted, the default value 1 is used.
Chapter 7: 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}). • Press b R 1 to store the list. 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. Example • Make a matrix mat A using list L1 as the first column and list L2 as the second column.
Chapter 7: 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 7: 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 7: 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. Note: If relative frequencies or probabilities are stored in the frequency list, please use P_stdDv. 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 7: List Features Calculations using VECTOR 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} These functions use lists as vectors. 1 CrossPro( CrossPro(list name1, list name2) Calculate the cross product (vector product) of two lists. Example • Calculate the cross product of L1 and L2. Note: 2 DotPro( Calculation range: up to 3-dimensional vector. The dimensions of the vectors have to be identical.
Chapter 7: List Features 5. Drawing families of curves using the list function Using list items as coordinates, you can simultaneously draw families of curves. 1. Press Y. 2. Enter the equation; Y1 = {3, -2}x2 + {5, 3}x + {2, 4} 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.
Chapter 7: 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 7: 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 8: Statistics & Regression Calculations Chapter 8 Statistics & Regression Calculations 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 8: 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 8: 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. 4. Press } to move the cursor to the next line (DATA). Selecting whether 5. Select X for 1-variable plotting and press E.
Chapter 8: 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 Window menu. Set the WINDOW settings 1. Press W. Window (Rect) setting menu will appear. 2.
Chapter 8: 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 8: Statistics & Regression Calculations 2.
Chapter 8: Statistics & Regression Calculations The web site access counts example on page 147 will be used again to demonstrate the calculation of statistical values.
Chapter 8: 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 8: 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 8: 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 8: 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.
Chapter 8: 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 8: 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 8: Statistics & Regression Calculations 3. • To set the all plotting ON: Press 1 (1 PlotON). • To set the all plotting OFF: Press 2 (2 PlotOFF). *Y ou 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 8: 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 136 for details. 2 sortD( sortD(list) Sorts the list in descending order.
Chapter 8: Statistics & Regression Calculations 5. Regression Calculations Accessing the regression menu 01 Med_Med 1. Press S D REG. The Regression menu is displayed. 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 8: Statistics & Regression Calculations 06 Rg_x3 Rg_x3 (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression line using the third degree polynomial. (cubic regression) Formula: y = ax3 + bx2 + cx + d Parameters: a, b, c, d, R2 07 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.
Chapter 8: Statistics & Regression Calculations 12 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 13 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 8: Statistics & Regression Calculations 16 x’ value or list x’ Finds the estimated value of x for a given value of y by applying the function determined by the regression. 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 6 E.
Chapter 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 8: 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 9 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 9: 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 9: 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 9: 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 9: Financial Features 2. 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 (–) Set the TAB and FSE (2 and FIX respectively) 1 2 3 Time flow PMT = 800 358 359 N = 360 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.
Chapter 9: 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 9: Financial Features 3. 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 9: 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 9: 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 30-year loan at an annual interest rate of 5% for the remaining $200,000.
Chapter 9: 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 9: Financial Features 4. 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 10 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 shares variables with other calculator features. These variables can be called up or defined within the SOLVER feature or any other features.
Chapter 10: 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 10: The SOLVER Feature Newton& bisection method Newton&bisection method is a technique of finding approximate solutions to a math problem via calculus, when conventional algebraic techniques just cannot work. If the Equation method fails, the calculator will automatically switch to Newton&bisection method. Example Solve “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 10: 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 10: 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 10: 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 10: 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 10: 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 11 Programming Features The calculator has programming features that enable automatic processing of a series of calculations any number of times. 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). Please note that complex numbers cannot be used in programming. 1. Try it! Display a message “HELLO WORLD” on the display. Creating a new program 1. Press P.
Chapter 11: Programming Features 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. Note: Entering a command Press @ j, and you can access all the available commands at once. 7. Select A 1. 8. Press P. 9. Select A 2. The characters following a double quotation mark can be manipulated as text.
Chapter 11: Programming Features 2. Programming Hints Editing the program Press P B and then the appropriate numbers to open the stored program. Press @ i to enter the insert type mode. Adding commands, strings or Press E to go to the next line. Be sure to press @ i command lines again to turn off the insert type mode and return to type over mode. to the program Press E twice to insert a blank line. Entering alphabetical characters (uppercase only) Press A to enter characters. Press @ .
Chapter 11: 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 11: 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 11: 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 11: Programming Features 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 11: Programming Features 04 Web 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. 05 Time Time Sets the graph coordinates as axes in sequence graphs. n is set to the X axis and u(n), v(n) and w(n) is set to the Y axis. 06 uv uv Sets the graph coordinates as the axes of sequence graphs. u(n) is set to the X axis and v(n) is set to the Y axis. 07 uw uw Sets the graph coordinates as the axes of sequence graphs.
Chapter 11: Programming Features F FORMAT menu P F F FORMAT menu commands are used to set the graph format. 01 RectCursor RectCursor Sets the graph coordinate display format to X - Y axes. 02 PolarCursor PolarCursor Sets the graph coordinates display format to polar coordinates. 03 ExprON 04 ExprOFF ExprON Sets the graph equation to be displayed on the graph screen. ExprOFF Sets the graph equation to not be displayed on the graph screen.
Chapter 11: 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 11: 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 11: Programming Features 07 For For variable, initial value, end value [, increment] 08 Next 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 11: Programming Features [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. 7.
Chapter 11: Programming Features 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). A EQVARS Specifies the graph equation (Y1 to Y9, and Y0, X1T•Y1T to X6T•Y6T, R1 to R6). B WINDOW Specifies the functions that set the graph display screen size (Xmin, Ymax, Tstep, etc.). C STOWIN Specifies the stored zoom (window) setting value (Zm_Xmin, Zm_ Ymax, etc.).
Chapter 11: Programming Features • Always enter the argument for functions requiring an argument at the end of the command, such as the CALC function (@ k). An error will be returned for commands not accompanied by an argument. Example Value 5 Example Set Xmin = -3, Xmax = 10, Xscl = 1, Ymin = -5, Ymax = 5, Yscl = 1 in the WINDOW screen. Use R to input the settings.
Chapter 11: Programming Features • 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. • In this way, the contents of an immediately preceding statistical calculation can be stored as statistical values. • These contents remain valid until the next statistical calculation is executed, even if the power is turned off. • The same is true even for regression calculations and verification calculations. 8.
Chapter 11: Programming Features Chapter 13: Programming Features 9. Preinstalled program There is one preinstalled program ("integral"). Calculating the area between graphs for a given interval Integral • Enter necessary equations before executing this program. 1. Press P A 0 1. 2. Press 1 to select “∫Y1dx”, 2 to select “∫Y1-Y2dx” or 3 to select "AREA BETWEEN Y1-Y2" to avoid the surface cancel each other. 3.
Chapter 11: Programming Features Calculation ranges are illustrated below. Program name integral Calculation range Note Xmin and Xmax are in the windows settings. Xmin ≤ LOWER ≤ Xmax Xmin ≤ UPPER ≤ Xmax Storage locations of the calculation result This program calculate by using the variables below. Therefore, please note that some numbers are stored in these variables if you execute the program.
Chapter 12 OPTION Menu The optional products (CE-451L and CE-LK4) are not available in some regions. 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.
Chapter 12: 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 12: 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 12: 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 12: 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 12: OPTION Menu Transmission between the EL9950 and PC • The optional kit CE-LK4 (cable and Windows software) is required for calculator to data communication with PC. And “SHARP CE-LK4 for EL-9950” (PC-Link software) must be installed on your Windows PC. • Refer to the CE-LK4 operation manual for details. • During communications between calculator and PC, no operation of the calculator is required.
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) Note: 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. • Please do not use rechargeable battery.
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. Note: Do not remove the lithium battery while the unit operation batteries are removed; otherwise all the calculator's stored memory will be lost. 4.
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, wait a few seconds and then press O. The following message will appear. 7. Press O. Do not press C.
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”. The calculator is not responding; the software appears to have crashed! • Press O. If this does not work, then press @, then O to tell the running application to quit. If everything fails, then the calculator’s memory may need to be reset.
Appendix 3. Specifications Model EL-9950 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 01 02 Syntax Calculate 03 Nesting Description Syntax error found in equation/program Calculation-related error found (division by 0, calculation beyond range, etc.) Cannot nest more than 14 numerical values, or 32 functions during execution. Graph equation variables (Y1, etc.) includes other graph equation variables (Solver features). 04 Invalid Matrix definition error or entering an invalid value.
Appendix Error Code Error Message Description 36 No solution No solution found. 37 No title No title entered. 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.
Appendix 5. Error Conditions Relating to Specific Tasks 1. Financial * Define constants “r” and “s” as used in the equation below. r= ( I (%) C/Y 100 +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) f (r) = PV + PMT × n + FV: (r = 0) r 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( f (χ2, df) = 1 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 n m 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 + 1) = (n – c) p 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 x 10 x-1 x2 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 Calculation range Decimal: |x| ≤ 9999999999 Binary: 1000000000000000 ≤ x ≤ 1111111111111111 dec 0 ≤ x ≤ 0111111111111111 bin oct Notes 4000000000 ≤ x ≤ 7777777777 Octal: x is an integer 0 ≤ x ≤ 3777777777 hex Hexadecimal: FDABF41C01 ≤ x ≤ FFFFFFFFFF 0 ≤ x ≤ 2540BE3FF →dms →deg xy → r xy → θ |x| < 1 × 10100 |x| < 1 × 10100, |y| < 1 × 10100 x2 + y2 r = x2 + y2 < 1 × 10100 -1 θ = tan y y | x | < 1 × 10100 x x = r cosθ rθ → x rθ → y y = r sinθ |r| < 1 × 10100 Binary:
Appendix Function Calculation range Notes |x| < 1 × 1050 |y| < 1 × 1050 |Σx| < 1 × 10100 2 100 Statistic Σx < 1 × 10 calculations |Σy| < 1 × 10100 2 100 Σy < 1 × 10 |Σxy| < 1 × 10100 |n| < 1 × 10100 _ x n ≠ 0 n>1 sx |Σx| < 1 × 1050 0≤ (Σx)2 n <1 n–1 Σx2 – × 10100 _ 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 r |Σy| < 1 × 1050 (Σy)2 (Σx)2 0 < (Σx2 – ) (Σy2 – ) <1 × 10100 n n |Σxy – ΣxΣy | < 1 × 10100 n < 1 × 10100 n>0 |Σx| < 1 × 1050
Appendix Function a y’ Calculation range _ |bx| < 1 × 10100 _ _ |y – bx | < 1 × 10100 |bx| < 1 × 10 Same as b for other. |a + bx| < 1 × 10100 |y – a| < 1 × 10100 y–a | b | < 1 × 10100 int÷ 0 ≤ x < 1010 remain 0 ≤ x < 1010 % |x| < 10100 → a b/c |x| < 1010 → b/c Matrix Same as above. 100 x’ List Notes Error is returned when the number of elements exceeds 1000. A number with 10 or less decimal places, or the 1010-th or above decimal places are 0.
Appendix 3. Complex number calculation In a complex number calculation, a calculation error may occur and increase due to inner continuous calculations.
Appendix 7. 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 Page M NUM abs( abs(value) B1 34 round( round(value [, digit number of decimals]) B2 34 ipart ipart value B3 35 fpart fpart value B4 35 int int value B5 35 min( min(value A, value B) or min(list) B6 35 max( max(value A, value B) or max(list) B7 35 lcm( lcm(natural number, natural number) B8 36 gcd( gcd(natural number, natural number) B9 36 M PROB random random [(number of trial)] C1 36 rndInt( rndInt(minimum value, ma
Appendix Functions Commands g Syntax value g Keystrokes Page E5 40 M INEQ = value A = value B F1 40 ≠ value A ≠ value B F2 40 > value A > value B F3 40 ≥ value A ≥ value B F4 40 < value A < value B F5 40 ≤ value A ≤ value B F6 40 M LOGIC and value A and value B G1 41 or value A or value B G2 41 not not value G3 41 xor value A xor value B G4 42 xnor value A xnor value B G5 42 conj(complex number) H1 42 real( real(complex number) H2 42 image( image(com
Appendix 2. LIST menus Functions Commands Syntax Keystrokes Page @ l OPE sortA( sortA(list name [, subordinate list name1, ... , subordinate list name n]) A1 136 sortD( sortD(list name [, subordinate list name1, ...
Appendix 3. STAT menus Functions Commands Keystrokes Syntax Page S EDIT/OPE EDIT No arguments AE 151 sortA( sortA(list [, subordinate list 1, ... , subordinate list n]) B1 161 sortD( sortD(list [, subordinate list 1, ... , subordinate list n]) B2 161 SetList SetList [list name 1, list name 2, list name 3, ... ] B3 161 ClrList ClrList list name1 [, list name 2, ...
Appendix Functions Commands Syntax Keystrokes Page Rg_abx Rg_abx (list name for x, list name for y [, frequency list] [, equation name to store]) D10 163 Rg_aebx Rg_aebx (list name for x, list name for y [, frequency list] [, equation name to store]) D11 163 Rg_x-1 Rg_x-1 (list name for x, list name for y [, frequency list] [, equation name to store]) D12 164 Rg_axb Rg_axb (list name for x, list name for y [, frequency list] [, equation name to store]) D13 164 Rg_logistic Rg_logistic (l
Appendix Functions Commands Syntax Keystrokes Page cdfnorm( cdfnorm(lower limit, upper limit [,mean, standard deviation]) F02 179 InvNorm( InvNorm(probability [, mean, standard deviation]) F03 180 pdfT( pdfT(value, degree of freedom) F04 180 cdfT( cdfT(lower limit, upper limit, degree of freedom) F05 181 pdfχ2( pdfχ2(value, degree of freedom) F06 181 cdfχ2( cdfχ2(lower limit, upper limit, degree of freedom) F07 181 pdfF( pdfF(value, degree of freedom of numerator, degree of free
Appendix Functions Commands Keystrokes Syntax Page Broken + No arguments B2 156 Broken No arguments B3 156 Norm •_X No arguments C1 156 Norm+_X No arguments C2 156 Norm _X No arguments C3 156 Norm •_Y No arguments C4 156 Norm+_Y No arguments C5 156 Norm _Y No arguments C6 156 NormDis No arguments D1 156 Box No arguments E1 157 MBox • No arguments E2 157 MBox+ No arguments E3 157 MBox No arguments E4 157 Pie No arguments F1 158 Pie% No arguments F
Appendix Functions Commands Syntax Keystrokes Page Draw Draw equation A 07 102 Shade( Shade(equation 1, equation 2 [, begin, end]) A 08 102 DrawInv DrawInv equation A 09 103 Circle( Circle(x-coordinate of center, y-coordinate of center, radius) A 10 103 Text( Text(column, row, “character strings”) Text(column, row, variable) A 11 104 @ d POINT PntON( PntON(x-coordinate, y-coordinate) B1 105 PntOFF( PntOFF(x-coordinate, y-coordinate) B2 105 PntCHG( PntCHG(x-coordinate, y-coor
Appendix Functions Commands Syntax Keystrokes Page In Zm_In No arguments A3 76 Out Zm_Out No arguments A4 76 Default Zm_Default No arguments A5 76 Square Zm_Square No arguments A6 76 Dec Zm_Dec No arguments A7 76 Int Zm_Int No arguments A8 76 Stat Zm_Stat No arguments A9 76 No arguments BE 77 Zm_x2 No arguments C1 77 x-1 Zm_x-1 No arguments C2 77 No arguments C3 77 Z FACTOR/POWER FACTOR x2 x Zm_ x Z EXP 10x Zm_10x No arguments D1 77 ex Zm_ex No arguments
Appendix Functions Commands Syntax Keystrokes Page sin-1 x Zm_sin-1 No arguments E4 78 cos-1 x Zm_cos-1 No arguments E5 78 tan-1 x Zm_tan-1 No arguments E6 78 Z HYP/STO/RCL sinh x Zm_sinh No arguments F1 78 cosh x Zm_cosh No arguments F2 78 tanh x Zm_tanh No arguments F3 78 sinh-1 x Zm_sinh-1 No arguments F4 78 cosh-1 x Zm_cosh-1 No arguments F5 78 tanh-1 x Zm_tanh-1 No arguments F6 78 StoWin No arguments G1 78 RclWin No arguments H1 78 PreWin No arguments H
Appendix 8. SLIDE SHOW menus Functions Commands Syntax Keystrokes Page ] CURR/PLAY/NEW/SELECT/EDIT CURR No arguments AE 119 PLAY No arguments B 119 NEW No arguments CE 119 SELECT No arguments D 119 MOVE No arguments E1 119 DEL No arguments E2 120 RENAME No arguments E3 120 9.
Appendix Functions Commands For Syntax Keystrokes 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 215 Return No arguments B12 215 Next While mode) SCRN P (in (in the the Programming Prgramming mode) SCRN ClrT No arguments C1 210 ClrG No arguments C2 210 DispT No arguments C3 210 DispG No arguments C4 210 mode) I/O P (in (in the the Programmi
Appendix Functions Commands Syntax Keystrokes 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 mode) FORMAT the Programming Prgramming mode) FORMAT RectCursor No arguments F01 212 PolarCursor No arguments F02 212 ExprON No arguments F03 212 ExprOFF No arguments F04 212 Y'ON No arguments F05 212 Y'OFF No arguments F06 212 AxisON No arguments F07 212 AxisOF
Appendix Functions Commands Keystrokes Syntax Page P (in mode) COPY (in the the Programming Prgramming mode) COPY StoLine No arguments H1 216 RclLine No arguments H2 216 10.
Appendix Functions Commands Keystrokes Syntax Page augment( augment(matrix name A, matrix name B) C04 127 identity identity dimension value C05 127 rnd_mat( rnd_mat(number of row, number of column) C06 127 row_swap( row_swap(matrix name, row number, row number) C07 128 row_plus( row_plus(matrix name, row number, row number) C08 128 row_mult( row_mult(multiplied number, matrix name, row number) C09 128 row_m.p.( row_m.p.
Appendix Functions Commands Syntax Keystrokes Page Irr( Irr(initial investment, list of following collected investment [, frequency list] [, assumed revenue rate]) B07 192 Bal( Bal(number of payments [, decimal place to round]) B08 193 ∑Prn( ∑Prn(initial number of payments, end number of payments [, decimal place to round]) B09 193 ∑Int( ∑Int(initial number of payments, end number of payments [, decimal place to round]) B10 193 →Apr( →Apr(effective interest rate, number of settlements)
Appendix Functions Commands Syntax Keystrokes Page 6 No arguments B6 66 2 No arguments C2 67 3 No arguments C3 67 13.