Casio fx-991ES manual

http://world.casio.com/edu/ RCA502160-001V01 E fx-115ES fx-991ES User's Guide[...]

CASIO Europe GmbH Bornbarch 10, 22848 Norderstedt, Germany[...]

E-1 About this Manual • The MA TH mark indicates an example that uses Math f ormat, while the LINE mark indicates Linear format. For details about input/output f or mats, see “Specifying the Input/Output F ormat”. •K e ycap mar kings indicate what a ke y inputs or what function it performs. Example: 1 , 2 , + , - , ! , A , etc. •P ressing[...]

E-2 • The follo wing shows an example of ho w a key oper ation to select an on-screen menu item is represented in this User’ s Guide. Example: 1 (Setup) Indicates the menu item that is selected b y the number ke y operation ( 1 ) bef ore it. Note that this is not part of the actual ke y operation you perf orm. • The cursor key is mark ed with[...]

E-3 Safety Precautions Be sure to read the f ollowing safety precautions bef ore using this calculator . K eep this manual handy for later ref erence. Caution This symbol is used to indicate inf or mation that can result in personal injury or mater ial damage if ignored. Battery •A fter removing the battery from the calculator, put it in a saf e [...]

E-4 Handling Precautions •B e sure to press the O ke y before using the calculator f or the first time. •E ven if the calculator is operating normally , replace the battery at least once every three years. A dead battery can leak, causing damage to and malfunction of the calculator . Nev er leav e a dead battery in the calculator. • The batte[...]

E-5 Befor e Using the Calculator k Removing the Har d Case Bef ore using the calculator, slide its hard case do wnwards to remov e it, and then affix the hard case to the bac k of the calculator as shown in the illustration below . k T urning P ower On and Off •P ress O to turn on the calculator. •P ress 1A (OFF) to turn off the calculator. k A[...]

E-6 k About the Display Y our calculator has a 31-dot × 96-dot LCD screen. Example: k Display Indicator s Sample Display: This Means this: indicator: The keypad has been shifted b y pressing the 1 ke y. The ke ypad will unshift and this indicator will disappear when you press a k ey . The alpha input mode has been entered by pressing the S ke y. T[...]

E-7 Important! •F or a very complex calculation or some other type of calculation that takes a long time to e xecute, the displa y ma y show only the abov e indicators (without any value) while it perf orms the calculation internally . Calculation Modes and Calculator Setup k Calculation Modes When you want to perf orm this type of Select this op[...]

E-8 •S ee “Adjusting Displa y Contrast” f or information about how to use “ ] CONT ' ”. Specifying the Input/Output Format For this input/output format: P erf orm this key operation: Math 1N 1 (MthIO) Linear 1N 2 (LineIO) •M ath format causes fractions, irrational n umbers, and other e xpressions to be displa yed as the y are writt[...]

E-9 •N orm: Selecting one of the tw o availab le settings (Nor m1, Norm2) determines the range in which results will be display ed in non- e xponential format. Outside the specified r ange, results are display ed using exponential f ormat. Norm1: 10 –2 >  x  ,  x  > 10 10 Norm2: 10 –9 >  x  ,  x  > 10 10 Ex[...]

E-10 k Initializing the Calculation Mode and Other Settings P erf or ming the follo wing procedure initializes the calculation mode and other setup settings as shown belo w . 1 9 (CLR) 1 (Setup) = (Y es) This setting: Is initialized to this: Calculation Mode COMP Input/Output Format MthIO Angle Unit Deg Display Digits Norm1 Fr action Display F orma[...]

E-11 Example: sin 30 = LINE s 30)= Pressing s inputs “sin(”. •N ote that the input procedure is different if y ou want to use Math fo rm at. For more inf ormation, see “Inputting with Math Format”. Omitting the Multiplication Sign Y ou can omit the multiplication sign ( × ) in any of the f ollowing cases . •B efore an open parentheses [...]

E-12 •N ormally the input cursor appears as a straight ver tical ( I ) or horizontal ( ) flashing line on the displa y screen. When there are 10 or fe wer bytes of input remaining in the current e xpression, the cursor changes shape to I to let you know . If the I cursor appears, terminate the expression at a con venient point and calculate the r[...]

E-13 Deleting a Character or Function Example: To correct the expression 369 × × 12 so it becomes 369 × 12 LINE Inser t Mode: 369**12 dd Y Ov erwrite Mode: 369**12 ddd Y Correcting a Calculation Example: To correct cos(60) so it becomes sin(60) LINE Inser t Mode: c 60) ddd Y s Ov erwrite Mode: c 60) dddd s Inserting Input into a Calculation Alwa[...]

E-14 k Displaying the Location of an Err or If an error message (lik e “Math ERROR” or “Syntax ERR OR”) appears when you press = , press d or e . This will display the part of the calculation where the error occurred, with the cursor positioned at the error location. Y ou can then mak e necessar y corrections. Example: When you input 14 ÷ [...]

E-15 Functions and Symbols Supported for Math Format Input • The “Bytes” column shows the n umber of bytes of memory that are used up by input. Function/Symbol Ke y Operation Bytes Improper F raction ' 9 Mixed F r action 1 ' ( ( )1 3 log(a,b) (Logarithm) & 6 10^ x (P ower of 10) 1l ( $ )4 e^ x (P ower of e ) 1i ( % )4 Square Roo[...]

E-16 Example 3: To input (1 + ) 2 × 2 = MA TH (1+ ' 2 c 5 e ) Math w *2= •W hen you press = and obtain a calculation result using Math fo rm at, par t of the expression y ou input can be cut off as shown in the Example 3 screen shot. If you need to vie w the entire input e xpression again, press A and then press e . Incorporating a V alue i[...]

E-17 Original Expression: Function Ke y Operation Resulting Expression Integral 7 Derivative 1 7 ( F ) Σ Calculation 1 & ( 8 ) Y ou can also incor porate v alues into the following functions. 1l ( $ ), 1i ( % ), ! , 6 , 1 ! ( # ), 1w (Abs) Displaying Calculation Results in a Form that Includes ' ' ' ' ' 2, π , etc. (I[...]

E-18 Example 2: sin (60) = (Angle Unit: Deg) MA TH s 60= Math Example 3: sin –1 (0.5) = π (Angle Unit: Rad) MA TH 1 s (sin –1 ) 0.5= Math • The follo wing are the calculations for which ' fo rm (form that includes ' within irrational number display) results can be display ed. a. Arithmetic calculations of values with square root sy[...]

E-19 The follo wing shows the range f or each of the coefficients ( a , b , c , d , e , f ). 1 < a < 100, 1 < b < 1000, 1 < c < 100 0 < d < 100, 0 < e < 1000, 1 < f < 100 Example: The underlined areas in the abov e examples indicate what caused decimal f or m to be used. Reasons why the results of the e xamples a[...]

E-20 • If a term is encountered during the calculation cannot be displayed as a root ( ' ) form or a fraction, the calculation result is displa yed in decimal f or m. Example: log3 + ' 2 = 1.891334817 Basic Calculations (COMP) This section e xplains how to perform arithmetic, fraction, percent, and sexagesimal calculations . All calcula[...]

E-21 Omitting a Final Closed P arenthesis Y ou can omit any closed parenthesis ( ) ) immediately preceding operation of the = ke y at the end of a calculation. This is true only in the case of Linear format. Example: (2 + 3) × (4 – 1) = 15 LINE (2+3)* (4-1= k Fraction Calculations How y ou should input fractions depends on the input/output forma[...]

E-22 Switching between Fraction and Decimal Format • The f or mat of the fraction depends on the currently selected fraction display f ormat setting (improper fraction or mixed fraction). •Y ou cannot switch from decimal f ormat to mixed fraction f or mat if the total number of digits used in the mix ed fraction (including integer , numerator ,[...]

E-23 Sexa gesimal Calculations •P erforming the following types of se xagesimal calculations produces a se xagesimal result. -A ddition or subtraction of two se xagesimal values -M ultiplication or division of a sexagesimal v alue and a decimal value Appendix <#012> 2 ° 20´30˝ + 39´30˝ = 3 ° 00´00˝ Con verting V alues between Sexage[...]

E-24 Using Calculation History Memory and Replay Calculation history memor y maintains a record of each calculation e xpression y ou input and e xecute, and its result. Modes that suppor t calculation history memor y: COMP ( N 1 ), CMPLX ( N 2 ), BASE-N ( N 4 ) Recalling Calculation History Memory Contents Press f to back-step through calculation h[...]

E-25 Using Calculator Memory Memory Name Description An sw er Memo ry Stores the last calculation result obtained. Calculation results can be added to or sub- Independent tracted from independent memory . The “M” Memory display indicator indicates data in independent memory . Va r iables Six variab les named A, B, C, D , X, and Y can be used fo[...]

E-26 Inputting Answer Memory Contents into an Expression Example: To perform the calculations shown below: LINE 123+456= 789- G = k Independent Memory (M) Y ou can add calculation results to or subtract results from independent memory . The “M” appears on the display when independent memory contains a value. Independent Memory Overview • The [...]

E-27 Calculation Examples Using Independent Memory • If the “M” indicator is on the displa y , perform the procedure under “Clearing Independent Memor y” before perf orming this example. Example: 23 + 9 = 32 23+9 m 53 – 6 = 47 53-6 m –) 45 × 2 = 90 45*2 1m (M–) 99 ÷ 3 = 33 99/3 m (T otal) 22 tm (M) Clearing Independent Memory Pres[...]

E-28 Using CALC The CALC feature lets y ou input a calculation e xpression that contains v ar iab les, and then assign values to the v ariables and perf or m the calculation. Y ou can use CALC in the COMP Mode ( N 1 ) and in the CMPLX Mode ( N 2 ). k Expressions Suppor ted b y CALC The f ollowing describes the types of expressions that can be used [...]

E-29 s (or = ) 10= •T o exit CALC , press A . • If the expression y ou are using contains more than one variable , an input prompt appears for each one . Appendix <#016> Cal culate a n +1 = a n + 2 n (a 1 = 1) as the value of a n changes from a 2 to a 5 . (Results: a 2 = 3, a 3 = 7, a 4 = 13, a 5 = 21) *1 Assigns 1 to a 1 .* 2A ssigns 1 t[...]

E-30 •A n error (V ariable ERR OR) occurs when the solution variable is not included in the expression being solv ed. k Example SOL VE Operation Example: To solve y = ax 2 + b for x when y = 0, a = 1, and b = –2. MA TH S f (Y) Ss (=) S y (A) S ) (X) w + S e (B) 1 ) (,) S ) (X) 1s (SOL VE) Math Prompts for input of a v alue f or Y . Current valu[...]

E-31 • SOL VE uses Newton’ s Method, so e ven if there are multiple solutions, only one of them will be returned. •N ew ton’s Method can ha ve prob lems obtaining solutions for the f ollowing types of functions. -A per iodic function ( y = sin( x ), etc.) -A function whose graph includes a steep slope ( y = e x , y =1/ x , etc.) -A disconti[...]

E-32 Function Calculations This section explains ho w to use the calculator’ s built-in functions. The functions av ailable to you depends on the calculation mode y ou are in. The e xplanations in this section are mainly about the functions that are av ailable in all calculation modes. All of the e xamples in this section sho w operation in the C[...]

E-33 k Con verting an Input V alue to the Calculator’ s Default Angle Unit After inputting a value , press 1G (DRG ' ) to displa y the angle unit specification menu shown belo w . Press the number ke y that corresponds to the angle unit of the input value . The calculator will automatically conv er t it to the calculator’ s default angle u[...]

E-34 Appendix <#023> to <#025> *1 A base of 10 (common logarithm) is used if no base is specified. k Po wer Functions and P ower Root Functions •P ower functions and power root functions can be used in the COMP , ST A T , EQN, MA TRIX, T ABLE, and VECTOR calculation modes . •T he X 2 , X 3 , X –1 functions can be used in complex n[...]

E-35 Tips on Impr oving Integration V alue Accuracy •W hen a periodic function or integration interval results in positive and negative f ( x ) function values P erf or m separate integrations f or each cycle, or f or the positive part and the negative par t, and then combine the results. P ositive P art Negative P art ( S P ositive) ( S Negative[...]

E-36 k Differential Calculations Y our calculator performs differential calculations b y approximating the derivativ e based on centered difference appro ximation. d / dx ( f ( x ), a , tol ) f ( x ): Function of X (All non-X v ariables are treated as constants.) a : Input a value to specify the point f or which the derivativ e should be obtained ([...]

E-37 k Σ Calculations With Σ (, you can obtain the sum of an input f ( x ) e xpression for a specific range . Σ calculations are perf ormed using the follo wing for m ula. Σ ( f ( x ), a , b ) = f ( a ) + f ( a + 1) + .... + f ( b ) f ( x ): Function of X (All non-X v ariables are treated as constants.) a :C alculation range start point b :C al[...]

E-38 • If you perf or m coordinate con version inside of an e xpression instead of a stand-alone operation, the calculation is performed using only the first value (either the r -v alue or the X-value) produced b y the conv ersion. Example: P ol ( ' 2, ' 2) + 5 = 2 + 5 = 7 Appendix <#036> to <#037> k Other Functions This sec[...]

E-39 Rounding Function (Rnd) This function rounds the value or the result of the e xpression in the function’ s argument to the number of significant digits specified by the number of displa y digits setting. Display Digits Setting: Norm1 or Nor m2 The mantissa is rounded to 10 digits. Display Digits Setting: F ix or Sci The value is rounded to t[...]

E-40 (Check rounded result.) *14= FIX k Practical Examples Appendix <#042> ∫ (sin X + cos X ) 2 dX = π 0 π ( tol : Not specified) <#043> Confirm that the two sides of the f ollowing equation are equal: e = Σ n ! 1 n = 0 ∞ Tr a n sfor ming Displayed Va l ues Y ou can use the procedures in this section to transform a displa yed va [...]

E-41 Note •W hen you transf or m from decimal f orm to standard form, the calculator automatically decides the standard form to use. Y ou cannot specify the standard form. Fr action: The current fraction displa y format setting determines whether the result is an improper fraction or mixed fraction. π : The f ollowing are the π fo rm s that are[...]

E-42 Complex Number Calculations (CMPLX) Y our calculator can perform the following comple x number calculations. •A ddition, subtraction, multiplication, division •A rgument and absolute value calculations •R eciprocal, square and cube calculations •C onjugate comple x number calculations All calculations in this section are perf ormed in [...]

E-43 •W ith Linear f or mat, the real par t and imaginary par t are shown in two diff erent lines. Example 2: ' 2 ∠ 45 = 1 + i (Angle Unit: Deg) MA TH ! 2 e 1 y ( ∠ ) 45= Math CMPLX Examples of Calculation Results Using P olar Coordinate Format ( r ∠ θ ) Example 1: 2 × ( ' 3 + i ) = 2 ' 3 + 2 i = 4 ∠ 30 (Angle Unit: Deg) [...]

E-44 k Absolute V alue and Argument (Abs, arg) Y ou can use the following procedure to obtain the absolute v alue (|Z|) and argument (arg) on the Gaussian plane f or a complex n umber of the f or mat Z = a + b i . 1w (Abs); 1 2 (CMPLX) 1 (arg) Appendix <#051> Obtain the absolute value and argument of 2 + 2 i . *1 Absolute V alue *2 Argument S[...]

E-45 ST A T Editor Screen There are two ST A T editor screen formats, depending on the type of statistical calculation you selected. Single-variable Statistics Paired-v ariable Statistics • The first line of the ST A T editor screen shows the value for the first sample or the values f or their first pair of samples. FREQ (Frequency) Column If y o[...]

E-46 ST A T Editor Screen Input Precautions • The number of lines in ST A T editor screen (the number of sample data values y ou can input) depends on the type of statistical data y ou selected, and on the Statistical Display setting of the calculator’ s setup screen. • The follo wing types of input are not allowed on the ST A T editor screen[...]

E-47 Deleting All ST A T Editor Contents (1) Press 1 1 (ST A T) 3 (Edit). (2) Press 2 (Del-A). • This clears all of the sample data on the ST A T editor screen. Note •N ote that you can perf orm the procedures under “Inser ting a Line” and “Deleting All ST A T Editor Contents” only when the ST A T editor screen is on the display . k ST [...]

E-48 Single-variab le Menu Item Select this When you want to do this: menu item: Displa y the Distr sub-menu of commands for normal distr ibution calculations 7 Distr •F or more information, see “Distr Sub-men u”. P aired-variable Menu Item Select this When you want to do this: menu item: Displa y the Reg sub-menu of commands for regression c[...]

E-49 Distr Sub-menu ( 1 1 (ST A T) 7 (Distr)) 1 P( 2 Q( 3 R( 4 ' t This menu can be used to calculate the probability of standard normal distribution. Normalized v ariate t is calculated with the e xpression shown below , using the mean value ( o ) and population standard de viation value ( x σ n ) obtained from the data input on the ST A T e[...]

E-50 Commands when Linear Regression Calculation (A+BX) Is Selected With linear regression, reg ression is performed in accordance with the f ollowing model equation. y = A + BX The follo wing are the commands that appear on the sub-menus that appear when you select 4 (Sum), 5 (V ar), 6 (MinMax), or 7 (Reg) on the ST A T menu while linear regressio[...]

E-51 Reg Sub-menu ( 1 1 (ST A T) 7 (Reg)) Select this When you want to obtain this: menu item: 1 AR egression coefficient constant term A 2 BR egression coefficient B 3 r Correlation coefficient r 4 m Estimated value of x 5 n Estimated value of y Appendix Linear Regression Calculation: <#061> to <#064> •E xamples <#062> through [...]

E-52 Comments f or Other T ypes of Regression F or details about the calculation f or mula of the command included in each regression type, ref er to the indicated calculation f ormulas ( Appendix <#069> to <#073>). Statistical Calculation Model Equation Calculation T ype Formula Logarithmic Regression y = A + B ln X <#069> (ln X)[...]

E-53 k Number Base Setting and V alue Input Use the ke ys listed below to specify the number base. The ke y markings used in this section are the ones that are above each ke y , on the right. Key Number Base Screen Indicator U Decimal Dec c He xadecimal Hex b Binary Bin q Octal Oct • The current number base setting is indicated in the second line[...]

E-54 Specifying the Base during Input The BASE-N Mode lets you o verride the current default n umber base setting and input a particular value using a different base. When inputting the value , press 1 3 (BASE) c to display page two of the BASE menu, and then press the number k ey that corresponds to the base you w ant to specify . Press this key: [...]

E-55 Press this key: When you want to input this: 5 (Not) “Not(” function, which returns the result of a bitwise complement 6 (Neg) “Neg(” function, which retur ns the result of a two’ s complement •N egative binary , octal, and hexadecimal values are produced b y taking the binary two’ s complement and then retur ning the result to t[...]

E-56 k Inputting Coefficients Use the coefficient editor screen to input the coefficients of an equation. The coefficient editor screen shows input cells f or each of the coefficients required by the currently selected equation type . Simultaneous linear Cubic equation equations with two unkno wns Rules for Inputting and Editing Coefficients •D a[...]

E-57 • In the case of simultaneous linear equations, y ou can use f and c to s witch the display between the solutions f or X and Y (and Z). •W hen there are multiple solutions f or a quadratic or cubic equation, y ou can use the f and c ke ys to scroll the displa y between X 1 , X 2 , and X 3 . The actual number of solutions depends on the equ[...]

E-58 (3 )P ress a number ke y ( 1 through 6 ) to specify the matr ix dimension you want to use . •P ressing a number key to specify the matrix dimension causes the matrix editor screen to appear. (4) Use the matr ix editor screen to input each of the elements into the matrix. •I nput is subject to the same r ules as those that gov ern the coeff[...]

E-59 •Y ou cannot edit the contents of a cell. •T o switch to the matrix calculation screen, press A . •W hile the MatAns screen is on the display , you can press an arithmetic operator key (lik e + or - ) and use the screen contents in a subsequent calculation, just as with Answ er Memor y contents. F or more inf ormation, see “Using Answ [...]

E-60 <#104> Obtain the absolute value (Abs(MatB)) of each element of Matrix B. •U se 1w (Abs). <#105> Determine the square (MatA 2 ) or cube (MatA 3 ) of Matrix A. •U se w to specify squar ing, and 1 w ( x 3 ) to specify cubing. Note that y ou cannot use 6 f or this input. Generating a Number T able from a Function (T ABLE) All calc[...]

E-61 (4) After specifying the star t value, press = . • This displa ys the end value input screen. •S pecify the end value. (5) After specifying the end value, press = . • This displa ys the step value input screen. •S pecify the step value. •F or details about specifying the star t, end, and step values, see “Star t, End, and Step V al[...]

E-62 Note •C ertain functions and Star t, End, Step value combinations can cause number table gener ation to take a long time. k Number T able Screen The number tab le screen shows x -values calculated using the specified Start, End, and Step values, as well as the v alues obtained when each x -value is substituted in the function f ( x ). •N o[...]

E-63 (4) Use the vector editor screen to input each element. •I nput is subject to the same r ules as those that gov ern the coefficient editor screen in the EQN Mode. F or more information, see “Rules for Inputting and Editing Coefficients”. • If you want to create another v ector , repeat this procedure from step (1). Copying the Contents[...]

E-64 Appendix <#106> Store VctA = (1, 2) and VctC = (2, –1, 2). <#107> Copy VctA = (1, 2) to VctB and then edit V ector B to VctB = (3, 4). • The follo wing examples use the v ectors input in Examples <#106> and <#107> (VctA, VctB, VctC). <#108> VctA + VctB (V ector Addition) <#109> 3 × VctA (V ector Scalar [...]

E-65 •T he values are based on ISO Standards (1992) and CODA T A Recommended V alues (1998). For details, see Appendix <#114>. Appendix <#115> and <#116> P erf or m all of these examples in the COMP Mode ( N 1 ). Metric Conversion The calculator’ s built-in metric conv ersion commands make it simple to conv er t values from on[...]

E-66 3. F ractions: a b / c 4. Prefix symbol: (–) (negative sign) d, h, b , o (base n symbol) 5. Metric conversion commands: cm ' in, etc. Statistical estimated value calculation: m , n , m 1 , m 2 6. P ermutations, combinations: n P r , n C r Complex polar f orm symbol: ∠ 7. Dot product: • (Dot) 8. Multiplication and division: × , ÷ M[...]

E-67 A Stack ERR OR occurs when the calculation you are perf orming causes the capacity of either stac k to be exceeded. Stack Issues to K eep in Mind for Each Mode •I n the CMPLX Mode, each input value uses two le vels of the numeric stack, regardless of whether the input v alue is a real number or a complex number . This means that the numeric [...]

E-68 Functions Input Range tanh x 0   x   9.999999999  10 99 tanh – 1 x 0   x   9.999999999  10 –1 log x /ln x 0  x  9.999999999  10 99 10 x –9.999999999  10 99  x  99.99999999 e x –9.999999999  10 99  x  230.2585092 ' x 0  x  1  10 100 x 2  x  1  10 50 1/ x [...]

E-69 k Error Messa g es The calculator will displa y an error message when a result exceeds the calculation r ange, when y ou attempt an illegal input, or whenev er any other similar problem occurs. When an error messa ge appears... The follo wing are general operations you can use when an y error message appears. •P r e ssing d or e displays to [...]

E-70 • Action •M a k e necessar y corrections. Dimension ERR OR (MA TRIX and VECT OR Modes only) • Cause • The matrix or vector you are trying to use in a calculation was input without specifying its dimension. •Y ou are trying to perform a calculation with matrices or vectors whose dimensions do not allow that type of calculation. • Ac[...]

E-71 k Before assuming malfunction of the calculator ... Pe rform the following steps whene v er an error occurs during a calculation or when calculation results are not what you e xpected. If one step does not correct the problem, mo ve on to the next step . Note that you should mak e separate copies of important data before performing these steps[...]

E-72 1 Press 1A (OFF) to tur n off the calculator . •T o ensure that you do not accidentally turn on power while replacing the batter y , slide the hard case onto the front of the calculator . 2 On the back of the calculator , remov e the screw and the battery cover . 3 Remove the old battery . 4 Wipe a new battery with a dr y cloth, and then loa[...]

CASIO COMPUTER CO. , L TD . 6-2, Hon-machi 1-chome Shibuya-ku, Tokyo 151-8543, Japan SA0411-B Printed in China[...]