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fx-95ms fx-100ms fx-115ms (FX-912MS) fx-570ms fx-991ms user's guide k FX-912MS owners please be sure to read the important notice of this manual. http://world.casio.com/edu_e/ e
casio electronics co., ltd. unit 6, 1000 north circular road, london nw2 7jd, u.k.
1 removing and replacing the calculators cover before starting ..... 1 holding the cover as shown in the illustration, slide the unit out of the cover. ? fter you are finished ..... 2 holding the cover as shown in the illustration, slide the unit out of the cover. ? lways slide the keyboard end of the unit into the cover first. never slide the display end of the unit into the cover. ..... 1 ..... 2
2 caution this symbol is used to indicate information that can result in personal injury or material damage if ignored. batteries ? fter removing the battery from the calculator, put it in a safe place where it will not get into the hands of small children and accidentally swallowed. ? eep batteries out of the reach of small children. if accidentally swallowed, consult with a physician im- mediately. ? ev er charge batteries, try to take batteries apart, or allow batteries to become shorted. never expose batteries to direct heat or dispose of them by incin- eration. ? isuse of batteries can cause them to leak and dam- age nearby items, and can create the risk of fire and personal injury. ? lways make sure that the batterys positive k and negative l ends are facing correctly when you load it into the calculator. remove the battery if you do not plan to use the calculator for a long time (fx-95ms/100ms/570ms). ? se only the type of battery specified for this calcu- lator in this manual. disposing of the calculator ?ever dispose of the calculator by burning it. doing so can cause certain components to suddenly burst, creating the risk of fire and personal injury. the displays and illustrations (such as key markings) shown in this users guide are for illustrative purposes safety precautions be sure to read the following safety precautions before using this calculator. keep this manual handy for later ref- erence.
3 only, and may differ somewhat from the actual items they represent. the contents of this manual are subject to change with- out notice. ? n no event shall casio computer co., ltd. be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials. moreover, casio computer co., ltd. shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. be sure to press the 5 key before using the calcu- lator for the first time. even if the calculator is operating normally, replace the battery at least once every three years for the fx- 115ms/fx-570ms/fx-991ms, or at least once every two y ears for the fx-95ms/fx-100ms. a dead battery can leak, causing damage to and mal- function of the calculator. never leave a dead battery in the calculator. the battery that comes with this unit discharges slightly during shipment and storage. because of this, it may require replacement sooner than the normal expected battery life. ? ow battery power can cause memory contents to become corrupted or lost completely. always keep written records of all important data. ? vo id use and storage in areas subjected to tem- perature extremes. ve ry low temperatures can cause slow display response, total failure of the display, and shortening of battery life. also avoid leaving the calculator in direct sunlight, near a window, near a heater or anywhere else it might be ex posed to very high temperatures. heat can cause dis- coloration or deformation of the calculators case, and damage to internal circuitry. handling precautions
4 ? vo id use and storage in areas subjected to large amounts of humidity and dust. ta ke care never to leave the calculator where it might be splashed by water or exposed to large amounts of hu- midity or dust. such conditions can damage internal cir- cuitry. ? e ver drop the calculator or otherwise subject it to strong impact. ? e ver twist or bend the calculator. avoi d carrying the calculator in the pocket of your trou- sers or other tight-fitting clothing where it might be sub- jected to twisting or bending. ? e ver try to take the calculator apart. ? e ver press the keys of the calculator with a ball- point pen or other pointed object. use a soft, dry cloth to clean the exterior of the cal- culator. if the calculator becomes very dirty, wipe it off with a cloth moistened in a weak solution of water and a mild neutral household detergent. wring out all excess mois- ture before wiping the calculator. never use thinner, ben- z ene or other volatile agents to clean the calculator. do- ing so can remove printed markings and can damage the case.
5 contents removing and replacing the calculators cover ................................... 1 safety precautions .................................. 2 handling precautions ............................. 3 tw o-line display ...................................... 7 before getting started... .......................... 7 k modes .................................................................... 7 k input capacity ........................................................ 8 k making corrections during input ........................... 9 k replay function ..................................................... 9 k error locator .......................................................... 9 k multi-statements .................................................. 10 k exponential display formats ............................... 10 k decimal point and separator symbols ................ 11 k initializing the calculator ...................................... 11 basic calculations ................................ 11 k arithmetic calculations ........................................ 11 k fr action operations ............................................. 12 k pe rcentage calculations ...................................... 14 k degrees, minutes, seconds calculations ............ 15 k fix, sci, rnd ..................................................... 15 memory calculations ............................ 16 k answer memory ................................................... 16 k consecutive calculations .................................... 17 k independent memory ........................................... 17 k va ri ables .............................................................. 17 scientific function calculations .......... 18 k tr igonometric/inverse trigonometric functions ... 18 k hyperbolic/inverse hyperbolic functions ............ 19
6 k common and natural logarithms/ antilogarithms ...................................................... 19 k square roots, cube roots, roots, squares, cubes, reciprocals, factorials, random numbers, , and pe rm utation/combination .................................... 20 k angle unit conversion ......................................... 21 k coordinate conversion (pol ( x , y ), rec ( r , )) ..... 21 k engineering notation calculations ...................... 22 equation calculations .......................... 22 k quadratic and cubic equations ........................... 22 k simultaneous equations ...................................... 24 statistical calculations ......................... 26 standard deviation .................................................. 26 regression calculations .......................................... 28 te c hnical information ........................... 32 k when you have a problem...... ............................. 32 k error messages ................................................... 32 k order of operations ............................................. 34 k stacks .................................................................. 35 k input ranges ....................................................... 36 po wer supply (fx-95ms only) ...................... 38 specifications (fx-95ms only) ..................... 39
7 t wo-line display the two-line display makes it possible to view both the calculation formula and its result at the same time. the upper line shows the calculation formula. the lower line shows the result. a separator symbol is displayed every three digits when the integer part of the mantissa has more than three dig- its. before getting started... k modes before starting a calculation, you must first enter the cor- rect mode as indicated in the table below. the following table shows the modes and required operations for the fx-95ms only. users of other mod- els should refer to the ?sers guide 2 (additional functions) for information about modes and their selection. fx-95ms modes to perform this type of perform this to enter calculation: key operation: this mode: basic arithmetic calculations f 1 comp standard deviation f 2 sd regression calculations f 3 reg solution of equations f f 1 eqn
8 ?re ssing the f ke y more than twice displays additional setup screens. setup screens are described in the sec- tions of this manual where they are actually used to change the calculator setup. ? n this manual, the name of the mode you need to enter in order to perform the calculations being described is indicated in the main title of each section. example: note! ? o return the calculation mode and setup to the initial defaults shown below, press a b 2 (mode) = . calculation mode: comp angle unit: deg exponential display format: norm 1 fra ction display format: a b / c decimal point character: dot mode indicators appear in the upper part of the display. be sure to check the current calculation mode (sd, reg, comp) and angle unit setting (deg, rad, gra) before beginning a calculation. k input capacity the memory area used for calculation input can hold 79 ?teps. one step is taken up each time you press a n umber key or arithmetic operator key ( + , , , - , \ ). a a or p ke y operation does not take up a step, so inputting a d , for example, takes up only one step. ? ou can input up to 79 steps for a single calculation. whenever you input the 73rd step of any calculation, the cursor changes from ? to k ? to let you know memory is running low. if you need to input more than 79 steps, y ou should divide your calculation into two or more parts. ? ressing the g ke y recalls the last result obtained, which y ou can use in a subsequent calculation. see ?nswer memory for more information about using the g key. equation calculations eqn
9 k making corrections during input ?se e and r to move t he cursor to the location you w ant. ?re ss [ to delete the number or function at the current cursor position. ?re ss a k to change to an insert cursor t . inputting something while the insert cursor is on the display in- serts the input at the insert cursor position. ? ressing a k , or = returns to the normal cursor from the insert cursor. k replay function ? ve ry time you perform a calculation, the replay function stores the calculation formula and its result in replay memory. pressing the [ key displays the formula and result of the calculation you last performed. pressing [ again back steps sequentially (new-to-old) through past calculations. ?re ssing the e or r ke y while a replay memory cal- culation is on the display changes to the editing screen. ?re ssing the e or r ke y immediately after you finish a calculation displays the editing screen for that calcula- tion. ?re ssing t does not clear replay memory, so you can recall the last calculation even after you press t . replay memory capacity is 128 bytes for storage of both ex pressions and results. replay memory is cleared by any of the following ac- tions. when you press the 5 key when you initialize modes and settings by pressing a b 2 (or 3 ) = . when you change from one calculation mode to another when you turn off the calculator. k error locator ?re ssing r or e a fter an error occurs displays the calculation with the cursor positioned at the location where the error occurred.
10 k multi-statements a multi-statement is an expression that is made up of two or more smaller expressions, which are joined using a colon ( : ). example: to add 2 + 3 and then multiply the result by 4 2 + 3 p \ g - 4 = = k exponential display formats this calculator can display up to 10 digits. larger values are automatically displayed using exponential notation. in the case of decimal values, you can select between two fo r mats that determine at what point exponential notation is used. ? o change the exponential display format, press the f ke y a number of times until you reach the exponential display format setup screen shown below. ?re ss 3 . on the format selection screen that appears, press 1 to select norm 1 or 2 for norm 2. u norm 1 with norm 1, exponential notation is automatically used fo r integer values with more than 10 digits and decimal va lues with more than two decimal places. u norm 2 with norm 2, exponential notation is automatically used fo r integer values with more than 10 digits and decimal va lues with more than nine decimal places. ? ll of the examples in this manual show calculation re- sults using the norm 1 format. 5. 2 + 3 disp 20. ans 4 1 2 3 fix sci n or m
11 k decimal point and separator symbols y ou can use the display setup (disp) screen to specify the symbols you want for the decimal point and 3-digit sepa- rator. ? o change the decimal point and separator symbol set- comp basic calculations ting, press the f key a number of times until you reach the setup screen shown below. 1 disp fx-95ms: 1 r other models: 1 r r ? ress the number key ( 1 or 2 ) that corresponds to the setting you want to use. 1 (dot): period decimal point, comma separator 2 (comma): comma decimal point, period separator k initializing the calculator ? erform the following key operation when you want to initialize the calculation mode and setup, and clear re- play memory and variables. a b 3 (all) = k arithmetic calculations use the f ke y to enter the comp mode when you w ant to perform basic calculations. comp ............................................................. f 1 negative values inside of calculations must be enclosed within parentheses. sin ?.23 s r d 1.23 t ? isplay the selection screen.
12 it is not necessary to enclose a negative exponent within parentheses. sin 2.34 10 ? s 2.34 e d 5 example 1: 3 (5 10 ? ) 1.5 10 ? 3 - 5 e d 9 = example 2: 5 (9 7) 80 5 - r 9 + 7 t = ? ou can skip all t operations before = . k fraction operations u fraction calculations ? alues are displayed in decimal format automatically whenever the total number of digits of a fractional value (integer + numerator + denominator + separator marks) e xceeds 10. 1 5 2 3 13 15. 00 13 15 example 1: 2 c 3 + 1 c 5 = example 2: 3 1 4 3 c 1 c 4 + 1 c 2 c 3 = 2 3 1 4 11 12 1 2 example 4: 1.6 2.1 1 c 2 + 1.6 = example 3: 2 c 4 = 2 4 1 2 results of calculations that mix fraction and decimal val- ues are always decimal. u decimal ? fraction conversion ? se the operation shown below to convert calculation results between decimal values and fraction values. note that conversion can take as long as two seconds to perform. 4 11 12. 00
13 1 2. 00 1 2 example 2: ? 0.5 (fraction ? decimal) 1 c 2 = c c 0.5 00 1 2. 00 2 3 4. 00 11 4. 00 example 1: 2.75 2 (decimal fra ction) 2.75 = 2.75 c a b 3 4 11 4 u mixed fraction ? improper fraction conversion example: 1 ? 1 c 2 c 3 = a b a b 5 3. 00 1 2 3. 00 5 3 2 3 1 2 3. 00 ? ou can use the display setup (disp) screen to specify the display format when a fraction calculation result is gr eater than one. ? o change the fraction display format, press the q key a number of times until you reach the setup screen shown below. 1 disp ? isplay the selection screen. fx-95ms: 1 other models: 1 r ? ress the number key ( 1 or 2 ) that corresponds to the setting you want to use. 1 (a b / c ): mixed fraction 2 (d /c ): improper fraction
14 an error occurs if you try to input a mixed fraction while the d/c display format is selected. k pe r centage calculations example 1 : to calculate 12% of 1500 (180) 1500 - 12 a v ? example 2: to calculate what percentage of 880 is 660 (75%) 660 \ 880 a v example 3 : to add 15% onto 2500 (2875) 2500 - 15 a v + example 4 : to discount 3500 by 25% (2625) 3500 - 25 a v , example 5: to discount the sum of 168, 98, and 734 by 20% (800) 168 + 98 + 734 = g a j 1 p 1 - 20 a v , *as shown here, if you want to use the current answer memory value in a mark up or discount calculation, you need to assign the answer memory value into a variable and then use the variable in the mark up/discount calculation. this is because the calculation performed when v is pressed stores a result to answer memory before the , key is pressed. example 6: if 300 grams are added to a test sample originally weighing 500 grams, what is the percentage increase in weight? (160%) 300 + 500 a v example 7: what is the percentage change when a value is increased from 40 to 46? how about to 48? (15%, 20%) 46 , 40 a v e e e e e e 8 = *
15 k degrees, minutes, seconds calculations ? ou can perform sexagesimal calculations using degrees (hours), minutes, and seconds, and convert between sexagesimal and decimal values. example 1: to convert the decimal value 2.258 to a sexagesimal value and then back to a decimal value 2.258 = 2.258 a o 2 15 28.8 i 2.258 example 2: to perform the following calculation: 12 34?6? 3.45 12 i 34 i 56 i - 3.45 = 43 24 31.2 k fix, sci, rnd ? o change the settings for the number of decimal places, the number of significant digits, or the exponential dis- play format, press the f ke y a number of times until y ou reach the setup screen shown below. 1 2 3 fix sci n or m ? ress the number key ( 1 , 2 , or 3 ) that corresponds to the setup item you want to change. 1 (fix): number of decimal places 2 (sci): number of significant digits 3 (norm): exponential display format example 1: 200 7 14 200 \ 7 - 14 = f ..... 1 (fix) 3 (specifies three decimal places.) 400. 00 400.000 00 fix
16 200 \ 7 = - 14 = (internal calculation continues using 12 digits.) 28.571 00 400.000 00 28.571 00 28.571 00 399.994 00 200 \ 7 = (internal rounding) a q - 14 = the following performs the same calculation using the specified number of decimal places. ?re ss f ..... 3 (norm) 1 to clear the fix specifica- tion. example 2: 1 3, displaying result with two significant digits (sci 2) f ..... 2 (sci) 2 1 \ 3 = 3.3 ?1 sci ?re ss f ..... 3 (norm) 1 to clear the sci specifica- tion. k answer memory ? henever you press = a fter inputting values or an ex- pression, the calculated result automatically updates an- sw er memory contents by storing the result. ?n addition to = , answer memory contents are also up- dated with result whenever you press a v , | , a { , or a j fo llowed by a letter (a through f, or m, x, or y). comp memory calculations use the f ke y to enter the comp mode when you w ant to perform a calculation using memory. comp ............................................................. f 1
17 ? ou can recall answer memory contents by pressing g . ? nswer memory can store up to 12 digits for the mantissa and two digits for the exponent. answer memory contents are not updated if the opera- tion performed by any of the above key operations re- sults in an error. k consecutive calculations ? ou can use the calculation result that is currently on the display (and also stored in answer memory) as the first va lue of your next calculation. note that pressing an operator key while a result is displayed causes the dis- played value to change to ans, indicating it is the value that is currently stored in answer memory. the result of a calculation can also be used with a sub- sequent type a function ( x 2 , x 3 , x ? , x !, drg ' ), +, ? ^( x y ), x , , , n p r and n c r . k independent memory ? alues can be input directly into memory, added to memory, or subtracted from memory. independent memory is convenient for calculating cumulative totals. ? ndependent memory uses the same memory area as variab le m. ? o clear independent memory (m), input 0 a j 3 (m+). example: 23 9 32 23 + 9 a j 3 (m+) 53 6 47 53 , 6 | ) 45 2 90 45 - 2 a { (total) ?1 0 3 (m+) k va riables there are nine variables (a through f, m, x and y), which can be used to store data, constants, results, and other val ues. ? se the following operation to delete data assigned to a
18 comp particular variable: 0 a j 1 . this operation de- letes the data assigned to variable a. ? erform the following key operation when you want to clear the values assigned to all of the variables. a b 1 (mcl) = example: 193.2 23 8.4 193.2 28 6.9 193.2 a j 1 \ 23 = p 1 \ 28 = scientific function calculations use the f ke y to enter the comp mode when you w ant to perform basic arithmetic calculations. comp ............................................................. f 1 certain types of calculations may take a long time to complete. ? ait for the result to appear on the display before start- ing the next calculation. = 3.14159265359 k tr igonometric/inverse trigonometric functions ? o change the default angle unit (degrees, radians, gr ads), press the f ke y a number of times until you reach the angle unit setup screen shown below. 1 2 3 deg rad g ra ? ress the number key ( 1 , 2 , or 3 ) that corresponds to the angle unit you want to use. (90 = radians = 100 grads) 2
19 example 1: sin 63 52 41 0.897859012 q ..... 1 ( deg) s 63 i 52 i 41 i = example 2: cos ( rad ) 0.5 q ..... 2 ( rad) w r a x \ 3 t = 3 example 3 : cos 1 q ..... 2 ( rad) a v r l 2 \ 2 t = g \ a x = 0.25 ( r ad) ( ( r ad) ) 4 2 2 example 4: tan 1 0.741 36.53844577 q ..... 1 ( deg) a g 0.741 = k hyperbolic/inverse hyperbolic functions example 1: sinh 3.6 18.28545536 m s 3.6 = example 2: sinh 1 30 4.094622224 m a j 30 = k common and natural logarithms/ antilogarithms example 1: log 1.23 0.089905111 r 1.23 = example 2: in 90 (= log e 90) = 4.49980967 t 90 = ln e 1 t p p = example 3: e 10 22026.46579 a u 10 = example 4: 10 1.5 31.6227766 a q 1.5 = example 5: 2 4 16 2 w 4 =
20 k square roots, cube roots, roots, squares, cubes, reciprocals, f actorials, random numbers, , and p ermutation/combination 1 1 3 4 1 example 6: 12 r 3 a , 4 a t a = example 7: 8! 40320 8 a f = example 4: 123 30 2 1023 123 + 30 k = example 5: 12 3 1728 12 n * = * a n in the case of fx-570ms/fx-991ms. 1 7 example 3: 7 123 ( = 123 ) 1.988647795 7 a h 123 = example 1: 2 3 5 5.287196909 l 2 + l 3 - l 5 = example 2: 3 5 3 27 ?.290024053 a d 5 + a d r d 27 t = 0.664 00 example 8: to generate a random number between 0.000 and 0.999 a m = (the above value is a sample only. results differ each time.) example 9: 3 9.424777961 3 a x = example 10: to determine how many different 4-digit va lues can be produced using the numbers 1 through 7 numbers cannot be duplicated within the same 4-digit va lue (1234 is allowed, but 1123 is not). (840) 7 a m 4 = example 11: to determine how many different 4-mem- ber groups can be organized in a group of 10 individuals (210) 10 n * 4 =
21 * a n in the case of fx-100ms/fx-115ms/fx-570ms/ fx-991ms. k angle unit conversion ?re ss a v to display the following menu. 1 2 3 d r g ?re ssing 1 , 2 , or 3 converts the displayed value to the corresponding angle unit. example: to c o n ve r t 4.25 radians to degrees q ..... 1 ( deg) 4.25 a v 2 ( r ) = 243.5070629 4 . 2 5 r k coordinate conversion (pol ( x , y ), rec ( r , )) calculation results are automatically assigned to vari- ables e and f. example 1: to c o nv ert polar coordinates ( r 2, 60 ) to rectangular coordinates ( x , y ) (deg) x 1 a f 2 p 60 t = y 1.732050808 0 o ?re ss 0 n to display the value of x , or 0 o to dis- play the value of y . example 2: to convert rectangular coordinates (1, 3) to polar coordinates ( r , ) (rad) r 2 f * 1 p l 3 t = * a f in the case of fx-100ms/fx-115ms/fx-570ms/ fx-991ms. 1.047197551 0 o ?re ss 0 n to display the value of r , or 0 o to dis- play the value of .
22 k engineering notation calculations 2 3 deg r ee? eqn example 1: to convert 56,088 meters to kilometers 56.088 10 3 56088 = j (km) example 2: to convert 0.08125 grams to milligrams 81.25 10 ? 0.08125 = j (mg) equation calculations the eqn mode lets you solve equations up to three de- gr ees and simultaneous linear equations with up to three unknowns. use the f ke y to enter the eqn mode when you want to solve an equation. eqn .......................... f f 1 (fx-95ms) f f f 1 (other models) k quadratic and cubic equations quadratic equation: ax 2 + bx + c = 0 cubic equation: ax 3 + bx 2 + cx + d = 0 entering the eqn mode and pressing r d isplays the ini- tial quadratic/cubic equation screen. use this screen to specify 2 (quadratic) or 3 (cubic) as the degree of the equation, and input values for each of the coefficients. 0. a? element value coefficient name arrow indicates direction you should scroll to view other elements.
23 0. x1= solution var iable name arrow indicates direction you should scroll to view other solutions. press the ] key to view other solutions. use [ and ] to scroll between all of the solutions for the equation. pressing the t ke y at this point returns to the coefficient input screen. certain coefficients can cause calculation to take more time. example 1: to solve the equation x 3 ?2 x 2 x + 2 = 0 ( x = 2, ?, 1) (degree?) 3 ( a ?) 1 = ( b ?) d 2 = ( c ?) d 1 = ( d ?) 2 = ( x 1 = 2) ] ( x 2 = ?) ] ( x 3 = 1) if a result is a complex number, the real part of the first solution appears first. this is indicated by the ? ? i symbol on the display. press a r to toggle the display between the real part and imaginary part of a solution. ? ny time until you input a value for the final coefficient ( c fo r a quadratic equation, d fo r a cubic equation), you can use the [ and ] ke ys to move between coefficients on the screen and make changes, if you want. ? ote that you cannot input complex numbers for co- efficients. calculation starts and one of the solutions appears as soon as you input a value for the final coefficient.
24 0.25 x1= 0.75 x1= i r ? i r ? i d d a r example 2: to solve the equation 8 x 2 ?4 x + 5 = 0 ( x = 0.25 0.75 i ) (degree?) 2 ( a ?) 8 = ( b ?) d 4 = ( c ?) 5 = ( x 1 = 0.25 + 0.75 i ) ] ( x 2 = 0.25 ?0.75 i ) simultaneous linear equations with two unknowns: a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 simultaneous linear equations with three unknowns: a 1 x + b 1 y + c 1 z = d 1 a 2 x + b 2 y + c 2 z = d 2 a 3 x + b 3 y + c 3 z = d 3 entering the eqn mode displays the initial simultaneous equation screen. k simultaneous equations 2 3 unkno w ns? use this screen to specify 2 or 3 as the number of un- knowns, and input values for each of the coefficients. 0. a1? element value coefficient name arrow indicates direction you should scroll to view other elements.
25 ? ny time until you input a value for the final coefficient ( c 2 for two unknowns, d 3 fo r three unknowns), you can use the [ and ] ke ys to move between coefficients on the screen and make changes, if you want. note that you cannot input complex numbers for coeffi- cients. calculation starts and one of the solutions appears as soon as you input a value for the final coefficient. 0. x= solution var iable name arrow indicates direction you should scroll to view other solutions. press the ] key to view other solutions. use [ and ] to scroll between all of the solutions for the equation. pressing the t ke y at this point returns to the coefficient input screen. example: to solve the following simultaneous equations 2 x + 3 y ? z = 15 3 x ?2 y + 2 z = 4 5 x + 3 y ?4 z = 9 ( x = 2 , y = 5 , z = 4) (unknowns?) 3 ( a 1 ?) ....... ( d 1 ?) 2 = 3 = d 1 = 15 = ( a 2 ?) ....... ( d 2 ?) 3 = d 2 = 2 = 4 = ( a 3 ?) ....... ( d 3 ?) 5 = 3 = d 4 = 9 = ( x = 2) ] ( y = 5) ] ( z = 4)
26 sd sd reg statistical calculations standard deviation use the f ke y to enter the sd mode when you want to perform statistical calculations using standard de- viation. sd .................................... f 2 (fx-95ms) f f 1 (other models) ? lways start data input with a b 1 (scl) = to clear statistical memory. ? nput data using the key sequence shown below. < x -data> s ? nput data is used to calculate values for n , x , x 2 , o , n and n - 1 , which you can recall using the key opera- tions noted nearby. to recall this type of value: perform this key operation: x 2 a u 1 x a u 2 n a u 3 o a x 1 n a x 2 n - 1 a x 3 example: to c a lculate n 1 , n , o , n , x , and x 2 for the following data : 55, 54, 51, 55, 53, 53, 54, 52 in the sd mode: a b 1 (scl) = (stat clear) 55 s each time you press s to register your input, the number of data input up to that point is indicated on the display ( n value). 54 s 51 s 55 s 53 s s 54 s 52 s sample standard deviation ( n 1 ) = 1.407885953 a x 3 = 1. n= sd
27 p opulation standard deviation ( n ) = 1.316956719 a x 2 = arithmetic mean ( o ) = 53.375 a x 1 = number of data ( n ) = 8 a u 3 = sum of values ( x ) = 427 a u 2 = sum of squares of values ( x 2 ) = 22805 a u 1 = data input precautions s s inputs the same data twice. ? ou can also input multiple entries of the same data us- ing a g . to input the data 110 ten times, for example, press 110 a g 10 s . ? ou can perform the above key operations in any order, and not necessarily that shown above. ? hile inputting data or after inputting data is complete, y ou can use the [ and ] ke ys to scroll through data y ou have input. if you input multiple entries of the same data using a g to specify the data frequency (number of data items) as described above, scrolling through data shows both the data item and a separate screen for the data frequency (freq). ? ou can then edit the displayed data, if you want. input the new value and then press the = key to replace the old value with the new one. this also means that if you w ant to perform some other operation (calculation, recall of statistical calculation results, etc.), you should always press the t key first to exit data display. ?re ssing the s ke y instead of = after changing a value on the display registers the value you input as a new data item, and leaves the old value as it is. ? ou can delete a data value displayed using [ and ] by pressing a u . deleting a data value causes all val ues following it to be shifted up. data values you register are normally stored in calcula- tor memory. the message ?ata full appears and you will not be able to input any more data if there is no memory left for data storage. if this happens, press the = key to display the screen shown below. 1 2 ed i t o ff es c
28 press 2 to exit data input without registering the value y ou just input. press 1 if you want to register the value you just input, without saving it in memory. if you do this, however, you will not be able to display or edit any of the data you have input. ?o delete data you have just input, press a u . ? fter inputting statistical data in the sd mode or reg mode, you will be unable to display or edit individual data items any longer after perform either the following operations. changing to another mode changing the regression type (lin, log, exp, pwr, inv, quad) 1 2 3 li n log e xp 1 2 3 p w r inv q uad re use the f ke y to enter the reg mode when you want to perform statistical calculations using regression. reg ................................. f 3 (fx-95ms) f f 2 (other models) entering the reg mode displays screens like the ones shown below. ? ress the number key ( 1 , 2 , or 3 ) that corresponds to the type of regression you want to use. 1 (lin) :l inear regression 2 (log) : logarithmic regression 3 (exp) :e xponential regression r 1 (pwr) :p ow er regression r 2 (inv) :i nv erse regression r 3 (quad) : quadratic regression reg regression calculations
29 ? lways start data input with a b 1 (scl) = to clear statistical memory. ? nput data using the key sequence shown below. < x -data> p < y -data> s the values produced by a regression calculation depend on the values input, and results can be recalled using the key operations shown in the table below. to recall this type of value: perform this key operation: x 2 a u 1 x a u 2 n a u 3 y 2 a u r 1 y a u r 2 xy a u r 3 o a x 1 x n a x 2 x n -1 a x 3 p a x r 1 y n a x r 2 y n -1 a x r 3 regression coefficient a a x r r 1 regression coefficient b a x r r 2 regression calculation other than quadratic regression correlation coefficient r a x r r 3 m a x r r r 1 n a x r r r 2 the following table shows the key operations you should use to recall results in the case of quadratic regression. to recall this type of value: perform this key operation: x 3 a u r r 1 x 2 y a u r r 2 x 4 a u r r 3 regression coefficient c a x r r 3 m 1 a x r r r 1 m 2 a x r r r 2 n a x r r r 3
30 the values in the above tables can be used inside of ex pressions the same way you use variables. u linear regression the regression formula for linear regression is: y = a + b x . example: atmospheric pressure vs. temperature pe rform linear regression to de- termine the regression formula terms and correlation coefficient fo r the data nearby. next, use the regression formula to estimate atmospheric pressure at 18 c and temperature at 1000 hpa. fi- nally, calculate the coefficient of determination ( r 2 ) and sample covariance . temper ature atmospheric pressure 10 c 1003 hpa 15 c 1005 hpa 20 c 1010 hpa 25 c 1011 hpa 30 c 1014 hpa in the reg mode: 1 (lin) a b 1 (scl) = (stat clear) 10 p 1003 s 1. n= reg each time you press s to register your input, the number of data input up to that point is indicated on the display ( n value). 15 p 1005 s 20 p 1010 s 25 p 1011 s 30 p 1014 s regression coefficient a = 997.4 a x r r 1 = regression coefficient b = 0.56 a x r r 2 = correlation coefficient r = 0.982607368 a x r r 3 = atmospheric pressure at 18 c = 1007.48 18 a x r r r 2 =
31 te mperature at 1000 hpa = 4.642857143 1000 a x r r r 1 = coefficient of determination = 0.965517241 a x r r 3 k = sample covariance = 35 e a u r 3 , a u 3 - a x 1 - a x r 1 f \ e a u 3 , 1 f = u logarithmic, exponential, power, and inverse regression ? se the same key operations as linear regression to re- call results for these types of regression. the following shows the regression formulas for each type of regression. logarithmic regression y a b in x exponential regression y a e b x (in y in a + b x ) po we r regression y a x b (in y in a + b in x ) inverse regression y a b 1 / x u quadratic regression the regression formula for quadratic regression is: y = a + b x + c x 2 . in the reg mode: r 3 (quad) a b 1 (scl) = (stat clear) 29 p 1.6 s 50 p 23.5 s 74 p 38.0 s 103 p 46.4 s 118 p 48.0 s example: pe rform quadratic regression to de- termine the regression formula terms f or the data nearby. next, use the regression formula to estimate the val ues for n (estimated value of y ) for x i = 16 and m (estimated value of x ) for y i = 20. x i y i 29 1.6 50 23.5 74 38.0 103 46.4 118 48.0
32 regression coefficient a = ?5.59856934 a x r r 1 = regression coefficient b = 1.495939413 a x r r 2 = regression coefficient c = 6.71629667 10 ? a x r r 3 = n when x i is 16 = ?3.38291067 16 a x r r r 3 = m 1 when y i is 20 = 47.14556728 20 a x r r r 1 = m 2 when y i is 20 = 175.5872105 20 a x r r r 2 = data input precautions s s inputs the same data twice. ? ou can also input multiple entries of the same data us- ing a g . to input the data ?0 and 30 five times, for ex ample, press 20 p 30 a g 5 s . the above results can be obtained in any order, and not necessarily that shown above. ? recautions when editing data input for standard devia- tion also apply for regression calculations. t echnical information k when you have a problem...... if calculation results are not what you expect or if an error occurs, perform the following steps. 1. press a b 2 (mode) = to initialize all modes and settings. 2. check the formula you are working with to confirm it is correct. 3. enter the correct mode and try performing the calcula- tion again. if the above steps do not correct the problem, press the 5 ke y. the calculator performs a self-check operation and deletes all data stored in memory if any abnormality is detected. make sure you always keep written copies of all important data. k error messages the calculator is locked up while an error message is on
33 the display. press t to clear the error, or press e or r to display the calculation and correct the problem. see ?rror locator for details. math error ? auses calculation result is outside the allowable calculation r ange. an attempt to perform a function calculation using a va lue that exceeds the allowable input range. an attempt to perform an illogical operation (division by zero, etc.) action check your input values and make sure they are all within the allowable ranges. pay special attention to va lues in any memory areas you are using. stack error ? ause the capacity of the numeric stack or operator stack is e xceeded. action ? implify the calculation. the numeric stack has 10 lev- els and the operator stack has 24 levels. ? ivide your calculation into two or more separate parts. syntax error ? ause an attempt to perform an illegal mathematical opera- tion. action ?re ss e or r to display the calculation with the cur- sor located at the location of the error and make re- quired corrections. arg error ? ause ? mproper use of an argument
34 action ?re ss e or r to display the location of the cause of the error and make required corrections. k order of operations calculations are performed in the following order of prec- edence. 1 coordinate transformation: pol ( x , y ), rec ( r , ) differentials: d/dx * integrations: dx * normal distribution: p(*, q(*, r(* 2 ty pe a functions: with these functions, the value is entered and then the function key is pressed. x 3 , x 2 , x 1 , x !, ? engineering symbols * normal distribution: t * m , m 1 , m 2 , n angle unit conversions (drg ' ) metric conversions** 3 po wers and roots: ^ ( x y ) , x 4 a b / c 5 abbreviated multiplication format in front of , e (natu- ra l logarithm base), memory name, or variable name: 2 , 3 e , 5a, a, etc. 6 ty pe b functions: with these functions, the function key is pressed and then the value is entered. , 3 , log, in, e x , 10 x , sin, cos, tan, sin 1 , cos 1 , tan 1 , sinh, cosh, tanh, sinh 1 , cosh 1 , tanh 1 , ( ) d*, h*, b*, o*, neg*, not*, det**, trn**, arg*, abs*, conjg* 7 abbreviated multiplication format in front of type b func- tions: 2 3, alog2, etc. 8 pe rm utation and combination: n p r , n c r * 9 dot ( )** 0 , ! , @ and* # xnor*, xor*, or*
35 * fx-100ms/fx-115ms/fx-570ms/fx-991ms only. ** fx-570ms/fx-991ms only. operations of the same precedence are performed from ri ght to left. e x in 120 e x {in( 120)} ? ther operations are performed from left to right. operations enclosed in parentheses are performed first. ? hen a calculation contains an argument that is a negative number, the negative number must be enclosed within parentheses. the negative sign (? is treated as a type b function, so particular care is required when the calculation includes a high-priority ty pe a function, or power or root operations. example: ( ?) 4 = 16 ? 4 = ?6 k stacks this calculator uses memory areas, called ?tacks, to tem- porarily store values (numeric stack) and commands (com- mand stack) according to their precedence during calcu- lations. the numeric stack has 10 levels and the command stack has 24 levels. a stack error (stack error) occurs whenever you try to perform a calculation that is so com- plex that the capacity of a stack is exceeded. ? atrix calculations use up to two levels of the matrix stack. squaring a matrix, cubing a matrix, or inverting a matrix uses one stack level. (fx-570ms, fx-991ms only) example: 1 2 3 45 1 2 3 4 5 6 7 numeric stack command stack 1 2 3 4 5 2 3 4 5 4 1 2 3 4 5 6 7
36 ? alculations are performed in sequence according to ?rder of operations. commands and values are de- leted from the stack as the calculation is performed. k input ranges internal digits: 12 accuracy * : as a rule, accuracy is 1 at the 10th digit. functions input range sin x deg 0 x 4.499999999 10 10 rad 0 x 785398163.3 gra 0 x 4.999999999 10 10 cos x deg 0 x 4.500000008 10 10 rad 0 x 785398164.9 gra 0 x 5.000000009 10 10 tan x deg same as sin x , except when x = (2 n -1) 90. rad same as sin x , except when x = (2 n -1) /2. gra same as sin x , except when x = (2 n -1) 100. sin ? x 0 x 1 cos ? x tan ? x 0 x 9.999999999 10 99 sinh x 0 x 230.2585092 cosh x sinh ? x 0 x 4.999999999 10 99 cosh ? x 1 x 4.999999999 10 99 tanh x 0 x 9.999999999 10 99 tanh ? x 0 x 9.999999999 10 ? log x / ln x 0 x 9.999999999 10 99 10 x ?.999999999 10 99 x 99.99999999 e x ?.999999999 10 99 x 230.2585092
37 functions input range x 0 x 1 10 100 x 2 x 1 10 50 1/ x x 1 10 100 ; x g 0 3 x x 1 10 100 x !0 x 69 ( x is an integer) n p r 0 n 1 10 10 , 0 r n ( n , r are integers) 1 { n !/( n r )!} 1 10 100 n c r 0 n 1 10 10 , 0 r n ( n , r are integers) 1 [ n !/{ r !( n r )!}] 1 10 100 p ol( x , y ) x , y 9.999999999 10 49 ( x 2 + y 2 ) 9.999999999 10 99 rec( r , ) 0 r 9.999999999 10 99 : same as sin x a , b , c 1 10 100 ? 0 b , c x 1 10 100 decimal ? sexagesimal conversions 0 0 0 x 999999 59 x 0: ? 10 100 y log x 100 ^( x y ) x 0: y 0 x 0: y n , ( n is an integer) however: ? 10 100 y log x 100 y 0: x g 0 ? 10 100 1/ x log y 100 x y y 0: x 0 y 0: x 2 n 1, ( n g 0; n is an integer) however: ? 10 100 1/ x log y 100 a b / c x 1 10 50 sd y 1 10 50 (reg) n 1 10 100 x n , y n , o , p : n g 0 x n 1 , y n 1 , a, b, r : n g 0, 1 to tal of integer, numerator, and denominator m ust be 10 digits or less (including division marks). 1 2 n +1 1 n
38 *for a single calculation, calculation error is 1 at the 10th digit. (in the case of exponential display, calculation error is 1 at the last significant digit.) errors are cumulative in the case of consecutive calculations, which can also cause them to become large. (this is also true of internal consecutive calculations that are performed in the case of ^( x y ), x y , x !, 3 , n p r , n c r , etc.) in the vicinity of a functions singular point and point of inflection, errors are cumulative and may become large. users of other models should refer to the ?sers guide 2 (additional functions). this calculator is powered by a single aa-size battery. replacing the battery dim figures on the display of the calculator indicate that battery power is low. continued use of the calculator when the battery is low can result in improper operation. re- place the battery as soon as possible when display fig- ures become dim. to replace the battery 1 press a i to turn power off. 2 remove the six screws that hold the back cover in place and then remove the back cover. 3 remove the old battery. 4 load a new battery into the unit with its positive k and negative l ends facing cor- rectly. 5 replace the back cover and secure it in place with the six screws. 6 press 5 to turn power on. power supply (fx-95ms only) screw screw
39 u a uto power off calculator power automatically turns off if you do not per- fo rm any operation for about six minutes. when this hap- pens, press 5 to turn power back on. specifications (fx-95ms only) users of other models should refer to the ?sers guide 2 (additional functions). po wer supply: single aa-size battery (r6p (sum-3)) battery life: approximately 17,000 hours continuous display of flashing cursor. approximately 2 years when left with power turned off. dimensions: 19.5 (h) 78 (w) 155 (d) mm 3 / 4 (h) 3 1 / 16 (w) 6 1 / 8 (d) w eight: 130 g (4.6 oz) including battery po wer consumption: 0.0002 w operating temperature: 0 c to 40 c (32 f to 104 f) important notice for FX-912MS owners the names FX-912MS (japan domestic model name) and fx-115ms (international model name) apply to the same model. owners of the FX-912MS should refer to the description of fx-115ms.
sa0206-e printed in china ca 310067-1 casio computer co., ltd. 6-2, hon-machi 1-chome shibuya-ku, tokyo 151-8543, japan sa0206-d printed in china ca 310063-1

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