Casio Calculator FX 115MSPLUS User Manual

fx-95MS  
fx-100MS  
fx-115MS  
fx-570MS  
fx-991MS  
(fx-912MS)  
User's Guide  
kfx-912MS owners  
Please be sure to read the important notice of this manual.  
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E
Removing and Replacing  
the Calculator’s Cover  
• Before starting .....1  
Holding the cover as shown in the illustration, slide the  
unit out of the cover.  
• After you are finished .....2  
Holding the cover as shown in the illustration, slide the  
unit out of the cover.  
• Always slide the keyboard end of the unit into the cover  
first.Never slide the display end of the unit into the cover.  
.....1  
.....2  
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Safety Precautions  
Be sure to read the following safety precautions before  
using this calculator. Keep this manual handy for later ref-  
erence.  
Caution  
This symbol is used to indicate information that can  
result in personal injury or material damage if ignored.  
Batteries  
• After 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.  
• Keep batteries out of the reach of small children. If  
accidentally swallowed, consult with a physician im-  
mediately.  
• Never 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.  
• Misuse of batteries can cause them to leak and dam-  
age nearby items, and can create the risk of fire and  
personal injury.  
• Always make sure that the battery’s 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).  
• Use only the type of battery specified for this calcu-  
lator in this manual.  
Disposing of the Calculator  
• Never 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 User’s Guide are for illustrative purposes  
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only, and may differ somewhat from the actual items they  
represent.  
• The contents of this manual are subject to change with-  
out notice.  
• In 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.  
Handling Precautions  
• Be sure to press the 5key 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  
years 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.  
• Low battery power can cause memory contents to  
become corrupted or lost completely. Always keep  
written records of all important data.  
• Avoid use and storage in areas subjected to tem-  
perature extremes.  
Very 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  
exposed to very high temperatures. Heat can cause dis-  
coloration or deformation of the calculator’s case, and  
damage to internal circuitry.  
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• Avoid use and storage in areas subjected to large  
amounts of humidity and dust.  
Take 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.  
• Never drop the calculator or otherwise subject it to  
strong impact.  
• Never twist or bend the calculator.  
Avoid 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.  
• Never try to take the calculator apart.  
• Never 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-  
zene or other volatile agents to clean the calculator. Do-  
ing so can remove printed markings and can damage  
the case.  
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Contents  
Removing and Replacing the  
Calculator’s Cover................................... 1  
Safety Precautions .................................. 2  
Handling Precautions ............................. 3  
Two-line Display ...................................... 7  
Before getting started............................. 7  
kModes .................................................................... 7  
kInput Capacity ........................................................ 8  
kMaking Corrections During Input ........................... 9  
kReplay Function ..................................................... 9  
kError Locator .......................................................... 9  
kMulti-statements .................................................. 10  
kExponential Display Formats ............................... 10  
kDecimal Point and Separator Symbols ................ 11  
kInitializing the Calculator...................................... 11  
Basic Calculations ................................ 11  
kArithmetic Calculations ........................................ 11  
kFraction Operations ............................................. 12  
kPercentage Calculations ...................................... 14  
kDegrees, Minutes, Seconds Calculations ............ 15  
kFIX, SCI, RND ..................................................... 15  
Memory Calculations ............................ 16  
kAnswer Memory ................................................... 16  
kConsecutive Calculations .................................... 17  
kIndependent Memory ........................................... 17  
kVariables .............................................................. 17  
Scientific Function Calculations.......... 18  
kTrigonometric/Inverse Trigonometric Functions ... 18  
kHyperbolic/Inverse Hyperbolic Functions ............ 19  
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kCommon and Natural Logarithms/  
Antilogarithms ...................................................... 19  
kSquare Roots, Cube Roots, Roots, Squares, Cubes,  
Reciprocals, Factorials, Random Numbers, π, and  
Permutation/Combination .................................... 20  
kAngle Unit Conversion ......................................... 21  
kCoordinate Conversion (Pol (x, y), Rec (r, )) ..... 21  
kEngineering Notation Calculations ...................... 22  
Equation Calculations .......................... 22  
kQuadratic and Cubic Equations ........................... 22  
kSimultaneous Equations ...................................... 24  
Statistical Calculations......................... 26  
Standard Deviation .................................................. 26  
Regression Calculations .......................................... 28  
Technical Information ........................... 32  
kWhen you have a problem...... ............................. 32  
kError Messages ................................................... 32  
kOrder of Operations ............................................. 34  
kStacks .................................................................. 35  
kInput Ranges ....................................................... 36  
Power Supply (fx-95MS only) ...................... 38  
Specifications (fx-95MS only) ..................... 39  
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Two-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 “User’s Guide 2 (Additional  
Functions)” for information about modes and their  
selection.  
fx-95MS Modes  
To perform this type of  
calculation:  
Perform this  
To enter  
key operation: this mode:  
Basic arithmetic calculations F 1  
COMP  
SD  
Standard deviation  
F 2  
Regression calculations  
Solution of equations  
F 3  
REG  
EQN  
F F 1  
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• Pressing the F key 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.  
• In 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:  
Equation  
Calculations  
EQN  
Note!  
To return the calculation mode and setup to the initial  
defaults shown below, press A B 2(Mode) =.  
Calculation Mode:  
Angle Unit:  
COMP  
Deg  
Exponential Display Format: Norm 1  
Fraction Display Format:  
Decimal Point Character:  
ab/c  
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  
“steps.One step is taken up each time you press a  
number key or arithmetic operator key ( +, ,, -, \ ).  
A A or p key operation does not take up a step, so  
inputting A D, for example, takes up only one step.  
You 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,  
you should divide your calculation into two or more parts.  
• Pressing the g key recalls the last result obtained, which  
you can use in a subsequent calculation. See “Answer  
Memory” for more information about using the g key.  
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k Making Corrections During Input  
• Use e and r to move the cursor to the location you  
want.  
• Press [ to delete the number or function at the current  
cursor position.  
• Press 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.  
• Pressing A K, or = returns to the normal cursor from  
the insert cursor.  
k Replay Function  
• Every 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.  
• Pressing the e or r key while a replay memory cal-  
culation is on the display changes to the editing screen.  
• Pressing the e or r key immediately after you finish  
a calculation displays the editing screen for that calcula-  
tion.  
• Pressing 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  
expressions and results.  
• Replay memory is cleared by any of the following ac-  
tions.  
When you press the 5key  
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  
• Pressing r or e after an error occurs displays the  
calculation with the cursor positioned at the location  
where the error occurred.  
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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
2 + 3 p \ g - 4 =  
5.Disp  
×
Ans  
4
=
20.  
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  
formats that determine at what point exponential notation  
is used.  
To change the exponential display format, press the F  
key a number of times until you reach the exponential  
display format setup screen shown below.  
F i x Sc i  
N
3
or  
m
1
2
• Press 3. On the format selection screen that appears,  
press 1 to select Norm 1 or 2 for Norm 2.  
uNorm 1  
With Norm 1, exponential notation is automatically used  
for integer values with more than 10 digits and decimal  
values with more than two decimal places.  
uNorm 2  
With Norm 2, exponential notation is automatically used  
for integer values with more than 10 digits and decimal  
values with more than nine decimal places.  
• All of the examples in this manual show calculation re-  
sults using the Norm 1 format.  
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k Decimal Point and Separator Symbols  
You can use the display setup (Disp) screen to specify the  
symbols you want for the decimal point and 3-digit sepa-  
rator.  
To change the decimal point and separator symbol set-  
ting, press the F key a number of times until you reach  
the setup screen shown below.  
Disp  
1
• Display the selection screen.  
fx-95MS:  
1 r  
Other Models: 1 r r  
• Press 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  
• Perform 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) =  
COMP  
Basic Calculations  
k Arithmetic Calculations  
Use the F key to enter the COMP Mode when you  
want to perform basic calculations.  
COMP .............................................................F 1  
• Negative values inside of calculations must be enclosed  
within parentheses.  
sin –1.23 S R D 1.23 T  
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• It is not necessary to enclose a negative exponent within  
parentheses.  
sin 2.34 ҂ 10–5 S 2.34 e D 5  
Example 1: 3҂(5҂10–9) ҃ 1.5҂10–8  
3 - 5 e D 9 =  
Example 2: 5҂(9ѿ7) ҃ 80  
5 - R 9 + 7 T =  
You can skip all Toperations before =.  
k Fraction Operations  
uFraction Calculations  
• Values are displayed in decimal format automatically  
whenever the total number of digits of a fractional value  
(integer + numerator + denominator + separator marks)  
exceeds 10.  
2
3
1
5
13  
15  
Example 1:  
ѿ
҃
13 15.00  
2 C 3 + 1 C 5 =  
1
4
2
3
11  
12  
Example 2: 3  
ѿ 1  
҃ 4  
3 C 1 C 4 +  
4 11 12.00  
1 C 2 C 3 =  
2
4
1
2
Example 3:  
Example 4:  
҃
2 C 4 =  
1
2
ѿ1.6 ҃ 2.1  
1 C 2 + 1.6 =  
• Results of calculations that mix fraction and decimal val-  
ues are always decimal.  
uDecimal Fraction Conversion  
• Use 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.  
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3
4
Example 1: 2.75 ҃ 2  
(Decimal Fraction)  
2.75 =  
2.75  
C
2
3 4.00  
11  
4
҃
A B  
11 4.00  
1
2
Example 2:  
0.5 (Fraction Decimal)  
1 C 2 =  
1 2.00  
0.500  
C
C
1 2.00  
uMixed Fraction Improper Fraction  
Conversion  
2
3
5
3
Example: 1  
1
1
2 3.00  
3.00  
2 3.00  
1 C 2 C 3 =  
A B  
A B  
5
You can use the display setup (Disp) screen to specify  
the display format when a fraction calculation result is  
greater than one.  
To change the fraction display format, press the q key  
a number of times until you reach the setup screen shown  
below.  
Disp  
1
• Display the selection screen.  
fx-95MS:  
1
Other Models: 1 r  
• Press the number key (1 or 2) that corresponds to  
the setting you want to use.  
1(ab/c): Mixed fraction  
2(d/c): Improper fraction  
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• An error occurs if you try to input a mixed fraction while  
the d/c display format is selected.  
k Percentage 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 =  
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k Degrees, Minutes, Seconds  
Calculations  
You 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 =  
A O  
I
2.258  
2°15°28.8  
2.258  
Example 2: To perform the following calculation:  
12°34’56” ҂ 3.45  
43°24°31.2  
12 I 34 I 56 I - 3.45 =  
k FIX, SCI, RND  
To change the settings for the number of decimal places,  
the number of significant digits, or the exponential dis-  
play format, press the F key a number of times until  
you reach the setup screen shown below.  
F i x Sc i  
N
3
or  
m
1
2
• Press 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 ҃  
400.00  
200 \ 7 - 14 =  
(Specifies three  
decimal places.)  
FIX  
.....  
(Fix)  
400.00000  
F
1
3
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(Internal calculation continues  
using 12 digits.)  
28.57100  
200 \ 7 =  
- 14 =  
400.00000  
The following performs the same calculation using the  
specified number of decimal places.  
200 \ 7 =  
A Q  
28.57100  
28.57100  
399.99400  
(Internal rounding)  
- 14 =  
.....  
• Press F  
3(Norm) 1 to clear the Fix specifica-  
tion.  
Example 2: 1 3, displaying result with two significant  
digits (Sci 2)  
SCI  
3.3–01  
.....  
(Sci)  
2 2 1 \ 3 =  
F
.....  
• Press F  
3(Norm) 1 to clear the Sci specifica-  
tion.  
COMP  
Memory Calculations  
Use the F key to enter the COMP Mode when you  
want to perform a calculation using memory.  
COMP .............................................................F 1  
k Answer Memory  
• Whenever you press = after inputting values or an ex-  
pression, the calculated result automatically updates An-  
swer Memory contents by storing the result.  
• In addition to =, Answer Memory contents are also up-  
dated with result whenever you press A v, |, A  
{, or A j followed by a letter (A through F, or M, X,  
or Y).  
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You can recall Answer Memory contents by pressing g.  
• Answer 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  
You can use the calculation result that is currently on the  
display (and also stored in Answer Memory) as the first  
value 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 (x2, x3, x–1, x!, DRG'), +, –,  
^(xy), x , ҂, , nPr and nCr.  
k Independent Memory  
• Values can be input directly into memory, added to  
memory, or subtracted from memory. Independent  
memory is convenient for calculating cumulative totals.  
• Independent memory uses the same memory area as  
variable M.  
To clear independent memory (M), input 0 A j 3  
(M+).  
Example:  
23 ѿ 9 ҃ 32  
53 Ҁ 6 ҃ 47  
23 + 9 A j 3(M+)  
53 , 6 |  
Ҁ) 45 ҂ 2 ҃ 90  
45 - 2 A {  
(Total) –11  
03(M+)  
k Variables  
• There are nine variables (A through F, M, X andY), which  
can be used to store data, constants, results, and other  
values.  
• Use the following operation to delete data assigned to a  
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particular variable: 0 A j 1. This operation de-  
letes the data assigned to variable A.  
• Perform 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  
COMP  
Use the F key to enter the COMP Mode when you  
want to perform basic arithmetic calculations.  
COMP .............................................................F 1  
• Certain types of calculations may take a long time to  
complete.  
• Wait for the result to appear on the display before start-  
ing the next calculation.  
π = 3.14159265359  
k Trigonometric/Inverse Trigonometric  
Functions  
To change the default angle unit (degrees, radians,  
grads), press the F key a number of times until you  
reach the angle unit setup screen shown below.  
Deg Rad  
G
3
r a  
1
2
• Press the number key (1, 2, or 3) that corresponds  
to the angle unit you want to use.  
π
2
(90° = radians = 100 grads)  
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Example 1: sin 63°52o41ꢁ ҃ 0.897859012  
.....  
(
q
1 Deg)  
S 63 I 52 I 41 I =  
π
3
Example 2: cos  
(
rad)҃ 0.5  
.....  
(
q
2 Rad)  
W RA x \ 3 T=  
2
2
π
4
.....  
Example 3: cosҀ1  
҃0.25 π (rad)(҃  
q
(rad))  
2 (Rad)  
A V RL 2 \ 2 T= g \ A x =  
Example 4: tanҀ1 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: sinhҀ1 30 ҃ 4.094622224  
M A j 30 =  
k Common and Natural Logarithms/  
Antilogarithms  
Example 1: log 1.23 ҃ 0.089905111  
R 1.23 =  
T 90 =  
Example 2: In 90 (= loge 90) = 4.49980967  
ln e ҃ 1  
T p P =  
A U 10 =  
A Q 1.5 =  
2 W 4 =  
Example 3: e10 ҃ 22026.46579  
Example 4: 101.5 ҃ 31.6227766  
Example 5: 24 ҃ 16  
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k Square Roots, Cube Roots, Roots,  
Squares, Cubes, Reciprocals,  
Factorials, Random Numbers, π, and  
Permutation/Combination  
Example 1: 2 ѿ 3 ҂ 5 ҃ 5.287196909  
L 2 + L 3 - L 5 =  
3
Example 2: 5 ѿ 3 ȕ27 ҃ –1.290024053  
A D 5 + A D RD 27 T=  
1
7
Example 3: 7 123 ( = 123 ) ҃ 1.988647795  
7 A H 123 =  
Example 4: 123 ѿ 302 ҃ 1023  
Example 5: 123 ҃ 1728  
123 + 30 K =  
12 N* =  
*
in the case of fx-570MS/fx-991MS.  
A N  
1
Example 6:  
҃ 12  
1
3
1
4
ȕ
3
4
a , a Ta =  
R
Example 7: 8! ҃ 40320  
8 A f =  
Example 8: To generate a random number between  
0.000 and 0.999  
0.66400  
A M =  
(The above value is a sample only. Results differ each time.)  
Example 9: 3π ҃ 9.424777961  
3 A x =  
Example 10: To determine how many different 4-digit  
values can be produced using the numbers 1 through 7  
• Numbers cannot be duplicated within the same 4-digit  
value (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 =  
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20  
* A n in the case of fx-100MS/fx-115MS/fx-570MS/  
fx-991MS.  
k Angle Unit Conversion  
• Press A v to display the following menu.  
D
R
G
1 2 3  
• Pressing 1, 2, or 3 converts the displayed value to  
the corresponding angle unit.  
Example: To conver t 4.25 radians to degrees  
.....  
q
1(Deg)  
r
4.25  
(
)
4.25 A v 2 R =  
243.5070629  
k Coordinate Conversion (Pol (x, y),  
Rec (r, θ ))  
• Calculation results are automatically assigned to vari-  
ables E and F.  
Example 1: To convert polar coordinates (r҃2, ҃60°)  
to rectangular coordinates (x, y) (Deg)  
x ҃ 1  
A F 2 P 60 T =  
0o  
y ҃ 1.732050808  
• Press 0n to display the value of x, or 0o 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.  
θ ҃ 1.047197551  
0o  
• Press 0n to display the value of r, or 0o to dis-  
play the value of .  
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21  
k Engineering Notation Calculations  
Example 1: To convert 56,088 meters to kilometers  
56.088 ҂103  
(km)  
Example 2: To convert 0.08125 grams to milligrams  
56088 = J  
81.25 ҂10 –3  
0.08125 = J  
(mg)  
Equation  
Calculations  
EQN  
The EQN Mode lets you solve equations up to three de-  
grees and simultaneous linear equations with up to three  
unknowns.  
Use the F key 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: ax2 + bx + c = 0  
Cubic Equation: ax3 + bx2 + cx + d = 0  
Entering the EQN Mode and pressing r displays the ini-  
tial quadratic/cubic equation screen.  
Deg ree?  
2 3  
Use this screen to specify 2 (quadratic) or 3 (cubic) as the  
degree of the equation, and input values for each of the  
coefficients.  
Arrow indicates  
direction you  
should scroll to  
view other  
Coefficient name  
a?  
elements.  
0.  
Element value  
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22  
• Any time until you input a value for the final coefficient (c  
for a quadratic equation, d for a cubic equation), you can  
use the [ and ] keys to move between coefficients  
on the screen and make changes, if you want.  
• Note 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.  
Arrow indicates  
direction you  
should scroll to  
view other  
Variable name  
x1=  
solutions.  
0.  
Solution  
Press the ] key to view other solutions. Use [ and ]  
to scroll between all of the solutions for the equation.  
Pressing the t key at this point returns to the coefficient  
input screen.  
• Certain coefficients can cause calculation to take more  
time.  
Example 1: To solve the equation  
x3 – 2x2 x + 2 = 0 (x = 2, –1, 1)  
(Degree?)  
(a?)  
3
1 =  
D 2 =  
D 1 =  
2 =  
]
(b?)  
(c?)  
(d?)  
(x1 = 2)  
(x2 = –1)  
(x3 = 1)  
]
• If a result is a complex number, the real part of the first  
solution appears first. This is indicated by the “RI”  
symbol on the display. Press A r to toggle the display  
between the real part and imaginary part of a solution.  
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23  
D
RI  
RI  
x1=  
x1=  
0.25  
A r  
D
0.75i  
Example 2: To solve the equation  
8x2 – 4x + 5 = 0 (x = 0.25 0.75 i)  
(Degree?)  
(a?)  
2
8 =  
D 4 =  
5 =  
(b?)  
(c?)  
(x1 = 0.25 + 0.75i)  
(x2 = 0.25 – 0.75i)  
]
k Simultaneous Equations  
Simultaneous Linear Equations with Two Unknowns:  
a
a
1x + b1y = c1  
2x + b2y = c2  
Simultaneous Linear Equations with Three Unknowns:  
a1x + b1y + c1z = d1  
a2x + b2y + c2z = d2  
a3x + b3y + c3z = d3  
Entering the EQN Mode displays the initial simultaneous  
equation screen.  
Unkno ns?  
w
3
2
Use this screen to specify 2 or 3 as the number of un-  
knowns, and input values for each of the coefficients.  
Arrow indicates  
direction you  
should scroll to  
view other  
Coefficient name  
a1?  
elements.  
0.  
Element value  
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• Any time until you input a value for the final coefficient  
(c2 for two unknowns, d3 for three unknowns), you can  
use the [ and ] keys 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.  
Arrow indicates  
direction you  
should scroll to  
view other  
Variable name  
x=  
solutions.  
0.  
Solution  
Press the ] key to view other solutions. Use [ and ]  
to scroll between all of the solutions for the equation.  
Pressing the t key at this point returns to the coefficient  
input screen.  
Example: To solve the following simultaneous equations  
2x + 3y z = 15  
3x – 2y + 2z = 4  
5x + 3y – 4z = 9  
(x = 2, y = 5, z = 4)  
(Unknowns?)  
3
(a1?) ....... (d1?)  
(a2?) ....... (d2?)  
(a3?) ....... (d3?)  
(x = 2)  
2 = 3 = D1 = 15 =  
3 = D 2 = 2 = 4 =  
5 = 3 = D 4 = 9 =  
]
]
(y = 5)  
(z = 4)  
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25  
SD  
Statistical  
Calculations  
REG  
SD  
Standard Deviation  
Use the F key 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)  
• Always start data input with A B 1(Scl) = to clear  
statistical memory.  
• Input data using the key sequence shown below.  
<x-data> S  
• Input data is used to calculate values for n, Σx, Σx2, o,  
σn and σn-1, which you can recall using the key opera-  
tions noted nearby.  
To recall this type of value:  
Perform this key operation:  
Σx2  
Σx  
n
A U 1  
A U 2  
A U 3  
A X 1  
A X 2  
A X 3  
o
σn  
σn-1  
Example: To calculate σnҀ1, σn, o, n, Σx, and Σx2 for  
the following data : 55, 54, 51, 55, 53, 53, 54, 52  
In the SD Mode:  
A B 1(Scl) = (Stat clear)  
SD  
n=  
55 S  
1.  
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 (σnҀ1) = 1.407885953  
A X 3 =  
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26  
Population Standard Deviation (σn) = 1.316956719  
Arithmetic Mean (o) = 53.375  
A X 2 =  
A X 1 =  
A U 3 =  
A U 2 =  
A U 1 =  
Number of Data (n) = 8  
Sum of Values (Σx) = 427  
Sum of Squares of Values (Σx2) = 22805  
Data Input Precautions  
S S inputs the same data twice.  
You 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.  
You can perform the above key operations in any order,  
and not necessarily that shown above.  
• While inputting data or after inputting data is complete,  
you can use the [ and ] keys to scroll through data  
you 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).  
You 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  
want to perform some other operation (calculation, recall  
of statistical calculation results, etc.), you should always  
press the t key first to exit data display.  
• Pressing the S key 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.  
You can delete a data value displayed using [ and ]  
by pressing A U. Deleting a data value causes all  
values following it to be shifted up.  
• Data values you register are normally stored in calcula-  
tor memory. The message “Data 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.  
Ed i t  
1
O
FF ESC  
2
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27  
Press 2 to exit data input without registering the value  
you 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.  
To delete data you have just input, press A U.  
• After 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)  
REG  
Regression Calculations  
Use the F key 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.  
L i n Log  
E
3
xp  
1
2
r
e
P r Inv  
Q
3
uad  
1w  
2
• Press the number key (1, 2, or 3) that corresponds  
to the type of regression you want to use.  
1 (Lin): Linear regression  
2 (Log): Logarithmic regression  
3 (Exp): Exponential regression  
r 1 (Pwr): Power regression  
r 2 (Inv): Inverse regression  
r 3 (Quad): Quadratic regression  
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• Always start data input with A B 1(Scl) = to clear  
statistical memory.  
• Input 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:  
Σx2  
Σx  
A U 1  
A U 2  
n
A U 3  
Σy2  
Σy  
Σxy  
o
A U r 1  
A U r 2  
A U r 3  
A X 1  
xσn  
xσn-1  
p
yσn  
yσn-1  
A X 2  
A X 3  
A X r 1  
A X r 2  
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
n
A X r r r 1  
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:  
Σx3  
A U r r 1  
A U r r 2  
A U r r 3  
Σx2y  
Σx4  
Regression coefficient C A X r r 3  
m
m
n
1
A X r r r 1  
A X r r r 2  
A X r r r 3  
2
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29  
• The values in the above tables can be used inside of  
expressions the same way you use variables.  
uLinear Regression  
• The regression formula for linear regression is:  
y = A + Bx.  
Example: Atmospheric Pressure vs. Temperature  
Perform linear regression to de-  
termine the regression formula  
Atmospheric  
Temperature  
Pressure  
10°C  
15°C  
20°C  
25°C  
30°C  
1003 hPa  
1005 hPa  
1010 hPa  
1011 hPa  
1014 hPa  
terms and correlation coefficient  
for 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 (r2) and sample  
covariance  
.
In the REG Mode:  
(Lin)  
1
A B 1(Scl) =(Stat clear)  
10 P1003 S  
REG  
n=  
1.  
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 P1010 S 25 P 1011 S  
30 P 1014 S  
Regression Coefficient A = 997.4  
Regression Coefficient B = 0.56  
A X r r 1 =  
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 =  
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Temperature 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 =  
uLogarithmic, Exponential, Power, and Inverse  
Regression  
• Use 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 ѿ BؒIn x  
Exponential Regression y ҃ AؒeB x (In y ҃ In A + Bx)  
·
Power Regression  
Inverse Regression  
y ҃ AؒxB (In y ҃ In A + BIn x)  
y ҃ A ѿ Bؒ1/x  
uQuadratic Regression  
• The regression formula for quadratic regression is:  
y = A + Bx + Cx2.  
Example:  
Perform quadratic regression to de-  
xi  
29  
yi  
1.6  
termine the regression formula terms  
for the data nearby. Next, use the  
regression formula to estimate the  
values for n (estimated value of y) for  
xi = 16 and m (estimated value of x)  
for yi = 20.  
50  
23.5  
38.0  
46.4  
48.0  
74  
103  
118  
In the REG Mode:  
(Quad)  
r 3  
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  
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Regression Coefficient A = –35.59856934  
Regression Coefficient B = 1.495939413  
Regression Coefficient C = – 6.71629667 i10–3  
A X r r 1 =  
A X r r 2 =  
A X r r 3 =  
n when xi is 16 = –13.38291067  
m1 when yi is 20 = 47.14556728  
m2 when yi is 20 = 175.5872105  
16 A X r r r 3 =  
20 A X r r r 1 =  
20 A X r r r 2 =  
Data Input Precautions  
S S inputs the same data twice.  
You can also input multiple entries of the same data us-  
ing A G. To input the data “20 and 30” five times, for  
example, press 20 P 30 A G 5 S.  
• The above results can be obtained in any order, and not  
necessarily that shown above.  
• Precautions when editing data input for standard devia-  
tion also apply for regression calculations.  
Technical 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  
5key. 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  
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32  
the display. Press t to clear the error, or press e or r  
to display the calculation and correct the problem. See  
“Error Locator” for details.  
Math ERROR  
• Causes  
• Calculation result is outside the allowable calculation  
range.  
• An attempt to perform a function calculation using a  
value 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  
values in any memory areas you are using.  
Stack ERROR  
• Cause  
• The capacity of the numeric stack or operator stack is  
exceeded.  
• Action  
• Simplify the calculation.The numeric stack has 10 lev-  
els and the operator stack has 24 levels.  
• Divide your calculation into two or more separate parts.  
Syntax ERROR  
• Cause  
• An attempt to perform an illegal mathematical opera-  
tion.  
• Action  
• Press 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  
• Cause  
• Improper use of an argument  
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33  
• Action  
• Press 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, θ)  
Differentials: d/dx*  
Integrations: dx*  
Normal distribution: P(*, Q(*, R(*  
2 Type A functions:  
With these functions, the value is entered and then the  
function key is pressed.  
x3, x2, xҀ1, x!,  
Engineering symbols  
° ’ ”  
*
Normal distribution: t*  
m m1 m2  
n
,
,
,
Angle unit conversions (DRG')  
Metric conversions**  
3 Powers and roots: ^(xy), x  
4 ab/c  
5 Abbreviated multiplication format in front of π, e (natu-  
ral logarithm base), memory name, or variable name:  
2π, 3e, 5A, πA, etc.  
6 Type B functions:  
With these functions, the function key is pressed and  
then the value is entered.  
3
,
, log, In, ex, 10x, sin, cos, tan, sinҀ1, cosҀ1  
,
tanҀ1, sinh, cosh, tanh, sinhҀ1, coshҀ1, tanhҀ1, (Ҁ)  
d*, h*, b*, o*, Neg*, Not*, Det**,Trn**, arg*, Abs*, Conjg*  
7 Abbreviated multiplication format in front ofType B func-  
tions: 2 3, Alog2, etc.  
8 Permutation and combination: nPr, nCr  
*  
9 Dot ()**  
0 ҂, ꢀ  
! ѿ, Ҁ  
@ and*  
# xnor*, xor*, or*  
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34  
* fx-100MS/fx-115MS/fx-570MS/fx-991MS only.  
** fx-570MS/fx-991MS only.  
• Operations of the same precedence are performed from  
right to left. exIn  
120 ex{In(  
120)}  
• Other operations are performed from left to right.  
• Operations enclosed in parentheses are performed first.  
• When 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  
Type A function, or power or root operations.  
Example: ( –2)4 = 16  
–24 = –16  
k Stacks  
This calculator uses memory areas, called “stacks,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.  
• Matrix 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
4
5
1
2
3
4
5
6
7
Numeric Stack Command Stack  
1
2
3
4
5
4
1
2
3
4
5
6
7
҂
2
3
4
5
ѿ
҂
ѿ
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• Calculations are performed in sequence according to  
“Order 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  
sinx  
DEG 0Ϲ xϹ4.499999999҂1010  
RAD 0Ϲ xϹ785398163.3  
GRA 0Ϲ xϹ4.999999999҂1010  
cosx DEG 0Ϲ xϹ4.500000008҂1010  
RAD 0Ϲ xϹ785398164.9  
GRA 0Ϲ xϹ5.000000009҂1010  
tanx DEG Same as sinx, except when x= (2n-1)҂90.  
RAD Same as sinx, except when x= (2n-1)҂π/2.  
GRA Same as sinx, except when x= (2n-1)҂100.  
sin–1x  
cos–1x  
0Ϲ xϹ1  
tan–1x 0Ϲ xϹ9.999999999҂1099  
sinhx  
coshx  
0Ϲ xϹ230.2585092  
sinh–1x 0Ϲ xϹ4.999999999҂1099  
cosh–1x 1Ϲ x Ϲ4.999999999҂1099  
tanhx 0Ϲ xϹ9.999999999҂1099  
tanh–1x 0Ϲ xϹ9.999999999҂10–1  
logx/lnx 0x Ϲ9.999999999҂1099  
x
10  
–9.999999999҂1099Ϲ x Ϲ 99.99999999  
–9.999999999҂1099Ϲ x Ϲ 230.2585092  
ex  
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36  
Functions  
Input Range  
x
x2  
0Ϲ x 1 ҂ 10100  
xꢂꢃ 1҂ 1050  
1/x  
xꢂꢃ 1҂ 10100  
xꢂꢃ 1҂ 10100  
;
x G  
0
3
x
x!  
0Ϲ x Ϲ 69 (x is an integer)  
0Ϲ n 1҂1010, 0Ϲ r Ϲ n (n, r are integers)  
nPr  
1Ϲ {n!/(nr)!} 1҂10100  
0Ϲ n 1҂1010, 0Ϲ r Ϲ n (n, r are integers)  
1Ϲ [n!/{r!(nr)!}] 1҂10100  
nCr  
x, yϹ9.999999999҂1049  
(x2+y2) Ϲ9.999999999҂1099  
Pol(x, y)  
0Ϲ r Ϲ9.999999999҂1099  
θ: Same as sinx  
Rec(r, )  
a, b, c 1҂10100  
0 Ϲ b, c  
xꢂꢃ1҂10100  
°’ ”  
Decimal Sexagesimal Conversions  
0°0°0°Ϲ xϹ999999°59°  
xŒ0: –1҂10100ylogx100  
^(xy)  
x҃0: yŒ0  
x0: y҃n,  
However: –1҂10100 ylogxꢂꢃ100  
1
(n is an integer)  
2n+1  
yŒ0: x G 0  
–1҂101001/x logy100  
x
y
y҃0: xŒ0  
y0: x҃2nѿ1,  
However: –1҂10100 1/x logyꢂꢃ100  
1
n
(n G 0; n is an integer)  
Total of integer, numerator, and denominator  
b
a /c must be 10 digits or less (including division  
marks).  
xꢂꢃ 1҂1050  
yꢂꢃ 1҂1050  
SD  
(REG)  
nꢂꢃ 1҂10100  
xn, yn, o, p : n G 0  
xn1, yn1, A, B, r : n G 0, 1  
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37  
* 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 ^(xy), x y , x!, 3 , nPr, nCr, etc.)  
In the vicinity of a function’s singular point and point of  
inflection, errors are cumulative and may become large.  
Power Supply  
(fx-95MS only)  
Users of other models should refer to the “User’s 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  
Screw  
Screw  
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  
and  
k
negative  
rectly.  
ends facing cor-  
l
5 Replace the back cover and  
secure it in place with the six  
screws.  
6 Press 5to turn power on.  
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38  
uAuto Power Off  
Calculator power automatically turns off if you do not per-  
form 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 “User’s Guide 2  
(Additional Functions).”  
Power 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) i 78 (W) i 155 (D) mm  
3/4(H) ҂ 31/16(W) ҂ 61/8(D)  
Weight:  
130 g (4.6 oz) including battery  
Power Consumption: 0.0002 W  
OperatingTemperature: 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.  
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39  
CASIO COMPUTER CO., LTD.  
6-2, Hon-machi 1-chome  
Shibuya-ku, Tokyo 151-8543, Japan  
SA0206-D Printed in China  
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CA 310063-1  

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