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.
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
1
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
2
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.
3
• 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.
4
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
5
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
6
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
7
• 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.
8
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.
9
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.
10
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
11
• 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:
҃
2 C 4 =
1
2
• Example 4:
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.
12
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
13
• 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 =
14
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
15
(Internal calculation continues
using 12 digits.)
28.57100
200 \ 7 =
400.00000
- 14 =
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).
16
• 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
17
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)
18
• 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 =
• Example 2: In 90 (= loge 90) = 4.49980967
T 90 =
ln e ҃ 1
• Example 3: e10 ҃ 22026.46579
• Example 4: 101.5 ҃ 31.6227766
• Example 5: 24 ҃ 16
19
T p P =
A U 10 =
A Q 1.5 =
2 W 4 =
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
123 + 30 K =
• Example 5: 123 ҃ 1728
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 =
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 =
y ҃ 1.732050808
0o
• 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 .
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
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 “R↔I”
symbol on the display. Press A r to toggle the display
between the real part and imaginary part of a solution.
23
D
R⇔I
x1=
x1=
0.25
A r
D
R⇔I
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
1x + b1y = c1
a2x + 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
24
• 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)
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 =
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
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
28
• 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
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
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 =
30
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
31
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
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
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*
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
35
• 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 ꢂxꢂ Ϲ4.499999999҂1010
RAD 0Ϲ ꢂxꢂ Ϲ785398163.3
GRA 0Ϲ ꢂxꢂ Ϲ4.999999999҂1010
cosx DEG 0Ϲ ꢂxꢂ Ϲ4.500000008҂1010
RAD 0Ϲ ꢂxꢂ Ϲ785398164.9
GRA 0Ϲ ꢂxꢂ Ϲ5.000000009҂1010
tanx DEG Same as sinx, except when ꢂxꢂ= (2n-1)҂90.
RAD Same as sinx, except when ꢂxꢂ= (2n-1)҂π/2.
GRA Same as sinx, except when ꢂxꢂ= (2n-1)҂100.
sin–1x
cos–1x
0Ϲ ꢂxꢂ Ϲ1
tan–1x 0Ϲ ꢂxꢂ Ϲ9.999999999҂1099
sinhx
coshx
0Ϲ ꢂxꢂ Ϲ230.2585092
sinh–1x 0Ϲ ꢂxꢂ Ϲ4.999999999҂1099
cosh–1x 1Ϲ x Ϲ4.999999999҂1099
tanhx 0Ϲ ꢂxꢂ Ϲ9.999999999҂1099
tanh–1x 0Ϲ ꢂxꢂ Ϲ9.999999999҂10–1
logx/lnx 0ꢃ x Ϲ9.999999999҂1099
x
10
–9.999999999҂1099Ϲ x Ϲ 99.99999999
–9.999999999҂1099Ϲ x Ϲ 230.2585092
ex
36
Functions
Input Range
x
x2
0Ϲ x ꢃ 1 ҂ 10100
ꢂxꢂꢃ 1҂ 1050
1/x
ꢂxꢂꢃ 1҂ 10100
ꢂxꢂꢃ 1҂ 10100
;
x G
0
3
x
x!
0Ϲ x Ϲ 69 (x is an integer)
0Ϲ n ꢃ 1҂1010, 0Ϲ r Ϲ n (n, r are integers)
nPr
1Ϲ {n!/(n–r)!} ꢃ 1҂10100
0Ϲ n ꢃ 1҂1010, 0Ϲ r Ϲ n (n, r are integers)
1Ϲ [n!/{r!(n–r)!}] ꢃ 1҂10100
nCr
ꢂxꢂ, ꢂyꢂ Ϲ9.999999999҂1049
(x2+y2) Ϲ9.999999999҂1099
Pol(x, y)
0Ϲ r Ϲ9.999999999҂1099
θ: Same as sinx
ꢂaꢂ, b, c ꢃ 1҂10100
Rec(r, )
°’ ”
0 Ϲ b, c
ꢂxꢂꢃ1҂10100
Decimal ↔ Sexagesimal Conversions
0°0°0°Ϲ ꢂxꢂ Ϲ999999°59°
xŒ0: –1҂10100ꢃylogxꢃ100
^(xy)
x҃0: yŒ0
xꢃ0: y҃n,
However: –1҂10100 ꢃylogꢂxꢂꢃ100
1
(n is an integer)
2n+1
yŒ0: x G 0
–1҂10100ꢃ1/x logyꢃ100
x
y
y҃0: xŒ0
yꢃ0: x҃2nѿ1,
However: –1҂10100 ꢃ1/x logꢂyꢂꢃ100
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).
ꢂxꢂꢃ 1҂1050
ꢂyꢂꢃ 1҂1050
SD
(REG)
ꢂnꢂꢃ 1҂10100
xn, yn, o, p : n G 0
xn–1, yn–1, A, B, r : n G 0, 1
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.
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
3/4ꢀ (H) ҂ 31/16ꢀ (W) ҂ 61/8ꢀ (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.
39
CASIO COMPUTER CO., LTD.
6-2, Hon-machi 1-chome
Shibuya-ku, Tokyo 151-8543, Japan
SA0206-D Printed in China
CA 310063-1
|