Casio FX-300MS - Manual (Page 2)

Manufacturer:
CASIO COMPUTER CO., LTD.
6-2, Hon-machi 1-chome
Shibuya-ku, Tokyo 151-8543, Japan
Responsible within the European Union:
CASIO EUROPE GmbH
Casio-Platz 1
22848 Norderstedt, Germany
This mark applies in EU countries only.
32 5 = 2 5 1M( x ') 32 = 2.
To calculate ' 2 × 3(= 3 ' 2 = 4.242640687...) to three
decimal places (Fix 3)
N 1(Fix) 3
1 2 * 3 = 4.243
To convert rectangular coordinates ( ' 2 , ' 2 ) to polar
coordinates v
fx-82MS/85MS/300MS/350MS:
r9 2 ,9 2 )= r = 2.
~t(F) Ƨ = 45.
• Press ~c(E) to display the value of r , or ~t(F) to
display the value of Ƨ .
fx-82SX PLUS/220 PLUS:
r9 2 ((,) 9 2 )= r = 2.
!q( y , Ƨ ) = Ƨ = 45.
• Press ! r ( x , r ) = to display the value of r , or
!q( y , Ƨ ) = to display the value of Ƨ .
To convert polar coordinates ( ' 2 , 45°) to rectangular
coordinates v
fx-82MS/85MS/300MS/350MS:
!r(Rec( ) 9 2 , 45 = x = 1.
~t(F) y = 1.
• Press ~c(E) to display the value of x , or ~t(F) to
display the value of y .
fx-82SX PLUS/220 PLUS: q9 2 ((,) 45 = x = 1.
!q( y , Ƨ ) = y = 1.
• Press ! r ( x , r ) = to display the value of x , or
!q( y , Ƨ ) = to display the value of y .
(5 + 3) ! = 40320 ( 5 + 3 )1E( x !) = 40320.
To obtain two random three-digit integers
1000 1.(Ran#) = 459.
= 48.
(Actual results will differ.)
To generate random integers in the range of 1 to 6 (fx-82SX
PLUS/220 PLUS only)
12(RanInt) 1 1((,) 6 )= 2.
= 6.
(Actual results will differ.)
To determine the number of permutations and combinations
possible when selecting four people from a group of 10
Permutations: 10 1{( n P r ) 4 = 5040.
Combinations: 10 {4 = 210.
To perform the following calculations when Fix 3 is selected
for the number of display digits: 10 ч 3 Ч 3 and Rnd(10 ч 3)
Ч 3
N 1(Fix) 3 10 / 3 * 3 = 10.000
10 / 3 =10(Rnd) * 3 = 9.999
15. Statistical Calculations (SD, REG*)
*fx-82MS/85MS/300MS/350MS only
To select this type of statistical
calculation: (Regression formula
shown in parentheses) Perform this key
operation:
Single-variable (X) ,2(SD)
Paired-variable (X, Y), linear
regression
( y = A + B x ) ,3 (REG) 1(Lin)
Paired-variable (X, Y), logarithmic
regression
( y = A + Bln x ) ,3 (REG) 2(Log)
Paired-variable (X, Y), e
exponential regression ( y = A e B x )
,3(REG)3(Exp)
Paired-variable (X, Y), power
regression
( y = A x B ) ,3 (REG) e1(Pwr)
Paired-variable (X, Y), inverse
regression
( y = A + B/ x ) ,3 (REG) e2(Inv)
Paired-variable (X, Y), quadratic
regression
( y = A + B x + C x 2 ) ,3 (REG) e3(Quad)
Inputting Data
• In the SD Mode and REG Mode, the l key operates as the 7
key.
• Always start data input with ! , (CLR) b (Scl) =
( rb(Scl) = on the fx-82SX PLUS/220 PLUS) to clear statistical
memory.
• Input data using the key sequence shown below.
SD Mode: <
x -data> 7
REG Mode: < x -data> , < y -data> 7
• 77 inputs the same data twice.
• You can also input multiple entries of the same data using !,(;)
( !)(;) on the fx-82SX PLUS/220 PLUS).
k
8 8
9 9
10 10
11 11
12 12
13 13
Data Input Precautions
• While inputting data or after inputting data is complete, you can use
the f and c keys to scroll through data you have input. If you
input multiple entries of the same data using !,(;) ( !)(;) on
the fx-82SX PLUS/220 PLUS) 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).
• 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, you should always press the
A key first to
exit data display.
• Pressing the 7 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 f and c by pressing
!l(CL). Deleting a data value causes all values following it to
be shifted up.
• 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.
Press c to exit data input without registering
the value you just input.
Press b if you want to register the value
you just input. If you do this, however, you will not be able to display
or edit any of the data you have input.
• 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.
• Entering the REG Mode and selecting a regression type (Lin, Log,
Exp, Pwr, Inv, Quad) clear variables A through F, X, and Y.
• Do not use variables A through F, X, or Y to store data when
performing statistical calculations.
Obtaining Statistical Values from Input Data
Supported statistical variables and the keys you should press to recall
them are shown below.
fx-82SX PLUS/220 PLUS:
Sum:
Σ x 2 , Σ x , Number of Items: n , Mean: o, Population Standard
Deviation: σ x , Sample Standard Deviation: s x
!e to j
fx-82MS/85MS/300MS/350MS:
For single-variable statistical calculations, the variables marked with
an asterisk (*) are available.
Sum:
Σ x 2 *, Σ x *, Σ y 2 , Σ y , Σ xy , Σ x 3 , Σ x 2 y , Σ x 4 , Number of Items: n *
Σ x 2 , Σ x , n ........... !b(S-SUM) b to d
Σ y 2 , Σ y , Σ xy ........ !b(S-SUM) e b to d
Σ x 3 , Σ x 2 y , Σ x 4 ..... !b(S-SUM) ee b to d(Quadratic
Regression only)
Mean: o*, p, Population Standard Deviation: σ x *, σ y , Sample
Standard Deviation: s x *, s y
o, σ x , s x .............. !c(S-VAR) b to d
p, σ y , s y ............... !c(S-VAR)e b to d
Regression Coefficients: A, B, Correlation Coefficient: r
Regression Coefficients for Quadratic Regression: A, B, C
!c(S-VAR)ee b to d
Estimated Values:
m, n
Estimated Values for Quadratic Regression: m 1 , m 2 , n
!c(S-VAR)eee b to c (or d)
•
m , m 1 , m 2 and n are not variables. They are commands of the type
that take an argument immediately before them. See “Calculating
Estimated Values” for more information.
To calculate the mean ( o) and population standard
deviation ( σ x ) for the following data: 55, 54, 51, 55, 53, 53,
54, 52
,c(SD)
55
7 54 7 51 7 55 7 53 77 54 7 52 7
fx-82SX PLUS/220 PLUS: !h( o) = 53.375
!i( σ x ) = 1.316956719
fx-82MS/85MS/300MS/350MS:
!c(S-VAR) b( o) 53.375
!c(S-VAR) c( σ x ) 1.316956719
2 fx-82MS/85MS/300MS/350MS: To calculate the linear
regression and logarithmic regression correlation
coefficients (
r ) for the following paired-variable data
and determine the regression formula for the strongest
correlation: (
x , y ) = (20, 3150), (110, 7310), (200, 8800),
(290, 9310). Specify Fix 3 (three decimal places) for results.
,3(REG) 1(Lin) , 1(Fix) 3
20
, 3150 7 110 , 7310 7 200 , 8800 7 290 ,
9310 7
!2(S-VAR) ee3(r) = 0.923
,3(REG) 2(Log)
20
, 3150 7 110 , 7310 7 200 , 8800 7 290 ,
9310 7
!2(S-VAR) ee3(r) = 0.998
!2(S-VAR) ee1(A) = −3857.984
!2(S-VAR) ee2(B) = 2357.532
Logarithmic Regression Formula:
y = –3857.984 + 2357.532ln x
k
k
1 1
Calculating Estimated Values
Based on the regression formula obtained by paired-variable
statistical calculation, the estimated value of
y can be calculated for
a given x -value. The corresponding x -value (two values, x 1 and x 2 , in
the case of quadratic regression) also can be calculated for a value
of
y in the regression formula.
To determine the estimate value for y when x = 160 in the
regression formula produced by logarithmic regression of
the data in
2 . Specify Fix 3 for the result. (Perform the
following operation after completing the operations in 2 .)
160 12(S-VAR) eee2( n) = 8106.898
Important: Regression coefficient, correlation coefficient, and
estimated value calculations can take considerable time when there
are a large number of data items.
16. Calculation Ranges, Number of
Digits, and Precision
Calculation Range and Precision
Calculation Range: ±1 × 10 –99 to 9.999999999 × 10 99 or 0
Number of Digits for Internal Calculation: 15 digits
Precision: In general, ±1 at the 10th digit for a single calculation.
Precision for exponential display is ±1 at the least significant digit.
Errors are cumulative in the case of consecutive calculations.
Function Calculation Input Ranges and Precision
Functions Input Range
sin x
cos x
DEG 0 Ϲ | x | Ͻ 9 × 10 9
RAD 0 Ϲ | x | Ͻ 157079632.7
GRA 0 Ϲ | x | Ͻ 1 × 10 10
tan x
DEG Same as sin x , except when | x | = (2 n –1) × 90.
RAD Same as sin x , except when | x | = (2 n –1) × π/2.
GRA Same as sin x , except when | x | = (2 n –1) ×
100.
sin –1 x
cos –1 x 0 Ϲ | x | Ϲ 1
tan –1 x 0 Ϲ | x | Ϲ 9.999999999 × 10 99
sinh x
cosh x 0 Ϲ | x | Ϲ 230.2585092
sinh –1 x 0 Ϲ | x | Ϲ 4.999999999 × 10 99
cosh –1 x 1 Ϲ x Ϲ 4.999999999 × 10 99
tanh x 0 Ϲ | x | Ϲ 9.999999999 × 10 99
tanh –1 x 0 Ϲ | x | Ϲ 9.999999999 × 10 –1
log x /ln x 0 Ͻ x Ϲ 9.999999999 × 10 99
10 x –9.999999999 × 10 99 Ϲ x Ϲ 99.99999999
e x –9.999999999 × 10 99 Ϲ x Ϲ 230.2585092
' x 0 Ϲ x Ͻ 1 × 10 100
x 2 | x | Ͻ 1 × 10 50
x –1 | x | Ͻ 1 × 10 100 ; x G 0
3 ' x | x | Ͻ 1 × 10 100
x ! 0 Ϲ x Ϲ 69 ( x is an integer)
n Pr 0 Ϲ n Ͻ 1 × 10 10 , 0 Ϲ r Ϲ n ( n , r are integers)
1 Ϲ { n !/( n – r )!} Ͻ 1 × 10 100
n Cr 0 Ϲ n Ͻ 1 × 10 10 , 0 Ϲ r Ϲ n ( n , r are integers)
1 Ϲ n !/ r ! Ͻ 1 × 10 100 or 1 Ϲ n !/( n – r )! Ͻ 1 × 10 100
Pol( x , y )
| x |, | y | Ϲ 9.999999999 × 10 99
x 2 + y 2 Ϲ 9.999999999 × 10 99
Rec( r , Ƨ) 0 Ϲ r Ϲ 9.999999999 × 10 99
Ƨ : Same as sin x
°’ ”
| a |, b , c Ͻ 1 × 10 100 ; 0 Ϲ b , c
The display seconds value is subject to an error of
±1 at the second decimal place.
| x | Ͻ 1 × 10 100
Decimal ↔ Sexagesimal Conversions
0°0´0˝ Ϲ | x | Ϲ 9999999°59´
x y
x Ͼ 0: –1 × 10 100 Ͻ y log x Ͻ 100
x = 0: y Ͼ 0
x Ͻ 0: y = n , 1
2 n +1 ( n is an integer)
However: –1 × 10 100 Ͻ y log | x | Ͻ 100
x ' y
y Ͼ 0: x G 0, –1 × 10 100 Ͻ 1/ x log y Ͻ 100
y = 0: x Ͼ 0
y Ͻ 0: x = 2 n +1, 1
n ( n G 0; n is an integer)
However: –1 × 10 100 Ͻ 1/ x log | y | Ͻ 100
a b / c
Total of integer, numerator, and denominator must
be 10 digits or less (including division marks).
RanInt#( a , b ) a Ͻ b ; | a |, | b | Ͻ 1 × 10 10 ; b – a Ͻ 1 × 10 10 ( a , b are
integers)
k
k
k
3 3
• Precision is basically the same as that described under “Calculation
Range and Precision”, above.
• Calculations that use any of the functions or settings shown below
require consecutive internal calculations to be performed, which can
cause accumulation of error that occurs with each calculation.
x y , x ' y , 3 ', x !, nPr, nCr; °, r , g (angle unit: radians); σ x , s x , regression
coefficient.
• Error is cumulative and tends to be large in the vicinity of a function’s
singular point and inflection point.
• Accumulation of errors tends to occur during statistical calculations
involving data in which there is a large number of decimal places
and there is little difference between data items. Input of statistical
data is limited to six decimal places.
17. Error Messages
The calculator will display an error message whenever an error occurs
for any reason during a calculation.
• Press
d or e to return to the calculation screen. The cursor will
be positioned at the location where the error occurred, ready for
input. Make the necessary corrections to the calculation and execute
it again. (Not included on the fx-82SX PLUS)
• Press A to return to the calculation screen. Note that this also
clears the calculation that contained the error.
Math ERROR
Cause: • The intermediate or final result of the calculation you
are performing exceeds the allowable calculation range. • Your
input exceeds the allowable input range. • The calculation you are
performing contains an illegal mathematical operation (such as
division by zero).
Action: • Check the input values and reduce the number of digits.
• When using independent memory or a variable as the argument of
a function, make sure that the memory or variable value is within the
allowable range for the function.
Stack ERROR
Cause: The calculation you are performing has caused the capacity
of the numeric stack or the command stack to be exceeded.
Action: • Simplify the calculation expression. • Try splitting the
calculation into two or more parts.
Syntax ERROR
Cause: There is a problem with the format of the calculation you
are performing.
Action: Make necessary corrections.
Arg ERROR
Cause: Improper use of an argument.
Action: Make necessary corrections.
18. Before Assuming Malfunction of the
Calculator...
Perform the following steps whenever an error occurs during a
calculation or when calculation results are not what you expected.
Note that you should make separate copies of important data before
performing these steps.
1. Check the calculation expression to make sure that it does not
contain any errors.
2. Make sure that you are using the correct mode for the type of
calculation you are trying to perform.
3. If the above steps do not correct your problem, press the O
key.
4. Initialize all modes and settings. See “Initializing Calculator
Settings”.
19. Replacing the Battery
Important: Removing the battery will cause all of the calculator’s
memory contents to be deleted.
1. Press 1A(OFF) to turn off the calculator.
• To ensure that you do not accidentally turn on power while
replacing the battery, slide the hard case onto the front of the
calculator (fx-350MS).
2. Remove the cover as shown in the illustration and replace the
battery, taking care that its plus (+) and minus (–) ends are facing
correctly.
Screw Screw Screw
Screw Screw
fx-82MS/82SX PLUS/
220 PLUS
fx-350MS fx-85MS/300MS
3. Replace the cover.
4. Initialize the calculator. See “3. Initializing the Calculator”.
• Do not skip the above step!
20. Specifications
Power Requirements:
fx-82MS/82SX PLUS/220 PLUS: AA-size battery R6P (SUM-3)
× 1
fx-350MS: Button battery LR44 (GPA76) × 1
fx-85MS/300MS: Built-in solar cell; button battery LR44 (GPA76)
× 1
Approximate Battery Life:
fx-82MS/82SX PLUS/220 PLUS: 17,000 hours (continuous display
of flashing cursor)
fx-350MS: 9,000 hours (continuous operation)
fx-85MS/300MS: 3 years (based on one hour of operation per day)
Power Consumption:
0.0001 W (fx-82MS/82SX PLUS/220 PLUS/350MS)
Operating Temperature: 0°C to 40°C (32°F to 104°F)
Dimensions (H × W × D)/ Approximate Weight (including the battery)
fx-82MS 18.6 Ч 85 Ч 156 mm
3 / 4 Љ × 3 3 / 8 Љ × 6 1 / 8 Љ
115 g
(4.1 oz)
fx-82SX PLUS
fx-220 PLUS 19.5 Ч 78 Ч 155 mm
3 / 4 Љ × 3 1 / 8 Љ × 6 1 / 8 Љ
115 g
(4.1 oz)
fx-85MS
fx-300MS
fx-350MS 12.2 Ч 85 Ч 155 mm
1 / 2 Љ × 3 3 / 8 Љ × 6 1 / 8 Љ
100 g
(3.5 oz)
RJA521989-001V01