Using Calculator fx-991MS

Lecture - 11^th August 2007

If one does not understand concept or formula then one need to form strategy to get answers

Eg: ⁿC₆ : ^n-3C₃ = 33/4 find N

_if you don’t remember formula or answer, you can put any value to n eg: n=10

then

¹⁰C₆ : ⁷C₃ will not be equal to 8.25 (33/4)

then try higher number say

¹¹C₆ : ⁸C₃ will be equal to 8.25 (33/4)

Please note above strategy is based on wild guess and is time consuming and should be used only when there is no other option

Cramer’s method of solving equation (17^th August 2007)

x + y +z = 6

x – y + z = 2

2x –y +3z = 9

Press Mode Mode Mode 1 3 (this will select Eqn 3)

a1? Prompt will be displayed

enter 1 = 1 = 1 = 6 =1 = -1 = 1 = 2 = 2 = -1 = 3 = 9 =

you will get values x = 1, press =, you will get y = 2, press =, you will get z = 2

press Shift Mode 3 = = (all values, memory and mode will be cleared)

Try question no. 80 from QM Paper I of July 2007

Karl Pearson’s co-efficient of co-relation (24^th August 2007)

Co-efficient of co-relation = r

If r = +1 (positive co-relation)

If r = -1 (negative co-relation)

If r = 0 (no co-relation)

If r = 0 to 0.5 (lower co-relation)

If r = 0.5 to 0.8 (moderate co-relation)

If r = 0.8 to 1 (higher co-relation)

Eg:

Sales (x) Profit (y)

50 13

57 15

59 19

64 24

72 29

94 32

96 46

press Mode Mode 2 1 (this will select Reg Lin)

enter values 50,13 M+ then 57,15M+ same way enter upto 96,46M+

shift 2 -> -> 3 = (this will select r)

-> means press right of Copy/Replay button (biggest button on calculator)

you will get answer 0.9322

Least Square Method of Regression (24^th August 2007)

Sales (x) Profit (y)

1 10

2 22

3 35

4 44

5 59

Mode Mode 2 1 (this will select Reg Lin)

Always remember to enter independent variable first and then dependent variable

enter values 1,10M+ then 2,22M+ same way enter upto 5,59M+

press = shift 2 -> -> 1 = (this will give you value of variable A which is x for us)

press = shift 2 -> -> 2 = (this will give you value of variable B which is y for us)

Matrices & determinant of Matrices

To calculate Determinant of

1 1 1

1 -1 1

2 -1 3

Mode Mode Mode 2 (this will select Mat)

Shift 4 1 1 (this will select Dim A)

m? will be displayed (it is asking for rows x columns)

enter 3 = 3 (that is for 3 rows x 3 columns)

MatA11? will be displayed

Now enter all values

1 = 1 = 1 = 1 = -1 = 1 = 2 = -1 = 3=

Press AC

Press Shift 4 -> 1 (this will select Det)

Press Shift 4 3 1 = (this will select MatA)

You will get answer

Same way you can perform addition, subtraction, multiplication, division of matrices

Try question no. 79 from QM Paper I of July 2007

Here once you enter values of all 3 matrices,

(shift 4 3 1 x shift 4 3 2) x shift 4 3 3

this way we are multiplying (MatA x MatB)MatC as required by question

Inverse of Matrices

this way we can find inverse of matrices. With the same data as above, we can

Press Shift 4 3 1 = (this will select MatA) and press x^-1 (function below mode key) =

Det of Mat A, sum of the products of the element of any row or column with the co-factor of any other row or column element is always equal to zero

Standard Deviation

Example 1:

X

1

2

3

4

5

Mode Mode 1 (this will select SD)

1 M+ 2M+ 3M+ 4M+ 5M+

Press AC

Shift 2 2 = (this will give you std dev)

It will give you answer of 1.4142 which is standard deviation

Once you press Shift 2

You will find option 1 2 3

Option 1 is mean, Option 2 is Population standard deviation, Option 3 is Sample Standard deviation. Use them as required by question. Read question carefully to find what is asked?

Example 2

Try question no. 72 from QM Paper I of July 2007

Class interval (x) and number of observations (f) are given

Class f

10-20 5

20-30 15

30-40 17

40-50 25

50-60 18

60-70 10

70-80 6

80-90 4

We will find Mid-point (x) and multiply that by frequency (f), you will get fx

Total of fx divide by f will give us mean

Here 2 set of data namely x & f are given hence we need to follow different method of calculating Std Dev

Mode Mode 2 1 (Reg Lin)

Here you can enter all values of Mid point (x) & frequency (f)

Eg: 15,5….till 85,4

Example After entering data

Shift 1 -> 3 (This will give you total of fx (4600))

Shift 1 -> 2 (This will give you total of f (100))

Now 4600/100 will give you mean of 46

Once mean is available with you, you can find x-mean, this result, lets call it a

Now you are required to find square of a, for that you can use x² function on calculator. This has to be done on paper (can’t perform on calculator to the best of my knowledge)

Now we have square of a data with us, this we will replace with x

Use top arrow of Copy/Replay button several times till you find x1 = 15

Now replace this with new data (a)

So

Square of x-mean (a)

961

441

121

1

81

361

841

1521

once this entry is done, now press AC

Shift 1 -> 3 (This will give you total of af (29700))

Now finding Std Dev is easy, divide 29700/100 and take square root of that

Answer = 17.23

This method may look lengthy, however it will take lesser time compare to manual calculations and it is reliable since most of operations are automated. Once you practice it couple of times, you will be able to do it faster.

Please note Standard Deviation of set of data is expressed in same unit as the observations in the data set.

Please note all the mathematical and positional averages are equal if there is no dispersion in a data set.

Number system (29^th September 2007)

Press Mode Mode 3 (this will select Base)

Press inverse key 3 times (this key is located below mode key)

You will find 4 options

d h b o

d = decimal = base number 10

h = hexadecimal = base number 2

b = binary = base number 8

o = octal = base number 16

Decimal to Binary

Select 1 option d (this will select decimal)

d will appear, type 25 and press shift log = (you should get answer 11001)

Binary to Decimal

Select 3 option b(this will select binary)

b will appear, type 11001 and press shift x² = (you should get answer 25)

Decimal to Octal

Select 1 option d (this will select decimal)

d will appear, type 85 and press shift ln = (you should get answer 125)

Octal to Decimal

Select 4 option o (this will select octal)

o will appear, type 125 and press shift x² = (you should get answer 85)

Binary addition

eg: 111001 + 11000

answer:

convert 11001 from bin to dec = 25

convert 11000 from bin to dec = 24

now sum of both numbers = 49

convert 49 from dec to bin

you should get answer 110001

eg: 111001 + 110011

answer:

convert 111001 from bin to dec = 57

convert 110011 from bin to dec = 51

now sum of both numbers = 108

convert 108 from dec to bin

you should get answer 1101100

If you find any errors in this file, please let me know so that I can correct it and distribute update file to all of you

If you find any new methods using this model of calculator, please share with us…. remember your invention is not worth it if you don’t share it.