Casio Fx82tl Manual

							16  Mastering the Calculator using the Casio fx-82TL
5. Fractions
How do you add  and ? Normally you would have to find a common denominator of 
252.
So:
Or you can use your calculator to add fractions. Find the
 key
On the  key the ‘a’ represents the whole part of a mixed 
number and the ‘’ represents the fraction part of a mixed number.
When the number you are typing is a proper or improper fraction the ‘a’ is zero and there is no 
need to type a value for it.
1
12 ------4
63 ------
1
1
2------4
63 ------ +
21
252 ---------
16
252 --------- +
37
252---------==
ab
c ---
fraction key
ab
c ---
b
c --- 
						

							Mastering the Calculator using the Casio fx-82TL  17
The key strokes required for the calculation  are:
and the display will show 37 ⎦ 252 which is read as 
Example
Find 
Using the calculator the key strokes are:
and the display will show 8 ⎦ 71 ⎦ 72 which is read as 
Note if you now press  the display will read . So this key turns a mixed 
fraction into an improper fraction.
If you press the  key a second time the decimal equivalent is displayed,  
i.e. 8.9861111
Example
Find 
(This means the square root of 25 cubed).
The calculator strokes are:
The display should read 125.
1
1
2------4
63------+
37
2
52 ---------
819 ---
63
72------+
87172------
647
72 ---------
25
3
2 --- 
						

							18  Mastering the Calculator using the Casio fx-82TL
6. Using the x-1 key
This is a very useful key in more complex calculations. Find the  key on your calculator.
(x-1 really means ; e.g. )
Example
Look at this example
 is the same as  or 
You can input this in your calculator by pressing
The answer should be 0.571428571. This would be the same as if you just typed 4 ÷ 7
1
x ---7-11
7 ---=
4
7 ---41
7 ---×1
7 --
-4× 
						

							Mastering the Calculator using the Casio fx-82TL  19
Take another example
Ty p e :
The answer should be 0.051948051
7. Scientific notation
Sometimes you may have numbers expressed in scientific notation, i.e., 7.24 × 103 instead of 
7240. When a number is multiplied by 10
3, you move the decimal point three places to the 
right. You can do this on the calculator by using the 
 key.
Press , the display should read 7240.
4
83+ ()7×-------------------------- 
						

							20  Mastering the Calculator using the Casio fx-82TL
If you want to multiply two numbers e.g. 8.34 × 10–2 × 4.28 × 105. Press
and the display will read 35695.2
If you press  the display will read 3.56952000004 which 
means 3.56952 × 104. Pressing the mode three times gives you the display
The  puts the calculator in scientific notation. The calculator then asks SCI 0~9? This 
gives the option of how many digits are displayed. The  gives you 10 digits. Notice a 
small sci appears in the screen.
If you press  the display will read 3.57004 which means 3.570 
× 104. This rounds the number to 4 digits. 
Practise using the  and  keys on your calculator  
						

							Mastering the Calculator using the Casio fx-82TL  21
8. Factorial x!
Look at your calculator and find the key with the symbol x! on it. You will come across this 
symbol when doing the Binomial Distribution. This is called the factorial key.
Use it to find the 3! and 5!. Press 
3! means 3 × 2 × 1  and 5! = 5 × 4 × 3 × 2 × 1
3! = 6 5! = 120
How many ways would you guess that we could arrange ten people?
That is, how large would you estimate 10! to be? Use your calculator to find 10!
You should get 3 628 800.
10! = 10 × 9 × 8 × ... × 3 × 2 × 1
(Thank goodness this can be done on the calculator.)
Use the shift key 
to activate x! 
						

							22  Mastering the Calculator using the Casio fx-82TL
9. Using memory
To calculate the following it may be useful to use the memory key for each term:
Example:
To make sure memory is clear, first press
or
and make sure you are in normal calculation mode [may need to press mode 1].
A small m appears in the display when you put something in memory.
916– ()2
16----------------------23 16– ()
2
16 -------------------------17 16– ()
2
16 -------------------------++
these keys are for memory
key to activate M- or M)(Use the 
						

							Mastering the Calculator using the Casio fx-82TL  23
To do the calculation above, press the following keys
- this puts the first term (3.0625) into the memory
then press
- this adds the second term (3.0625) into memory
then press
- this adds the third term 0.0625 to memory.
To find the answer press 
The answer should be 6.1875.
Example 2
calculate the following:
first  to clear the memory then
press the following keys:
your answer should be 11.39917438
(There are other memory keys in your calculator – the A to F keys, accessed by using SHIFT 
STO and RCL – try them yourselves.)
18
17----------17
17 ----------
12
17----------++ 
						

							24  Mastering the Calculator using the Casio fx-82TL
10. Statistics
10.1 Mean and standard deviation – single data
The formula for the mean is 
The formulas for the sample standard deviation are
(Theoretical formula)
(Working formula)
Your calculator will calculate the mean and standard deviation for you (the population 
standard deviation 
 or the sample standard deviation  – in data calculations you will 
usually use the sample standard deviation.)
The differentiation between σ and s varies with different calculators. On the Casio fx-82TL, σ 
is denoted by σ
n and s is denoted by . The positions of these keys is shown on the 
diagram below.
xΣx
n------=
sΣxix – ()2
n1 – ------------------------=
sΣxi2Σxi()2n⁄ –
n1 – ---------------------------------------=
σnn-1
σn-1
input data key
(key for population 
standard deviation)
(key for mean)(key for sample 
standard deviation)
A, B, C, D, E, F
M, X and Y
used with  
						

							Mastering the Calculator using the Casio fx-82TL  25
To find the mean and standard deviation,
firstly you must access the statistics mode of the calculator by using the keys  followed 
by  SD will appear in the centre of the screen.
Note that once you are in the statistics mode, the keys shown within the blue lines and pink 
letters are active. There are 14 blue keys and 9 pink keys on the Casio fx-82TL. Make sure you 
can locate them. Before starting any computations always clear the statistic’s memories using 
Mcl. Press 
I will use the data set A (–5, 2, 3, 4, 11) to demonstrate the use of the calculator. Note that I 
have shown the use of the 
 key where necessary.
Step 1: Input the observations.
Use the  key to input data (no need to press ).
Step 2: Check that the correct number of observations have been inputted. [Note this is shown 
on the inside cover of your calculator under statistical data.]
Press 
The display should read 5.
Step 3: Display the mean
 and the display should read 3
Step 4: Display the standard deviation (assume the data set is a sample)
 and the display should read 5.7008771
__________________________________________________________________________