Calculator Basics:

    The TI-25X is a solar powered calculator.  This means you will never have to put batteries in it and it will always be ready for you to use.  Also, there's no OFF key.  Power shuts off when the case/cover is replaced and the light to the solar cells is cut off or after a short period of non-use.

    Before a calculation is done, it is a good practice to press the CE/C key a couple of times.  CE stands for Clear Entry and C stands for Clear.  Doing so will insure the calculator does not have any values or pending operations in memory that may be merged with your input.

    The TI-25X is not a rugged device.  As you can see, the whole case is a bit flexible.  Perhaps the weakest part is its display which may become defective by not displaying every character in entirety.  This can cause a result to be misread.  Take care of the calculator.  Don't drop it or pile books on it.  I purchased two of them for $5.00 each and both displays went bad as I described, but at least one lasted two years so for $5.00 I'm not complaining.

    The numeric keys, including [.] and [+/-], are arranged in a rectangular array in the center bottom of the keypad.

    Most keys, but not all keys, have two purposes.  The first or primary purpose is printed on the key in white print.  To access this just press the key.  The second purpose is printed over the key in orange print and is accessed by pressing the orange [2nd] key in the upper left corner of the key pad and then pressing the key with the desired second purpose.  When the [2nd] key is pressed the display will show 2nd in the upper left corner of the display

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Other Basic Scientific Calculators:

    The instructions that follow are generally applicable to all basic scientific calculators.  Differences occur only because different models arrange and label the keypad differently, but the basic operation is the same.  Some common differences are listed below.

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Basic Arithmetic Operations:

    Arithmetic operations are addition, subtraction, multiplication and division.  Each requires two values.  The basic sequence is to enter value 1, then the operation, then value 2, then press the equal key to see the result. The four arithmetic operation keys and the equal key are the black keys on the right of the keypad with the equal key in the bottom right corner of the keypad.

Example: Add 5.6 and 7.4
     How It's Done: key in the following:   5.6 [+] 7.4 [=]
     Result: If you performed this calculation correctly, the display should show 13.
Example: Add 9.4 to the product of 6.3 and 2.6
     How It's Done: key in the following:      6.3 [x] 2.6 [+] 9.4 [=]
or                                 9.4 [+] 6.3 [x] 2.6 [=]
     Result: The display should show 25.78
     Explanation:  The calculator will do multiplication and division operations before addition and subtraction when they are entered in sequence.  It is important to understand this because it does have an impact on the result of a calculation.  If you add 5 to 3 and multiply the result by 2 you may expect the answer to be 16; (5+3=8, 8x2=16).  However if you use the calculator and type in 5 [+] 3 [x] 2 [=] you'll get 11 for the result.  The calculator will first multiply 3 by 2 and then add 5 to the result (3x2=6, 6+5=11.)  What's going on is calculators do multiplication and division before addition and subtraction operations.  Addition and subtraction operations that have not yet been evaluated become pending operations that will subsequently operate on the result of the multiplication or division operations that precede them.  If you were to type 5 [+] 3 [=] [x] 2, the [=] key executes the addition before multiplication is selected so the result becomes 16 as expected.  For each of the following calculations, see if you can predict what the calculator will display:

2 + 3 x 4 =
8 x 2 + 3 x 3 =
8 - 2 2 =
8 - 2 = 2 =

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Arithmetic Operations Using Parentheses:

    In the center of the keypad you'll find the [(] and [)] keys.  These are the left and right parentheses keys also known as open and closed parentheses.  They are used to surround, enclose, or bracket a portion of a larger calculation so that the portion enclosed by the parentheses is fully evaluated before it is used by the remainder of the calculation.

Example: Divide the quantity  5 + 4 by the quantity 4 - 1.
     How It's Done: key in the following:   [(]  5  [+]  4 [)]  []  [(]  4  [-]  1  [)]  [=]
     Results: the display should show   3.
     Explanation: You're entering ( 5 + 4 ) ( 4 - 1 )  =.  The first set of parentheses forces the operation 5 + 4 to be evaluated and replaced by the result 9.  The second set of parentheses forces the operation 4 - 1 to be evaluated and replaced by the result 3. When the [=] key is pressed the calculator evaluates 9 3 displaying the result 3.  Notice, when using parentheses and the [)] key is pressed the display immediately shows the result of the calculation enclosed by parentheses.

    It's recommended that long calculations be written out on paper before they are keyed into the calculator.  This will help you see the entire calculation, evaluate how the calculator will handle it in terms of which operations will be performed first.  As you key in the calculation, following what you wrote, you will likely make fewer mistakes and have better results.

    If you are ever in doubt about the order in which a calculation will be done, you can always place parentheses around portions of the calculation to make it calculate the way you desire.

    See how the following calculations come out differently when parentheses are used.  Try to understand why based on the explanation above.

2 + 3 x 4 = 14
8 x 2 + 3 x 3 = 15
8 - 2 2 = 7
( 2 + 3 ) x 4 = 20
8 x ( 2 + 3 ) x 3 = 120
( 8 - 2 ) 2 = 3

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Entering Values In Scientific Notation:

             The number 4,895,000,000 can be written in a compact form known as scientific notation using powers of 10.  First, the number is written as a single digit whole number with the remaining digits following the decimal point:  4.895.  Then the number is multiplied by the power of 10 that converts it to the original value. 4.895109.  This is scientific notation and most calculations involving physical data will use values in this form.

    Numbers in scientific notation that have positive powers of 10 are large numbers.  If they have negative powers of 10, they are small numbers.  For example 3.2610-5 is 0.0000326. 

    To enter 4,895,000,000 in scientific notation type in 4.895.  To enter the power of 10 press the key [EE]; it's the second key in the third row.  Then enter the power of 10, in this case 9.  The entire sequence is 4.895 [EE] 9.  You'll notice the power of 10 (called an exponent) is displayed as 09 in the right of the display.

    To enter 0.000326 the key sequence is 3.26 [EE] 5 [+/-].  Since the power of 10 in this case is negative the [+/-] key had to be used to turn the 5 into -5.  The [+/-] key is called the "change sign" key and is used when entering negative values. Remember it is pressed AFTER the value is entered.

    Now let's try -0.00071, which is -7.110-4.  Key in 7.1 [+/-] [EE] 4 [+/-].  That's a lot of work but if you learn to make sense of it, it will become almost second nature to enter it correctly.  Here the entire number is negative.  The first [+/-] makes the number itself negative. [EE] is then pressed to enter an exponent and the second [+/-] makes the exponent negative.

Example: Enter 76,200,000 in scientific notation
     How It's Done: 7.62 [EE] 7
     Result: The display should show   7.62  07
Example: Enter -0.000067 in scientific notation
     How It's Done: 6.7 [+/-] [EE] 5 [+/-]
     Result: The Display should show    -6.7-05
Example: Do the following calculation in scientific notation:
8,200,000 728,000
     How It's Done: The key sequence is:
8.2 [EE] 6 [] 7.28 [EE] 5 [=]
     Result: The display should show    5.9696  12

    If the display shows a value in scientific notation and you want to show it in common form (not in scientific notation), press [2nd] [EE].  If the value can be displayed without scientific notation, the calculator will do so.  Otherwise the display will stay in scientific notation.

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The Reciprocal:    

    The [1/x] key in the top row performs the reciprocal operation on the value currently in the calculator display.  If the display shows 4  when [1/x] is pressed, the calculator will compute the reciprocal of 4 and display 0.25.  Since this acts only on the value in the display, it will not effect any pending operations.  On the calculator keys wherever you see an x that key will act only on the value in the display.

Example: Perform the operation 1/5 + 1/4 using reciprocals
     How It's Done: The key sequence is 5 [1/x] [+] 4 [1/x] [=]
     Result: The display should show   0.45

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The Square Root:

    The square root, , is a common operation but causes students a lot of grief.  Remember, when the square root key is pressed, the operation will act on the value in the display.  The result may not be what you expect if a previous operation is pending.         

    When a number is multiplied by itself we say it has been squared.  The square root is the opposite operation, it un-squares a number.  When 9 is un-squared the result is 3.  When 16 is un-squared the result is 4.  Thus the square root of 25 is 5 because 55= 25.

    To access the square root you must press the [2nd] key first followed by [].  You'll find [] behind the [x2].  These two operations are opposites of each other (technically called inverse operations) and it is common to place opposite operations on keys one-behind-the-other.

    To understand squares, [x2], and square roots, [], try the following:  enter the number 82.6.  Press [2nd] [] and the display shows 9.0884542.  With this in the display press [x2] and the display becomes 82.6.  This works the other way too.  Enter 5.7 and press [x2], the display becomes 32.49.  Now press [2nd] [] and the display becomes 5.7 again.

    Often the square root operation will be performed on some previously calculated result.  Here's where trouble begins.  Students tend to forget that the calculator doesn't know ahead of time what you intend to do.  So it follows a set of rules without any variation.  If you intend the square root to act on a result, that result must be completed and in the display before the square root is selected.  This is most easily done by placing the previous calculation in parentheses or by pressing [=] before the square root operation is done.   For example take the square root of 7 plus 9.    If you do this the wrong way and enter 7 [+] 9 [2nd] [] [=] the result will be 10 and is of course wrong. You see, only the 9 was in the display when the square root was executed so it returned 3 which was then added to the 7.  You want the 7 and the 9 to be added first and the square root to be taken of their sum.  Here's the correct way to do this:  [(] 7 [+] 9 [)] [2nd] [].  When the parentheses are closed the display shows 16, the sum of 7 and 9. Then the square root will operate on 16 giving the correct result of 4.  An alternate way of entering this calculation is  7 [+] 9 [=] [2nd] [].

Example: Take the square root of  32 + 42
     How It's Done: 3 [x2] [+] 4 [x2] [=] [2nd] []
or   [(] 3 [x2] [+] 4 [x2] [)] [2nd] []
     Result: The display should show 5.

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Angular Modes:

    There are three angular modes available; degree, radian, and gradian.  The trigonometric functions operate on a value representing an angular quantity.  The calculator must be in the same angular mode as the value being operated on. For example, suppose you want the value of the sine (sin) of 2.0 radians.  The sine of  2.0 radians is 0.9092974.  But if the calculator is in degree mode, the display will show 0.0348936.  This is the wrong answer.

    To change angular mode press the [DRG] key in the top row of the keypad.  As you repeatedly press this key you will see tiny letters in the lower left corner of the display cycle through D, R, and none.  When D is shown the calculator is in degree mode and all trig functions will be computed assuming all angular values are measured in degrees.  When R is shown all angles are assumed to be in radians.  When the display is clear all angles are assumed to be in gradians.

    Make it a habit to check the angle mode display before you do any trigonometric calculations.

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Using Trig Functions:

    If you haven't read the section on angular modes, it's best to do so now.

    The basic trigonometric or trig functions you need are sine, cosine, and tangent.  These are designated by the keys [sin], [cos], and [tan].  Like other operations they will operate only on the value in the display and assume it is measured in units consistent with the current angular mode of the calculator.

    One additional function you will need is the inverse tangent.  You'll find it above the [tan] key so you'll have to press [2nd] [tan] to access it.

    A note of caution: when doing calculations involving trig functions do not press keys faster than the calculator can keep up.  It takes a full second for the calculator to return a value from a trig function and you have to wait for it to finish before you press any other keys.

Example: Evaluate  sin2 (30o) + cos2 (30o)
     How It's Done: First ensure the calculator is in degree mode.
Type in 30 [sin] [x2] [+] 30 [cos] [x2] [=]
     Result: The display should show   1.
Example: Evaluate 5 sin (3.0 rad) / sin (4.0 rad)
     How It's Done: First ensure the calculator is in  radian mode.
Type in 5 [] 3 [sin] [] 4 [sin] [=]
     Result: The display should show    -0.9323437
Example: Evaluate  tan-1 (4/3)  in degree mode
     How It's Done: First ensure the calculator is in degree mode.
4 [] 3 [=] [2nd] [tan]
or    [(] 4 [] 3 [)] [2nd] [tan]
     Result: The display should show    53.130102
(This value will be in degrees)

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Evaluating An Algebraic Expression:

    Just about every calculation you'll need to do for a science course will involve evaluating an equation or formula.  Follow these steps.

  1. On paper, solve the equation for the quantity you need to find a value for.

  2. List all the values for all the other quantities in the equation.  Make sure all the values are expressed in the same system of units.  If any aren't, you will have to convert them before they can be used.

  3. Write out how the calculation should be typed in.

  4. Type in the values and operations as expressed in the equation.  You may have to use parentheses to ensure the calculation is done correctly.  Remember you do not have to enter the physical units associated with the values.  In fact there's no way to do so, so don't worry about it.

  5. The result will be a value whose units are in the same system as the data used to calculate it.

Example: K = mv2/2  where 
K = 500 J,    energy in joules
m = 5 kg,    mass in kilograms
solve for v,    speed in meters per second
    How It's Done: 1.  Solve equation for v...       v = Square Root (2K/m)
2.  K = 500 J,  m = 5 kg
3.  ( 2 500 5 )
4.  [(] 2 [] 500 [] [)] [2nd] []
    Result: The display should show    14.142136
This value represents a speed in m/s.
Example: F = G m1m2/r2   where
G = 6.67 10-11 Nm2/kg2,   constant
m1 = 4.5 106 kg,   mass in kilograms
m2 = 9.2 105 kg,   mass in kilograms
r = 10.2 m ,   distance in meters
Solve for F,  force of gravity in newtons
    How It's Done: 1.  The equations is already solved for the desired variable.
2.  The data as give is ready to use.
3.  6.67 10-11 4.5 106 9.2 105 / 10.22
4.  6.67 [EE] 11 [+/-] [] 4.5 [EE] 6 [] 9.2 [EE] 5 [] 10.2 [x2] [=]
    Result: The display should show    2.6542  00
Press [2nd] [EE] to leave scientific notation mode and the display becomes  2.6541522.
This value represents a force in N (newtons).

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