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Brief User Guide for TI-82 Calculators

Contents:  How to do graphing, intersections of graphs, finding roots, derivative, matrices, and much more.


To facilitate lookup, the instructions are divided into the following categories:

         I.   Basic Math – Capabilities, Math operations, how to change settings, and how to obtain certain symbols.
        II.  Special Expressions – Absolute Value, Greatest Integer, etc.
       III.  Graphing and Evaluating Functions – Graphing, finding roots, finding intersections of graphs,
            graphing inequalities, etc.
       IV.  Special Functions – Greatest Integer, Piecewise Functions, Trig Functions, Logic & Truth    
              Tables, Sequences, Recursion Formulas, arithmetic of lists,  etc.
         V.  Calculus – Finding the derivative at a certain point, finding the integral.
        VI.  Matrices – Determinant, Transpose, Row Operations, solving systems of equations, source for program for
               rref and ref.
        VII.  Transferring Programs and Data – Transferring data or programs from one calculator to
       VIII.  Problems with the calculator.
         IX.  Appendices - Instructions for using my programs REFRREF2 and INEQGRAF.

RELEASE DATE:  10/5/03         DATE LAST REVISED:  5/7/09
Printer friendly page here.

NOTE:  Copy limitations and printing hints are listed at the end of  this document.

 GENERAL:   All keys have at least two functions and some have three.  The default function for a key is the white
print on the key.  When 2nd is pressed, the key function is as indicated in blue print (gray on some later models) on
the panel immediately above the key.  When ALPHA is pressed, the function is the white label immediately above
and, in most cases, near the right end of the key. 

    General Capabilities:
Students should be aware that the TI-82, TI-83 Plus, and TI-84 will not manipulate variables.   That is,
    they will not simplify expressions, factor expression such as quadratic equations, and they will not do multiplications of variables
    such as in the FOIL method.  Furthermore, the TI-82
will not  do the row-echelon or reduced row-echelon method of solving a system
    of equations without a separate program.
The TI-82 will generally evaluate expressions using a particular value for an expression,
    it will find roots of equations, intersections of graphs, do arithmetic on matrices, and many other operations which are listed in
    the index above.

 1.  Turning the calculator ON and OFF.
        a)  To turn on: Press the ON key.
         b)  To turn off:  Press 2nd; then OFF (the second function for the ON key.)

 2.  Adjusting the contrast of the screen.
         a) To make the screen display darker: Press the 2nd key; then hold down the UP arrow     
             key until the contrast is satisfactory.
         b) To make the screen display lighter: Press the 2nd key;
then hold down the DOWN arrow     
             key until the contrast is satisfactory.

3. Clearing the Calculator Screen.
         a) To clear the calculator screen: Press the CLEAR key.
         b)  Note that CLEAR may also take you to another screen if you are using one of
              the screens that does not permit data entry.

4.  To move to another screen:
         a)  Press 2nd, QUIT.
         b)  You can also use CLEAR if you are not using a screen such as Y=, List, or                      
              PRGM where entries can be made.

5. Correcting errors or changing characters.   
         a) To replace a character at the cursor position, just press the new
         b) To insert a character in the position of the cursor, press  2nd, press
             the INS key, and then press the key for the desired character.
         c) To delete a character in the position of the cursor, press the
DEL key.

 6. Changing the MODE:
      (Use the MODE for such things as changing from degrees to radians, displaying numbers as powers of ten,
      using split screen, and other similar things.)
         a) Press the MODE key.
         b) Use the arrow keys to move the cursor to the desired item.
         c) Press ENTER to highlight the selected item.
         d) Press CLEAR or 2nd, QUIT to return to the home screen,

 7. Performing numerical calculations:
       a) On the graphing calculator screen, the multiplication symbol will appear    
       as * and the division symbol will appear as /.
      b) Parentheses can be used to denote multiplication or as grouping symbols to  
         clarify the order of operations.
       c) To enter an exponent use the ^ key for any exponent.  You can also use the x2
           to raise a number to the second power.
       d) Use the (-) key for negative numbers and the - key for subtraction.

 8. Raising a number to a power:
      a) Enter the number.
      b) Press the ^ key
      c) Enter the number for the power.  Enclose fractional exponents in parentheses.
      d) Press ENTER.
      e) For an exponent of 2 only, you can use the x2 key after entering the
         number that you want to raise to the second power.
      f) Alternate method for raising to the third power only:  Enter your number,
         press MATH; then 3; then ENTER. (Note that using ^ is more efficient.)

 9. Finding the root of a number:
For square root only, press 2nd, the square root key, enter the number whose square root you
     want and press ENTER.  For other roots, do the following:
      a) Enter the number for the root index.
      b) Press the MATH key.
      c) Press 5 to paste the unspecified root symbol to the screen.   
      d) Enter the number you want to find the root of.
      e)  Press ENTER.
      f)  As an alternate method for cube root only, you can also choose to press 
           MATH, enter 4 to select item 4, and enter your number. Finally, press ENTER.

 10.  Operations with fractions:
         a)  Use the divide symbol between the numerator and denominator. Ex: ¼ is 
              entered as 1÷4.
         b)  Use the correct operator symbol (divide, multiply, add, subtract) between
         c)  Pressing ENTER will give you the answer in decimal format.  To get the answer
             as a fraction, skip step c) and continue as below.
         d)  Press MATH to select Frac; then ENTER.  Press ENTER again to display the answer.
               NOTE:  You can convert decimals to fractions using step d), but the decimal
              must have 12 decimal places.  Example:  To convert the decimal equivalent of
             1/3 to a fraction, you must enter this number, .333333333333.  Otherwise the
             calculator will just return the decimal you entered.


  1. To enter the symbols, =, , >, <, , or :
         a) Press the 2nd ; then the TEST key.
         b) Enter the item number for the desired symbol.

  2. To find the absolute value of a number:
       a)   Press the, 2nd, ABS (blue print above the x-1 key).
       b)  Enter your number.
       c)  Press ENTER.

  3. Finding the greatest integer function of a number.
         a) Press the MATH key.
         b) Use right arrow to move the highlight to NUM.
         c) Press 4 to select lnt.
          d) Enter your number.
          e) Press ENTER.


  1. Graphing a function:  (Note that all equations must be in the Y= form before entry.)
         a) Press the Y= key.
         b) Enter the function(s) using the [X,T,Θ] key to enter the variable X.
         c) Press GRAPH to graph the function.  (If you don’t see your graph, press
            TRACE and use the arrows to find the maximum or minimum value of your 
            function.  Press ENTER.)
         d) To leave the screen without graphing: press 2nd, QUIT.
         e) Press CLEAR while the cursor is on the same line as the function to erase the
         f)  To deselect a function, move the cursor to the equal sign and press ENTER.

  2.  To obtain the standard size viewing window:
           a) Press the ZOOM key.
           b) Press 6 to execute Z Standard.

  3.   To change the viewing window to a custom size:
           a) Press the Window key.
           b) Use the arrow keys to move the cursor to the value to be changed.
           c) Enter the new value.
           d) Press Graph to see the new graph, or press, 2nd, QUIT to return to the calculations 
           e) ZSquare keeps the y-scale the same and adjusts the x-scale so that one unit 
              on the x-axis equals one unit on the y-axis.
           f)  ZDecimal makes each movement of the cursor equivalent to one-tenth of a
           g) ZInteger makes each movement of the cursor equivalent to one unit.

    4.  Evaluating a function without going to the Graph screen: (Note that the function must be entered
         in the Y= screen.)
         a) Press 2nd, Y-VARS.
         b) Press ENTER.
         c) Select the name of a function, e.g., Y1, and press ENTER.
         d) Enter an x-value such as YI (3) or a list of x-values in the format Y1 ({2,3,4,5}).  (In the
             last format, make sure the interior grouping symbols are braces rather than
         e) Press ENTER.

   5.  To change or erase a function:
         a) Press the Y= key.
         b) Use the arrow keys to move the cursor to the desired location and make
             changes by inserting, deleting, or changing the desired characters.
         c) To erase a function, with the cursor on the same line as the function, press the
             CLEAR key.

   6. To use the trace function:
         a) Press the TRACE key.
          b) Use the right and left arrow keys to move the cursor along the graph. The
              coordinates of the cursor location are shown.
         c) If more than one graph is on the screen, you can press the up or down arrows
            to jump between graphs.

  7.  Finding the maximum and minimum points.
         a) Enter the function and graph.
         b) Press 2nd; then the CALC key.
         c) Press 3 for minimum or 4 for maximum.
         d) Move the cursor to the left of the point and press ENTER.
         e) Move the cursor to the right of the point and press ENTER
         f) Press Enter again.
         g) The values for maxima or minima will appear at the bottom of the screen.

  8.  Finding the value of a function at a given value of x.
         a) Enter the function and the graph.
         b) Press 2nd; then the CALC key.
         c) Press 1 to select "1: value."
         d) Enter the x-value and press ENTER.

   9.  To zoom in using a box.
          a) Enter the function and graph.
          b) Press the ZOOM key.
          c) Press 1 to select ZBox.
          d) Move the cursor above and to the left of the location you want enlarged and
              press ENTER.
          e) Move the cursor below and to the right of the location you want enlarged and
              press ENTER.
          f) The box is then enlarged to fill the screen.

10.  Finding the intersection point of two graphs.
          a) Press "Y=" and enter two equations whose intersection you want to find.
          b) Press 2nd,  CALC.
          c) Press 5 to select Intersect.
          d) Using the left or right cursor, move the cursor near the point of intersection if it's not already
              there.  If it's on the intersection, you might want to move it away slightly.
          e) The prompt "First curve" should appear on the screen.
          f)  Press ENTER and the prompt "Second curve," will appear and the cursor will have moved to
              to the second curve.
         g)  The prompt "Guess,"  should now be displayed.  Move the cursor near the intersection and
              press ENTER.
          f) The values for the coordinates of the point of intersection will appear at the bottom of the screen.

 11.  Solving an equation in one variable. (Also know as finding the roots.)
          a) Press "Y=" and enter the equation you want to solve.
          b) Press 2nd, CALC.
          c) Press 2 to select root.
          d) Move the cursor to the left of the intercept and press ENTER.
          e) Move the cursor to the right of the intercept and press ENTER.
          f)  Move the cursor between the above two points and press ENTER again.
          g) The "x" and "y" coordinates of the root will appear at the bottom of the screen.

12.  Graphing inequalities:
       Graphing inequalities with the standard TI-82 is tedious.  Use my program, INEQGRAF.  The        
       instructions for using this program are in Appendix IA of this manual.


  1.  Changing from radian measure to the degree mode.
          a) Press the MODE key.
          b) Move the cursor to either Radian or Degree to match the units of your angle.
          c) Press ENTER.
          d) Press CLEAR or 2nd, QUIT to return to the calculator screen.

  2. Graphing piecewise functions or  functions on an interval.
          a) To graph a function on the interval x < a, enter the function in parentheses, followed by
             (x<a).  For example, to graph x² -2 on the interval x<1, enter this:  (x²-2)(x<1)
          b) To graph a function on the interval x > a, enter the function in parentheses, followed by (x>a).
          c) To graph a function of the interval a<x<b, enter the function in parentheses, followed by

   3.  Graphing trigonometric functions:
          a)  You must have the calculator set to radians to graph a trig function.  See the MODE section if
               you don't know how to do that.
          b)  Press "Y=" and then press the button for the function you want to graph.
          c)  Enter the argument of the function, e.g., X, and press GRAPH.

  4.  Using the LOGIC functions:
       NOTE:  You can use the logic functions such as "and", "or," "xor," or "not," to do things such as
                   Boolean algebra and truth tables.  Note that you must use "1" for true and "0" for false.  As
                   a simple example, suppose you wanted to do p ^ q.  (Unfortunately, the TI-82 will not get
                   data from a list and perform operations on it, so we'll have to work around that.)
          a)  Press STAT, ENTER and enter the proper combination of 1s and 0s in for p in the table under
b)  Enter the proper combination of 1s and 0s for q in L2.
          c)  Enter an equivalent number of 0s in L3 to dimension it, otherwise you will get a dimension error
          d)  Press 2nd, QUIT to go to the home screen. 
          e)  Press 1, STO, x:  (Make sure you have the colon.
           f)  Now enter L1(x) and L2(x), STO, L3(x) and press ENTER. The first row in the tables will be
               evaluated and stored in L3. The "and" statement is obtained by pressing 2nd, TEST, selecting
               LOGIC, and pressing number 1 for "and."
           g)  Press 2nd, ENTER and the expression 1
→x:L1(x) and L2(x) L3(x) will be redisplayed.
           h)  Change the expression "1
→x" to "2→x" and press ENTER.
            i)  Continue this until all entries in the lists have been evaluated.
                Obviously, you can also use the other logic operations in place of "and."  All of this is much
                 easier done with a program, but for those of you not into programming, this will work.

  5.  Finding terms of sequences.
           a)  Press 2nd, LIST, 5 to paste Seq( to the home screen.
           b)  Enter the sequence information in the following format. 
                    Seq(formula, variable, beginning, end, step). 
                    Example:  Find the first five terms of : an = 3n +4. 
                       1)  Convert the variables in the formula  to ‘x’; then enter: Seq(3x+4, x,1, 5, 1).  Press ENTER to
                            get the answers.
            c)  If you want the answer in fractions rather than decimals do this:
                   1)  After  you’ve entered the information for the sequence, press MATH, ENTER.  That will  
                         paste ►Frac to the end of the sequence information. 
                   2) Press ENTER to get the answer in fractions.

  6.  Recursion formula:        
         Let’s take this recursion formula:  an = 3an-1 +2, when a1 = 5.
           a)  From the home screen, Press 5; then ENTER to place the value for
a1 to the variable Ans.
           b)  Enter the formula as follows:  Press 3, 2nd, Ans, +, 2.
           c)  You will now get a new term each time you press ENTER.

7.  Arithmetic of Lists:
Arithmetic of lists, multiplication, squaring, addition, subtraction, etc., can always be done from the
      home screen, but sometimes it's much easier to do it from the lists.  Let's take a look at how to multiply
      the corresponding elements of list L1 times those in list L2 and store the data in L3.
      a)  Press STAT, ENTER to go to the list tables.
      b)  Enter the data in L1 and L2.
      c)  Place the cursor on the title, L3, and press CLEAR, ENTER to clear the list if necessary.
     d)  Place the cursor on the title, L3, and press 2nd, L1, x (the multiply symbol), 2nd, L3. You should have
          L1*L2 opposite L3= at the bottom of the screen.
     e)  Press ENTER and the products of corresponding elements will be stored in L3.


  1.   Finding the numerical derivative from a function:
(Note that the function must be entered on the Y= screen before using this method. Also set the
         Window to ZDecimal before using this method by pressing ZOOM, 4.)
          a) Press the MATH key.
          b) Press 8 to select nDeriv(.
          c)  Press 2nd, Y-VARS, ENTER; select the variable you want and press ENTER.
          d)  Enter the name of the independent variable, probably X. 
          e)  Enter the value of the point where you want the derivative evaluated. For example if you want
               the derivative for Y1 evaluated at 3, you would have this: nDeriv(Y1, x,3). 
           f)  Press ENTER and the value will be displayed.

  2.  Determining the value of the derivative from points on a graph.
          a) Enter the function and graph.
          b) Press 2nd, CALC.
          c) Press 6 to choose dy/dx.
          d) Move the cursor to the desired point and press ENTER. The value of the
              numerical derivative at the point you selected will appear at the bottom of the screen.

  3.  Drawing a tangent line at a point:
          a) Enter the function and graph.
          b) Press 2nd, DRAW.
          c)  Press 5 to select Tangent(.
          d)  Move the cursor to the point of tangency desired and press ENTER.
          e)    To clear the tangent line, press 2nd, DRAW and then  ENTER.

  4.  Calculating the value of a definite integral:
         a) Press the MATH key.
          b) Press 9 to select fnInt(.
          c) You will now enter an expression in the form Y,X,a,b inside the parentheses.
              In that expression, Y is the expression you’re integrating; for example Y1, X is the
              variable of integration, usually X; a is lower limit and b is the upper limit.   
          d) For the expression to be integrated, you can either choose a variable entered
              into the Y= screen, or you can enter the expression itself.  As an example,
              you might have  fnInt(Y1,X,1,2 with your expression entered into Y1, or you
              might have fnInt( x2,x,1,2 where you have entered the expression x2 yourself.
              Notice that you must enter Y1 from the Y-VARS menu if you use that
          e) Press the ENTER key to see the value of the definite integral.

  5.  Alternate procedure for finding the value of a definite integral:
          a) Press the ZOOM key.
          b) Press 4 to select ZDecimal.  (You don’t have to do this step, but it probably will be
              easier to set your limits if you do.)
          c) Press the Y= key.
          d) Enter the function you are integrating.
          e) Press the GRAPH key.
          f) Press 2nd, CALC.
          g) Press 7 to select Integral.
          h) Move the cursor to the lower limit of integration and press the ENTER key.
   i) Move the cursor to the upper limit of integration and press the ENTER key.
         j) The integrated region will be shaded, and the value of the definite integral will
            appear at the bottom of the screen.  
          k)  To clear the shading from the screen, Press 2nd, DRAW, ENTER. 


       1)  Entering a matrix:
               a)  Press MATRIX, move the cursor to EDIT.
               b)  Move the cursor to the matrix number you want to edit or enter numbers in,
                   and press ENTER.
               c)  Enter the number of rows and press ENTER; then enter the number of
                   columns and press ENTER.
               d)  Enter each value of the matrix and press ENTER after each value.
               e)  Press 2nd, QUIT to go to the home screen.       

       2)  Multiplying two matrices [A] * [B]:
              a)  Enter the data into matrices [A] and [B] and press 2nd, QUIT to go to the
                   home screen.
              b)  Press MATRIX, select the matrix you want as the first in the product, [A],
                  and press ENTER.
              c)  Press the multiply symbol.
              d)  Press MATRIX, select the matrix you want as the second in the product,
                  [B], and press ENTER.
              e)  Press ENTER to perform the multiplication step.
              f)  Remember that the numbers of columns in [A] must equal the number of
                  rows in [B] or you will get a dimension error.

         3)  Doing other matrix math:
                 a)  Press MATRIX and cursor over to MATH.  There you will see a list of
                     operations that you can do.  To find the determinant, use Det.  To find
                     the transpose, use T. 
                 b)  After you select the operation you want, press ENTER.
                 c)  Press MATRIX, select the matrix you want to operate on, and press
                 d)  Press ENTER again to get your answer. 

        4)  Solving systems of equations:
             The TI-82 does not have the ref and rref functions as the TI-83 Plus and TI-84 do.  You can use my program,
             see item 5) below.  Perhaps the easiest way is to make use of this equation:
              [A][X] =[K]  where [A] is the matrix of coefficients, [X] is the variables, and [K] is the matrix of coefficeints.
              Now, we solve that equation for this:
              [X] =[A]-1 [K]
             To perform the math for this, do the following:
             a) Enter the coefficients in matrix [A] or whatever matrix you choose.
             b) Enter the  constants in matrix [B] or whatever matrix you choose other than the one you have the
               coefficients in.
            c) From the home screen, press 2nd, MATRIX, and press 1 for matrix [A].
            d) Press the inverse button, x-1.
            e) Press the multiply button.
             f) Press 2nd, MATRIX, 2 for matrix [B]. You should now have [A]-1 *[B] on the home screen.
            g) Press ENTER and the answer will be displayed

 NOTE:  You can do any of the elementary row operations.  They are very useful for doing the arithmetic for Gauss or Gauss-Jordan elimination, but a little time is required to get the hang of solving a matrix a row at a time. So, since most students don’t take the time to use those functions, I’m not going to include them.  Instead, I’ll give you my Website as a reference for finding out how to do those operations if you want to do them.  First go to my Website:  http://www.grafcalcwhiz.com/
Go to the listing “TI FAQs” in the navigation bar on the left.  Click on the link “More Detailed Page 1”. That will take you to a long page of 40 FAQs.  Cursor down to the answers and then down to answer (21). That will give you the procedure for doing the row operations.  Alternately, to find item 21,  you can use Find under the Edit menu and enter (21) in the dialog box.  Then click Next to find the answer.    

       5)  Doing rref and ref:
           a)  You cannot do these operations on the TI-82 without a program.  There is a program on
                my Website for doing this.  Go to my Website at the URL listed above.     
               The program takes about 25 minutes to enter by hand.  For STCC students, as time permits,
               I will transfer this program electronically from a TI-82 that I have the program stored in to the
              student's calculator.  To set up a time to have this done, email me at 
              dkizer@southwest.tn.edu  .  The instructions for this program are in Appendix IB of this


     1)  I will assume that both calculators are TI-82:
  a) Turn both calculators off and plug in the unit-to-unit cable for both calculators.
               b) Turn on both calculators and press 2nd, LINK on both. Cursor over to
                  RECEIVE on the receive calculator, the calculator that you're transferring the
                  program to.
               c) Press ENTER on the receive calculator. The word "Waiting"  should appear.
              d) On the sending calculator, cursor down to Prgm and press ENTER.
              e) Cursor down to the program you want to transfer and press ENTER. The program that 
                  you selected will be marked with a square "dot."
              f) Cursor over to TRANSMIT press ENTER.
              g)  If everything is connected satisfactorily, transmission of the program should start.  
                   Otherwise,  you'll get a transmit error after a few seconds.
              h)  If you get a transmit error, rotate the plugs on the cable slightly back and forth and try again.


          a)  Problems with trigonometric functions:  The most common problem with trig functions is not
        having the MODE set to the to the dimension of the number entered.  For example, students may
        have entered degrees, but have their calculator MODE set to radians.  To correct that, see
        “Changing the MODE in section I.
           b)  In the graph function mode, you may get a strange graph or maybe even an error message.  If
        that occurs, the first thing to check is whether one or more of the Plot functions is turned on.  To take
        care of that, Press 2nd, STAT PLOT, press 4, and press ENTER.

           c)  If your calculator hangs up and you are unable to correct the problem, first try online or other
                places that provide help.  If you are unable to get help, you can reset the calculator.  Do that as follows:
                  1)  Press 2nd, MEM, press 3.
                  2)  Decide if you really want to RESET.  Resetting will erase all of your programs.


 Appendix IA:  Graphing Inequalities:    
This program, INEQGRAF, may be downloaded from my website www.angelfire.com/pro.fkizer in either text or .82P format.  It will graph up to three inequalities on the same screen.  After the calculator has graphed the equation in Y1=, it then moves on to the equation in Y2=.  If you want to interrupt the graphing for some reason, press the ON button. 

Graphing is done as follows:
For many Finite Math problems you will get the best display (the feasible region) if you set Xmin and Ymin both at 0.

1)  Put your inequalities in the slope-intercept form, y = ax+b, and enter the part to the right of the equal
    sign into the Y= screen.  Either clear or deselect all other equations on this screen. 
2)  Press 2nd, QUIT to leave the Y= screen.

1)  Press PRGM and select the program INEQGRAG by either pressing the number before it on the
     keyboard or highlighting its number and pressing ENTER.
2)  Press ENTER. The menu will appear on the screen and wait for you to choose a number.  If you
    press 1, the equation in Y1= will be selected for graphing. 
3)  Another menu will appear asking what type inequality you want to graph.  Press the
    appropriate number and press ENTER.  All equations will be graphed and the appropriate graph(s) will
    be shaded.  The menu will appear again and wait for you to tell it what to do by selecting a number.
4)  When you are done, press the number 3 for DONE, and the calculator will display the shaded
     inequalities.  Notice that the calculator does not draw the dashed line for < or >.  It only draws a 
    solid line.
5)  When you are finished with the graph for a particular problem, press ENTER.  The shading will be
     erased and the graphs will be redrawn.  Be sure to do this last step because the program keeps
     running until you do.

 Appendix IB: Doing ref and rref:  
 1)  Enter the matrix data according to Item 1, in section VI.
 2)  Press PRGM; then press the number before the program name RREFREF2.  The matrix that you
     entered will be displayed for checking for accuracy.  Press ENTER.
 3)  When the menu appear, select the number for the operation that you want to perform.
 4)  The solution will be displayed in decimal form.  Note that you can scroll to the right if the last
      columns are not displayed on the screen.
 5)  Press ENTER to display the matrix in fractions.
 6)  Finally, press ENTER to quit the program.


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Revised: 12/12/07