Appendix C - How to use the TI-83 Plus

 

1. ON and OFF-To turn on the calculator press the on key in the lower left corner. To turn the calculator off, press and release the yellow 2nd key then press the on key. The yellow 2nd key makes the calculator do the function in yellow above the key.

 

2. 2ND-The yellow 2nd button on the upper left hand side causes the calculator to perform the function in yellow above each key. Remember to press and release this button every time you want to use a function written in yellow

 

3. ALPHA-To get any of the letters in green, press and release the ALPHA key.

 

4. ENTER-Use the ENTER key in the lower right hand corner to get the solution to a problem after you type it in.

 

5. Negative numbers and Subtraction -To type in negative numbers use the (-) negative key located below the 3 key. This key is for putting in negative numbers.  The – key above the + key is for subtraction .

Example To type in -5 – (-2) type in the negative key,(-), then 5, then the subtraction key,-, then the left parenthesis key,(, then the negative key (-), then 2, then the right parenthesis key, ), then ENTER.

 

 

 

6.  Parenthesis- Use parenthesis any time there is parenthesis in the problem or if more than one term is in the numerator, denominator, or exponent.

Example To find the answer to , enter parenthesis around the numerator and parenthesis around the denominator.  Type

 

 

7.  Fractions- If the fraction is a mixed number you must first write it as an improper fraction.  For example, if the fraction was  you would have to write this as .  Press the MATH button (below the green ALPHA key), then 1 for FRAC.

Example To add the fractions, , first rewrite .  Now just type in 

(-5. Before pressing ENTER, press the MATH button then 1 for FRAC, then ENTER.

      

 

8. X2-To square a number, type in the number then press the X2 key, then ENTER.

Example To get 52, type in 5 then press the X2 key, then ENTER. You should get 25.

 

9. To get the square root of a number or a variable, press the square root key (press the 2nd key then X2 key) and type the number or variable you want to take the square root of. 

Example To get the square root of 30, press the square root key (2nd X2) then type in 30, then ENTER.

 

 

 


10.  Power Key ^To raise a number or a variable to any power, type in the number then press the ^ (power key), then type in the power that you want to raise the number or variable to. 

Example to get 510, type in 5^10, then ENTER.  The answer is  9765625.

Example- To find the answer to type in . 

Notice you need parenthesis around the base and the exponent since they are both fractions.

 




 

11.  xTo get any root of a number, type in the root, then press MATH key, then press 5 for  , then enter the number you want to take the root of and press ENTER.

Example To get the 4th root of 30, , type in 4, then press the MATH key, then press 5 for  , then 30 and press ENTER.

 


     

 

 

12.  Editing your expressions and equations-If you type in something wrong you can use your arrow keys to edit your expressions.  If you have already hit ENTER and want to edit an expression, press 2nd then ENTRY (ENTER).

 

13.  DEL-Use the DEL (delete) key to delete any part of your expression.

 

14. INS-Use the INS (insert) key (2ND then DEL) to insert into your expressions.

 

15. Scientific Notation-There are two ways to calculate scientific notation on your calculator.

Example-To find the answer to  type in the following

(6.024 X 10^-24 )  (8.23 X 10^-8) then ENTER. You should get 7.319E –17.  This means 7.319 X 10-17 in scientific notation or expanded out .00000000000000007319.

 

 

 

 

 

 


You could have also used the EE key (2nd then the comma key). Type in 6.024 EE-24  8.23 EE -8 then ENTER.

 

 

 

 

16.  The X,T,Q,N key- Use the X key X,T,Q,N  when you are solving or graphing equations.

 

17. Imaginary and Complex numbers-  To enter imaginary or complex numbers press the 2nd key then the decimal point.

 

18. Absolute value-  To get absolute value, press the MATH key then arrow to the right (for NUM), then 1 (for abs).

 

 

 

19.  Log- Log base 10 key.  To find the log10  (1000) type in log(1000). You should get 3

 

20.  Ln-  Natural log key. To find the loge  (1000) type in LN(1000). You should get 6.9077

 

21.  ex-  To get the ex key, press 2ND then the natural log key (ln). 

 

Tables

 

1. To make tables of values press the blue Y= key and type in the equation and press ENTER. The equation must be solved for y. Then press the 2nd key then the blue WINDOW key (for TBL SET).  Enter the start of your table and the D TBL (how much the values of x are increasing) and make sure Indpnt: and Depend: are set to Auto. Then press 2nd key then the blue GRAPH key (for TABLE)

 

Example: Complete the following table for the equation y = 2x + 3.

 

X

Y

0

 

2

 

4

 

6

 

 

First press the blue Y= key and type in the equation (you just type in 2x + 3. Do not type in Y=, and you must use the X,T,Q,N key.

 

Now press the 2nd key then the blue WINDOW key (for TBL SET). There you will enter the start of your table the D TBL (how much the values of x are increasing) and make sure Indpnt: and Depend: are set to Auto.  Then press 2nd key then the blue GRAPH key (for TABLE).

 

     

 

2. If you want to evaluate an equation for a particular value, press the 2nd key then the blue WINDOW key, and arrow down to the first Auto and arrow to the right for Ask.

 

 

 

 

 


Now press the 2nd GRAPH for table and type in the number you want to evaluate the equation for. For example let’s say we want to evaluate the equation y = 2x + 3 for x = 4.12.

 

 



EQUATIONS

1. Solving Quadratic, Cubic equations and higher- To solve quadratic, cubic equations or higher, you must first have the application PolySmlt copied to your TI-83 Plus.  If you have a TI graph link cable, you can copy the application from the Internet at http://www.ac.cc.md.us/Department/math.html/ti.html.  If you do not have the PolySmlt application and are unable to copy it, see Example 3 in the next section on Graphing. Once you have the application copied on your calculator press the blue APPS key, then press the number for the PolySmlt Application, then press ENTER, then press 1 for Poly Root Finder.  Then enter the order of the equation (Quadratic = 2, cubic = 3, etc.), then press ENTER.  Now enter your coefficients pressing ENTER after each one (the equation must be in standard form and set equal to 0).  Then press the blue GRAPH key for solve.

 

Example- To solve the quadratic equation (2x-3)2 + 5 = x + 3 first put the equation in standard form. Expanding (2x-3)2 we get 4x2 -12x + 9 + 5 = x + 3.  Setting the equation equal to zero we get, 4x2 -12x + 9 + 5 - x - 3 = 0.  Combining like terms we have, 4x2 -13x + 11 = 0. 

 

Now we are ready to enter the coefficients into our calculator. Press the blue APPS key, then press the number for the PolySmlt Application, then press ENTER, then press 1 for Poly Root Finder.  Then enter the order of the equation 2 (for this example), then press ENTER.  Now enter your coefficients pressing ENTER after each one.  Then press the blue GRAPH key for solve. You should get 1.63 + .33i and 1.63 - .33i

 

         

 

 

2. Solving Systems of Equations- To solve systems of equations press the blue APPS key, then press the number for the PolySmlt Application, then press ENTER, then press 2 for Simult Eqn Solver. If you have a TI graph link cable you can copy the PolySmlt application from the Internet at http://www.ac.cc.md.us/Department/math.html/ti.html. If you do not have the PolySmlt application and are unable to copy it, see Example 2 in the last section of this appendix on Matrices. 

 

Enter the number of equations and number of unknowns and enter in the coefficients (the equations need to be in standard form).  Then press the blue GRAPH key (for solve).

Example- Solve the system of equations:

x + 2y +3z = 4
2y - 3z = 7
4x + 5y = -2

First we will need to write these equations in standard form ax +by +cz = d. We get,

pulling off the coefficients we get, . Now we are ready to use the calculator.

Press the blue APPS key, then press the number for the PolySmlt Application, then press ENTER, then press 2 for Simult Eqn Solver. Type in 3 for the number of equations then ENTER and 3 for the number of unknowns then ENTER. Now enter in your coefficients from the table above and press the blue GRAPH key (for solve).

       

 

3. Solving linear equations- To solve linear equations, or any equation that only has one solution, first use paper and pencil to set the equation equal to zero.  On the calculator press the MATH key then 0 for Solver. Now type in your equation (note you must use the X,T,Q,N key for the variable.

Example- Solve the linear equation 2x + 4 = 10.  First set the equation equal to zero by subtracting 10 from both sides of the equation and we get, 2x + 4 – 10 = 0.  Now press the MATH key then 0 for Solver.  You may need to arrow up to get to where you can type in the equation.  Type in 2x + 4 – 10 then press ENTER, then ALPHA ENTER (for Solve).
We get x = 3.

   

 

 

Graphing

 

1. Y = To graph an equation it must be solved for y. Press the blue Y = key to type in the equation to graph.

 

2. Zoom- Press the  blue ZOOM key to either; Zoom In, Zoom Out, Zstandard (this sets your viewing window to have an x min and y min of –10 and an x max and y max of –10),

Zoom Stat, or ZoomFit (zoomFit will at least get some part of your graph to show on your calculator). If you use zoom in, you will zoom in on the location of the cursor. Move the cursor with the arrow keys to the area you want to zoom in on, then press ENTER.

 

3. Adjusting the WINDOW - Use the blue WINDOW key to change your viewing window and scale. It’s generally a good idea to have your Ymax and Xmax be positive and your Ymin and Xmin to be negative by about the same amount so you can see the x and y-axis.

 

4. TRACE- Trace is for tracing your graph

 

*5. CALC- If you press the 2nd key then TRACE you will have choices for value, zero (which means root or x-intercept), minimum, maximum intersect, and other choices. Use these to find the values for y for a given x value, roots, max, mins, and intersection points.

 

Example 1 – Graph the equation y = 2x + 5 and find the y – intercept.

 

Press the Y = key and type in 2x + 5 and press ENTER. Now press the blue Zoom key and choose 6 for Zstandard (the reason for choosing Zstandard is because when looking at the numbers in this equation, the graph should be able to be seen on the Standard Viewing Window.  If the graph did not show up, we could press the Zoom key again and choose 3 for Zoom Out and press ENTER.)

 

     

 

Now to find the y –intercept, we need to realize that the y –intercept has a x value of 0.

Press the 2nd key then TRACE (for CALC) and choose 1 (for value). Type in 0 after the x = and press ENTER and we get the y-intercept of (0,5).

 

      

 

 

 

 

Example 2 – Graph the equation y = 2x + 5 and find the x – intercept.

Press the Y = key and type in 2x + 5 and press ENTER. Now press the blue Zoom key and choose 6 for Zstandard.

 

     

 

Another name for the x-intercept or root is the zero of a graph. So to find the x –intercept or Zero, press the 2nd key then TRACE (for CALC) and choose 2 (for zero). Then the arrow to the left of the x intercept and press ENTER. Then arrow to the right and press ENTER, then press ENTER again and we get the x-intercept to be the point (-1.5,0)

 

           

 

Note that you must arrow to the left and press Enter and arrow to the right and press Enter and press Enter again to find roots (zeros), maximums or minimums.

 

Example 3 – Find the roots for the quadratic equation y = 2x2 – 5x – 300.

 

First use the blue Y= key to type in the equation. Then press the blue GRAPH key. Your graph may not show up, so press the blue ZOOM key and choose 3 to zoom out and press enter (do not forget to press Enter). If your roots do not show up, zoom out again until they show on your calculator screen.

 

      

 

Now that the roots (zeros) are showing, press 2nd then the blue TRACE key (for CALC) and choose 2 (for zero). Arrow to the left of the first root and press Enter and arrow to the right of the first root and press Enter and press Enter again. We get our first root to be (-11.0617,0). Do the same thing for the second root and we get (13.561072,0).

 

       

 

      

 

Example 4 - Find the vertex point for the previous quadratic equation y = 2x2 – 5x – 300.

 

Even though the vertex point is not showing on the graph, it is still within the domain of the graph on the calculator screen, so we will not need to zoom out. Press the 2nd key then TRACE (for CALC) and choose 3 for minimum (by looking at the shape of the graph we can tell that the vertex point is going to be a minimum not a maximum. Arrow to the left of the minimum and press Enter and arrow to the right of the minimum and press Enter and press Enter again. We get our vertex point to be at the coordinate (1.25,-303.125).

 

      

We can check this with the vertex formula . The a = 2, the b = -5 and the c = -300 and we get x = 1.25. Evaluating the equation when x = 1.25 we get –303.125.

 

 

 

STAT

(Used for finding equations of lines and curves and other statistical information)

 

Example 1- Let’s say we know that 32 degrees Fahrenheit is equal to 0 degrees Celsius, and 212 degrees Fahrenheit is equal to 100 degrees Celsius. However, we do not know the conversion formula from Fahrenheit to Celsius. To get the linear conversion formula we need at least two points. We could set up our points (F,C). So, from the fact that 32 degrees Fahrenheit is equal to 0 degrees Celsius, we get the point (32,0) and from the fact that 212 degrees Fahrenheit is equal to 100 degrees Celsius, we get the other point (212,100). To find the equation of the line that goes through the points (32,0) and (212,100) press the STAT key and press 1 for EDIT and enter the Fahrenheit values on list1 and their associated Celsius values for list2. Press the STAT key again, and arrow to the right to CALC and choose 4 (for LinReg(ax + b)), then press ENTER.

        

We should get  a = .555555, b = -17.7777 and r = 1 and the slope intercept form of  linear equations y = ax + b. So the equation that goes through our points is y =.5555x - 17.7777.

 

Example 2- Let’s say you want to find the equation of the line (linear equation) that best fits the points (5,3) (4,2) and (1,-3) and the correlation coefficient (r) and the coefficient of determination (r2).

First we must get the calculator to show us the r and the r2. To do this press the 2nd key then 0 (for Catalog) and arrow down to the word diagnostics on and press ENTER and press ENTER again.

    

Now press STAT key and press 1 for EDIT and enter the x values on list1 and the y values for list2. Press the STAT key again, and arrow to the right to CALC and choose 4 (for LinReg(ax + b)), then press ENTER and we will get a = 1.538, b = -4.46, r = .9962, r2 = .9962. So the equation of the line of best fit is y = 1.538x - 4.46.

 

         

Matrices

 

1. Entering a matrix-To enter a matrix, press the 2nd key then the x-1 key (for MATRX), then arrow to the right to EDIT and arrow down to the letter you want to call the matrix and press ENTER.  Now put in the size of your matrix.  Then enter the elements of your matrix.  Now press 2nd MODE (for quit) to exit.

 

2. Operations with matrices- To add, subtract, or multiply matrices, or find the inverse of a  matrix, or solve a system of equations using matrices, press the 2nd key then the x-1 key (for MATRX), then arrow down to the matrix you want to use and press ENTER,  then times or whatever operation you want, then press the 2nd key then the x-1 key (for MATRX), then arrow down to the other matrix you want to use and press ENTER then press ENTER again to get the solution.

 

Example 1 – Multiply these two matrices.

 

First, press the 2nd key then the x-1 key (for MATRX), then arrow to the right to EDIT and arrow down to the letter you want to call the matrix (might as well use A) and press ENTER.  Now put in the size of your first matrix (3 Enter 4 Enter). Then enter the elements of your matrix.  Now press 2nd MODE (for quit).

 

   

 

Now, press the 2nd key then the x-1 key (for MATRX), then arrow to the right to EDIT and arrow down to the letter you want to call the matrix (might as well use B) and press ENTER.  Now put in the size of your second matrix (4 Enter 2 Enter). Then enter the elements of your matrix.  Now press 2nd MODE (for quit).

 

  

 

Now press the 2nd key then the x-1 key (for MATRX), and press 1 for matrix A, press the multiplication key. Get back to the Matrix area (2nd key then the x-1 key) and press 2 for matrix B then press Enter for your solution.

 

        

Example 2 - Solve the system of equations:

x + 2y +3z = 4
2y - 3z = 7
4x + 5y = -2

First we will need to write these equations in standard form ax +by +cz = d. We get,

Pulling off the coefficients we get the matrix, . Now we are ready to use the calculator.

Press the 2nd key then the x-1 key (for MATRX), then arrow to the right to EDIT and arrow down to the letter you want to call the matrix (might as well use A) and press ENTER.  Now put in the size of your first matrix (3 Enter 4 Enter). Then enter the elements of your matrix.  Now press 2nd MODE (for quit).

 

Now press the 2nd key then the x-1 key (for MATRX), then arrow to the right to MATH and arrow down to choice B (rref) and press Enter.

    

 

Now press the 2nd key then the x-1 key (for MATRX), and press 1 for matrix A and press Enter.

    

So the solution to x is –5.7272, the solution to y is 4.1818, and the solution to z is .4545.