# TI-83/84 Calculator Help in MATH 141

Finding an Exact Fractional Value of a Decimal
From your home screen, if you have calculated a value which is not an integer value, you can determine whether or not it is a rational number and can be written as an exact fraction by hitting MATH and choosing option 1: Frac and then hitting ENTER. The reduced fraction for your value should appear if it is a rational number.

Finding the Intersection Point of Two Lines
1. Graph the two functions by entering the slope-intercept form of the lines into Y1 and Y2. These are located under the Y= button.
2. Go to CALC which is found by pressing 2nd TRACE.
3. Select option 5:intersect.
4. The calculator will prompt you for the first and second curves you want to intersect. The cursor will blink on a function and show the function name in the upper left corner of the screen. When it blinks on Y1, press ENTER & when it blinks on Y2, press ENTER.
5. The calculator will then ask you to guess where the intersection point is located. Use your right and left arrow keys to move to the intersection point and press ENTER.
6. The intersection point will appear at the bottom of the screen.

Linear Regression
1. Enter your x and y values into lists. To do this, hit STAT and select 1:Edit.... If you have anything in L1 or L2, cursor up to the name of the list, hit CLEAR and ENTER. Now just enter in your values one at a time by pressing ENTER after each number.
2. To find the regression equation, first hit STAT, cursor right to CALC and select option 4:LinReg(ax+b). Now press 2nd 1 , 2nd 2 , to specify the x list and y list. (REMEMBER THE COMMAS! You do not have to specify the lists if you are using L1 and L2 for your x and y-values, respectively.) Hit VARS, cursor right to Y-VARS, select 1:Function... and Y1 (or whichever function you would like) to specify where the regession equation will be saved. You should now see the following on your home screen:

LinReg(ax+b) L1, L2, Y1 or LinReg(ax+b) Y1 (if you are using L1 and L2 for your lists)

3. Now, press ENTER. The following should appear on your screen:

LinReg(ax+b)
y=ax+b
a=....
b=....
r^2=....
r=....

Your regression line is the equation now saved under Y1. If you don't have the r stuff, then you need to turn your diagnostics on. To do this, hit 2nd 0, and cursor down to select DiagnosticOn. When this comes up on your home screen, press ENTER and it should say Done.
4. To graph the regression line with the data points, first make sure your stat plot is turned on. To do this, hit 2nd Y= and select 1.... by pressing ENTER. You can then highlight any of the options you would like. Now just hit GRAPH. If you don't see anything, adjust your window size under WINDOW and ZOOM.
5. To find a y value from your regression line when given an x value, go to the main calculator screen and call up your function name (VARS, cursor right to Y-VARS, select 1:Function... and Y1 (or whichever function your line is in)) and then open the left parenthesis, type the x value and close your parenthesis. OR... hit CALC (2nd TRACE) and select option 1:value. Then just enter the value for x.
6. To find an x value from your regression line when given a y value, enter the y value under Y2 and then find the intersection point between Y1 (your regression line) and Y2.

Matrices
If you have a TI-83 Plus or any version of the TI-84, when you see directions to hit the MATRX button, you need to hit 2nd x^(-1).
• Entering a Matrix
1. Hit MATRX.
2. Cursor right two places to EDIT and hit ENTER.
3. Enter the size of the matrix. (ROW NUMBER FIRST, COLUMN NUMBER SECOND!!!)
4. Enter the matrix elements. If you enter the elements and press ENTER after each element, the cursor will move left to right across the rows and then down to the next row and continue in the same fashion until you reach the last element of the matrix. You can always move around to different elements with your cursor keys, too.

• Calling a Matrix for Computation
1. Make sure you are on the home screen before you begin. To do this, hit 2nd MODE to quit.
2. Press MATRX and cursor down under the NAMES list until you get to the matrix you want and hit ENTER. The name of the matrix you need to do computations with will now be on your homescreen.

• Matrix Transpose
1. Call the matrix you would like to transpose from the home screen.
2. Hit MATRX, cursor right to MATH and select option 2:T.
3. You should now see the symbolic representation of transposing your matrix. To actually see the transpose, hit ENTER.

• Square Matrix Inverses
1. Enter the matrix for which you would like to find the inverse.
2. Call that matrix from your home screen.
3. Hit the x inverse button (x^-1) which is directly below the MATH key and press ENTER.

• Fast RREF (This only works when the #rows is less than or equal to #columns)
1. Enter the matrix you want to reduce.
2. Go to your home screen.
3. Press MATRX, cursor right to MATH, and select B:rref.
4. Call the matrix you want to reduce and hit ENTER.

Counting
• Factorials
1. Enter n on your home screen.
2. Press MATH, cursor over to PRB, and down to 4:!.
3. Press ENTER.

• Permutations
1. Enter n on your home screen.
2. Press MATH, cursor over to PRB, and down to 2:nPr.
3. Enter r.
4. Press ENTER

• Combinations
1. Enter n on your home screen.
2. Press MATH, cursor over to PRB, and down to 3:nCr.
3. Enter r.
4. Press ENTER

Statistics
• Histograms
1. Enter Data into Lists. Your random variable(X) values should be entered into L1 and the corresponding probabilities should be entered into L2.
2. Turn on Stat Plot. Press 2nd Y= and choose which plot you want. In class I used the first one. When on the Stat Plot screen, highlight the following options:

On
Histogram (Bar Graph) picture - the last picture in the top row
Xlist: L1
Freq: L2

NOTE: Once you've done this the plot will be turned ON until you turn it OFF.
3. Set Window. Use X values to choose Xmin and Xmax. Set Y values between 0 and 1 and choose Yscl by looking at your data.
4. Graph. (Make sure you don't have anything entered on Y= screen.)

• Expected Value/Standard Deviation/Variance
1. Enter data into L1 and L2 as in the above.
2. Press STAT cursor right to CALC and down to 1: 1-Var Stats.
3. When you see 1-Var Stats on your home screen, add L1,L2 so that your screen reads 1-Var Stats L1,L2 and press ENTER.
4. The expected value is the first number listed : x bar.
5. The standard deviation is the fifth number listed: sigma x.
6. To find the variance, use the standard deviation. Press VARS, cursor down to 5:Statistics, and down again to 4:sigma x. Then press the x-squared key and hit ENTER.

• Binomial Distribution
1. Single Probability Calculation: binompdf() -> Press 2nd VARS and select option 0:binompdf. The format of the command is as follows: binompdf(n,p,r), where n = the number of trials, p = the probability of success in each trial, and r = the desired number of successes. This calculates P(X=r).
2. Cumulative Probability Calculation (Sum of Many): binomcdf() -> Press 2nd VARS and select option A:binomcdf. The format of the command is as follows: binomcdf(n,p,r), where n = the number of trials, p = the probability of success in each trial, and r = the desired number of successes. This calculates P(0 <= X <= r).

• Normal Distribution
1. P(a < Z < b) = normalcdf() -> Press 2nd VARS and select option 2:normalcdf. The format of the command is as follows: normalcdf(left endpoint, right endpoint, mean, standard deviation).
2. P(Z < z)= a - Press 2nd VARS and select option 3:invNorm. The format of the command is as follows: a = invNorm(probability, mean, standard deviation).

Compound Interest and Effective Rates of Interest for Non-Continually Compounded Accounts
For both of these types of problems, go to FINANCE on your calculator. If you have the regular TI-83, this is found by hitting 2nd x^(-1). If you have the TI-83 Plus, this is found by hitting the blue APPS button and selecting option 1:Finance....

• Compound Interest
1. Select option 1:TVMSolver. You should have the following on your screen:

N =
I%=
PV=
PMT=
FV=
P/Y=
C/Y=

2. If you are making payments, make sure that END is highlighted at the bottom of the screen.
3. Fill in all but one of the above options (the one you are trying to solve for) as follows: N = the total number of times compounded (the number of times compounded per year times the number of years), I% = interest rate (not in decimal form), PV = present value (the amount you invest), PMT = value of payments (0 if you are not making any payments), FV = future value (the amount of money you have at the end of your investment), P/Y = the number of payments per year (the number of times compounded per year if you are not making any payments), C/Y = the number of times compounded per year. If you fill in PV and FV, one must be negative in order for your calculator to find an answer. (Simulating the flow of money between you and the bank.) Make sure you have some kind of value entered in the spot for whichever variable you are solving for or else the calculator will not let you proceed to input values for the rest of the variables.
4. Move your cursor to the value you are solving for and hit ALPHA and then ENTER.

• Effective Rates of Interest
1. Select option C:Eff(.
2. Input the nominal interest rate (not in decimal form) followed by a comma and then the number of times the account is compunded per year.
3. Hit ENTER.