TI-83 Plus Workshop. Al Maturo,

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1 Solving Equations with one variable. Enter the equation into: Y 1 = x x 6 Y = x + 5x + 3 Y 3 = x 3 5x + 1 TI-83 Plus Workshop Al Maturo, AMATURO@las.ch We shall refer to this in print as f(x). We shall refer to this in print as g(x). We shall refer to this in print as h(x). Notice that the = sign is highlighted. This means that the equation is active. In order to de-activate the equation move the cursor to the = sign and press ENTER. This will allow you to work with one graph at a time. What are the roots of Y 1? Find the roots of Y 1 using the calculator. Evaluating Equations at different values of x. Find f(0) = f(-3) = f(4.35) = g(0) = g(-3) = g(4.35) = h(0) = h(-3) = h(4.35) = Find minima of f(x) and g(x). Find the intersection point of f(x) and h(x). Find the derivative / Slope of h(x) at the following points: h (-1) = h (0) = h () = Add the above values together using variable storage. Find the area under h(x) on: 0 hx ( ) dx = hx ( ) dx= 1

2 Graphing graphs that do not appear on the Standard screen. Radioactive Decay: Substance Ra 6 has a half-life of 160 years. The quantity after t years is given by the equation: t 1 Qt () = Find the amount present initially. After 1000 years. Graph it. Population Growth: A town s population increases according to the model: Pt 0.093t () = 500e Find P(0). Find P(15). Graph it. Combinations / Permutations C = C = P = P = Find Matrices for solving Simultaneous Equations: A -1 B Solve: 3x y= 6 x 7y= 10 5x+ 3y= 9 5x 6y= 1x+ 1y+ 1z= 1 3x+ 5y+ 4z = 3x+ 6y+ 5z= 0 Enter {,,5,,8,5,4,7,,5,} STO L1 Sort, Mean, Median, Mode of Lists of Values Enter {3,3,5,3,8,5,3,7,3,5,} STO L Sort, Mean, Median, Mode of Lists of Values Enter {15,15,158,18,148,165,147,173,17,165,168} STO L3 {38,34,39,35,37,40,37,44,43,40,4} STO L4 Var Stats for a Correlation Study

3 All the information is available for the slope and coefficient. xy x y xy x y m= r = σ σ σ x x y Financial Functions (Loans, Payments, etc.) For a loan of $6000 at 6.5% APR, paid monthly, starting at the beginning of the first period, what would the monthly payment be? For a mortgage of $150,000, paid over 30 years monthly, at a rate of 7% APR, starting at the beginning of the first period, what would the monthly payments be? If it were paid quarterly? If it were paid quarterly at the end of the first period? Mode Settings excellent for external exams (3 decimal places)

4 Solving Equations with one variable. Enter the equation into: Y 1 = x x 6 To find the roots of Y 1 using the calculator nd CALC :zero TI-83 Plus Workshop - Solutions Left Bound: Pick a point before the root, hit ENTER Right Bound: Pick a point after the root, hit ENTER Guess: Do not guess, just hit ENTER Evaluating Equations at different values of x. Find f(0) = 0 STO X VARS Right arrow key to Y-VARS 1:Function Choose the desired function, Y 1 f(-3) = - 3 STO X Follow the same steps as above. Find minima of f(x) nd CALC 3:minimum Left bound: Pick a point before the root, hit ENTER Right bound: Pick a point after the root, hit ENTER Guess: Do not guess, just hit ENTER Find the intersection point of f(x) and h(x) nd CALC 5:intersect It will ask for First Curve, then Second Curve, then guess. Up/Down arrows change curve. For the First Curve, move BLINKY near the point of intersection, hit ENTER. For the Second Curve, move BLINKY near point of intersection, hit ENTER. 4

5 Make sure you are on different curves. Make sure that you are on the correct curves. Guess: Do not guess, just hit ENTER. Find the derivative/slope of h(x) at x = -1 (remember h(x) is Y ) nderiv(y,x,-1) nderiv is found at Math8 Find the area under h(x) on: 0 hx ( ) dx = fnint(y,x,-,0) fnint is found at Math9 Graphing graphs that do not appear on the Standard screen Radioactive Decay: Substance Ra 6 has a half-life of 160 years. The quantity after t years is given by the equation: t 1 Qt () =. Enter this function into Y 1. Use parenthesis. Find the amount present initially. 0 STO X (STO is next to 1) Y 1 (found in VARS, Y-VARS, Function, then choose Y 1 ) Answer = 5. After 1000 years STO X (STO is next to 1) Y 1 (found in VARS, Y-VARS, Function, then choose Y 1 ) Answer = Graph it. You will need to change Window Settings From the information found above, I will choose the x & y min & max. For x, maybe 1 (because I like to see the axis) to 5000 For y, maybe 1 (because I like to see the axis) to 30 (a bit more than 5) Xmin = -1 Ymin = -1 Xmax = 5000 Ymax = 30 Xres = whatever it is Xscl = 1000 Yscl = 5 (anyone know what this is?) 5

6 Combinations / Permutations Find 1C 7 = 1 MATH PRB (move across to the right, not down) 3:nCr 7 Remember, you need to pre-load the 1 before getting the C, then enter 7. Find 1P 5 = 1 MATH PRB (move across to the right, not down) :npr 5 Remember, you need to pre-load the 1 before getting the C, then enter 5. Enter {,,5,,8,5,4,7,,5,} STO L1 STAT CALC 1:1-Var_Stats ndl 1 (move to the right, not down) (if you want L, the specify it.) Toggle up and down to see all the information available. Enter {15,15,158,18,148,165,147,173,17,165,168} STO L3 {38,34,39,35,37,40,37,44,43,40,4} STO L4 Var Stats for a Correlation Study After entering the lists STAT CALC :-Var_Stats ndl 3,L 4 Toggle up and down to see all information available. (move to the right not down) 6

7 Financial Functions (Loans, Payments, etc.) For a loan of $6000 at 6.5% APR, paid monthly, starting at the beginning of the first period, what would the monthly payment be? Find the Finance feature. It is either under nd Finance or APPS 1:TVM Solver Enter the information into the fields: N = 36 (number of months for 3 years) I% = 6.5 (no need to change to 0.065, already in percent form) PV = 6000 (Present value of loan) PMT (come back to this later) FV = 0 (Future value of loan should be 0 if you want to pay it off) P/Y = 1 (Payments per year: 1 for monthly, 4 for quarterly, etc) C/Y = 1 (Compounded per year: most banks do same as payments) PMT (First payment is due at the beginning or end of first period?) Move BLINKY to PMT, because that is what we are trying to find and hit ALPHA (Green button) SOLVE (ENTER button) Notice answer is negative because payment is an outflow of cash. Wherever BLINKY is what will be solved. I hope that is clear. The best way to learn is practice, practice, practice. Students are great sources for help, and other ways to do these. Sometimes they can find out how to do something more easily Remember: AMATURO@las.ch if you have questions/suggestions. 7