Your calculator will serve as an extremely useful tool if you
take advantage of all of its functions. We will base all of the
following tips and programs on the TI-82, which most calculus
students use today.
On the AP Calculus Exam, you will need your calculator for Part B of Section I and for Section II. You will need to know how to do the following:
1. simple calculations
2. find the intersection of two graphs
3. graph a function and be able to find properties listed under
Elementary Functions in the Topics to Study section
(e.g. domain, range, asymptotes)
Here are some of the functions available that you should know how to use:
In the CALC menu: | 1. calculate the value of a function at x = c |
2. calculate the roots of a function | |
3. find the minimum of a function | |
4. find the maximum of a function | |
5. find the point of intersection of two functions | |
6. find the slope of the tangent at (x, y) | |
7. find the area under the curve from a to b |
In the MATH MATH menu: | 6. find the minimum of a function |
fMin(expression, variable, lower, upper) | |
7. find the maximum of a function | |
fMax(expression, variable, lower, upper) | |
8. find the numerical derivative at a given value | |
nDeriv(expression, variable, value) | |
9. find the numerical integral of an expression | |
fnInt(expression, variable, lower, upper) | |
0. calculate the root of an expression | |
solve(expression, variable, guess, {lower, upper}) |
Calculator Programs
One of the easiest programs to create is one that will solve for
f(x). You can also run the program multiple times to find other
values for the same function.
PROGRAM: SOLVE | |
: Input X | |
: 3x2 + 2 X | [type your function here and place X at the end] |
: Disp X |
Here is a program to solve for a quadratic equation:
PROGRAM: QUADRAT |
:Input "A? ", A |
:Input "B? ", B |
:Input "C? ", C |
:(- B + (B2 - 4AC) ) / 2A D |
:(- B - (B2 - 4AC) ) / 2A E |
:B2 - 4AC F |
:ClrHome |
:Disp "+ EQUALS" |
:Disp D |
:Disp "- EQUALS" |
:Disp E |
:Disp "B2 - 4AC EQUALS" |
:Disp F |
To Run: Enter a, b, and c for ax2 + bx + c. |
"+ EQUALS" and "- EQUALS" give the roots of the equation |
Here is a program that will use the trapezoidal rule to approximate
a definite integral:
PROGRAM: TRAP |
:ClrHome |
:Input "F(X) IN QUOTES:", Y0 |
:Input "START(A):", A |
:Input "END(B):", B |
:Input "NO. OF DIV. (N):", N |
:(B - A) / N D |
:0 S |
:For (X, A, B, D) |
:S + Y0 S |
:End |
:A X : Y0 F |
:B X : Y0 L |
:D * (-F + S - L) A |
:ClrHome |
:Disp "EST AREA=" |
:Disp A |