QuickClassPad II

Reference Guide

Press these keys for numbers, basic operations,and the most common variables
Tap any icon to select the application.
Tap m at any time to return to the menu screen.
Tap M at any time to return to the Main menu.
Tap to advance to the next page.
In any menu application, press k forthe onscreen keyboard.
Press c to power on. Then press c
to clear commands. Press Kc topower off.
Press these keys for numbers, basic operations,and the most common variables
Press E to execute commands.

Press these keys for numbers, basic operations,and the most common variables

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If an object, such as a ball, is dropped from a initial height, c, the height, h, in feet, as afunction of time, t, in seconds, can be modeled by h = -16t2 + c.
If the object is tossed upwards with an initial velocity, v, then the model becomes
h = -16t2 + vt + c. These models ignore air resistance.

1. If a ball is dropped from a height of 120 feet,compute the height after 2 seconds.
Tap M for the Main menu.
Press:
z16*2^2+120E.

For a more mathematical display, the raised exponent
template can be used from the Math1 Keyboard.
Press:
z16*2kO2:+120E.

This expression can also be evaluated using a variable forsubstitution. A command in the form expression | variable =value means evaluate the expression with the given value(s)substituted for the variable(s).
Pressz16k_[)O2:+120-U_[=2E.

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2. Compute the time when the height of the ball is84 feet.
The value can be computed using the square rootand fraction templates from Math1.

Tap
k5N84120Cz16E.
The value can also be computed using a solvecommand from Math1. The format is(equation,variable) even if there is only one variablein the equation.

Tap)`z16_)O2:+120=84,_[)E.

3. A ball is tossed upwards with an initial velocityof 56 feet/second, from an initial height of 120 feet.
Compute the time and the height when the ball is at
a maximum height.
Commands such as fMax are found under theInteractive and the Action menus. The Interactive commands open a dialogue box which givesprompts for the input. The fMax command uses x
as the default variable, but another variable suchas t can be used.

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Tap Interactive, Calculation, fMin/fMax, fMax
and complete the inputs as shown. (Part of the firstcoefficient, -16, has scrolled off the screen.)
Then tap OK.

4. Rewrite the expression from Question 3 infactored form.
Tap Interactive, Transformation, factor, factor.

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Enter the expression in the box. Then tap OK.

5. This model expresses height, or position, as afunction of time. Construct a model for velocity as afunction of time.
The velocity would be the derivative of the position
function.
Tap Interactive, Calculation, diff.

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Enter the expression in the box. (Again, part of thefirst coefficient, -16, has scrolled off the screen.)
Then tap OK.

Alternately, the template for a derivative from
Math2 can be used; the result will look the same.

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6. Compute the instantaneous velocity at time
2 seconds.
The only difference is to tap the bullet for Derivative
at value, and to enter the value in the last box.

For a more intuitive display, use the derivative
template from Math2 and the “with” (U) commandon Math3.

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7. Compute the total net distance that the balltravels.
The ball had an initial height of 120 and fell to heightof 0, so the net distance should be -120.
For a calculus connection, integrate the velocity
function.

Tapk9P.
Enter the integrand, the variable, and the limits.
The variable t can be found at 9, then tap
E.
8. Compute the total distance that the ball travels.
The initial height and the maximum height are
known, so the total distance can be easily
computed.
For another calculus connection, another integral
can be used. The traditional approach is to use two
integrals, but it is quicker to use the absolute value
template. The template is also in 9.

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The ClassPad has a symbolic algebra system, sometimes called a computer algebra system,or CAS. An important distinction is a calculator using symbolic algebra can manipulate undeclared variables. The factoring example from Question 4 was an illustration. It is usually a goodidea to tap Edit, then Clear All Variables to ensure that the variables do not have a value
stored in memory. The next 2 questions illustrate additional symbolic algebra.
9. If a model for the height of a ball thrown upwards
as a function of time is given by h = -16t2 + vt + c,compute an expression for the time when the ballhits the ground.
Tap Interactive, Equation, solve.

Enter the equation in the box by pressing kand tap 0 to view the variables. The negative
sign is to the left of 16 and has scrolled off.
Enter the variable in the second box and tap E,or press the E key; then tap OK.

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Both solutions are shown; the first solution would benegative and is not in the domain.

10. If a model for the height of a ball, thrown
upwards, as a function of time, is given by
h = -16t2 + vt + c, compute an expression forvelocity as a function of time.
Pressk and tap 9].

Enter the expression and the variable and tap E,or press the E key.

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