Casio FX-CG500 User manual

QUICK START GUIDE
fx-CG500
Tap any icon to select the application.
Tap mat any time to return to the
menu screen.
Tap Mat any time to return to the Main menu.
Tap to advance to the next page.
In any menu application, press kfor
the onscreen keyboard.
Press cto power on. Then press c
to clear commands. Press Kc to
power off.
Press these keys for numbers, basic
operations, and the most common variables
Press Eto execute commands.
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fx-CG500

QUICK START GUIDE
fx-CG500
Main Menu ............................................ Page 3
Numerical Solve Menu ......................... Page 12
Graph and Table Menu ......................... Page 14
Conic Menu ......................................... Page 24
Statistics Menu .................................... Page 31
Author:
John Diehl
Casio Teacher Advisory Council
Editors:
Nathan Austin, Amber Branch, Amy Chow
Casio Education, Curriculum and Training Department
INDEX

fx-CG500 Quick Start Guide 3
If an object, such as a ball, is dropped from a initial height, c, the height, h, in feet, as a
function 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 Mfor the Main menu.
Press z16*2^2+120E.
For a more mathematical display, the raised exponent
template can be found on the Math1 Keyboard.
Press z16*2kO2:
+120E.
This expression can also be evaluated using a variable for
substitution. A command in the form expression | variable =
value means evaluate the expression with the given value(s)
substituted for the variable(s).
Press z16k_[)O2:
+120-U_[=2E.
MAIN MENU

fx-CG500 Quick Start Guide4
2. Compute the time when the height of the ball is
84 feet.
The value can be computed using the square root
and fraction templates from Math1.
Tap k5N84-
120Cz16E.
The value can also be computed using a solve
command from Math1. The format is
(equation,variable) even if there is only one variable
in the equation.
Tap)`z16_[)O
2:+120=84,_
[)E.
3. A ball is tossed upwards with an initial velocity
of 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 the
Interactive and the Action menus. The Interactive
commands open a dialogue box which gives
prompts for the input. The fMax command uses x
as the default variable, but another variable such
as tcan be used.
MAIN MENU

fx-CG500 Quick Start Guide 5
Tap Interactive, Calculation, fMin/fMax, fMax
and complete the inputs as shown. (Part of the rst
coefcient, -16, has scrolled off the screen.)
Then tap OK.
4. Rewrite the expression from Question 3 in
factored form.
Tap Interactive, Transformation, factor, factor.
MAIN MENU

fx-CG500 Quick Start Guide6
Enter the expression in the box. Then tap OK.
5. This model expresses height, or position, as a
function of time. Construct a model for velocity as a
function of time.
The velocity would be the derivative of the position
function.
Tap Interactive, Calculation, diff.
MAIN MENU

fx-CG500 Quick Start Guide 7
Enter the expression in the box. (Again, part of the
rst coefcient, -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.
MAIN MENU

fx-CG500 Quick Start Guide8
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) command
on Math3.
MAIN MENU

fx-CG500 Quick Start Guide 9
7. Compute the total net distance that the ball
travels.
The ball had an initial height of 120 and fell to height
of 0, so the net distance should be -120.
For a calculus connection, integrate the velocity
function.
Tap k9P.
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, which can be found in 9.
MAIN MENU

fx-CG500 Quick Start Guide10
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 good idea 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 ball
hits the ground.
Tap Interactive, Equation, solve.
Enter the equation in the box by pressing k
and tap _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 Ekey; then tap OK.
MAIN MENU

fx-CG500 Quick Start Guide 11
Both solutions are shown; the rst solution would be
negative 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 for
velocity as a function of time.
Press kand tap 9].
Enter the expression and the variable and tap E,
or press the Ekey.
MAIN MENU

fx-CG500 Quick Start Guide12
To use the Numerical Solve menu, tap the icon, enter the equation in the box, then enter
values for the variables. Tap the bullet for the unknown variable and tap 1.
1. If a ball is tossed upwards with an initial velocity
of 56 ft/sec, from an initial height of 120 feet,
compute the times when the ball is at height
150 feet.
Enter the equation. Note that a times symbol is
needed between vand tto distinguish the product
from a single variable named vt.
Enter the values of 150, 56, and 120, select the bullet
for tand tap 1.
NUMERICAL
SOLVE MENU

fx-CG500 Quick Start Guide 13
To compute the second value for t, enter an initial
estimate, say 4, for tand tap 1.
2. If a ball is tossed upwards from an initial height of
120 feet, and has height of 160 feet after 2 seconds,
compute the initial velocity.
Enter the values of 160, 2, and 120, select the bullet
for vand tap 1.
NUMERICAL
SOLVE MENU

fx-CG500 Quick Start Guide14
1. If a ball is tossed upwards with an initial velocity
of 56 ft/sec from an initial height of 120 feet, graph
the height of the ball, as a function of time.
From the Menu, select the Graph & Table icon.
Enter the function as y1.
To set a window, tap 6, enter the values and tap
OK.
Tap $to graph.
GRAPH &
TABLE MENU
GRAPH &
TABLE MENU

fx-CG500 Quick Start Guide 15
Tap rto plot the graph in a full screen. To adjust
the window, use#"23 to scroll in any of
the four directions, +to zoom in, and -
to zoom out.
2. Compute the height of the ball at time 4 seconds.
To trace, tap =. To nd a specic value, press any
one of the number keys; this will open a dialogue
box. Then tap OK.
GRAPH &
TABLE MENU

fx-CG500 Quick Start Guide16
Press Eto mark the point and keep the
coordinates on the display.
GRAPH &
TABLE MENU

fx-CG500 Quick Start Guide 17
3. Compute the times when the ball is at height
150 feet.
Tap Analysis, G-Solve, x-Cal/y-Cal, x-Cal.
Enter the value for yand tap OK.
GRAPH &
TABLE MENU

fx-CG500 Quick Start Guide18
Press Eto mark the point and keep the coordi-
nates on the display.
Press 3to move to the second point.
4. Compute the time when the ball hits the
ground.
To compute an x-intercept, tap the 3icon at the
top of the screen, then tap Y.
GRAPH &
TABLE MENU

fx-CG500 Quick Start Guide 19
5. Compute the coordinates of the maximum point.
For a maximum point, tap the 3icon at the top of
the screen, then tap U.
6. Construct a table of values for times
{0, 1, 2, 3, 4, 5}.
To set the table, tap 8.
Enter the values and tap OK.
GRAPH &
TABLE MENU

fx-CG500 Quick Start Guide20
To view the table, tap #.
GRAPH &
TABLE MENU