Casio CFX-9850GB PLUS Manual de usuario

CASIO

Introductory

Graphics Calculator

Workshop

Using the Casio CFX-9850GB PLUS

Casio Education Division

Ph (02) 9370 9100

Fax (02) 9417 8957

Email casio.ed[email protected]m.au

GETTING STARTED WITH THE CFX-9850 GB PLUS

Turning ON

•Press the AC/ON key.

When you turn your CFX 9850 on, you will see the main menu screen. Each icon on

the main menu screen stands for a MODE on the calculator.

Below is a short summary of the main purpose(s) of each mode.

RUN – The scientific calculator

STAT – For statistical calculations

MAT – To enter, and perform row/column operations upon, matrices

LIST – To manipulate lists (can also be done in STAT mode) or change

List Files.

GRAPH – To graph and analyse functions, parametric graphs and polar

graphs.

DYNA – To look at the effect of a changing constant on the graph of a

function.

TABLE – Will produce a table of values for any function.

RECUR – To produce tables and graphs from and analyse recursive

relations.

CONICS – To graph and analyse conics.

EQUA – Will solve simultaneous equations and polynomials. Also

contains an equation solver to find the value of any pronumeral in an

equation.

PRGM – Program mode. Use this mode to write programs. Stores and

executes programs also.

TVM – Time Value of Money. For financial calculations.

LINK – Allows the calculator to link to a PC or another calculator to

transfer programs and data.

CONT – Contrast. Adjusts the contrast and colour balance.

MEM – Memory. Shows memory usage and allows you to reset

individual memories or the entire calculator. Note that resetting the

calculator will delete stored data and programs.

Resetting the Calculator

Resetting the calculator serves two main purposes:

1. It clears any previous operations that the current user may not be familiar with

or want to use.

2. It returns the calculator to its initial default settings.

♦To reset the calculator, using the arrow keys highlight the MEM (memory) icon

and press the blue EXE key. To select RESET, use the down arrow followed by

EXE. Press YES (F1) followed by the MENU key to return back to the menu

screen.

The Function Keys – F-Key(s)

To use the calculator effectively, it is important to

understand how the function keys work, that is the F1 to

F6 keys. These keys actually correspond to options that

appear along the bottom of the calculator screen once a

mode has been entered. This is illustrated in the screen

shown opposite which is in the GRAPH mode. These

functions keys are continuously used and you should be

very familiar with how they work. F1 F2 F3 F4 F5 F6

Other important keys:

(-) is the change of sign key and should only be used for this purpose

The four arrow keys to move the cursor around the screen

EXE should be pressed to enter a mode and also after typing information into

the calculator

EXIT will take you back a step

MENU will take you back to the main menu

THE SCIENTIFIC CALCULATOR

The CFX-9850 GB PLUS has identical capabilities to that of a scientific calculator. It

has a keyboard almost identical to that of a scientific calculator. All those operations

performed on a scientific calculator can be accessed using the RUN mode (MENU

1). To complete a calculation, first type an expression into the command line and

press the blue EXE key to execute the command. The EXE key (located in the

bottom right hand corner) replaces the ‘=’ key on the scientific calculator.

♦The yellow SHIFT key enables the user to access the yellow (secondary)

functions located above the calculator keys.

♦Casio Scientific and Graphic Calculators use S-VPAM (Super Visually Perfect

Algebraic Method), that is ‘how you say / write it, is how you enter it’. For

example, the square root of 12 is entered by SHIFT then X2followed by 12, i.e.

√12.

♦The power (exponentiation) function is accessed using the ∧key (next to the EXIT

key. For example, 26is entered as 2 ∧6 followed by EXE.

♦The (red) ALPHA key will allow you to access the red secondary functions.

♦The F↔D key converts a fraction to a decimal or a decimal to a fraction once a

calculation has been completed (non terminating decimals are not included!).

The Run Mode

Enter into the RUN mode from the main menu by using the arrows to highlight the

RUN mode then press EXE, or from the main menu simply press 1.

Because the calculator has been reset, it has returned to its initial default settings. To

examine the default settings of the RUN mode press SHIFT then MENU (SETUP).

Notice, for example, that the default setting for an angle is currently radians. Scroll

down the screen, using the arrows, to highlight Angle. At the bottom of the screen

you have three options for Angle:

Deg (degrees), Rad (radians) and Gra (gradients)

F1 F2 F3

Press the F-key that corresponds to degrees (i.e. F1) and note that the option has

now been changed on your screen. Press the EXIT key, then enter 10cos60 and

press EXE.

Note that you have now changed the angle setting of the calculator to degrees. The

calculator will remain in degrees until you either reset the calculator or alter the

setting as you have recently done.

Memories

Results can be stored in one of twenty six variable memories by using the key

followed by any of the letters A – Z. Recall, that to access a letter first press the red

ALPHA key followed by the corresponding letter that you want to use, then press the

EXE key.

(N.B: the letters are in red and are secondary key functions).

The calculator understands the mathematical syntax, such that LB is interpreted as

L x B.

Number patterns – A.P’s and G.P’s

The last command line is automatically stored in the Independent Memory. Useful

and practical applications of this feature involve generating Arithmetic or Geometric

Progressions, generating Time Payment or Superannuation sequences.

Store the first term of the sequence by entering the number then pressing EXE. For

example, to generate an A.P enter the first term 5 EXE, then enter the common

difference + 7, then press EXE repeatedly; this will generate the A.P which has been

constructed.

GRAPHING FUNCTIONS

Enter the GRAPH mode from the main menu.

The X,θ

θθ

θ,T Key

The variable key is located just under the red ALPHA key. This key is the only key to

be used when entering a variable in an equation.

The View-Window

The view-window option displays the dimensions and scale of the axes that appear

on the calculator screen. To access this screen, press SHIFT F3. There are three

default windows that are set up for you already. These are INITIAL (F1),

TRIGONOMETRY (F2) and STANDARD (F3). The default setting is INITIAL.

Press EXIT to leave this screen.

Drawing a Function

Type into Y1 the equation .1X(X+3)(X-3) then press EXE to store the function. To

draw, press DRAW (F6).

Trace the function by pressing TRACE (SHIFT F1). By using the left and right arrows,

you can trace the graph. Use the trace function to find the roots of this equation.

G-Solve

G-Solve stands for Graph Solve. To access G-Solv

press SHIFT then F5. With G-Solve, you can find roots,

maximums, minimums, the y intercept, intersection

points, as well as perform integrations. Press F1

(ROOT) to find the first root of the equation. To access

the second and third roots, press the right arrow key.

Integration

Press G-SOLV (SHIFT F5) then F6 (the continuation key) and finally ∫dx (F3). Use

the left arrow key to set the lower limit at X=-3 then press EXE. Set the upper limit at

X=0 and press EXE.

Finding the gradient of the tangent at a point

Press SHIFT MENU to enter the SETUP of the graph mode. Highlight Derivative,

and press ON (F1). Press EXIT and DRAW (F6) then trace the function again by

pressing TRACE (SHIFT F1). This will now show the derivative at each point on the

function.

Graphing The First and Second Derivative

To graph the derivative of this function, press EXIT to allow you to type in another

function and highlight Y2. Press OPTN, CALC, d/dx (F1). Then press VARS, GRPH

(F4), Y (F1). Then type 1, X and close the brackets. Press EXE and DRAW (F6). You

can trace these graphs by pressing TRACE (SHIFT F1). To trace the graph of the

derivative, press the down arrow. It is possible to draw the derivative in a different

colour than the original function.

It is possible to draw the second derivative of the function using the same process.

Zooming and Sketching

Once you have drawn a particular function, by pressing SHIFT F2 you will activate

the Zoom option. This allows the user to zoom in or out from a particular point on the

function by a given or specified factor. It will also allow the user to zoom in on a

specific part of the graph, for example a root or point of intersection.

Again, once a function has been drawn, you can activate the Sketch option by

pressing SHIFT F4. Using this option allows us to sketch tangents, normals, inverse

functions, draw a circle with a specified radius, sketch vertical and horizontal lines

and more!

Absolute Value Graphs

To draw an absolute value function first press OPTN

followed by NUM (F5) then Abs (F1). If there is more than

one term in the function to be sketched, make sure that

brackets are used after the Abs notation.

Inequalities

From the text screen in the GRAPH mode, press TYPE (F3) then the continuation

key (F6) and the options for sketching inequalities will appear on the screen. Press

Y> (F1) and note the change at the top of the screen. Enter the equations as shown

below, draw and observe the region satisfied by the two inequalities.

Families of Functions / Restricted Domains

The GRAPH will allow us to investigate families of functions in a very purposeful and

constructive manner. For example, if a student wants to understand the effect of the

addition of a constant in a quadratic function.

The { } parentheses, secondary functions above the multiplication and division keys,

allow us to construct and draw a family of functions. To complete this investigation

make Y1 = x2+ {-2, -1, 0, 1, 2}, store and draw the function using the initial view

window. Note that all five functions will be draw on the same coordinate plane.

To restrict the domain of a function use the

‘square’ parentheses [ ].

GRAPHING FUNCTIONS

Sketching Trigonometric Functions

Before sketching a trig function you must decide whether to sketch in degrees or

radians. For the purposes of this example, it is imperative that we sketch in radians.

From the RUN mode enter the SET UP (SHIFT

MENU) and check that the Angle setting of the

calculator is set to radians. If not, scroll down using

the down arrow to Angle, then press Rad (F2).

EXIT the SET UP, press MENU and enter into the

GRAPH mode of the calculator (MENU 5). Once in the

GRAPH mode, alter the View-Window (SHIFT F3) to

the TRIG (F2) setting.

Note that the default trig setting sketches the trig

function for {x: -3π≤x ≤3π}

Press EXIT to return to the text screen. Use the functions available in the GRAPH

mode to sketch y = sin x, and find its derivative in the given domain.

To enter the ‘d/dx’ symbol press OPTN then CALC

(F2) (to access the calculus options) followed by F1

(d/dx).

You may wish to draw Y2 in a different colour. If so,

press COLR (F4) then choose the colour that you want

to use. Orange (F2) is an excellent contrast to blue or

green. To draw the two functions press DRAW (F6).

To enter the ‘Y’ symbol press VARS (variables) then

GRPH (F4) followed by Y (F1). Notice that the graph

of cos x has been drawn against the graph of sin x,

exposing the result that the first derivative of sin x w.r.t

x is actually cos x.

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