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TI 84 HELP MANUAL

INDEX

Topic Page Number

Angles (degrees, minutes, seconds) and Time 29 Composite Functions 31 Equation of a Line (Graphing) 11 Error messages when graphing (see Graphs) 16 Financial Mathematics 7 Fractions 5 Graphs 16 Histogram 19 Introduction 2 Lists (entering data) 14 Math( emetics) Menu 7 Operating System 32 Operations with TI84 3 Settings 4 Scattergram (Scatterplot, point graph etc) 22 Scientific Notation 6 Statistics (Singular and Multiple Frequencies) 13 Storing Values 30 Table Function 9 Transmitting Data/Lists/Programmes/Applications etc 24 Trouble Shooting (Errors in graphing) 16 Y Variables 11

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TI 84 HELP MANUAL

This manual is to be used in conjunction with the manual/CD supplied with the TI 84 calculator.

The second functions on the calculator are printed in yellow on the calculator face. To access these functions, you must press y keypad first. For example, press y [DRAW] to work with the drawing functions.

The home screen is the screen where calculations take place.

Press . Before you press to calculate the value, you wish to change the sum. Press . This clears the line.

Suppose you had pressed and the answer was 131. Your next problem to evaluate was . You wish to clear the screen. If you press twice you will clear the screen. The first clears the line and the second clears the screen. If there was nothing in the new line, then pressing would clear the screen first time round.

To move from one menu to home screen, always use y [QUIT] (it will save many problems in the future).

The only way to become proficient in the use of the TI84 is to use it frequently.

At times, the batteries will run down and you will find it hard to see the screen (or the screen may be too dark).

Press y (take your finger off the keypad) and press (hold down) } or to adjust your screen. (You may find it easier to type a few numbers first before

you adjust the contrast)

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OPERATIONS (ARITHMETIC) WITH THE TI84

Evaluate (a) 62 (b) 54 (c) 36

Press

Press

Press y [ ]

Second Entry At times, you can save time by accessing previous calculations that you have entered by pressing y [ENTRY]. Each time that you press these keypads you can recall what you have previously calculated. Press y [ENTRY] repeatedly.

At times, you may have entered a long calculation and pressed before you realised that you had made a typing error. Do not panic. Press y [ENTRY] and use the | and ~ keypads to place the cursor where you want to correct the error.

The should have been a . Press y [ENTRY] and place the cursor (using the arrow keypads) over the and press and press .

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SETTINGS ON THE TI 84

Press z to see/check the settings. Generally you will have all the settings highlighted on the left hand side of the screen.

To highlight other settings use your arrow keys (|, ~, }, ) and press .

Sci mode displays all numbers on the screen in scientific notation.

Float displays up to 9 decimal places on the screen. To show the number of decimal places you want press then ~ and then .

This allows you to display 2 decimal places on the screen. As well, it shows 6 as 6.00.

To check your answer to a rounding decimal problem, set your calculator to the required number of decimal places and then type in your number and then press .

For example, round 16.37198 to three decimal places. Set to 3 decimal places, type in 16.37198 and press .

Split Screen As seen below with a horizontal split, you will see your graphs and any calculations.

If you select G-T, you will see graphs and tables of values (or selected table of values depending on your calculator settings. In the example below you will see a graph of y = 2x + 3 and co-ordinates starting at (-3, -3).

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FRACTIONS

There is only a conversion fraction button on the TI 84. For example you wish to convert 0.4 to a fraction. Type in 0.4, press and then .

What about 1.8 to a fraction? Follow the above procedure. You will notice that the calculator will return an improper fraction. To get around this, only convert 0.8 to a fraction.

The answer is 541 .

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517 ? Type in the question as it appears

using brackets.

You could convert it to an improper fraction by utilising the menu. Press then and you will notice that the decimal answer is replaced by Ans.

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The best-written answer is written as a mixed fraction. Follow the above procedures and you will establish the mixed fraction.

The answer is 1584 .

Addition, multiplication and division of fractions follow the same procedures.

SCIENTIFIC NOTATION

To have every number on the main screen appearing in scientific notation, set the mode screen.

Now, any number typed in and entered will appear in scientific notation.

Reminder: 6.96 E 3 is written as 31096.6 .

4.5 E -2 is written as 2105.4 .

To enter a number in scientific notation can be done two ways. You can enter using the [EE] (which is the second function of the key) or using the power button .

3.2 x 1011. Press y[EE] or 10 .

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MATH(EMATICS) MENU

The is one menu screen that you will use a great deal. Press and you will see near the 7, it shows there are more commands below. By using the , you will find -

Using either | or ~, you will see the other menus.

See manual/CD for correct syntax when using commands from these menus.

FINANCIAL MATHEMATICS

To access the financial mathematics on the TI 84 is slightly different to the TI 84 Plus.

TI 84 TI 84 Plus y [FINANCE] then [APPS]

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Press

Press to access the finance menu.

The TVM Solver is a very useful for financial mathematics. For example, you wish to invest $5 000 for 4 years at 6.5% per annum compounding monthly. How much would you have after 4 years?

N = 4 * 12 = 48 (number of interest periods) Interest Rate = 6.5 Present Value = $5 000 Payment (PMT) = 0 (You are not making a payment) Future Value = ???? Payment per year = 12 Compounding per year = 12

Place the cursor on the line of Future Value and press [SOLVE]

Another example:

I wish to borrow $280 000 to purchase a house. The interest rate is 6.57% per year, compounding monthly. How much would my weekly payments be if I wish to pay off the loan in 15 years?

N = 15 * 52 = 780 I% = 6.57 PV = 280 000 PMT = ???? (Does not matter if there is another value from another calculation in PMT) FV = 0 (loan is to be paid off) P/Y = 52 C/Y = 12

Place the cursor on the line of PMT and press [SOLVE]

Do not worry about the negative value as it represents money going out from you (i.e. a payment).

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Another example:

How much should I invest now to receive $5 000 (it includes interest and the amount invested) if invest for 2 years at 3.5% p.a. compounding quarterly?

N = 2 * 4 = 8 I% = 3.5 PV = ????? (As stated before, do not worry about the value in PV) PMT = 0 FV = 5 000 P/Y = 4 C/Y = 4

Place the cursor on the line of PV and press [SOLVE]

Do not worry about the negative value as it represents money going out from you (i.e. a payment).

TABLE FUNCTION

Press o and enter Press y [TBLSET] and input the data as shown.

Press y [TABLE]

This shows the values of y = 2x + 5 for values of x starting at x = -3 and increasing by 1 each time.

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What if you wanted to start at 2.3 and increase in increments of 0.2?

Press y [TBLSET] and input the data as shown.

Press y [TABLE]

This shows the values of y = 2x + 5 for values of x starting at x = 2.3 and increasing by 0.2 each time.

If you wish to enter the x-values yourself, press y [TBLSET]. Change the independent to ask by using ~ . This gets the TI 84 to prompt you for the x-values.

Press y [TABLE] to input values.

Press and the value of 13 is shown in the Y1 column.

Y1 = 2*4 + 5. You can have more equations (i.e. Y2)

Press o enter 3x - 1 into Y2

y [TABLE] . For x = 3, the values of Y1 and Y2 are calculated (Y1 = 2*3 + 5 and Y2 = 3*3 - 1).

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Y VARIABLES

Calculate the value of y = 3x + 1 when x = 2.

Into o type y [QUIT] ~

You may wish to evaluate the expression with other values for the variable. ~ y { y } . i.e. x =2, y = 7 and x = 5, y = 16.

EQUATION OF A LINE

Press p to view the default domain (x values) and range (y values) of the drawing window. You can change the values of each of the components.

Xscl and Yscl refers to the scales on each of the axes. The default setting is that the scale increases by one starting from -10 going up to 10.

Press o . If there are any equations, press when you are in the line corresponding to each of the equations. until all equations have been cleared.

Input y = 2x + 3 into Y1. Press .

If you have the default settings and then pressing s, you will see the following:

Do not panic if there are other graphs (histogram, scattergram, box-and-whisker) drawn as well. (See Graphs section (fixing errors) page 16).

If there are other graphs, press y [STAT PLOT] and press then (turns off all plots). Press s to draw line again.

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Press p and change the settings to: and pressing s , you will see:

If you wish to know the co-ordinates of specific points, whilst you are viewing the graph, press r . In the top left corner you will see the equation that you are tracing and the co-ordinate that the cursor is on.

Press, for example , you will see:

You then can check other co-ordinates, but be careful as if you enter , you will get an error message. Do not panic, it is just that the cursor is off the screen and you have set it to view a small portion. Press ( to quit) and you will be back at the home screen. Press p and change your window to suit your requirements.

To change the window to the default settings press q then and you will have a new graph(s) drawn with the new settings (window). The following shows that y = 2x + 3 plotted and tracing the point (2, 7).

If you then press either the left | or right | arrow keypads, then you will notice that the points on the screen have decimal points.

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Do not be alarmed as the TI 84 has very good resolution, but it is not as good as a computer. The TI 84 screen is made up of pixels (larger than that of a computer). The calculator is still tracing the points.

If you wish to view a table of values (i.e. x and y co-ordinates) of an equation, use the TBLSET and TABLE functions. Y = 2x + 3 is still in Y1. Press y [TBLSET] and set the calculator to the following. The table of values (x) will start at -3 and increase by 1 each time.

Press y [TABLE]

The y-values are calculated for you. By using the } and keypads, you can see the calculated values that are not on the screen. For example, x = 2, y = 7 (y = 2*2 + 3).

A reminder, you could use the table setup menu to ask for the value of the independent variable (x). Press y [TBLSET]. Press y [TABLE] to input values of the independent variable.

STATISTICS

To enter data in the statistics function, press . Whilst here, notice the CALC command. If you wish to do any calculations involving statistics, you will find them here.

Press or .

There is data in the lists. To clear the data press } (the cursor will be on L1) and then press . This will clear all the data in list 1. Press to start entering data in list 1. Clear other lists if you wish. You do not have to clear all lists if you only wish to work with, for example, list 1 and list 2.

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Sometimes you may delete a list instead of clearing it. Do not panic. If you have used your cursor to highlight L2 (for example) and pressed { (delete), you will find that the entire column will disappear. To insert a list, place your cursor where you want to insert a list and press y [INS] and then name the list by pressing y .

The previous data has not been deleted. Clear the lists by pressing the keypad.

To enter data in a list

Press to display the Lists screen and use the above information to clear L1. Enter data in L1 and press or after each entry.

To correct a value, place the cursor over the incorrect value, type the correct value and press or .

To insert a value, highlight the value below the required insertion point, press y [INS], type the value and press or .

To delete a value, highlight the value and press or .

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For example, you wish to perform some calculations on the following 12, 14, 8, 19, 15 (single frequency data). Enter the data in a list (usually L1). If you enter the data in a list other than L1 (which is the default list), be careful with calculations you may require (read carefully). The following example has the same data in L1 and L4.

Press y [QUIT] to return to the home screen. Press ~ to show the CALC menu. Press to perform some calculations.

Because the data is not in L1 (the default), you must tell the calculator that the data is in another list. Press y [L4].

Pressing to show calculations.

Use to see other calculated values (and you can use } to go back up to the other calculated values).

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Multiple frequency data.

For example, Goals per game

0 1 2 3 4

Frequency 5 8 9 4 1

Enter the Goals per game into L2 and the Frequency in L3 (it does not matter which list you input the data into).

As with the single frequency data (above), you must tell the calculator where the data is stored. Press y [L2] [L3] and press .

Again, you can use your } and keypads to look at the calculated values.

GRAPHS (HISTOGRAMS, SCATTERGRAM, BOX-AND-WHISKER)

One of the many questions asked is why the graphs are not being drawn correctly. As well, many ask why there are other graphs drawn.

Suggestion: use some of the following procedures before you enter data into lists, enter equations into o or press s .

Procedures to follow before graphing

1 Check window values (i.e. portion of the cartesian plane is what you want to see). Press p . For example, you may want to see the graph for the values of x between 5 and 9 and this window will not allow you to do this.

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2 Check that the data entered in lists match up (i.e. for example, 6 values in L1 and 5 values in L2).

If you press s , the TI84 will give you an error message. For example, if you enter the data shown, have a STATPLOT on and press s, the TI84 will give you an error message.

3 Another problem could be that you have graphs turned on, but there is no data for the TI84 to graph. The TI84 has been told to graph a connected line graph for data in L2 and L3, but there is no data to graph.

4 Due to games and programming, the [FORMAT] menu will be changed. Press y [FORMAT] and have the menu as shown. Highlight the options on the left-hand side of the menu. Use }, , |, ~ keys to put cursor over the commands then press .

5 Delete equations in the o menu. Use your arrow keys and the button to delete the equations.

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Looking at this screen, you can see that Plot 1 is ON. Whilst in this menu, you can use the arrow keys to put the cursor on Plot 1 and press . Plot 1 is turned OFF. (You can also turn plots on.)

6 Turn off all Stat Plots. Press y [STAT PLOT]. For example, 2 plots have been turned on.

Press and .

All plots have been turned off.

You could individually turn off some plots, but it is just as easy to turn all plots off.

7 To turn off the equations (and leave them in the lines), place the cursor on the = and press .

8 Another procedure is to reset the defaults. Press y [MEM] . Only use this method as a last resort.

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You are now ready to draw graphs.

Histogram

Graph the following data:

Score 2 3 4 5 6 Frequency 3 6 12 8 4

Enter the Scores in L1 and the Frequency in L2 (Refer to Statistics Section Page 13)

Press y [STAT PLOT]. Select a number for a plot ( , , or ). Move cursor to be over ON and press .

Of course, move your cursor key and position it over the and press to highlight the histogram.

You will notice that the Xlist has changed to the default and the frequency is changed to the default value of 1. Use your arrow keys and place your cursor over L1 and press y (to select L1) (only if you have entered the scores in a list other than L1). As with the frequency, press y (to select L2).

Do not press s yet. You must check your window (your viewing section).

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If you press q and (sets the default x and y values for the cartesian plane)

If no graphs have been set to draw, you will get the screen shown left.

If you press p , you will see the default values for the cartesian plane.

Before you press s , read the Procedures to follow before graphing on page 16 .

Pressing s will result in the following screen.

You do not want the all of the cartesian plane and the graph goes off the screen.

Press p and use your arrow keys to determine the axes values. Generally the score is the x-axis and the frequency is the y-axis.

The scores went from 2 to 6 and the frequency went from 4 to 12.

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For a correct histogram, start Xmin at -0.5 and the Xscl (x scale) equal to 1 (each column in 1 unit wide).

For each axis, go one value higher to fit the graph neatly on the viewing window.

Press s .

By starting the x-values at -.0.5, you have a correct graph that is easier to read values.

Pressing r and using your arrow keys, you can see what the scores and the frequencies are. For example, the bar highlighted does show x = 3, but if you look below the bar, you will see a stroke that signifies 3 (between 2.5 and 3.5).

As well, you noticed that when using the r facility, the trace values are over the graph. Press p and change your lowest y-value to -5 and this will allow optimum viewing of your graph. Press r and use your arrow keys as before.

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SCATTERGRAM, SCATTER PLOT, POINT GRAPH (MANY NAMES)

Graph the following data:

Score 4 5 6 7 8 Frequency 6 12 15 9 5

Enter the Scores in L3 and the Frequency in L4 as there is data in L1 and L2. You could always clear the previous data. (Refer to Statistics Section Page 13)

Press y [STAT PLOT]. Before you select a number for a plot ( , , or ), decide whether to keep Plot 1 on or turn the setting off.

We shall keep the setting for Plot 1 (histogram), but turn the setting off.

Press and move your cursor to the Off position and press to turn off Plot 1.

You could use your arrow key to move up to Plot 2 and press to change the settings for Plot 2.

Another way is to Press y [STAT PLOT] again and press to select Plot 2.

Move cursor to be over ON and press .

Of course, move your cursor key and position it over the " and press to highlight the scattergram.

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We must change the Xlist and Ylist.

Use your arrow keys and place your cursor over L1 and press y (to select L3). As with the frequency, press y (to select L4).

It is up to you to choose which mark to use.

Before you press s , read the Procedures to follow before graphing on page 16 .

If you had pressed s , you would have seen the screen. What is the problem? Your viewing window is still set for the histogram.

Press p and change the viewing window to your settings. Generally, the score is the x-axis and the frequency is the y-axis.

If you had changed the window to the settings shown and then pressed s , you would get the following graph, but no axes. If you wish to see the two axes, start the scales at 0.

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TRANSMITTING LISTS/PROGRAMMES/DATA/APPLICATIONS (and other data) TO ANOTHER TI84

By pressing y[LINK], you will see

Pressing the } and keypads, you will see what can be transmitted between calculators.

Transmitting Lists

Connect both TI84 calculators via the link cable. Ensure the cable is firmly pushed in on both calculators.

Press y[LINK] on both calculators

Receiving TI84 Transmitting TI84

Press ~ Press then press then on the lists you which to send

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Press ~ to highlight TRANSMIT

You must press on your TI84 first (i.e. the receiving TI84). Now press on the calculator you are transferring data from.

You may find that you will need to press to overwrite the lists on your TI84.

As well, you can highlight everything by pressing whilst you are in the [LINK] screen.

Press ~ to highlight TRANSMIT on the sending calculator.

You must press on your TI84 first (i.e. the receiving TI84). Now press on the calculator you are transferring data from.

You may find that you will need to press to overwrite on your TI84.

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Transmitting Programmes

Connect both TI84 calculators via the link cable. Ensure the cable is firmly pushed in on both calculators.

Press y[LINK] on both calculators

Receiving TI84 Transmitting TI84

Press ~ Press then press then on the programmes you which to send

Use } and and keypads to highlight which programmes to transmit.

Press ~ to highlight TRANSMIT on the sending calculator.

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You must press on your TI84 first (i.e. the receiving TI84). Now press on the calculator you are transferring data from.

You may find that you will need to press to overwrite the programmes on your TI84.

Transmitting Applications

Many applications can be transmitted from calculator to calculator. They can also be downloaded from www.education.ti.com.

Connect both TI84 calculators via the link cable. Ensure the cable is firmly pushed in on both calculators.

Press y[LINK] on both calculators

Receiving TI84 Transmitting TI84

Press ~ Press then press when cursor is on C (corresponds to Apps).

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Press and use your } and and keypads to highlight which Applications to transmit.

Press ~ to highlight TRANSMIT on the sending calculator.

You must press on your TI84 first (i.e. the receiving TI84). Now press on the calculator you are transferring data from.

You may find that you will need to press to overwrite the Applications on your TI84.

Transmitting a mixture of lists, programmes, applications etc.

Connect both TI84 calculators via the link cable. Ensure the cable is firmly pushed in on both calculators.

Press y[LINK] on both calculators

Receiving TI84 Transmitting TI84

Press ~

To highlight a mixture of lists, programmes and data, press on the transmitting TI84. Highlight the ones you wish to send by using your } and and keypads.

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Press ~ to highlight TRANSMIT on the sending calculator.

You must press on your TI84 first (i.e. the receiving TI84). Now press on the calculator you are transferring data from.

You may find that you will need to press to overwrite the programmes on your TI84.

ANGLES (DEGREES, MINUTES, SECONDS) AND TIME

To enter angles, you must know where the symbols are. Press y [ANGLE]. Degrees and Minutes are here and to access seconds, you must use .

To enter 16o 37' 18" (16 degrees, 37 minutes and 18 seconds);

Press y [ANGLE] y [ANGLE] 18

If you press enter, you will see that the answer on the screen has been changed to degrees.

If you wish to convert the answer back to degrees, minutes and seconds, access the ANGLE menu.

Press . Press

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As well, the degrees/minutes/seconds corresponds to hours, minutes and seconds. You may wish to find the difference in time. For example, what is the time difference between 6:40am and 7:03pm? You must work in 24 hour time and hence, 7:03pm is 1903 hours. Use the angle facility to find the difference in time and convert back to hours and minutes.

You must be careful when checking time differences over 2 or more days.

As shown on the left, you can do all the calculations in one step.

The answer is 12 hours and 23 minutes.

To enter any time between 12am and 1am, you must enter 0o first.

For example, what is the time difference between 12:53am and 4:12 pm?

The answer is 15 hours and 19 minutes.

STORING VALUES

Storing values on the TI84 is very easy. Yes, you can use the calculator as a telephone directory. For example, 4 is stored in B and 3390 1234 is my friend Graphica's home number.

Press [B] and .

Press [G] and .

To access these numbers, you simply use the and the corresponding letter.

You can also store another answer.

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COMPOSITE FUNCTIONS

The effect of applying one function, Y1, then another function, Y2, can be achieved via the composite function Y2(Y1).

If f(x) = 3x + 1 and g(x) = 2x2 - 5

Enter the equations into Y1 and Y2 by pressing the o.

Press y [QUIT] to display the home screen.

Press ~ (Y-Vars) (Function) (for Y1) and type in . This will calculate f(2).

This screen capture shows the calculations f(2) and g(7) which is the same as g(f(2)).

As well, you can find the inverse of functions. For example, (f(3))-1.

For the inverse, use the .

Another way in which to find values of composite functions and inverses is to use the o.

In Y3 enter Y2(Y1) which represents g(f(x)) and if you wish to enter Y1-1 which represents f-1(x).

See Table Function, Page 9, (set the TBLSET Independent to ASK).

Press y [TABLE] to access table and enter 2. To access Y3 and Y4 use your ~ and | keys.

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OPERATING SYSTEM

One of the benefits of having a TI84 plus calculator is that you can update your operating system. You can log onto www.education.ti.com and download the operating system or download it from another TI84 plus calculator.

Warning: Updating operating system will delete RAM memory (i.e. programmes, lists, games etc). Backup your data on another calculator or on your computer (TI Connect software).

Connect both TI84 calculators via the link cable. Ensure the cable is firmly pushed in on both calculators.

Press y [LINK] on both calculators

Receiving TI84 Transmitting TI84

Press ~ Press } and place cursor over G.

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You must press on your TI84 first (i.e. the receiving TI84). Now press on the calculator you are transferring the Operating System from.