**Introduction**

Mathematics is the father of all sciences. Human beings need mathematics to calculate, evaluate, and integrate different aspects of science. We cannot survive without mathematics and its uses, whether it may be a thing as basic as paying the bill in the restaurant, a little specific thing like the calculation of profit and loss, or a far more complex calculation of a partial differential equation having ten or more independent variables to solve a complex physical behavior in the environment. The use of calculators in solving mathematical problems has become a need of time as nowadays researches are becoming more complex and solving mathematical equations by hand has become impossible. It is now necessary to develop methods that can provide us with quick and accurate results for mathematical problems with precision. The need for calculators is essential to analyze different complex problems and how they will affect our lives. We need calculators to physically see the behavior of processes and observe their decline and increase as they change.

Many students and teachers recommend the use of a calculator and believe that a calculator is a need of time. In America, 99% of schools recommend the use of calculators and allow their students to use calculators during their school time and while completing assignments. With the development of mathematics research and its applications in science, our calculators have become more and more complex. As more and more functionalities are added to calculators, the more difficult it becomes to use them and understand how their functionalities can be used to solve problems. Nowadays, complex mathematical equations and formulas are integrated into calculators, and they save us time when calculating these equations by hand. Discrete mathematics is the gateway to research in modern mathematics. In the field of discrete mathematics, calculators are needed to perform computer operations. In this field, an analysis of graphs is needed to find out about discrete structures like trees and networks.

#### TI-84 Plus CE

Graphing calculators are used to perform the simplest thematic, from sum and multiplication to complex calculations of probability and statistics. The TI-84 Plus series is a new series of graphical calculators that was recently introduced by Texas Instruments. This series contains TI-84 Plus C Silver, TI-84 Plus CE, and TI-84 Plus. This paper will focus on the features of TI-84 Plus CE. Next, we will describe the functions of this calculator from basic to very complex.

**Keyboard**

This section covers basic functions in the TI-84 CE calculator

#### Turning ON

- Press ON
- To continue to the home screen, press 1

An information box will appear and suggest keys for the shortcut menu

To locate short, cuts press alpha [f1] – [f4].

To add a shortcut to cartilage, press +

#### Turning OFF

To turn off the calculator, press 2^{nd} + OFF

Turning off the calculator will clear all memory, settings, and errors.

Automatic Power Down

To conserve battery, TI-84 CE has a built-in timer that turns it off after a 3-minute inactive period.

By turning it off automatically, the memory will not clear, and it will return to the screen where it was left.

**Keyboard Functions**

The keyboard contains 48 keys, including the four arrow keys. Based on their functionalities, these keys are categorized below.

#### Graph/Plot Setup Keys

These are the 5 top row keys that are used for interactive graphing features; these keys are y=( state plot f1), window (tablet f2), zoom (format f3), trace (calc f4), graph ( table f5)

#### Editing Keys

These are the second and third-row keys to edit the written expressions and values on the screen; these keys are 2^{nd}, mode, del, alpha, (X, T, θ, n), and stat.

#### Maths And Statistics Keys

These are the five basic math and statistics operation keys.

#### Scientific Keys

These are the nine trigonometric, logarithmic, and power and inverse function keys.

#### Number Keys

These are the 9 number keys to enter numbers

#### Common Math Function Keys

To perform basic math operations of sum, subtract, divide, and multiplication.

**Function Keys**

These are the function keys to use functions written above keys:

2^{nd}

To use the second function written on the top left of the first row keys

#### Alpha

To use the third function written above each key

#### Alpha [F1]- [F4]

To use the fraction format, p/q, matrix entry, Math menu, and VARS menu functions

#### Alpha [F5]

To use options for the DRAW command while using GRAPH.

**Function Keys Usage**

- Primary Functions: functions written on the keys. Example: To use the sine function, press sin.
- Secondary Functions: the functions written above keys are accessible after using the 2
^{nd}Example: to take cos inverse, press 2^{nd}+ cos. - Pressing the 2
^{nd}key toggles all functions to secondary functions above each key. - Alpha (Tertiary) Functions: These are the functions written above the keys in the same color as the alpha key.
- These functions allow users to add special symbols and SOLVE shortcut menus. For example, to use the letter A, press alpha + math.
- To add a series of alphabetical characters, use 2
^{nd}+ A-Lock. This function enables multiple entries of alphabetical letters. Pressing alpha again will disengage the function.

#### Home Screen Usage

The home screen has two parts: right and left. The left part displays entered expressions, and the right part displays answers.

The home screen will display the current characters used in the expression and the history of previous expressions. Press ˄ and ˅ to see the history of previous calculations.

#### Example:

Press 2^{nd} √ 3 *x*^{2} + 4 ˃ + 6 enter

To evaluate the following expression:

Note: when you are using the MathPrint template, the cursor turns into the right arrow, which requires pressing ˃ to get out of the MathPrint template.

#### Mathprint Mode

When an expression is long, the ˃ key is used to see the whole expression.

**Calculator Modes**

Mode settings govern how the calculator displays and interprets:

- Answers
- Elements of lists and matrices
- Graphs
- Language settings
- Numbers

#### Setting Up Calculator Mode

The calculator has the following modes:

- Answers
- Elements of lists
- Graph
- Language
- Numbers

- To set the mode, press up and down to scroll between the lines where you want to change mode.
- Use left and right to move the cursor between settings
- Press enter to select a setting

#### Mathprint Classic

This mode is used to display the expressions in a natural way.

#### Normal Sci Eng

This mode is used to display answers in standard format when there is a decimal in the answer.

NORMAL, ENG and SCI modes can be switched to display answers in each format.

#### Float

This setting displays answers up to 10 digits. Selecting the desired number of digits will display after the decimal point.

__Example:__

- An answer that has a decimal value is displayed on the screen.
- A graph which has x and y quadrants, to display the values of coordinates in x and y
- To express a point in the slope of the tangent line.
- Result of an angle calculation in radians or degrees.

#### Radian Degree

This mode will switch the answer calculated between radians and degrees.

RADIAN: takes values as input in radians and provides answers in radians.

DEGREE: takes values as input in degree and provides an answer in degree.

**Evaluating Expressions**

An expression may include numbers, variables, characters, and function operators.

#### Order Of Operations

The order of operations defines the way expressions are added and evaluated in the calculator.

Note: the functions appearing first in the expression are evaluated first

#### Implied Multiplication

The calculator understands the implied multiplication even when the multiplication sign is not used in the expression.

#### Parentheses

The calculator evaluates the characters used in parentheses first.

#### Negation

The negation value is taken as input if we use the “-” sign before any number; the same rule applies to powers.

The use of parentheses is required when taking the power of more than one character expression.

**Graphs**

The TI 84 CE can represent graphs and draw points on the graph. Further, we will explain its various features.

#### Use Of Color In Display

The calculator has many different colors.

To edit the color, Y= can be used to change the line color.

Draw commands can be used to change between colors.

The left and right arrow keys switch between color options.

#### Setting A Background Image

The calculator also has the option to set the background color. The images vary in size, so TI Connect software can be used to send images of different sizes to the calculator. QuickPlot and Fit Equation can be used to auto-adjust the equation or graph in shape.

#### Quick plot And Fit Equation

This allows the user to add points to the displayed graph. The user can select the color and style of the plot and select an equation for the plot.

#### Images In Graph

The calculator can incorporate graphs in the plot. It needs software by Texas Instruments TI Connect CE from where images can be selected, adjusted in size, and sent to the calculator.

#### Piecewise Function

The calculator can also add a piecewise function

#### Tables

When a table is used, x and y coordinates are to be used. The user can view a table by selecting the table option. The table set function can be used to see how the values will be displayed.

**Matrices**

The calculator can perform matrix operations of Matrix addition, Matrix multiplication, division, inverse, subtraction, and elementary row operations.

#### Matrix Editor

To use the matrices, the user will have to use the matrix editor to enter the matrix menu.

There are a total of ten matrices allowed for matrix operations in one calculation.

To use the matrices, the user first enters the dimension of the matrix and then enters the values.

Example: a 3×3 matrix saved in memory

#### Matrix Calculation

To use the matrix operation, first, the user has to return to the home center and enter the matrix submenu to use a matrix command. The matrix name will be displayed above the matrix. Matrices names cannot be added manually in the calculator.

__Example:__

Determinant of a 3×3 matrix.

To perform the determinant of a matrix, we first have to enter the matrix submenu by the 2^{nd} / matrix key.

Next, enter the command 1:det( command

Press 2^{nd}/ matrix Names: 3: [C]

**Probability Functions**

The calculator can also perform functions of probability and statistics. The probability functions consist of random numbers generated by the system in the calculator.

#### Features

The probability functions can be used by the PROB submenu in the math menu.

__Example:__

Generating five random numbers between 10 and 25.

Go to the PROB submenu and enter command 5: randl( and press enter.

Enter the min value of the range and press enter.

Enter the maximum value and press enter.

Enter the number integers (n) and press enter

Press enter twice to see the generated random numbers.

Note: the calculator will present the same random number for a given sequence. We can also use different sets of integers by saving a non-zero value in rand memory and then computing the answer.

**Statistics**

Statistics functions allow one to make a list of data and analyze and plot the results. There are a number of commands that can be used for statistics operations. Users can create a list of data and analyze the data using statistics commands.

The following functions are available in statistics:

- Regressions
- Statistic plot definitions
- Distributions
- Statistical analysis of lists.
- Sine and Logistic analysis of regressions
- Multiple variable analysis.
- Statistical tests.

__Examples:__

To generate a list of data:

Enter the statistics menu and go to the EDIT submenu.

Enter the data into the list editor.

Lists 1 to 6 are built-in lists. Users can also create customized name lists.

__Plotting the data:__

To plot the data of lists, the user will have to enter the stat plot submenu. In this example, the stat plots of lists 1 and 2 are generated.

Highlight the row by using the left button.

The user can also zoom in to auto-adjust the view of the graph and manually zoom in on the graph and certain points.

The statistical data can be plotted in multiple ways in this calculator

- XY-line plot
- Histogram plot
- Scatter plot
- Modified box and whisker plot
- Probability plot

__Example:__

Two variable statistics for lists 1 and 2

Select the start menu

Select CALC submenu

Select 2:2-Var Stats and press enter

Select calculate, and press enter

The following screen will display the variable statistics of lists 1 and 2

**Variables**

The calculator can deal with multiple types of variables, including real and complex numbers, list functions, statistics plots, graph databases, and pictures.

#### Storing Values In Variables

To store a value in a variable, the user has to go to the “to” key

- Enter the value to be stored
- Press sto.
- Press alpha, select the character for which you want to store the value, and then press enter.
- The calculator will store the value in the character.

#### Display A Stored Value

The user can see the value stored in a variable by typing the character and pressing enter. If the value has not been initialized, the character will show the last saved value or zero if no value is stored.

#### Recalling Variable Values

The user can also recall and copy the value of the variable to the cursor location

Example:

- To recall a value, press 2
^{nd}/ rcl. - To recall the value of a variable, enter the character whose value needs to be recalled.
- To recall values in a list, press 2
^{nd}/rcl and select the name that needs to be recalled. - To recall a matrix, select the matrix, select 2
^{nd}/rcl, and select the name of the matrix that needs to be recalled.

Pressing VARS will display all the current variables stored

**Equations**

The calculator can solve a wide range of equations with multiple characters in each row. The equations can contain numbers, characters, terms, and mathematical operators.

#### Expression

To solve an expression, go to the math menu, go to the Numeric solver submenu, enter equation 1 and equation 2, and press ok.

The value stored in the variable will be overwritten by a new value, and it can be seen by recall operation.

The screen will also show what the bounds are for that solution, and their range can also be set manually.

**Error Conditions**

There are four types of errors that can arise when performing operations on the TI-84 CE calculator.

- Expression errors
- Instruction execution error
- Graph plotting errors
- Value storing errors.

#### Rectification

The error rectification process for any type of error is described below:

- The first step is to determine the error. This information can be gathered from the display screen, but it is also possible that it is not too explained.
- Correct the expression.
- Notice the error type.
- Go to the previous screen to find the error location.
- Take help from the error message.
- Determine the error type.
- Correct the expression.

**Management Of Calculator Files**

The calculator also has the facility to transfer files from the calculator to another calculator if their operating systems are compatible with each other.

#### OS Transfer Between Calculators

To transfer operating systems, two calculators are connected to each other by a two-way USB port. The communication between the calculators is started when, after connecting, the receiver calculator enables the RECEIVE option by following the prompt: 2nd/ [link]/ > / [enter].

After the first calculator is enabled, the receiving will display a message of waiting to show that it is now waiting for the other calculator to respond.

The sending calculator will now follow the prompt: 2^{nd}/ [link]/ > / ^ / [enter]. Then, it can select the OS to transfer.

#### Compatibility Between OS

The TI-84 Plus CE calculator series is compatible with other versions of this series. However, some of them are not compatible with some file transfers. The table below will provide the compatibility of file transfers between certain versions.

#### References

Guidebooks, T. (2018). TI-84 Plus CE Guidebooks. Education.ti.com. Retrieved 24 February 2018, from https://education.ti.com/guidebook/details/en/3BBF042421644CE2AF713484B03A8B11/ti-84-plus-ce