TI-Nspire™ CAS – Computer Algebra System

Working with variables

You can store values using variable_name := value or the other way around value =: variable_name. All defined variables are available across pages within the same problem. This allows for building dynamic, interconnected content. Sliders, table columns and graph functions are stored automatically. To remove a variable, use the DelVar command. Alternatively, you can insert a new problem to clear all previous variables.

Basic calculations with TI-Nspire CAS

TI-Nspire CAS handles not only complex operations but also basic arithmetic, roots, powers, and logarithms—making it easy to check and explore everyday math.

Working with fractions

Work with fractions, convert between decimals and exact forms. Try propFrac and exact.

Simplifying expressions

TI-Nspire CAS simplifies algebraic expressions, handles absolute values, logarithms and roots—making it a powerful tool for both practice and verification.

Expanding expressions

The expand command opens parentheses and rewrites expressions.

Factoring expressions

The factor command rewrites expressions as a product of terms.

Solving equations

With the solve command, TI-Nspire CAS solves equations symbolically or numerically. Note the use of the | operator.

Logical operators

Logical operators (and, or, not, xor, nor, nand, ⇒, ⇔) are used to work with conditions and logical statements. Parentheses are important because they determine the order in which conditions are evaluated. The same notation can be used, for example, to simplify solution sets of inequalities.

Solving systems of equations

The guided tool for solving systems of equations is found under 3: Algebra > 7: Solve System of Equations.

You can add more equations later using SHIFT ENTER on a computer keyboard, or with the key on the calculator. The system template can also be typed manually: system(eq1, eq2).

Domain of functions

Use domain to find where an expression is defined.

Differentiation

Derivatives can be calculated symbolically. Use the | operator to evaluate at a specific point. A guided option is available if needed.

Integration

You can calculate definite and indefinite integrals. Add conditions using the | operator.

Limits

You can calculate limits.

Vector calculations

Vector operations and commands work as shown in the example.

Exploring limits with a slider

In the Notes app, results update automatically when values change. You can store values using := or add a slider from the menu.

Matrix operations

You can input matrices using a template or from the keyboard in the form [1,2;3,4]. The transpose symbol T can be entered using @T.

Taylor approximation and dynamic values

In the Notes app, results update automatically when values change. You can store values using := or add a slider from the menu.

Binomial expansion with slider

In the Notes app, results update automatically when values change. You can store values using := or add a slider from the menu.

Dynamic sum of arithmetic sequence

There are several ways to calculate the sum of numbers from 1 to n: using a list, a sigma expression, or a known formula. With the slider you can dynamically explore the results.

Solving a quadratic equation step by step

With CAS, calculations can be done step by step, helping to develop your own thinking. You can use ans to refer to the previous equation or copy it. Make sure to enclose the entire equation in parentheses.

Sum, product and mean of quadratic roots

Statistics commands like sum, mean and product can be used with CAS too. Note how the mean of the roots matches the x-coordinate of the parabola's vertex.

Circle and sphere with CAS

You can calculate the area of a circle or the volume of a sphere using definite integrals. The solve command is used to isolate y from the equation of a circle.

Integral as a sum

An approximate value of an integral can be calculated using a sum by dividing the interval into subintervals. The number of subintervals can be adjusted with a slider, improving the accuracy of the sum. As the number of subintervals increases without bound, the limit of the sum equals the exact value of the integral.

Area between curves using integrals

The area between curves can be calculated by integrating the absolute value of the difference between the functions. Integrals involving absolute values may lead to difficult calculations, so an exact result is not always obtained directly. The problem can then be divided into parts by determining the order of the functions.

Vector perpendicularity and parallelism

Vector problems can be solved by combining the solve command with vector commands. The image shows examples of perpendicular, parallel, and same-direction vectors.

Three points on the same line

Whether three points lie on the same line can be examined using vectors. If vectors AB and AC are parallel, the points lie on the same line. Parallelism can be checked using the solve command or alternatively using the cross product.

Distance from a point to a line

The well-known formula for the distance from a point to a line can be derived using the Pythagorean Theorem and finding the shortest distance.

Factorial

Factorials are calculated by simply appending the ! symbol. You can also calculate the factorial of a list or use it in spreadsheets. In simple cases, expressions with factorials can be simplified using CAS.

Permutations

Permutations can be calculated using factorials or directly with the nPr command. You can find the command in the menu under 5: Probability > 2: Permutations. CAS commands can also be used in these calculations.

Combinations

Combinations can be calculated using factorials or directly with the nCr command. You can find the command in the menu under 5: Probability > 3: Combinations. CAS commands can also be used in these calculations.

Normal distribution

To calculate probabilities for a normal distribution, you can first define the probability density function using normPdf 5: Probability > 5: Distributions > 1: Normal Pdf..., and compute the result with an integral. The same result can be obtained more directly using the guided normCdf function 5: Probability > 5: Distributions > 2: Normal Cdf....

Equations related to the normal distribution

The guided normCdf command, found in the menu 5: Probability > 5: Distributions > 2: Normal Cdf..., allows you to calculate probabilities. Combined with solve, you can find missing values such as upper bound, mean, or standard deviation. Some equations require an initial guess to find a solution. Alternatively, you can use the density function and an integral.

Binomial distribution

The binomial probability function can be defined using the binomPdf command 5: Probability > 5: Distributions > A: Binomial Pdf.... To calculate the probability for a range of values, you can use a sum or the guided binomCdf command 5: Probability > 5: Distributions > B: Binomial Cdf..., which evaluates the sum for you.

Basic trigonometric functions

Trigonometric functions are entered by typing sin(, cos(, tan(, arcsin(, arccos( or arctan(. The functions are also available via the TRIG key on the calculator keypad. Calculations use the angle unit defined in the settings unless a different unit is specified in the input.

Angle settings

By default, TI-Nspire uses the angle unit defined in the document settings. If the input includes a unit, it is converted to the unit specified in the settings. On Windows, the ° symbol can be entered using CTRL + *, and Mac keyboards include a dedicated key. Units can also be entered using @d or @r.

ℹ️ See more

Computer view: The angle unit is shown at the bottom of the screen. Double-click Settings to open the document settings. Selecting Make Default applies the same setting to new documents. Selecting OK applies the settings only to the current document.

Handheld view: The angle unit can be changed directly by tapping the unit shown at the top of the screen (e.g. RAD).

Tip: The angle setting of a math box can also be changed per calculation. This is useful when the result is needed in different units. Unit conversion can also be performed using the commands @>DD and @>Rad.

Manipulating trigonometric expressions

In addition to the standard expand() and factor() commands, you can use tExpand() and tCollect() with trigonometric functions. These allow trigonometric expressions to be represented in alternative forms.

Solving trigonometric equations

Solving trigonometric equations can be done in the CAS environment using the solve() command. Solutions can be expressed in a general form using an integer parameter or restricted to a specific interval by adding a condition. If needed, the solutions can also be converted into a list for further processing.

Integer constant (@n1)

An integer constant can be used to test the equivalence of different representations and to work with trigonometric expressions in a general form. An integer constant is written in the form @n1, where the number is a freely chosen index. This makes it possible to distinguish between multiple integer constants when more than one is used in the same expression.

Derivatives in Lists & Spreadsheet

In the Lists & Spreadsheet application, derivatives can be computed directly in table cells. A common use case is to define expressions in one column and compute their derivatives in another. Derivatives can also be entered directly using the math template. Higher-order derivatives can be computed directly using the math template.

Calculating logarithms

Logarithms can be entered as log(number, base) or using the logarithm template . If the base is omitted, the logarithm is interpreted as base 10. The natural logarithm is written with ln(). The number e (Euler's number) can be typed as @e, or selected from the menu or symbol palette.

Simplifying logarithmic expressions

Many logarithmic expressions can be simplified simply by pressing Enter. If the expressions include variables, it is often necessary to define a domain to allow simplification. You can also try using expand and factor. These tools can be helpful, but may sometimes lead to unwanted forms, such as factorizations of base numbers.

Domain of the logarithmic function

The command domain(expression, variable) shows the values of the variable for which the expression is defined.

Change of base for logarithms

Use the logbase() or ln command to convert the base of a logarithm. These can be found under 3: Algebra > A. Convert Expression. The arrow can be typed as @>.

Solving logarithmic and exponential equations

Use the solve command to solve logarithmic and exponential equations. To define the base of the logarithm, append logbase().

Base conversions

In TI-Nspire, integers can be converted between different number systems, such as decimal, binary, and hexadecimal. Binary numbers use the prefix 0b and hexadecimal numbers use 0h. Without a prefix, a number is interpreted as decimal. Conversions can be performed using Base commands or by typing, for example, 10@>Base2 from the keyboard. If the document’s base setting is changed, results are shown by default in the selected base. Individual results can still be converted separately if needed.

Logical simplifications and tautologies

Logical expressions can be simplified and tested for tautologies. Implication can be written as => and equivalence as <=>.