The ** toolbox** key gives you access to an organized library of advanced functions. Press the

When viewing a graph, the ** toolbox** key gives you access to settings and additional features.

When writing an expression, the first functions in the **Toolbox** menu include: **Absolute value**, **n-th root** and **Logarithm base a**. When inputting expressions for the **Grapher**, the menu will also include **Inequalities**. Within the **Sequences** applicaiton, the **Toolbox** menu will also include defined sequences.

The **Toolbox** menu is then divided into several thematic sub-sections:

- Calculus
- Complex numbers
- Probability
- Units and constants
- Matrices and vectors
- Lists
- Arithmetic
- Trigonometry
- Decimal numbers
- Logic

`abs(x)`

Calculates the absolute value of the argument you enter in parentheses. `abs(-4.5)`

gives the value of $\mid -4.5\mid$, that is $4.5$.

`root(x,n)`

Calculates the $n$-th root of a number. You must enter $n$ and $x$ in parentheses. `root(x,n)`

gives the value of $\sqrt[n\,]{x}$. The value of $n$ doesn’t have to be an integer.

`log(x,a)`

Calculates the logarithm with base $a$. You must enter $a$ and $x$ in parentheses. `log(x,a)`

gives the value of $\log_{a}(x)$.

`diff(f(x),x,a)`

Calculates the derivative of a function at a point. `diff(f(x),x,a)`

gives the value of $f'(a)$. For example, to calculate the derivative of a square root at 5: `diff(sqrt(x),x,5)`

.

`diff(f(x),x,a,n)`

Calculates the nth derivative of a function at a point. `diff(f(x),x,a,n)`

gives the value of $f^{n}(a)$. For example, to calculate the 3rd derivative of a square root at 5: `diff(sqrt(x),x,5,3)`

.

`int(f(x),x,a,b)`

Calculates the integral of a function between two bounds. `int(f(x),x,a,b)`

gives the value of $\int_{a}^{b} f(x) \, \mathrm{d}x$. For example, to calculate the integral of the square root between $0$ and $5$: `int(sqrt(x),x,0,5)`

.

`sum(f(n),n,nmin,nmax)`

Calculates the sums of terms in $n$. `sum(f(n),n,nmin,nmax)`

gives the value of $\sum_{n=n_{min}}^{n_{max}} f(n)$.

`product(f(n),n,nmin,nmax)`

Calculates the products of terms in $n$. `product(f(n),n,nmin,nmax)`

gives the value of $\prod_{n=n_{min}}^{n_{max}} f(n)$.

`abs(x)`

Modulus of a complex number. `abs(2+3i)`

gives the value of $\mid 2+3i\mid$.

`arg(z)`

Argument of a complex number. `arg(2+3i)`

gives the value of $arg(2+3i)$ in radians.

`re(z)`

Real part of a complex number. For example, `re(2+3i)`

returns $2$.

`im(z)`

Imaginary part of a complex number. For example, `im(2+3i)`

returns $3$.

`conj(z)`

Conjugate of a complex number. `conj(2+3i)`

returns the conjugate of $2+3i$, that is $2-3i$.

`binomial(n,k)`

Number of ways to choose a subset of size $k$ elements, disregarding their order, from a set of $n$ elements. For example, $\dbinom{n}{k}$ returns $\frac{n!}{k! (n-k)!}$.

`permute(n,k)`

Number of different ordered arrangements of a $k$-element subset of an $n$-set. `permute(n,k)`

returns $A_{n}^k$, that is $\frac{n!}{(n-k)!}$.

`n!`

Returns the product of the entered integer and all integers below it. For example, $5!$ returns $120$.

`normcdf(a,µ,σ)`

$P(X<a)$ where X follows the normal distribution $N(\mu,\sigma)$.

`normcdfrange(a,b,µ,σ)`

$P(a<X<b)$ where X follows the normal distribution $N(\mu,\sigma)$.

`invnorm(a,µ,σ)`

Returns $m$ where $P(X<m)=a$ and X follows the normal distribution $N(\mu,\sigma)$.

`normpdf(x,µ,σ)`

Probability density function of $N(\mu,\sigma)$.

`tcdf(a,k)`

$P(X<a)$ where X follows the t-distribution with k degress of freedom.

`tcdfrange(a,b,k)`

$P(a<X<b)$ where X follows the t-distribution with k degress of freedom.

`invt(a,k)`

Returns $m$ where $P(X<m)=a$ and X follows the t-distribution with k degress of freedom.

`tpdf(x,k)`

Probability density function of $t(k)$.

`binompdf(m,n,p)`

$P(X=m)$ where X follows the binomial distribution $B(n,p)$.

`binomcdf(m,n,p)`

$P(X \leq m)$ where X follows the binomial distribution $B(n,p)$.

`invbinom(a,n,p)`

Returns $m$ where $P(X \leq m)=a$ and X follows the binomial distribution $B(n,p)$.

`poissonpdf(m,λ)`

$P(X=m)$ where X follows the Poisson distribution with parameter λ.

`poissoncdf(m,λ)`

$P(X \leq m)$ where X follows the Poisson distribution with parameter λ.

`geompdf(m,p)`

$P(X=m)$ where X follows the geometric distribution with probability p.

`geomcdf(m,p)`

$P(X \leq m)$ where X follows the geometric distribution with probability p.

`geomcdfrange(m,n,p)`

$P(m \leq X \leq n)$ where X follows the geometric distribution with probability p.

`invgeom(a,p)`

Returns $m$ where $P(X \leq m)=a$ and X follows the geometric distribution with probability p.

`hgeompdf(m,N,K,n)`

$P(X=m)$ where X follows the hypergeometric distribution with population size N, number of featured items K and sample size n.

`hgeomcdf(m,N,K,n)`

$P(X \leq m)$ where X follows the hypergeometric distribution with population size N, number of featured items K and sample size n.

`hgeomcdfrange(m,q,N,K,n)`

$P(m \leq X \leq n)$ where X follows the hypergeometric distribution with population size N, number of featured items K and sample size n.

`invhgeom(a,N,K,n)`

Returns $m$ where $P(X \leq m)=a$ and X follows the hypergeometric distribution with population size N, number of featured items K and sample size n.

`random()`

Returns a floating point number in [0,1).

`randint(a,b)`

Returns a random integer in [a,b].

`randintnorep(a,b,n)`

Returns n unique random integers in [a,b].

This menu contains sub-menus for constants and each type of measurement listed below. Units and constants can be selected from the menu or typed manually.

`a→b`

This menu item is a template that allows you to perform a unit conversion.

Abbreviation | Unit |
---|---|

`in` |
Inch |

`ft` |
Foot |

`yd` |
Yard |

`mi` |
Mile |

`au` |
Astronomical unit |

`ly` |
Light year |

`pc` |
Parsec |

Abbreviation | Unit |
---|---|

`pm` |
Picometer |

`nm` |
Nanometer |

`µm` |
Micrometer |

`mm` |
Millimeter |

`cm` |
Centimeter |

`m` |
Meter |

`km` |
Kilometer |

Abbreviation | Unit |
---|---|

`°` |
Degree |

`°'"` |
Degree minute second |

`rad` |
Radian |

`gon` |
Gradian |

Abbreviation | Unit |
---|---|

`ns` |
Nanosecond |

`µs` |
Microsecond |

`ms` |
Millisecond |

`s` |
Second |

`min` |
Minute |

`h` |
Hour |

`day` |
Day |

`week` |
Week |

`month` |
Month |

`year` |
Year |

Abbreviation | Unit |
---|---|

`Hz` |
Hertz |

`kHz` |
Kilohertz |

`MHz` |
Megahertz |

`GHz` |
Gigahertz |

Abbreviation | Unit |
---|---|

`tsp` |
Teaspoon |

`tbsp` |
Tablespoon |

`floz` |
Fluid ounce |

`cup` |
Cup |

`pt` |
Pint |

`qt` |
Quart |

`gal` |
Gallon |

Abbreviation | Unit |
---|---|

`mL` |
Milliliter |

`cL` |
Centiliter |

`dL` |
Deciliter |

`L` |
Liter |

Abbreviation | Unit |
---|---|

`acre` |
Acre |

Abbreviation | Unit |
---|---|

`ha` |
Hectare |

Abbreviation | Unit |
---|---|

`oz` |
Ounce |

`lb` |
Pound |

`shtn` |
Short ton |

`lgtn` |
Long ton |

Abbreviation | Unit |
---|---|

`µg` |
Microgram |

`mg` |
Milligram |

`g` |
Gram |

`kg` |
Kilogram |

`t` |
Metric ton |

Abbreviation | Unit |
---|---|

`µA` |
Microampere |

`mA` |
Milliampere |

`A` |
Ampere |

Abbreviation | Unit |
---|---|

`µV` |
Microvolt |

`mV` |
Millivolt |

`V` |
Volt |

`kV` |
Kilovolt |

Abbreviation | Unit |
---|---|

`Ω` |
Ohm |

`kΩ` |
Kiloohm |

Abbreviation | Unit |
---|---|

`µF` |
Microfarad |

`mF` |
Millifarad |

`F` |
Farad |

Abbreviation | Unit |
---|---|

`H` |
Henry |

`C` |
Coulomb |

`S` |
Siemens |

`T` |
Tesla |

Abbreviation | Unit |
---|---|

`mN` |
Millinewton |

`N` |
Newton |

`kN` |
Kilonewton |

Abbreviation | Unit |
---|---|

`Pa` |
Pascal |

`hPa` |
Hectopascal |

`bar` |
Bar |

`atm` |
Atmosphere |

Abbreviation | Unit |
---|---|

`mJ` |
Millijoule |

`J` |
Joule |

`kJ` |
Kilojoule |

Abbreviation | Unit |
---|---|

`µW` |
Microwatt |

`mW` |
Milliwatt |

`W` |
Watt |

`kW` |
Kilowatt |

`MW` |
Megawatt |

`GW` |
Gigawatt |

Abbreviation | Unit |
---|---|

`meV` |
Millielectronvolt |

`eV` |
Electronvolt |

`keV` |
Kiloelectronvolt |

`MeV` |
Megaelectronvolt |

Abbreviation | Unit |
---|---|

`K` |
Kelvin |

`°F` |
Fahrenheit |

`°C` |
Celsius |

Abbreviation | Unit |
---|---|

`cd` |
Candela |

Abbreviation | Unit |
---|---|

`µmol` |
Micromole |

`mmol` |
Millimole |

`mol` |
Mole |

Abbreviation | Unit |
---|---|

`c` |
Speed of light in a vacuum |

`e` |
Elementary charge |

`G` |
Gravitational constant |

`g0` |
Acceleration of gravity |

`k` |
Boltzmann constant |

`ke` |
Coulomb constant |

`me` |
Mass of an electron |

`mn` |
Mass of a neutron |

`mp` |
Mass of a proton |

`Na` |
Avogadro constant |

`R` |
Molar gas constant |

`ε0` |
Vacuum permittivity |

`µ0` |
Vacuum permeability |

`hplanck` x |
Planck permeability |

`New matrix or vector`

Create a new matrix or vector. This option creates a template. Enter your numbers using the directional keys.

`transpose(M)`

Transpose the matrix M. For instance, `transpose([[1,2][3,4]])`

returns $\left[\begin{array}{cc}1 & 3 \\ 2 & 4 \end{array}\right]$.

`dim(M)`

Size of the matrix M. For instance, `dim([[1,2][3,4]])`

returns `[2,2]`

.

`det(M)`

Determinant of the matrix M. For instance, `det([[1,2][3,4]])`

returns $-2$.

`inverse(M)`

Inverse of the matrix M. For instance, `inverse([[0.25,0][0,0.25]])`

returns $\left[\begin{array}{cc}4 & 0 \\ 0 & 4 \end{array}\right]$.

`identity(n)`

Identity matrix of size n.

`trace(M)`

Trace of the matrix M. For instance, `trace([[1,2][3,4]])`

returns $5$.

`ref(M)`

Returns the scaled shape of matrix M.

`rref(M)`

Returns the scaled form of matrix M.

Vectors can be row vectors or column vectors.

`dot(U,V)`

Calculates the dot product of two vectors.

`cross(U,V)`

Calculates the cross product of two vectors of size 3.

`norm(U)`

Calculates the magnitude of a vector.

`New list`

Create a new list. This option provides opening and closing curly braces. Enter your elements using the number keys with a comma to separate each element.

`List of f(k) for k from 1 to n`

Create a new list using a function. This option creates a template. Enter your function f(k) and your upper bound.

`mean(L)`

Calculates the mean of L.

`stddev(L)`

Calculates the standard deviation of L.

`samplestddev(L)`

Calculates the sample standard deviation of L.

`med(L)`

Calculates the median of L.

`var(L)`

Calculates the variance of L.

`dim(L)`

Returns the length of L.

`min(L)`

Returns the minimum element of L.

`max(L)`

Returns the maximum element of L.

`sort(L)`

Sorts the elements of L in ascending order.

`sum(L)`

Calculates the sum of the elements of L.

`prod(L)`

Calculates the product of the elements of L.

`gcd(p,q)`

Greatest Common Divisor of two integers. For instance, `gcd(55,11)`

returns $11$. This function accepts more than two integers as arguments.

`lcm(p,q)`

Least Common Multiple of two integers. For instance, `lcm(13,2)`

returns $26$. This function accepts more than two integers as arguments.

`factor(n)`

Integer factorization of $n$. For instance, `factor(24)`

returns $2^3 \times 3$.

A template to input a mixed fraction.

`rem(p,q)`

Remainder of the Euclidian division of $p$ by $q$. For instance, `rem(50,45)`

returns the remainder of the division of $50$ by $45$ that is $5$.

`quo(p,q)`

Quotient of the Euclidian division of $p$ by $q$. For instance, `quo(80,39)`

returns the quotient of the division of $80$ by $39$ that is $2$.

`sinh(x)`

Hyperbolic sine.

`cosh(x)`

Hyperbolic cosine.

`tanh(x)`

Hyperbolic tangent.

`arsinh(x)`

Inverse hyperbolic sine.

`arcosh(x)`

Inverse hyperbolic cosine.

`artanh(x)`

Inverse hyperbolic tangent.

`csc(x)`

Cosecant

`sec(x)`

Secant

`cot(x)`

Cotangent

`arccsc(x)`

Arccosecant

`arcsec(x)`

Arcsecant

`arccot(x)`

Arccotangent

`floor`

Floor function. For instance, `floor(5.8)`

returns $5$.

`frac(x)`

Fractional part. For instance, `frac(5.8)`

returns $0.8$.

`ceiling`

Ceiling function. For instance, `ceil(5.4)`

returns $6$.

`round(x,n)`

Rounds a number to $n$ digits after the decimal point. For instance round(8.6576,2) returns $8.66$.

`piecewise(-x,x<0,x,x≥0`

A piecewise template. Input an expression followed by its domain or conditions

`≤`

Less than or equal to

`≥`

Greater than or equal to

`≠`

Different

`and`

And

`or`

Or (inclusive)

`not`

Not

`xor`

Or (exclusive)

`nor`

Not or (inclusive)

`nand`

Not and