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# Mathematical Methods UDFs

## Calculus

**Average Rate of Change (avgroc)**

**Function: **Determines the average rate of change of a function

**Syntax: **avgroc(function, variable, lower, upper)

**Example:**

**Average Value (avgval)**

**Function: **Calculates the average value of a function

**Syntax: **avgval(function, variable, lower, upper)

**Example:**

**Bound Area (boundarea)**

**Function: **Determines the area bound by two graphs (if any) across their maximal domains

**Syntax: **boundarea(function1, function2, variable)

**Example:**

**Bound Area with domain (boundaread)**

**Function: **Determines the bound area between two functions in a restricted domain

**Syntax: **boundaread(function1, function2, variable, lower, upper)

**Example:**

**Integral Solve (intsolve)**

**Function: **Determines the answer for the integration multiple choice questions

**Case 1: One integral given, find transformed integral**

**Syntax: **intsolve({lower1,upper1, value1}, {transformations}, {lower2, upper2})

**Example:**

**Case 2: Two integrals given, find untransformed integral**

**Syntax: **intsolve({lower1, upper1, value1}, {lower2, upper2, value2}, {lower3, upper3})

**Example:**

**Case 3: Two integrals given, find transformed integral**

**Syntax: **intsolve({lower1, upper1, value1, lower2, upper2, value2}, {transformations}, {lower3, upper3})

**Example:**

**Newton's Method (newtons)**

**Function: **Estimates the root of a function using newton's method

**Syntax: **newtons(function, variable, x0, iterations)

**Example:**

**Number of Roots (nroot)**

**Function: **Determines the value(s) of a parameter required for a specified number of roots.

**Syntax: **nroot(polynomial, variable, parameter, number of roots)

**Example:**

**Number of Stationary Points (nstp)**

**Function: **Determines the value(s) of a parameter required for a specified number of stationary points.

**Syntax: **nstp(polynomial, variable, parameter, number of stationary points)

**Example:**

**Number of Points of Inflection (npoi)**

**Function: **Determines the value(s) of a parameter required for a specified number of points of inflection.

**Syntax: **npoi(polynomial, variable, parameter, number of points of inflection)

**Example:**

**Points of Inflection (pois)**

**Function: **Determines the points of inflection of a function

**Syntax: **pois(function, variable)

**Example:**

**Sign Table (signtab)**

**Function: **Uses a sign table to determine the stationary points of a function and their nature

**Syntax: **signtab(function, variable)

**Example:**

**Stationary Points (stps)**

**Function: **Determines the stationary points of a function

**Syntax: **stps(function, variable)

**Example:**

**Tangent Solve (tangsolve)**

**Function: **Determines the equation of the tangents to a function which pass through a specified point

**Syntax: **tangsolve(function, variable, x-coordinate, y-coordinate)

**Example:**

**Trapezoid Approximation (trapapprox)**

**Function: **Approximates an integral using the trapezoidal rule

**Syntax: **trapapprox(function, variable, lower, upper, number of trapezia)

**Example:**

## Continuous Probability

**Continuous Conditional Probability (ccondpr)**

**Function: **Determines conditional probability for a continuous distribution

**Case 1: Probability density function**

**Syntax: **ccondpr(Probability Density Function, Lower Bound, Upper Bound, Condition 1, Condition 2)

**Example:**

**Case 2: Normal Distribution**

**Syntax: **ccondpr(Blank String, Mean, Standard Deviation, Condition 1, Condition 2)

**Example:**

**Confidence Interval (confint)**

**Function: **Determines a confidence interval as well as the z-score, margin of error and standard deviation

**Syntax: **confint(Sample Size,P_hat, . confidence)

**Example:**

**Confidence Interval Solve (confintsolve)**

**Function: **Determines the sample size, standard deviation or percentage confidence depending on the provided data

**Syntax: **confintsolve(Lower Bound, Upper Bound, Sample Size or Sample Standard Deviation or . Confidence)

**Example:**

**Continuous Distribution Information (continfo)**

**Function: **Determines the expected value, mean, variance, standard deviation of a continuous probability distribution

**Syntax: **continfo(function, variable, lower, upper)

**Example:**

**Inverse Normal (invnormvals)**

**Function: **Determines the left, right and centre possibilities for probability of a distribution

**Syntax: **invnormvals(mean, standard deviation, probability)

**Example:**

**Normal Solve (normsolve)**

**Function: **Determines the mean and standard deviation for lower and upper type questions

**Case 1: Both Lower and Upper given**

**Syntax: **normsolve(Lower, Probability of Lower, Upper, Probability of Upper)

**Example:**

**Case 2: Lower and Mean given**

**Syntax: **normsolve(Lower, Probability of Lower, Mean, Blank String)

**Example:**

**Case 3: Lower and Standard Deviation given**

**Syntax: **normsolve(Lower, Probability of Lower, Blank String, Standard Deviation)

**Example:**

**Case 4: Upper and Mean given**

**Syntax: **normsolve(Mean, Blank String, Upper, Probability of Upper)

**Example:**

**Case 5: Upper and Standard Deviation given**

**Syntax: **normsolve(Blank String, Standard Deviation, Upper, Probability of Upper)

**Example:**

## Discrete Probability

**Binomial Distribution Information (binominfo)**

**Function: **Determines the expected value, variance, standard deviation, sample expected value, and sample standard deviation for a binomial distribution

**Syntax: **binominfo(Sample Size, Probability of Success)

**Example:**

**Binomial Solve (binomsolve)**

**Function: **Determines the number of trials required to achieve a certain probability

**Syntax: **binomsolve(outcome, probability of success, threshold value)

**Example:**

**Discrete Conditional Probability (dcondpr)**

**Function: **Determines conditional probability for a discrete distribution

**Case 1: Binomial Distribution**

**Syntax: **dcondpr(number of trials, probability of success, condition 1, condition 2)

**Example:**

**Case 2: Discrete Probability Table**

**Syntax: **dcondpr({List containing outcomes}, {List containing probabilities}, condition 1, condition 2)

**Example:**

**Case 3: Probability Mass Function**

**Syntax: **dcondpr({List containing outcomes}, PMF, condition 1, condition 2)

**Example:**

**Hypergeometric Cumulative Probability Function (hypergeocdf)**

**Function: **Determines the probability of selecting items without replacement, but over an interval of outcomes

**Syntax: **hypergeocdf(sample size, population size, number of successful items, lower bound, upper bound)

**Example:**

**Hypergeometric Probability Density Function (hypergeopdf)**

**Function: **Determines the probability of selecting items without replacement, but for specific outcomes

**Syntax: **hypergeopdf(sample size, population size, number of successful items, outcome)

**Example:**

**Inverse Binomial (invbinomial)**

**Function: **Determines the outcome required to achieve the probability

**Syntax: **invbinomial(number of trials, probability of success, known probability value)

**Example:**

**Probability Table (prtable)**

**Function: **Determines the mean, variance, standard deviation of a probability table

**Syntax: **prtable({outcomes}, {probabilities})

**Example:**

**Sample Distribution Binomial (samplebinom)**

**Function: **Determines the distribution for the sample proportion of a binomially distributed sample

**Syntax: **samplebinom(Sample Size, Probability of Success)

**Example:**

**Sample Binomial Probability (samplebinompr)**

**Function: **Determines the probability for the sample proportion for a binomially distributed sample

**Syntax: **samplebinompr(Sample Size, Probability of Success, Lower, Upper)

**Example:**

**Sample Distribution Hypergeometric (samplehypergeo)**

**Function: **Determines the distribution for the sample proportion of a hypergeometrically distributed sample

**Syntax: **samplehypergeo(Sample Size, Population Size, Number Successful)

**Example:**

**Sample Hypergeometric probability (samplehyppr)**

**Function: **Determines the probability for the sample proportion for a hypergeometrically distributed sample

**Syntax: **samplehyppr(Sample Size, Population Size, Number Successful, Lower, Upper)

**Example:**

## Functions

**Asymptotes (asymp)**

**Function: **Determines the vertical and horizontal asymptotes of a function

**Syntax: **asymp(function, variable)

**Example:**

**Composite Check (ccheck)**

**Function: **Checks whether a composite function is valid, and the maximal domain required for the composite to be valid.

**Syntax: **ccheck(function 1, function 2)

**Example:**

**Discriminant (discrim)**

**Function: **Calculates the discriminant of an inputted quadratic expression

**Syntax: **discrim(quadratic Expr, variable)

**Example:**

**Domain and Range (domrang)**

**Function: **Determines the domain and range of a function

**Syntax: **domrang(function, variable)

**Example:**

**Intercepts (intercepts)**

**Function: **Finding the x and y intercepts of a function

**Syntax: **intercepts(function,variable)

**Example:**

**Intersects (intersects)**

**Function: **Determines the points of intersection of two functions across their maximal domains.

**Syntax: **intersects(function1,function2,variable)

**Example:**

**Intersects with domain (intersectsd)**

**Function: **Determines the points of intersection between two functions in a restricted domain

**Syntax: **intersectsd(function1, function2, variable, lower, upper)

**Example:**

**Inverse Function (inverse)**

**Function: **Determines the inverse of a function

**Syntax: **inverse(function, variable, x in domain of f)

**Example:**

**Inverse Intersections (invints)**

**Function: **Determines the values of a parameter, k, required for a function and its inverse function to have a certain number of intersections

**Case 1: Square Root**

**Syntax: **invints(function, number of intersections with inverse)

**Example:**

**Case 2: Parabola**

**Syntax: **invints(function, number of intersections with inverse) *You will be prompted to enter an initial condition

**Example:**

**Case 3: Exponential**

**Syntax: **invints(function, number of intersections with inverse)

**Example:**

**Case 4: Logarithm**

**Syntax: **invints(function, number of intersections with inverse)

**Example:**

**Case 5: Hyperbola**

**Syntax: **invints(function, number of intersections with inverse)

**Example:**

**Case 6: Simple Cubic (Either 0 or 1 turning points)**

**Syntax: **invints(function, number of intersections with inverse)

**Example:**

**Case 7: Complicated Cubic (More than 1 turning point)**

**Syntax: **invints(function, number of intersections with inverse) *You will be prompted to enter the domain

**Example:**

**Angle Between Two Lines (lineang)**

**Function: **Determines the angle between two lines in degrees (Assumes CAS in raidans mode)

**Syntax: **lineang(Line 1, Line 2, Variable)

**Example:**

**Unique, None, Infinite Solution (linesolve)**

**Function: **Determines when two linear equations will have an unique, none or infinitely many solutions. Note: Equations must be in the form: Ax + By = C , rather than Ax + By + C = 0

**Syntax: **linesolve(Equation1, Equation2)

**Example:**

**Property Check (pcheck)**

**Function: **Determines which function satisfies a specific property

**Syntax: **pcheck(function, variable, LHS, RHS)

**Example:**

**Point Information (pointinfo)**

**Function: **Determines the gradient, perpendicular gradient, line, x and y intercepts of a line, midpoint, distance

**Syntax: **pointinfo(x1, y1, x2, y2)

**Example:**

**Polynomial Fit (polyfit)**

**Function: **Determines the equation of a polynomial which passes through a set of points.

**Syntax: **polyfit({x1, y1, x2, y2, ...})

**Example:**

**Transformations (transform)**

**Function: **Determines the transformed function after applying certain transformations

**Syntax: **transform(function, {transformations})

**Example:**

## Miscellaneous

**Column Augment (ca)**

**Function: **Converts answer into easily readable matrix form

**Case 1: One Variable**

**Syntax: **surfarea(Function, t, Lower Bound, Upper Bound)

**Example:**

**Case 2: Multiple Variables (Up to 5)**

**Syntax: **ca(Ans, {var1, var2,..., var5}

**Example:**

**Domain Solve (dsolve)**

**Function: **Solves equations in a restricted domain

**Syntax: **dsolve(Equation, Variable, Lower Bound, Upper Bound)

**Example:**

**Graph Information (graphinfo)**

**Function: **Determines the endpoints, x-intercepts, y-intercepts, stationary points, points of inflection of a function

**Case 1: Restricted Domain**

**Syntax: **graphinfo(Function, Variable, Lower Bound, Upper Bound)

**Example:**

**Case 2: Across Maximal Domain**

**Syntax: **graphinfo(Function, Variable, Blank String, Random Character)

**Example:**

**Rewrite (rr)**

**Function: **Gets the right hand side of an equation/answer

**Syntax: **rr(Equation/Answer)

**Example:**

**Triganometric Solve (tsolve)**

**Function: **Gives exact values of circular function equations (Ones which TiNspire cannot properly solve on its own)

**Case 1: Trigonometric Equation**

**Syntax: **tsolve(Equation, Variable, Lower Bound, Upper Bound)

**Example:**

**Case 2: Trigonometric Inequality**

**Syntax: **tsolve(Inequality, Variable, Lower Bound, Upper Bound)

**Example:**

# Specialist Mathematics UDFs

## Calculus

**Arc Length (arclength)**

**Function: **Determines the arc length for parametric curve

**Case 1: Function**

**Syntax: **arclength(Function, Variable, Lower Bound, Upper Bound)

**Example:**

**Case 2: Parametric Equation**

**Syntax: **arclength(Vector, Variable, Lower, Upper)

**Example:**

**Bound Volume (boundvol)**

**Function: **Determines the volume of the solid formed by the region(s) bound by two curves

**Syntax: **boundvol(Function 1, Function 2, Variable)

**Example:**

**Bound Volume Domain (boundvold)**

**Function: **Determines the volume of the solid formed by the region(s) bound by two curves in a restricted domain

**Syntax: **boundvold(Function 1, Function 2, Variable, Lower Bound, Upper Bound)

**Example:**

**Euler's Method (eulers)**

**Function: **Uses euler's method to estimate the solution to a differential equation

**Syntax: **eulers(Differential Equation, Independent Variable, x0, xn, y0, step-size)

**Example:**

**Mixing Problems (mix)**

**Function: **Determines the differential equation of the mixing problem

**Syntax: **mix() (You will be prompted for inputs)

**Example:**

**Rational Function (rational)**

**Function: **Determines holes, straight line asymptotes, and oblique asymptotes of a rational function.

**Syntax: **rational(numerator, denominator, variable)

**Example:**

**Surface Area of Solid (surfarea)**

**Function: **Determines the surface area of a solid of revolution

**Case 1: Function of x rotated about x-axis**

**Syntax: **surfarea(Function, Variable, Lower Bound, Upper Bound)

**Example:**

**Case 2: Function of y rotated about y-axis**

**Syntax: **surfarea(Function, Variable, Lower Bound, Upper Bound)

**Example:**

**Case 3: Function of x rotated about y-axis**

**Syntax: **surfarea(Function, y, x-lower, x-upper)

**Example:**

**Case 4: Parametric Equation**

**Syntax: **surfarea(Function, t, Lower Bound, Upper Bound)

**Example:**

## Complex Numbers

**De Moivre's Theorem (demoiv)**

**Function: **Determines the solutions to roots of unity questions

**Syntax: **demoiv(Power , Number)

**Example:**

**Circle Locus First Form (locicir1)**

**Function: **Determines cartesian equation of circle loci in the form |z - a| = r

**Syntax: **locicir1(Point , Radius)

**Example:**

**Circle Locus Second Form (locicir2)**

**Function: **Determines cartesian equation of circle loci in the form |z - a| = k|z - b|

**Syntax: **locicir2(Point 1, Point 2, k)

**Example:**

**Ellipse Locus (lociellp)**

**Function: **Determines cartesian equation of ellipse loci

**Syntax: **lociellp(Point 1, Point 2, Length)

**Example:**

**Hyperbola Locus (locihyp)**

**Function: **Determines cartesian equation of hyperbola loci

**Syntax: **locihyp(Point 1, Point 2, Length)

**Example:**

**Line Locus (lociline)**

**Function: **Determines cartesian equation of line in the form |z - a| = |z - b|

**Syntax: **lociline(Point 1, Point 2)

**Example:**

**Quadratic Roots (quadroots)**

**Function: **Determines quadratic roots of a complex number algebraically

**Syntax: **quadroots(Number)

**Example:**

**Ray (ray)**

**Function: **Determines the cartesian equation of a ray given a point and an angle

**Syntax: **ray(Point, Angle)

**Example:**

## Kinematics

**Collision Detector (collision)**

**Function: **Determines whether two particles collide and where their paths intersect

**Syntax: **collision(Position Vector 1, Position Vector 2)

**Example:**

**Projectile Motion (projm)**

**Function: **Determines the accleration, velocity, position, max height, max displacement, return speed of a particle

**Syntax: **projm(Initial Position, Initial Velocity, Launch Angle, Initial Acceleration)

**Example:**

**Constant Acceleration Equations (suvat)**

**Function: **Enter 3 known values and 2 unknown variables, it will determine the unknowns

**Syntax: **suvat(s (displacement), u (initial velocity), v (final velocity), a (acceleration), t (time))

**Example:**

## Vectors

**Unit Vector Bisector (bisec)**

**Function: **Determines the unit vector which bisects the angle between two vectors

**Syntax: **bisec(vector 1, vector 2)

**Example:**

**Colinear (colin)**

**Function: **Determines value(s) of a variable required for points to be collinear

**Syntax: **colin(Point 1, Point 2, Point 3)

**Example:**

**Linear Dependence (lindep)**

**Function: **Determines value(s) of a variable required for 3 vectors to be linearly dependent

**Syntax: **lindep(Vector 1, Vector 2, Vector 3)

**Example:**

**Angle between Vectors (vecang)**

**Function: **Determines the angle between the two inputted vectors.

**Syntax: **vecang(Vector1, Vector2)

**Example:**

**Vector Projection (vproj)**

**Function: **Determines vector, scalar resolute, & angle for two inputted vectors

**Syntax: **vproj(Vector 1, Vector 2)

**Example:**

## Linear Algebra

**Line Cartesian to Vector (car2vecline)**

**Function: **Converts equation of line from cartesian form to vector form

**Syntax: **car2vecline(line Cartesian)

**Example:**

**Plane Cartesian to Vector (car2vecplane)**

**Function: **Converts equation of plane from cartesian form to vector form

**Syntax: **car2vecplane(Plane Cartesian)

**Example:**

**Line Vector to Cartesian (vec2carline)**

**Function: **Converts equation of line from vector form to cartesian form

**Syntax: **vec2carline(line Vector)

**Example:**

**Plane Vector to Cartesian (vec2carplane)**

**Function: **Converts equation of plane from vector form to cartesian form

**Syntax: **vec2carplane(Plane Vector)

**Example:**

**Minimum Distance between 2 lines (dist2l)**

**Function: **Determines minimum distance between two lines

**Syntax: **dist2l(Line Vector 1, Line Vector 2)

**Example:**

**Minimum Distance between 2 planes (dist2pl)**

**Function: **Determines minimum distance between two planes

**Syntax: **dist2pl(Plane Cartesian 1, Plane Cartesian 2)

**Example:**

**Minimum Distance between line and plane (distlpl)**

**Function: **Determines the minimum distance between a plane and line

**Syntax: **distlpl(Line Vector, Plane Cartesian)

**Example:**

**Minimum Distance between line and point (distlp)**

**Function: **Determines minimum distance between a line and point

**Syntax: **distlp(Line Vector, Point)

**Example:**

**Minimum Distance between plane and point (distplp)**

**Function: **Determines minimum distance between a plane and point

**Syntax: **distlp(Plane Equation, Point)

**Example:**

**Intersection between 2 lines (ints2l)**

**Function: **Determines the point of intersection & angle between two lines

**Syntax: **ints2l(Line Vector 1, Line Vector 2)

**Example:**

**Intersection between 2 planes (ints2pl)**

**Function: **Determines the line of intersection & angle between two planes

**Syntax: **ints2pl(Plane Cartesian 1, Plane Cartesian 2)

**Example:**

**Intersection between plane and line (intslpl)**

**Function: **Determines the point of intersection & angle between line and plane

**Syntax: **intslpl(Line Vector, Plane Cartesian)

**Example:**

**Create line with 2 points (line2p)**

**Function: **Determines the equation of a line given two points

**Syntax: **line2p(Point 1, Point 2)

**Example:**

**Create line with direction vector and point (linedp)**

**Function: **Determines the equation of a line given a direction vector and point

**Syntax: **linedp(Direction Vector, Point)

**Example:**

**Create plane with 3 points (plane3p)**

**Function: **Determines the equation of a plane given three points

**Syntax: **plane3p(Point 1, Point 2, Point 3)

**Example:**

**Create plane with normal and point (planenp)**

**Function: **Determines the equation of a plane given a normal vector and a point

**Syntax: **planenp(Normal Vector, Point)

**Example:**

**Plane formed by intersecting lines (planeintl)**

**Function: **Determines the equation of the plane formed by two intersecting lines

**Syntax: **planeintl(Line Vector 1, Line Vector 2)

**Example:**

## Probability

**Sample Mean Confidence Interval (confint)**

**Function: **Determines the confidence interval for the sample mean

**Syntax: **confint(Sample Mean, Population Standard Deviation, Sample Size, . confidence)

**Example:**

**Hypothesis Testing (hyptest)**

**Function: **Determines whether the null hypothesis should be rejected by calculating p-values

**Syntax: **hyptest() (You will be prompted for inputs)

**Example:**

**Probability of Error (prerror)**

**Function: **Determines the probability of Type I and Type II errors occuring

**Syntax: **prerror() (You will be prompted for inputs)

**Example:**

**p-value (pval)**

**Function: **Determines the p-value of a hypothesis test

**Syntax: **pval() (You will be prompted for inputs)

**Example:**

# Download

### UDF Files:

**Note: **Latest version is v2.1. for MM and v2.4 for SM. Please ensure that the version you install is up to date.

###### Latest Changes (v2.1 - v2.4)

Bug fixes to

**sm_linalg\intslpl**and**sm_linalg\ints2pl**(fixed issues when letting z = t gave weird solution)Bug fix to

**sm_linalg\dist2l**(fixed parallel line detection)Bug fix to

**sm_kin\suvat**and**sm_pr\prerror**(fixed working out so it formated correctly)Added working out to

**sm_linalg\ints2pl**Added E(X), Var(X), Sd(X) to

**mm_dpr/samplebinom**and**mm_dpr/samplehypergeo**Made

**sm_linalg\ints**UDFs find acute angle, as that's what questions usually ask for

### UDF Guides:

__Mathematical Methods UDF Guide__

__Specialist Mathematics UDF Guide__

**Note: **The latest version is v2.0. for SM and v2.1 for MM Please ensure that the version you install is up to date.

### Version Updates & Mailing List

**New version v2: **New version released! 10 new UDFs :D also some bug fixes included. Asymtpote UDF issue with exponentials resolved!

Join our mailing list so you don't miss the latest updates :D sign up here

### Program Bugs:

After extensive testing our beta testers identified only a few bugs, with the vast majority of the programs working fine! :D

While many of the programs worked fine for us, if you encounter any issues or difficulties, please contact us and we will try to help you out.

##### Bugs Unresolved:

nroots, nstps, npois don't work for

**non-polynomial**functions, documentation has been updated to reflect this.Domain and Range function does not handle parameters well

Domain and Range may give inaccurate results if the domain is not restricted for complicated functions.

Domain and Range function does not handle rational functions well. Beware of auto-simplification.

Domain and Range function may round undefined endpoints into defined endpoints.