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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:
Points of Inflection (pois)
Function: Determines the points of inflection of a function
Syntax: pois(function, variable)
Example:
Stationary Points (stps)
Function: Determines the stationary points of a function
Syntax: stps(function, variable)
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:
Unique, None, Infinite Solution (linesolve)
Function: Determines when two linear equations will have an unique, none or infinitely many solutions
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:
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:
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:
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:
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: The latest version is v1.0. Please ensure that the version you install is up to date.
UDF Guides:
Mathematical Methods UDF Guide
Specialist Mathematics UDF Guide
Note: The latest version is v1.0. Please ensure that the version you install is up to date.
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 Identified:
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
