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Characteristic poly, eigenvalues and eigenvectors 3x3, digonailsability (non-randomised)
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Question in Ugur's workspace by Ugur Efem and 1 other

Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)

Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".
GEMIDDELD: Valbeweging van een balletje
Draft
Question in Panamaconferentie by Alexander Holvoet and 1 other

1) Schrijf een modeloplossing. Houd rekening dat je bij randomisatie dit anders zal moeten schrijven.

2) Randomiseer de snelheid, en controleer welke effecten dat heeft op de andere variabelen.
SA9 Calculate Median from a list
Ready to use
Question in Skills Audits for Maths and Stats by Upuli Wickramaarachchi and 6 others

This question provides a list of data to the student. They are asked to find the "median".
SA6 Calculate Range
Ready to use
Question in Skills Audits for Maths and Stats by Lauren Desoysa and 5 others

This question provides a list of data to the student. They are asked to find the "range".
SA8 Calculate Mode From a list
Ready to use
Question in Skills Audits for Maths and Stats by Lauren Desoysa and 4 others

This question provides a list of data to the student. They are asked to find the "mode".
Find characteristic polynomial, eigenvalues and eigenvectors of a 2x2 matrix
Ready to use
Question in Julia Goedecke's contributions by Julia Goedecke and 1 other

Example of an explore mode question. Student is given a 2x2 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvector is recognised by the marking algorithm, also multiples of the "obvious" one(s) (given the reduced row echelon form that we use to calculate them).

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".
Characteristic poly, eigenvalues and eigenvectors 3x3 non-randomised
Ready to use
Question in Julia Goedecke's contributions by Julia Goedecke

Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)

Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".
Calculate the distance between two points
Needs to be tested
Question in Glasgow Numbas Question Pool by Elizabeth Petrie and 2 others

Calculate the distance between two points along the surface of a sphere using the cosine rule of spherical trigonometry. Context is two places on the surface of the Earth, using latitude and longitude.

The question is randomised so that the numerical values for Latitude for A and B will be positive and different (10-25 and 40-70 degrees). As will the values for Longitude (5-25 and 50-75). The question statement specifies both points are North in latitude, but one East and one West longitude, This means that students need to deal with angles across the prime meridian, but not the equator.

Students first calculate the side of the spherical triangle in degrees, then in part b they convert the degrees to kilometers. Part a will be marked as correct if in the range true answer +-1degree, as long as the answer is given to 4 decimal places. This allows for students to make the mistake of rounding too much during the calculation steps.
Gaussian elimination calculator
Ready to use
Question in Julia Goedecke's contributions by Julia Goedecke and 1 other

Educational calculation tool rather than "question".

This allows the student to input a linear system in augmented matrix form (max rows 5, but any number of variables). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the system. This question has no marks and no feedback as it's just meant as a "calculator".

It has some rounding to 13 decimal places, as otherwise some fraction calculations become incorrectly displayed as a very small number instead of 0.

It would be possible to extend to more than 5 rows, one just has to put in a lot more variables and so on. I just had to choose some place to stop.
Inverse algorithm calculator
Ready to use
Question in Julia Goedecke's contributions by Julia Goedecke and 1 other

Educational calculation tool rather than "question".

This allows the student to input a square matrix (max rows 5). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the matrix and the identity matrix (or what it has got to). This question has no marks and no feedback as it's just meant as a "calculator". It has some checks in so students know when they are not entering a square matrix or a valid row number etc.

It has some rounding to 13 decimal places, as otherwise some fraction calculations become incorrectly displayed as a very small number instead of 0.

It would be possible to extend to more than 5 rows, one just has to put in a lot more variables and so on. I just had to choose some place to stop.
Direct sum and is sum whole space
Ready to use
Question in Julia Goedecke's contributions by Julia Goedecke and 1 other

Student decides on four different examples whether two subspaces form a direct sum and whether the sum is the whole vectorspace.

No randomisation, just the four examples. The question is set in explore mode, so that after deciding, students are asked to give reasons for their choices.
Invertibility via eigenvalues
Ready to use
Question in Julia Goedecke's contributions by Julia Goedecke

Example of an explore mode question. Student is given a 2x2 matrix with eigenvalues and eigenvectors, and is asked to decide if the matrix is invertible. If yes, second and third parts are offered where the student should give the eigenvalues and eigenvectors of the inverse matrix.

Assessed: remembering link between 0 eigenvalue and invertibility. Remembering link between eigenvalues and eigenvectors of matrix and its inverse.

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".
Numbas demo: Motion under gravity
Ready to use
Question in Demos by Christian Lawson-Perfect

Customised for the Numbas demo exam

Motion under gravity. Object is projected vertically with initial velocity $V\;m/s$ . Find time to maximum height and the maximum height. Now includes an interactive plot.
Julie's copy of Second order differential equations 2
Draft
Question in Julie's workspace by Julie Crowley

Method of undermined coefficients:

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$ . (Equal roots example). Includes an interactive plot.

rebelmaths
Julie's copy of Second order differential equations 1
Draft
Question in Julie's workspace by Julie Crowley

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$ .

rebelmaths
First order differential equations 8
Ready to use
Question in Bill's workspace by Bill Foster

Solve for $x(t)$ , $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$
Choose most appropriate model from Minitab output of AR(1) model and AR(2) stationary series
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Minitab was used to fit both an AR(1) model and an AR(2) to a stationary series. A table is given summarising the results obtained from Minitab. Choose the most appropriate model and make a forecast based on that model.
Interpret Minitab output of AR(1) model
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Minitab was used to fit an AR(1) model to a stationary time series. Given the output answer the following questions about the model and use the model to make forecasts.
Input 1 PSY
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Entering numbers in Numbas, Part 1.
Probability - sum of two numbers drawn without replacement
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Two numbers are drawn at random without replacement from the numbers m to n.

Find the probability that both are odd given their sum is even.
Probability - draw without replacement
Doesn't work
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

A box contains $n$ balls, $m$ of these are red the rest white.

$r$ are drawn without replacement.

What is the probability that at least one of the $r$ is red?
How to enter numbers and algebraic symbols - Getting Started
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Entering numbers and algebraic symbols in Numbas.
Second order ODE with constant coefficients and boundary conditions
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$ .
Solve a second order ODE with repeated roots,
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$ . (Equal roots example).
Separable first order ODE with boundary condition
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x(t)$ , $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$
Limiting speed given acceleration function,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

An object moves in a straight line, acceleration given by:

$\displaystyle f(t)=\frac{a}{(1+bt)^n}$ . The object starts from rest. Find its maximum speed.
Calculate mean, median, mode, range, and standard deviation of a sample
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Topics covered are calculating the mean, median, mode, range, and standard deviation.
Weight of a scoop in two ice cream parlours
Ready to use
Question in Transition to university by Stanislav Duris

Given two distributions, calculate the measures of average and spread and make some decisions based on the results.
Calculate the measures of central tendency for a sample
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Question in Transition to university by Stanislav Duris and 2 others

This question provides a list of data to the student. They are asked to find the mean, median, mode and range.
Julie's copy of Jack's copy of SOEE5154 - Mean, median, mode and standard deviation
Draft
Question in Julie's workspace by Julie Crowley

Exam covering questions on the Errorsr part of the SOEE5154M Maths course.

Topics covered are calculating the mean, median, mode and standard deviation.

rebelmaths

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