19 results authored by Andrew Iskauskas  search across all users.

Question in BUYS
Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Question in Durham Test Questions
Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Question in Andrew's workspace
Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non spaceseparated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.
Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Question in Custom Scripts
Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Question in Andrew's workspace
Solving a secondorder constant coefficient ODE. Uses the differentiation extension: https://github.com/Tandethsquire/Differentiation, and the Differential Equation custom part type, to differentiate a student answer and ensure it satisfies the equation.

Exam (2 questions) in Andrew's workspace
A sample of what can be done with the differentiation extension, and the corresponding custom part type.

Question in Custom Scripts
Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non spaceseparated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.
Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Question in Andrew's workspace
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Students are given six graphs, corresponding to curves $\gamma(t)$. They must match each with its signed curvature function, $\kappa(t)$.
The graphs are generated by calculating $\theta(t)=\int \kappa(t) \mathrm{d}t$ (by hand: these are given to the question as functions of a variable '#', in string form), and solving $x^{\prime}=\cos(\theta(t)\theta(0))$ and $y^{\prime}(t)=\sin(\theta(t)\theta(0))$ numerically (using the RKF method) with a JavaScript extension.

Question in Durham Test Questions
Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non spaceseparated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.
Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Question in Durham Test Questions
Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non spaceseparated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.
Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Question in Shared Questions
Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non spaceseparated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.
Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Exam (5 questions) in Mathematical Logic
A collection of questions (frequently updated) to demonstrate the usage of the Logic extension.
Current questions:
 Make syllogisms (either valid, invalid or valid under an additional assumption);
 Write statements in Polish and reverse Polish notation, find the truth table, determine satisfiability;
 Test whether a collection of statements $\Gamma$ models a statement $\phi$;
 Write the Disjunctive and Conjunctive Normal Forms for a statement.
Needs the Logic Extension!

Question in Andrew's workspace
The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.
To find the script, look in the Scripts tab of part a.

Question in Andrew's workspace
Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Question in Linear Algebra Applications
Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Exam (5 questions) in Custom Scripts
A collection of questions (frequently updated) to demonstrate the usage of the Logic extension.
Current questions:
 Make syllogisms (either valid, invalid or valid under an additional assumption);
 Write statements in Polish and reverse Polish notation, find the truth table, determine satisfiability;
 Test whether a collection of statements $\Gamma$ models a statement $\phi$;
 Write the Disjunctive and Conjunctive Normal Forms for a statement.
Needs the Logic Extension!

Question in Andrew's workspace
A method of randomly choosing variable names  use the
expression()
JME function to create a variable name from a randomly chosen string.(This question also uses a custom marking script to check that the student has simplified the expression)

Question in Custom Scripts
The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.
To find the script, look in the Scripts tab of part a.

Question in Andrew's workspace
Multiplication of $2 \times 2$ matrices.