Solving a differential equation of the form $\frac{dy}{dx}=ax^n e^{-y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=\frac{a \cos(x)}{y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=x(y-a)$ using separation of variables.

Solving a quadratic equation of the form $ax^2+bx+c=0$ using the quadratic formula.

Using Gaussian Elimination to solve 3X3 systems of equations

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

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This question demonstrates how to plot a graph of a function using JSXGraph.

Questions testing understanding of the precedence of operators using BIDMAS. That is, they test Brackets, Indices, Division/Multiplication and Addition/Subtraction.

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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".

This question demonstrates a few ways of interacting with a Venn diagram drawn using JSXGraph.

Find the forces in the members of a truss using the method of joints.

Find the moment of inertia of semi and quarter circles using the parallel axis theorem.

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.

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Gives a plot of a velocity-time graph using JSXgraph, and a description of the motion shown in the graph. The student is asked to calculate the acceleration at different stages of the motion, and the displacement at the end of the motion.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Practice using the log rules to add and subtract logarithms

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

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