Calculating the derivative of a function of the form $k(ax^m+b)^n$ using the chain rule.

Calculating the derivative of a function of the form $k(ax+b)^n$ using the chain rule.

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".

Calculating two unknown coefficients of a cubic expression when given two of the expression's linear factors.

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".

Short question in recognising errors in binary strings transmitted over a binary symmetric channel, as well as calculating probabilities of these errors occuring. Randomised 7-bit strings between 64 and 128, randomised probability between 0.05 and 0.1. Randomised error pattern.

A resource for Business students to practise calculating Normal probabilities and finding $Z$-values. 

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

Calculating the square root of a complex number using De Moivre.

Calculating complex numbers raised to an natural number exponent

Question 1 of Electric Drives Tutorial Sheet 2019/20 – AC Questions

These questions focus on calculating percentages in numerical reasoning tests.

This question focusses on calculating a percentage form a speific pie chart.

Calculating with vectors of random size, including resolving brackets. Advice (i.e. solution) has conditional visibility to show only the correct size.

A combination of tasks: checking which matrix products exist, calculating some of these products, calculating transpose matrices. Comparing product of transpose with transpose of product. Experiencing associativity of matrix multiplication. Not much randomisation, only in which matrix product is computed as second option.

Comprehensive solution written out in Advice.

Calculating with vectors in \(\mathbb{R}^4\), including resolving brackets. The fixed vector size is so that a test is fair to all students.

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Questions for calculating perimeters and areas of shapes.

Calculating limits using algebraic techniques

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

A resource for Business students to practise calculating Normal probabilities and finding $Z$-values. 

Exercises on calculating the determinant of 2x2 and 3x3 matrices.

Exercise using a given uniform distribution $X$, calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$.

The students are given the magnitude and angle (in degrees) of a vector. They have to find its alpha and beta components.

A function of the form (ax+b)/(x+c) is plotted. Student is asked to calculate the shaded area. Area is both above and below the x-axis.