Add (a/b).x +/- (c/d) where a,b,c,d are randomised positive integers, and x is a randomised letter.

Determine the correct parametric representation of a given curve.  Curve is randomly chosen from a set of 20.

The graph of the curve was not displayed on my machine.

Given $f(x)=(x+b)^n$. Find the gradient and equation of the chord between $(a,f(a))$ and $(a+h,f(a+h))$ for randomised values of $a$, $b$ and $h$.

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

This question assesses the learner's ability of calculating confidence intervals for numerical data and conducting a one-sample t-test.

Randomized input values: sample summary statistics and confidence level.

Adapted from question 7.12 in OpenIntro Statistics (4th ed).

Question Covering AC power and frquency response

Students are supposed to use Excel (or similar) to find the answers (e.g., enter coordinates of two points then plot and add trendline).

Uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

This question aims at getting the students to demonstrate their ability to apply the Euclidean algorithm to find the GCD between two numbers.

We provide two randomly generated numbers and ask the students to enter the steps of the Euclidean algorithm, as well as the GCD between the numbers.

A random graph is drawn and students are asked whether it represents a function or not.

Expand $\ln(\dfrac{a^{x}}{b^{y}})$ into $x\ln(a)-y\ln(b)$, x and y randomised.

Expand $\ln(a^{x}b^{y})$ into $x\ln(a)+y\ln(b)$, x and y randomised.

This question assesses the learner's ability to compute a confidence interval for a difference of two means, given two samples.

Randomized variables: sample raw data and confidence level. 

Adapted from section 7.3.1 in OpenIntro Statistics (4th ed).

Choosing whether given random variables are qualitative or quantitative.

A normal curve is shown, with the mean and +/- 1, 2 and 3 standard deviations marked. An area of the curve is shaded and students are asked to estimate the shaded area using the heuristic rule. There are 6 possible areas: (-infty, mu-2sd), (mu-2sd, mu-1sd), (mu-1sd,mu), (mu, mu+1sd), (mu+1sd, mu+2sd), (mu+2sd, infty). The mean and standard deviation are randomised.

Student is presented with a clock showing a random time (in 15 minute increments) with an idication of whether it is morning or afternoon, along with a scheduled meeting time (in 24 hour mode). Question asks them to calculate difference between times and whether they are early or late.

Trolley on a slope

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Find and compare means and standard deviation using EXCEL (downloadable randomised dataset)

Friction and Accelration of a block with 2 forces applied

Question covering DC and Step response circuits

This question tests students' ability to use repeated squaring to perform modular exponentiation.  Moduli are random numbers between 30 and 70, the base is a number between 10 and 29.  To generate questions of approximately uniform difficult the exponent is taken to be 256 plus two smaller powers of 2. 

Student needs to solve a quadratic equation to calculate time taken for a diver to hit the water after diving from a diving board. Height of the board and initial upward velocity of the diver are randomly generated values. student needs to know that surface of the water is height 0, and only positive root of quadratic has physical meaning. Question is set to always give one positieve and one negative root.

Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.

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".

Real numbers $a,\;b,\;c$ and $d$ are such that $a+b+c+d=1$ and for the given vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3,\;\textbf{v}_4$ $a\textbf{v}_1+b\textbf{v}_2+c\textbf{v}_3+d\textbf{v}_4=\textbf{0}$. Find $a,\;b,\;c,\;d$.

Given a randomised square root function select the possible ways of writing the domain of the function.

GIve a random linear program and ask the students to convert it to canonical form.

Sometimes randomisation creates error with variable: c4

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

A random graph is drawn and students are asked whether it represents a function or not.