Students are asked to rearrane the formula giving the voltage drop across a resistor in terms of emf of battery, resistance of resistor and internal resistance of battery to make the internal resistance the subject. They are then asked to calculate the internal resistance given values for the other variables (randomised).

Given a circle equation in the form (x-a)^2+(y-b)^2=r^2, write down the radius and centre coordinates.

In this question the students have to solve a linear recurrence of order 2. The sequence is asked in recurrence form and the goal is to find its closed form.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to rewrite the solution correctly. No variables but this is version 5 of 5 versions of the question. This version uses a much more mangled AI generated solution that the other 4 versions and does not ask for the line with the first error, just for the student to rewrite the solution correctly.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is version 4 of 5 versions of the question.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is version 2 of 5 versions of the question.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is 1 of 5 versions of the question.

Determine the radius and centre coordinates of a circle with equation expressed in expanded form.

Rearrange a homogeneous circle equation into the form (x-xc)^2+(y-yc)^2=r^2 to find the centre and radius.

Two part question, student has to rearrange the parallel resistors formula (stated in the question) to make L_1 or L_2 the subject (variable is chosen randomly), then find the value of this variable when values of the other variables in the formula are given. These values are randomly chosen.

Note that the advice for this question has two versions, the one displayed to the student depends on which variable is selected by the question.

Two part question, student has to rearrange the parallel inductors formula (stated in the question) to make L_1 or L_2 the subject (variable is chosen randomly), then find the value of this variable when values of the other variables in the formula are given. These values are randomly chosen.

Note that the advice for this question has two versions, the one displayed to the student depends on which variable is selected by the question.

Two part question, student has to rearrange the heat flow formula (stated in the question) to make T_1 or T_2 the subject (variable is chosen randomly), then find the value of this variable when values of the other variables in the formula are given. These values are randomly chosen.

Note that the advice for this question has two versions, the one displayed to the student depends on which variable is selected by the question.

Find the equation of a line passing through two points in the form y=mx+b. The question is set up so that m and b will be integers.

State the general form of the equation of a straight line explaining the role of each of the terms in your answer.

The student is shown a plot of a mystery function. They can enter values of $x$ check, within the bounds of the plot.

They're asked to give the formula for the function, and then asked for its value at a very large value of $x$.

A plot of the student's function updates automatically as they type. Adaptive marking is used for the final part to award credit if the student gives the right value for their incorrect function.

Students need to solve a quadratic equation and recognise that only the positive root has physical significance. Roots are randomised with one always negative and one positive. Equation can be factorised fairly easily or the quadratic formula can be used to find the solution. Advice gives solution by factorisation.

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

A two part question. Students are first given the formula for the time for a ball to come to rest after being dropped on a block. Part a) asks the students to rearrange the formula to make e, the coefficient of restitution, the subject of the formula. Part b) gives students realistic values for variables in the formula and asks them to calculate the coefficient of restitution using the formula derived in part a). 

Question asks students to find the time taken for an object thrown vertically upward from a platform to reach the ground. Set up randomly chooses environment to be on Earth, Mars or the Moon and uses appropriate acceleration due to gravity. The initial velocity of the body and height of the platform above the ground are randomly selected. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance.

Using given information to complete the equation $c= A \cos{ \left( \frac{2 \pi}{P} \left( t-H \right) \right) }+V $ that describes the concentration, $c$, of perscribed drug in a patient's drug over time, $t$. Calculating the maximum concentration and the concentration at a specific time. 

Calculating the rate of change of the temperature during a chemical reaction using the chain rule in a function of the form $T=ate^{-t}$, and finding the maximum temperature of the reaction.

Calculating area under curves of the form $ax^2+bx$ and $ax^4+bx^3+cx^2+dx+e$ in a contextualised problem.

The relationship between the frequency of an allele A, $x$, at a genetic locus in a diploid population and the fitness of a population with this frequency of allele A, $w$, is described by the function $w=ax^2+x(b-x)+c(b-x)^2$ . The aims are (a) ti simplify the algebraic expression, (b) calculate the fitness of a population with a given allele A frequency, and (c) calculate the allele A frequency when the fitness of the population is given.

The proportion of the sodium carbonate, $p$, which has dissolved by time $t$ seconds is given by the formula $ p=\frac{bt-at^2}{c}$. The aim is to calculate the proportion of sodium carbonate in a solution at a given time and vice versa.

Calculations involving Standard form.

Convert numbers between 0 and 1 intro standard form/scientific notation.

Convert numbers greater than 1 into standard form/scientific notation.

Rewriting a trigonometric expression of the form $A\cos(\theta)\pm B\sin(\theta)$ to either $R\sin(\theta+\alpha)$ or $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$. 

Rewriting a trigonometric expression of the form $A\sin(\theta)-B\cos(\theta)$ to $R\sin(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.