Students need to rewrite a given trig espression in terms of one trig ratio only, Written as a scan solution and upload question, no randomisation.

Students need to rewrite a given trig espression in terms of one trig ratio only, Written as a scan solution and upload question, no randomisation.

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

Write down the equation of a circle centre C and radius R.

Given a circle centre and radius, write an appropriate inequality for the region either inside or outside the circle.

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.

Question asks student to find zeros of a quadratic equation - disguised as finding time for particle to reach a given position. 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. Coefficients of the quadratic are randomly chosen within linits which give one positive and one negative root.

Fixed question: Given two points at opposite ends of a diameter, write down the equation of the circle.

Given a circle centre and a point on the circumference, write down the circle equation.

Given the radius and centre coordinates of a circle write down its equation.

Given a graph of a circle, write down its equation.

Question about use of trig identities, student has to use identities to find exact value of \(\sin \frac{\pi}{12}\). Question is used in exam where student has to write out the solution and upload it for grading.

Question about use of trig identities, student has to use identities to find exact value of \(\cos \frac{7\pi}{12}\). Question is used in exam where student has to write out the solution and upload it for grading.

Students are asked to solve two simulatineous linear equations in an application of mixing two liquids to arrive at a given final volume and concentration. Students are expected to write up working for their solution and upload it seperately. Final volume, final concentration and concentrations of each solution are randomised.

 Question asks student to find zeros of a quadratic equation. 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.

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.

Knowing the half-life of Carbon-14 and the initial mass of Carbon-14 when a tree was cut (a) write an expression that describes the relationship between the remaining mass and time, (b) calculate the remaining mass after $t$ years, and (c) given the remaining mass calculate how many years ago the tree was cut down. 

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $b$, for integers $a$, $b$, $m$ and $n$.

Plot the Fourier series coefficients for a piece-wise linear function.  Write a Python script to reproduce the same figure.

In the first part, the student must write any linear equation in three unknowns. Each distinct variable can occur more than once, and on either side of the equals sign. It doesn't check that the equation has a unique solution.

In the second part, they must write three equations in two unknowns. It doesn't check that they're independent or that the system has a solution. The marking algorithm on each of the gaps just checks that they're valid linear equations, and the marking algorithm for the whole gap-fill checks the number of unknowns.

A random proper fraction $a/b$ with denominator in the range 2 to 30 is picked, and the student must write $\frac{a}{b} \pi$.

The point of this question is to demonstrate that the correct answer is shown as a multiple of $\pi$ rather than a decimal.

Two functions given in words. Write down the function definition. The numbers in the function definitions are randomised.

In the first part, the student must write an R function to compute the first $n$ terms of the series $\frac{1}{k!}$.

In the second part, they must use that function to calculate an approximation to $e$ using a given number of terms of the series.

The student must write R code to assign the given value to the variable x.

Given an unknown list, the student must write Python code to create a copy of it.

There's an alternative to catch the case where the student's variable is just a reference to the original list.