Determinig the CoG of a composite part

Friction & Centripital Motion

2 bodies on an incline plane

3 Forces Applied to an Eye bolt.  Use force components to calculate the Reaction force.

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.

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.

Evaluación de una expresión algebraica con dos variables

This question models an experiment: the student must collect some data and enter it at the start of the question, and the expected answers to subsequent parts are marked based on that data.

The student's values of the variables width, depth and height are stored once they move on from the first part.

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). 

This question is an application of a quadratic equation. Student is given dimensions of a rectangular area, and an area of pavers that are available. They are asked to calculate the width of a border that can be paved around the given rectangle (assuming border is the same width on all 4 sides). The equation for the area of the border is given in terms of the unknown border width. Students need to recognise that only one solution of the quadratic gives a physically possible solution.

The dimensions of the rectangle, available area of tiles and type of space are randomised. Numeric variables are constructed so that resulting quadratic equation has one positive and one negative root.

Subtracting a decimal with 3 decimal places from a decimal with 2 or 3 decimal places. borrowing is necessary. This was modified from a subtraction question using integers with each number divided by 1000 so the variables have names referring to ones, tens, hundreds etc.

The student must solve a pair of simultaneous equations in $x$ and $y$.

The variables are generated backwards: first $x$ and $y$ are picked, then values for the coefficients of the equations are chosen satisfying those values.

This question shows how to use the question's JavaScript preamble to request data from an external source, and use that data in question variables.

Note that this means the question only works when the external source is available. Use this very carefully, and avoid it if you possibly can!

This question shows how explore mode can be used to loop through several versions of the same question. The variables for each version are stored in a list of "scenarios", and a counter works through that list each time the student moves on to the next part, labelled "try the next version of this question".

Give f(x)=ax^2+b a simple function input (like 6x-3) and evaluate. Constants and variables, and the function input are all randomised.

A custom marking algorithm picks out the names of the constants of integration that the student has used in their answer, and tries mapping them to every permutation of the constants used in the expected answer. The version that agrees the most with the expected answer is used for testing equivalence.

If the student uses fewer constants of integration, it still works (but they must be wrong), and if they use too many, it's still marked correct if the other variables have no impact on the result. For example, adding $+0t$ to an expression which otherwise doesn't use $t$ would have no impact.

Rearrange an equation for a variable e in k.1/(1-e) and then evaluate for e, given values for the variables.

Rearrange a linear formula au + bv + cw = d to make one of u,v,w the subject.

Rearrange a linear function in x and y to make y the subject. Line variables are randomised.

evaluate a function (4a)/(pi*b^2cd) given random values for a,b,c,d.

Simplify (a) a fully-factorised fraction with common factors, and (b) a fraction where the numerator is a product and the denominator a sum sharing the same variables (that cannot be simplified). The variables are randomised. Part of HELM book 1.4

Simplify an algebraic fraction that is fully factorised with common factors between the numerator and denominator, and one of the variables has a larger index on the denominator. Part of HELM Book 1.4

Solving first order differentials by separation of variables.

Show one of several blocks of text depending on the value of a question variable.

As well as a simple check for the value of a variable, the condition to display a block of text can be a complex expression in any of the question variables - in this example, depending on the discriminant of the generated quadratic.

Given an expression in one or two variables, with two or three terms, collect like terms, if possible. Part of HELM Book 1.3