Student is given a rational function, h(x), with randomised coefficients, and a linear function, k(x), also with randomised coeffieients and asked to find:

1. h(k(x)) or k(h(x)) (randomly selected) for a randomised value of x
2. The domain of h(x) - multiple choice part
3. A general expresion for k(h(x)) or h(k(x)) - opposite combination to first part.

Variables are constrained so that h(x) is not a degenerate form and that when evaluating h(x) denomiator is not 0.

This question gives the student the formula for the charge on a capacitor as a function of time then asks them to find the value of k, the exponential constant given other values and hence write out the formula for the given case. A custom function (in Extensions & scripts) extracts the student's formula and plots it on a JSXGraph object in the question. The student is then asked to evaluate the function at a given point using the plot or other methods. The value of the capacitor (Q_0), time (t) and charge at time t are randomised as is the value at which the formula is to be evaluated.

Simple Veriosn of Exam with randomised values

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).

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.

Describe the effect of changing the value of a constant term in a linear function. Part of HELM Book 2.5.1.

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.

Use parametric equations to find x for a given value of y. Part of HELM Book 2.2.2.

Identify the value that is not part of the domain of a function. Part of HELM Book 2.2.1.

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.

Given 2 randomised functions f(x) (linear) and g(x) (quadratic), find one of f(f), f(g), g(f) or g(g) at a randomised integer x-value

Simultaneous equations question. values for the coefficients are generated to be small numbers, random values are generated for the weights and the resultant energies are calculated for the question. Student needs to solve equations to find coefficients. Advice gives solution using method of elimination.

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.

Question requires students to determine if the smallest angle of a triangle is smaller than a given value. Answer is Yes/No but students need to use cosine rule to find the smallest angle and to know that smallest angle is oppositeshortest side (otherwise they will need to find all angles of the triangle). Designed for a test where students upload handwritten working for each question as a check against guessing. Also designed to make it difficult for students to google or use AI to find the answer.

Question requires students to determine if the largest angle of a triangle is smaller than a given value. Answer is Yes/No but students need to use cosine rule to find the largest angle and to know that largest angle is opposite longest side (otherwise they will need to find all angles of the triangle). Designed for a test where students upload handwritten working for each question as a check against guessing. Also designed to make it difficult for students to google or use AI to find the answer.

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). 

Useful for a review of the base 10 number system before introducing different bases and also just ensuring students understand how the base 10 system works.

Useful for a review of the base 10 number system before introducing different bases and also just ensuring students understand how the base 10 system works.

old question, way too many things in one question! I have made better questions out of each part now.

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.

The student is given a quadratic formula and asked to fill in a table of values of $f(x)$ for a given range of $x$.

There is also a plot of the points, which updates when the table is filled in, or the student can move the points to fill in the table.

The table uses the spreadsheet and JSXgraph extensions.

Friction

Student estimates, then calculates exactly and symbolically the value of $k$ for a parabola $y = k x^2$ which passes through a given point.

Evaluate a given, randomised, linear function at a given, randomised, value.

A difficult question that involves rearranging a complicated formula, then applying unit conversions to variable values, then evaluating the formula for the selected value. The variable values are randomised.