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".

Shows that you can embed a 3D GeoGebra applet in a content area.

The student is shown a passage of code in the prompt to a "choose several from a list" part.

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.

The number entry part in this question has an alternative answer which is marked correct if the student's number satisfies an equation specified in the custom marking algorithm.

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

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Given f(x)=1/(a-x)^2, evaluate f(x/z) where a is a randomised constant, and z is a randomised letter.

Given one of ax^2, ax^3, a/x (where a is a positive integer), calculate f(x+h) and f(x+h)-f(x) 

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.

evaluate a function with randomised alphanumeric expressions as inputs.

Evaluate a linear function at 3 numerical inputs.

HELM book 2.1.2 exercises

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

"Explain what is meant by the argument of a function."

Unmarked: Answer: "The argument is the input."

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.

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Student is shown a simple (randomised) function and asked to describe its behaviour. This is an information only question. Students need to view the advice to check their answer.

Given a function definition in words, evaluate the function with various variable and numeric inputs

HELM Book 1.5 Formulae and substitution exercises.

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.

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.

Choice of 2 formulae. The first is a fraction of the form y=(r+x)(1-rx). The second is of the form y=sqrt[(1-x)/(1+x) ]. Rearrange to make x the subject.

Rearrange a formula with a square root to make a variable under the root the subject.

Rearrange a complex formula involving squares, square roots, fractions and additions. This is a fixed question with no randomisation.

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

Transpose PV=RT to make a random variable the subject.

Convert a random number of cubic metres into cubic centimetres