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.

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.

HELM Book 1.5 Formulae and substitution exercises.

HELM Book 1.5.1: using formulae and substitution: task 1

The student is asked to calculate a division by the method of long division, which they should enter in a grid.

The process is simulated and the order in which cells are filled in is recorded, so the marking feedback tries to identify the first cell that the student got wrong, or should try to fill in next.

They're asked to give the quotient as a plain number in a second part, to check that they can interpret the finished grid properly.

Shows how the "give a number which satisfies an equation" part type can be used to makr the student's number correct if it satisfies an equation of the form $f(x) = 0$.

rebelmaths

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Given an equation with variable x in the power on two different bases, students must solve for x. Hints are included in the question to aid the student as needed.

Given an equation where x is the base of a log term, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation involving x as a power on e, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

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Shows different ways to load a geogebra applet.

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This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

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This test contains a few easy questions on subjects covered in the GCSE syllabus. I made it to try out the "School" theme, adapted for younger students.