Replace three tangential forces with an equivalent force-couple system acting at the center of a circle.

Homework set.  Find statically equivalent systems of forces.

Homework set.  Calculate resultant moment of one or more couples. 

Rigid body equilibrium problem.  Easiest to solve by replacing forces on the perimiter of the pulley with equivalent forces at the axle.

Picking a ratio out of a list that is not equivalent to the others.

This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number. 

This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number. 

You can enter an equation in 2 or more variables and rearrange it in the following steps. Numbas checks that the lines of working are all equivalent to the original equation. 

You can enter an expression and rearrange it in the following steps. Numbas checks that each arrangement is equivalent to the original expression.

A quick knowledge and understanding check of:

1) Work done concept.

2) Work done formulae: W = Fx and W = Fxcos(y).

3) Equivalent units of work.

Identify well-known fractional equivalents of decimals. Convert obscure decimals and recurring decimals into fractions.

https://numbas.mathcentre.ac.uk/question/22784/decimals-to-fractions/ by Lauren Richards

Translated to German.

The student has to enter `diff(y,x,2)`, equivalent to $\frac{\mathrm{d}^2y}{\mathrm{d}x^2}$, as their answer. It's marked by pattern matching, using a custom marking algorithm.

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This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number. 

Match prefixes with their abbreviations, from nano to giga. Match prefixes with equivalent scientific notation.

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Replace two forces with a equivalent force-couple system at a specified point.

Simplify an algebraic fraction where the numerator is a factor of the quadratic on the denominator. Posed as a yes/no question, is this fraction equivalent to this simplified form? The answer is always yes. Part of HELM Book 1.4

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Finding X-Y intercepts for quadratic and cubic equations.

The student is asked to integrate a given function. The marking algorithm differentiates the student's answer, and checks that it is equivalent to the original function.

Questions that gives either an am or pm time displayed on a 12-hour clock and asks for its equivalent time in 24-hour mode. The question uses JSXGraph to generate the displayed 12-hour time. Times are randomly generated in 5 minute increments.

Students must match the decimals 0.1, 0.01 and 0.001 to their fraction equivalents. The order in which they appear is randomised but it is always the same three decimals.

Arithmetic operations involving fractions; converting between decimals and fractions; deciding if fractions are equivalent.

Replace two parallel forces with an equivalent single force

Compute tables of Hamming distances in given codes, then determine which codes are equivalent.

The answer to this question is a differential equation involving $y''$, $y'$ and $y$.

A variable value generator for $y$ ensures that the right values are tested to check that the student's answer is equivalent to the expected equation.

Calculating rates and scaling rates. Drops per mL and drops per minute questions unit rate to equivalent rate.

Equivalent fractions, simplifying, adding, subtracting, multiplying and dividing fractions. Converting between mixed numbers and improper fractions.

Identify well-known fractional equivalents of decimals. Convert obscure decimals and recurring decimals into fractions.

Given the polar coordinates of a point $P$, calculate the equivalent cartesian coordinates