Fractions already have a common denominator. Addition and subtraction 50:50 split, when subtracting, the answer is negative half the time. Students shouldn't have to worry about reducing fractions by design.

Students seem to not realise that $\frac{a}{b}\times c=c\times\frac{a}{b}=\frac{a\times c}{b}=\frac{c\times a}{b}=a\times c \div b=a\div b\times c=c\div b \times a \ne c \div (b\times a)\ldots $ etc. This question is my attempt to help rectify this.

There's one question, which you have to get right 5 times in a row. If you get it wrong, you have to start again.

This makes more sense if the question is randomised!

This shows one way of laying out matrix cells in a table, so that some cells can be filled in by the student.

At the time this was written, there's an open issue for allowing some entries in the matrix entry part to be filled-in, which would make this technique redundant.

Some CSS in the preamble adds the brackets around the table - it has to have the attribute class="matrix-gaps"

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".

Convert a random number of cubic metres into cubic centimetres

Convert a random value in square metres to square centimetres.

convert a random length in m to centimetres

Calculate the time taken for a certain distance to be travelled given the average speed and the distance travelled.

Small, simple question.

A measurement is performed multiple times for the same object, the student will

• calculate the mean result
• calculate the standard error on the mean 
• write the mean±error to the correct precision as defined by the error written to 1 significant figure 

Advice is provided including on performing the calculations in Python or spreedsheets together with further reading. 

Factorise an expression of 2 or 3 terms where the gcd is a letter times a number. Part of HELM Book 1.3.4

Part of HELM Book 1.1

Simplifying an expression of the form $a^3 \times (a^4)^{1/2}$ to $a^5$, where $a$ is an integer. 

This question demonstrates how to use GeoGebra applets in explore mode.

The student must construct a polygon by adding points one at a time. At any point, they can answer the question, "Is the centroid inside the polygon?"

GeoGebra's IsInRegion command is used to decide if the centroid is inside the polygon.

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.

No description given

Multiplication of $2 \times 2$ matrices.

Calculate distance given speed and time.

Given speed and time, calculate distance.

Given speed and distance, find time. convert time units.

Is this number divisible by 2? Half the time the number is, half the time it isn't. Steps give the divisibility test.

Students are shown a graph of the value of a machine over time. The line equation is randomised.

They are asked to evaluate value at a given time, and the time at which a given value is reached. They are asked when the machine has no value, and the range of times over which the model is valid. They are also asked to explain the physical meaning of the gradient.

Solving a separable differential equation that describes the population growth over time with a known initial condition to calculate the population after $n$ years. 

Integrating a polynomial functions which describe the rate of change of a population over time to find and use an equation that describes the total population according to time.

A question to practise the following skills in the context of Earth Sciences:

• using a data set to deduce a linear relationship
• using the graph to make predictions

Calculate a rate of pay (in pounds per week) given the total pay over a given period of time.

Paired t-test to see if there is a difference between times taken to complete a task.

Topics: Trigonometeric equations and complex numbers
Students must complete the exam within 90 mins (standard time).
Questions have variables to produce randomised questions.

A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.

Calculate the average speed in km/h and m/s given distance in kilometres and time in hours and minutes.