$x$ is given and (sin(x),cos(x)) is plotted on a unit circle.  Then the student is asked to determine sin(y) and cos(y), where y is closely related to x (e.g. y=-x, y=180+x, etc.) Also find values and sign of cos/tan/sin(x).

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

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.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

Given a data sheet with distances between cities and costs for different forms of transport, and some information about modes of transport used, fill in a form for a journey.

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.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.

Parametric form of a curve, cartesian points, tangent vector, and speed.

Parametric form of a curve, cartesian points, tangent vector, and speed.

Intersection points, tangent vectors, angles between pairs of curves, given in parametric form.

Determine frictional force acting on a block on an incline.  Coefficients of friction, weight and a horizontal force are given

Students are given a positive whole number less than one hundred and are asked to find either 1/10, 1/100 or 1/1000 of it.

Students are given a positive whole number less than one thousand and are asked to divide it by either 10, 100, 1000 or 1,000,000.

Students are given a number with two decimal places and are asked to multiply it by either 10, 100 or 1000.

Powers of 10 from 10^3 to 10^6. 10 to the power 4 is excluded as it is given as an example.

Students are given a decimal in the form 0.X and asked to identify its value, either X units, X tenths, X hundredths or X tens.

In the first part, the student must write an R function to compute the first $n$ terms of the series $\frac{1}{k!}$.

In the second part, they must use that function to calculate an approximation to $e$ using a given number of terms of the series.

The student must write R code to assign the given value to the variable x.

The student must write a list comprehension to map the elements of a given list.

The student must write code to filter a given list of numbers, returning only the positive elements.

Given an unknown list, the student must write Python code to create a copy of it.

There's an alternative to catch the case where the student's variable is just a reference to the original list.

Given an unknown list, the student has to write code to return the last item in the list.

Given a randomly-generated list, the student must write code to return its first value.

There's an alternative to check if they get the second item, which they might do if they don't realise Python lists are zero-indexed.

Students are given a number with two decimal places and are asked to divide it by either 10, 100 or 1000.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown a column graph and asked to calculate the net benefit given the amount invested (randomly generated) and the intervention type (one of seven possible).

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given the number of people that are fed with 200g of rice (randomised), and the total number of people to be fed (randomised). They need to calculate the weight of rice using proportional reasoning.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given the number of pages read (randomised) and number of pages remaining (randomised), and asked to write the proportion read as a simple fraction.