Factorise a cubic expression into the product of three linear factors of the form $mx+c$, where one of the factors is given. 

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given a proportion of students who DO speak a language other than English at home, and are asked to find the percentage who do NOT. The fraction denominator is either 20 or 25, and the numerator is randomised.

Given either (a) ax+bx+cy+dy, or (b) ax^2+bx+c, (c) ax^2+bx^2+cx^2, where a,b,c,d are randomised constants, and x and y are randomised letters, simplify by collecting like terms (if possible).

Part of HELM Book 1.3

Given an expression in one or two variables, with two or three terms, collect like terms, if possible. Part of HELM Book 1.3

State if a function is increasing at given points or on given intervals

Given an expression (either a^-k or 1/a^-k) with a negative index, rewrite it with a positive index.

The variable a and the index k are randomised.

Part of HELM Book 1.2

Given an expression 10^-k, rewrite it as a fraction with no index. k is a random positive integer from 1 to 6.

Part of HELM Book 1.2

Given an expression (either a^-k or 1/a^-k) with a negative index, rewrite it with a positive index.

The variable a and the index k are randomised.

Part of HELM Book 1.2

Given an arbitrary polynomial, identify its degree. Part of HELM Book 1.2

Students are given three expanded products and asked to write them in index notation. Part of HELM Book 1.2

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.

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.