Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Provided with information on a sample with sample mean and known population variance, use the z test to either or reject a given null hypothesis. One sided.

Download a file and scan the values into R to obtain a numeric vector of values. Then use R to explore your numeric vector in order to find the answers to these questions.

The custom function rectangle(width,height) draws a rectangle with the given dimensions, along with some labels.

Provided with information on a sample (>30) with sample mean and standard deviation, use the z test to either accept or reject a given null hypothesis.

Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

Q1. True/false questions about basic facts.

Q2 and Q3. Velocity-time graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, definite integrals of v ar eto be determined.

Simple counting exercise, with combinations

Introduction to counting with permutations and combinations

Introduction to first order recurrence relations with a simple example, including homogenous and non-homogenous solutions.

Q1. True/false questions about basic facts.

Q2 and Q3. Velocity-time graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, changes in position, distances are to be calculated.

Graphs are given with areas underneath them shaded. The area of the shaded regions are given and from this the value of various integrals are to be deduced.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

More work on differentiation with trigonometric functions

Question requires students to interchange units of Hz with MHz, GHz, THz. Question is not very efficient at present- frequencies spanning many orders of magnitude are generated by variables in a clumsy way. Could be improved by having frequency generated by a 10^((random(1000..4000)/1000) variable instead, for example. 

The student must enter a number in scientific notation, with separate boxes for significand and exponent. They only get the marks if both elements are correct.

These questions show how to use JSON data to represent structured information.

Show a list of the factors of a number.

Works by testing each number up to $n$ for divisibility by $n$, so won't do well with really big numbers. Certainly fast enough for numbers up to 4 or 5 digits.

Choose from one of several pre-defined scenarios, and set variables to the corresponding values, defined in lists.

This question has three variables: city, population, and percent_like_chocolate. These differ for each city. We've defined a list for each variable, with the corresponding values. A variable called scenario picks a random position in the list, so the value of city, for example, is cities[scenario].

Some custom CSS restyles the matrix input so it looks like a fraction, with input boxes on top and bottom.

Ideally, there should be a fraction input part type, or an option for the number entry part to display a fraction input.

This question shows how to ask for a number in scientific notation, by asking for the significand and exponent separately and using a custom marking algorithm in the gap-fill part to put the two pieces together.

Answers not in standard form, i.e. with a significand not in $[1,10)$, are accepted but given partial marks.

This question asks the student to give a function with a particular root. It then asks them to divide by (x-{root}), and uses adaptive marking to mark against the previous answer.

This uses the "expression" data type, which is currently undocumented and experimental.

A "match choices with answers" part where the student either gets all the marks or none. Any incorrect choice is penalised with a huge negative mark, so they end up with the minimum mark of 0.

A fill-in-the-blank style question to test vocabulary within the topic of Algebra.