This question demonstrates a few ways of interacting with a Venn diagram drawn using JSXGraph.

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

Questions testing understanding of the precedence of operators using BIDMAS applied to integers.

Calculate probability using P(A) = 1-P(not A)

Using geogebra to draw lines tangent to a curve and calculate their gradient.

Questions testing understanding of the precedence of operators using BIDMAS. That is, they test Brackets, Indices, Division/Multiplication and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS applied to integers.

Subtracting a decimal with 3 decimal places from a decimal with 2 or 3 decimal places. borrowing is necessary. This was modified from a subtraction question using integers with each number divided by 1000 so the variables have names referring to ones, tens, hundreds etc.

The subtraction algortihm using the borrow and pay back method with integers.

These question are designed to be completed without using a calculator.

Student is given a triangle with the value of 2 sides and 1 or 2 angles and asked to find the value of the third side using the cosine rule. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.

Students are shown a right angled triangle and asked to find the value of an angle using a trig identity.

The triangle is a fixed image, but the angles and side lengths are randomly selected.

The angle is to be given in degrees and minutes.

There are 4 orientations of the triangle in the diagram. The orientation is randomly chosen.

Students are shown a right angled triangle and asked to compute a side length using a trig identity.

The triangle is a fixed image, but the angles and side lengths are randomly selected.

The angle is given in degrees and minutes, and students are asked for the side length correct to 1 decimal place.

There are 4 different triangle orientations that can display.

Using the given information to complete the equation $y= A \cos{ \left( \frac{2 \pi}{P} x  \right) }+V $ that describes an electromagnetic wave and calculating the smallest angle, $x$, for which $y=y_0$.

Given the cost of hiring a room for a given number of hours, compare with competing prices given per hour and per minute.

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

Questions testing understanding of the precedence of operators using BIDMAS. These questions only test BDMAS. That is, they test Brackets, Division/Multiplication and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS. These questions only test BDMAS. That is, they test Brackets, Division/Multiplication and Addition/Subtraction.

This question assesses

• the students ability to apply both theoretical and experimental probability to calculate expected values 
• the students understanding of how to calculate the relative frequency of an outcome

The question also helps to show students how using experimental probability and theoretical probability results in different expected values of an outcome.

This question assesses the students ability to calculate and convert between different types of compound units, including rates of pay, speed and unit pricing.

Questions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.

Calculating the derivative of a function of the form $\sin(ax^m+bx^n)$ using the chain rule.

Several questions on rounding number and using approximations to estimate. Several real-world examples.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown an infographic, given the details of one man and asked how many routine screenings they should have. There are seven possible questions.

This question demonstrates a few ways of interacting with a Venn diagram drawn using JSXGraph.

Short question to test encoding some random binary strings using repetition and parity bit. Randomised 5-bit strings.

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.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force acts in the positive $x$ and positive $y$ direction.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ and negative $y$ direction.