Simple multiplication of complex conjugates. Complex numbers are of the form $a+bi$ where $a$ and $b$ are randomised between 1 and 9 inclusive. 

The student is shown a diagram with a line between two points. They must make the line cross the axes at $x=1$ and $y=2$. They can drag the points around, or type a gradient in to move the points accordingly.

The student is shown a diagram containing a line between two points. They're given a gradient and $y$-intercept.

They must manipulate the line or the points so that the line has the given gradient and $y$-intercept.

The student is shown a diagram containing a line between two points. They're given a gradient and $y$-intercept.

They must manipulate the line or the points so that the line has the given gradient and $y$-intercept.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

A diagram showing the difference between lines, rays and segments in Eukleides.

Ask for the squares of five randomly-chosen numbers between 0 and 15.

The shuffle function puts a list in random order.

Use the CSS preamble to give a bit more space between multiple choice answers.

One way of checking an equation is valid is to check that the difference between the LHS and RHS is 0.

Asks the student whether a map between two finite sets, given schematically "by arrows" is injective/surjective/bijective.

Multi-choice question, differentiate between code for upper / lower case characters

Use a table of properties to find the Area Moment of inertia for simple shapes: rectangle, triangle, circle, semicircle, and quarter circle.

 The parallel axis theorem is not required for any of these shapes.  One situation requires subtracting a triangle from a rectangle however.

Distinguish between centroidal and non-centroidal moments of inertia.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

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Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Arithmetic operations involving fractions; converting between decimals and fractions; deciding if fractions are equivalent.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Differentiate between linear and quadratic sequences and arithmetic and geometric sequences through a series of multiple choice questions. Spot different patterns in sequences like the triangle sequence, square sequence and cubic sequence and then use this pattern to find the next three terms in each of the sequences.

Given a population size and data on a test for a condition on that population, use a tabular approach to find the increase in risk after a positive test in which there is a small chance of a false positive i.e. the probability that the test is positive even though  the condition is not present. See Advice for a graphical version.

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Used for LANTITE preparation (Australia). NC = Non Calculator strand. SP = Statistics & Probability strand.This question provides a list of data to the student. They are asked to find the difference between the mean and the median. This question was based on a Newcastle Uni question which also asked the mode, hence the surplus legacy variables (too tricky to delete).

Fragen zum Abbildungsbegriff / Questions regarding the notion of map between two sets.

A bill (for a random amount) is divided equally between a number of people.

Students evaluate the per-person cost for a random number of people.

They then complete a table showing the cost per person for various numbers of people.

Finally they are asked to identify the shape of the graph that represents this function. They are given 2 exponentials, a hyperbola and a line to choose from.

Converting between metres (m) and centimetres (cm). 

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised.