Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Finding x and y values for straight line graphs

Looking at gradients and values for x and y for straight-line graphs

Given data on probabilities of three levels of success of three options and projections of the profits that the options will accrue depending on the level of success, find the expected monetary value (EMV) for each option and choose the one with the greatest EMV.

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four version of this question: I: cubic, II: linear, III: quadratic, IV: sinusoisal.

A block lies on rough horizontal ground. The coefficient of friction is given and students find the maximum value of friction $F_{\text{MAX}} = \mu R$. This is then used to determine the magnitude of force that must be exceeded to achieve movement when the force is applied horizontally and at two different angles to the horizontal.

Finding the acceleration of a particle on an inclined plane which is at an angle to the horizontal. Smooth then with value for coefficient of friction.

No description given

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

multiple choice testing sin, cos, tan of angles that are negative or greater than 360 degrees that result in nice exact values. 

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

This question provides a sample of 20 data values and requires the calculation of mean, median, and standard deviation. The data are presented as a column so they can be easily copy-pasted into a spreadsheet.

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.

Substitute values into formulae for the area or volume of various geometric objects.

No description given

Substitute values into formulae for the area or volume of various geometric objects.

(Calculating estimate and actual value of temperature using given formulas, and hence finding the percentage error)

rebelmaths

This question demonstrates sending commands to geogebra and getting geogebra values and using them as part of a marking algorithm.

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$.

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

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Given a statement in words of a relationship between two variables, write down a corresponding formula. It's marked correct if values satisfying the relationship satisfy the formula, and values not satisfying the relationship don't.

Then, given a value for one of the variables, work out the value of the other one. They're substituted into the formula given in the first part and marked correct if it's satisfied.

Both parts use custom marking algorithms.

A cubic with a maximum and minimum point is given. Question is to determine coordinates of the minimum and maximum point.

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

Show one of several blocks of text depending on the value of a question variable.

As well as a simple check for the value of a variable, the condition to display a block of text can be a complex expression in any of the question variables - in this example, depending on the discriminant of the generated quadratic.

A static block of given mass is sits on a flat plane with defined static and kinetic friction values. It is pushed with enough force to start it moving - calculate the speed of the block after a given distance.

A block of given mass is sits on a flat plane with defined static and kinetic friction values. Randomly, it does one of two things, it is either:

1) pushed with enough force to start it moving - calculate the force on the block or the static friction.

2) moving over a distance - calculate the work done or the kinetic friction

(are these uneven calculations)