Calculate the marginal and average cost for a given cost function. Find the corresponding startup/shutdown price.
Maximize the profit function at a given price.

Drag points on a graph to the given Cartesian coordinates. There are points in each of the four quadrants and on each axis.

Find the equation of the line that passes through given points

Given a randomised square root function select the possible ways of writing the domain of the function.

The student is given the equations of a line and a circle, and has to find the coordinates of the points of intersection. They're always at integer coordinates.

The student is shown a set of axes with three lines. They must move the lines so they match the given inequalities, then move a point inside the region satisfied by the inequalities.

Given cost of production and price of sale of a product; a percentage increase in cost of production; and unit sales before and after; work out the extra profit.

Based on question 6 from section 3 of the maths-aid workbook on numerical reasoning.

This exercise will help you round off decimals to given decimal places.

This exercise will help you round off decimals to given decimal places.

Find the area under a curve. The step is given.

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

This question is a variation on another version which asks the student to find the height of a bridge arch and width of the river given a formula for the arch of the bridge (also available in the Numbas database)

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean and standard deviation of a sample. The population variance is not given and so the t test has to be used. Various scenarios are included.

Unmarked question, with advice.

Write down an example of a polynomial of given degree and given variable.

Write down a non-polynomial function.

Explain why a polynomial with a fractional index is not a polynomial.

Given an arbitrary polynomial, identify its degree.

Interpreting line graphs depicting the melting temperature of DNA depending on the percentage of GC content. Estimating the melting temperature given a GC percentage and vice versa.

An application of quadratic functions based on the Gladesville Bridge in Sydney, Australia. Student is given an equation representing the arch of the bridge and asked to find the height of the arch and the width of the river. Requires and understanding of the quadratic function and where and how to apply correct formulae.

An application of quadratic functions based on the Gateshead Bridge in the UK city of Newcastle. Student is given an equation representing the arch of the bridge and asked to find the height of the arch and the width of the river. Requires and understanding of the quadratic function and where and how to apply correct formulae.

Student is given a rational function, h(x), with randomised coefficients, and a linear function, k(x), also with randomised coeffieients and asked to find:

1. h(k(x)) or k(h(x)) (randomly selected) for a randomised value of x
2. The domain of h(x) - multiple choice part
3. A general expresion for k(h(x)) or h(k(x)) - opposite combination to first part.

Variables are constrained so that h(x) is not a degenerate form and that when evaluating h(x) denomiator is not 0.

This question gives the student the formula for the charge on a capacitor as a function of time then asks them to find the value of k, the exponential constant given other values and hence write out the formula for the given case. A custom function (in Extensions & scripts) extracts the student's formula and plots it on a JSXGraph object in the question. The student is then asked to evaluate the function at a given point using the plot or other methods. The value of the capacitor (Q_0), time (t) and charge at time t are randomised as is the value at which the formula is to be evaluated.

Students are asked to rearrane the formula giving the voltage drop across a resistor in terms of emf of battery, resistance of resistor and internal resistance of battery to make the internal resistance the subject. They are then asked to calculate the internal resistance given values for the other variables (randomised).

Basic trigonometry question, students are asked to find the diameter of a circular tunnel given distance from edge of a roadway to centre top of tunnel (randomised) and angle from edge of road to centre top of tunnel (randomised).

Students need to prove a given trig identity, Written as a scan solution and upload question, no randomisation.

Students need to prove a given trig identity, Written as a scan solution and upload question, no randomisation.

Students need to prove a given trig identity, Written as a scan solution and upload question, no randomisation.

Students need to rewrite a given trig espression in terms of one trig ratio only, Written as a scan solution and upload question, no randomisation.

Students need to rewrite a given trig espression in terms of one trig ratio only, Written as a scan solution and upload question, no randomisation.

Students need to prove a given trig identity, Written as a scan solution and upload question, no randomisation.

Students need to prove a given trig identity, Written as a scan solution and upload question, no randomisation.