Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis.  

Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

Horizontal and vertical shifts and scales of a random cubic spline

Simple questions on interval notation. If you are not randomising the order of your questions please turn on randomise choices in these questions.

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.

Use a piecewise linear graph of speed against time to find the distance travelled by a car.

Finally, use the total distance travelled to find the average speed.

The student is shown a Cartesian diagram containing a point $P$ and a circle. They must move the point and change its radius so that the point $P$ is touching the circle.

They can type the radius and coordinates in, or move the circle around on the diagram.

The student is shown a diagram containing a single point at the origin. They must move the point to the given integer coordinates.

A 2D linear programming problem: optimise the profit from producing two different kinds of product, which both use the same limited resources.

A JSXGraph diagram illustrates the problem and can be used to find an answer.

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 must make a spanning tree of the complete graph $K_5$. They can tick boxes to include or exclude edges, or toggle them by clicking on a visual representation of the graph.

Add, subtract, multiply and divide algebraic fractions.

This question shows how to pick a GeoGebra worksheet to show to the student from a list, based on the value of a question variable.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

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Simple multiplication practice.

Simple multiplication including multiples of 10, with answer that can be multiples of up to 1000.

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Some questions demonstrating the JSXGraph extension, for my talk at the JSXGraph conference 2021.

Solving 2nd order differential equation for pendulum, with and without damping.

The student is shown a diagram containing a single point at the origin. They must move the point to the given integer coordinates.

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.

Compute a table of values for a quadratic function. A JSXgraph plot shows the curve going through the entered values.

Customised for the Numbas demo exam

Motion under gravity. Object is projected vertically with initial velocity $V\;m/s$. Find time to maximum height and the maximum height. Now includes an interactive plot.

A simple multiplication test.