Solve two quadratic equations (with real coefficients) in the complex numbers. The solutions have non-zero imaginary part, fractions can appear (but the denominators are rather small).

Questions on differentiation from first principles, and continuity and differentiability.

Problem on a closed cylindrical tank having minimum surface area

Another practical application of differentiation

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This question uses the technique of allocating zero marks to gaps so that they act as holders of values input by the user but are not assessed. The values so input are then gathered using the code found in the preamble and suitable combinations are assigned as answers to gap fills which are then assessed to see if they meet the requirements of the question. Note that is a gap fill is created, but not addressed in the prompt of the part then it is hidden from the user.

Compute a table of values for a quadratic function. Calculate the slope and intercept of a line.

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Get the student to upload their experimental data in a CSV file, then ask them to compute statistics on it.

Horizontal and vertical shifts and scales of a random cubic spline

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A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

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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.