Gives a plot of a velocity-time graph using JSXgraph, and a description of the motion shown in the graph. The student is asked to calculate the acceleration at different stages of the motion, and the displacement at the end of the motion.

The student is shown two labelled graphs. They are asked:

• Number of vertices in each
• Number of edges in each
• Degree sequences for each
• Is there an isomorphism between them? If so, write one.

The number of vertices is always equal, so this is a gimme.

If the edges or degree sequences are different, the student is expected to realise that there cannot be an isomorphism.

If these values are the same, then there will be an isomorphism (else the question is a bit too tricky).

Numbas expects a particular isomorphism, but there may be more than one, all of which would be accepted.

sin horizontal shifted Working 1_11_16

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. SP = Statistics & Probability strand. Students read the annual hours worked from the chart and calculate the weekly hours given the number of weeks annual leave. There are 7 different versions of this question.

Given the graph of the line determine the equation of the line.

Given th original formula the student enters the transformed formula

Multiple solution of sin

Given the original formula the student enters the transformed formula

Given the original formula the student enters the transformed formula

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

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

This is a copy of a question by Ben Brawn. It replaces the JavaScript construction of the diagram with JSXGraph+JME.

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

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Four sinusoidal graphs are given. Student should select the one which is sine and cosine.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Four sinusoidal graphs are given. Student should select the one which is sine and cosine.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

given random circle on graph with centre in 2nd or 3rd quadrant. find loci in complex form

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students need to calculate the proportion of calls for one given emergency, after reading the number of calls, and total number of calls from the supplied infographic. There are 4 different versions of this question.

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11 questions that test trig equations including use of identities and those needing stretches and translations. Also some questions related to trig graph shapes and applications.

given plot of a graph. find amplitude, period and phase shift

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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.

Horizontal and vertical shifts and scales of a random cubic spline

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.