These question are designed to be completed without using a calculator.

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Students are shown a graph with 6 vertices and asked to find the length of the shortest path from A to a random vertex.

There is only one graph, but all of the weights are randomised.

They can find the length any way they wish. In the advice, the steps of Dijkstra's algorithm used in solving this problem are displayed. It is not a complete worked solution but it should be sufficient to figure out the shortest path used to reach each vertex.

Students are given a diagram with 2 triangles. They are given 2 randomised lengths, and a randomised angle of depression.

They need to compute an angle by subtracting the angle of depression from 90°. Then they need to use the sine rule to calculate a second angle. Then they need to use the alternate angles on parallel lines theorem to work out a third angle. They use these to calculate a third angle, which they use in the right-angle triangle with the sine ratio to compute the third side. They then use the cos ratio to compute the length of the third side.

Students are given 2 right-angle triangles - two ramps of differing steepness up a step, and are asked to find one of a selection of randomly chosen lengths. The height of the step is given - it is randomised. Students are also given either the angle of incline of the steeper ramp or its length, both of which are randomised. They are also given the angle of incline of the shallower ramp, which is also randomised.

The student is given a triangle with one side running N-S. They are given bearings for the other two sides. They are given the length of the N-S side.

The bearings and the length are randomised.

They are then asked to find the area and the perimeter of the triangle.

Student is given a triangle with the value of 2 sides and 1 or 2 angles and asked to find the value of the third side using the cosine rule. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.

Student is shown a random bearing with the true bearing marked. They are asked to write it as a compass bearing.

Student is given a triangle with the value of 3 sides and asked to find the value of an angle. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.

Student is given a triangle with the value of 1 side and 2 or 3 angles and asked to find the value of another side. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.

Student is given a triangle with 2 or 3 side lengths given and asked to use the sine rule to find the value of an angle. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.

Student is shown a graph with a parabola and asked to identify the correct equation. Multiple choice question.

Derive the expressions for the shear and bending moment as functions of $x$ for a cantilever beam with a uniformly varying (triangular) load.

Show a list of the factors of a number.

Works by testing each number up to $n$ for divisibility by $n$, so won't do well with really big numbers. Certainly fast enough for numbers up to 4 or 5 digits.

Solving a separable differential equation that describes the population growth over time with a known initial condition to calculate the population after $n$ years. 

Given the cost of hiring a room for a given number of hours, compare with competing prices given per hour and per minute.

A question made for the FYiMaths December meeting, to show off some of the more adventurous things you can do with Numbas.

Solve a trigonometric equation involving a conversion to tangent by division by cosine.

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Made for my TALMO talk. This demonstrates how you can use a part with no marks as an oracle to perform calculations, to help the student check their working.

This question demonstrates a few ways of interacting with a Venn diagram drawn using JSXGraph.

This test will assess a students ability to work with piecewise and composite functions.

A line with random $x$- and $y$- intercepts is plotted, and you have to drag two dots over the points where the line crosses the $x$ and $y$ axes.

Calculations involving elementary probability, and several questions designed to draw out misconceptions to do with probability.

Denominators with linear factors, repeated factors and non-factorisable quadratics.

Topics: Trigonometeric equations and complex numbers
Students must complete the exam within 90 mins (standard time).
Questions have variables to produce randomised questions.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Inverse and division of complex numbers.  Four parts.

Trigonometric equations with degrees

Simple trig equations with radians