Equivalent fractions, simplifying, adding, subtracting, multiplying and dividing fractions. Converting between mixed numbers and improper fractions.

Quiz for expanding brackets and factorising

Given a regular n-gon, students are asked for the sum of external angles, sum of internal angles, and the values of the external and internal angles.

Given n-1 angles inside a polygon, students have to calculate the value of the last internal angle.

Students are shown 4 exponential equations, and 4 graphs and asked to match them.

Students explore the relationship between length and area of a rectangle.

The perimeter of the rectangle is randomised. Students are given 11 different lengths, and asked to compute rectangle width and area for each. They are then asked to graph the function, identify it as a parabola, and estimate the maximum value.

Students are asked to find either the initial production cost, or a gradient, or the break even point from a graph.
They are then asked to determine the profit or loss from the graph for the production of a particular number of units. This number is randomised.

Students are shown 4 network diagrams (randomly selected from a pool of 20) and asked to identify which of them are trees.

Students are awarded 1 mark for each correct identification, and lose 1 mark for each non-tree they select.

As the number of trees can change, the number of marks that this question is worth can also change, ranging from 1 to 4.

Students are randomly shown one of two networks. They are shown four sub-networks, and asked to identify which one is a minimum spanning tree for the network. Thus, there are 2 versions of this question.

Students are randomly shown one of 3 networks.

They are given 4 sub-networks and asked to identify which one is a spanning tree

Students are shown one of a disconnected graph, a tree, and a graph containing cycles. They are asked the yes/no question: "Is this a connected graph?"

This question displays one of 6 graphs and asks the yes/no question, "Does this graph contain a cycle"?

This question displays one of 10 graphs. It asks the student to either 

(a) count the vertices, or

(b) count the edges, or

(c) state how many vertices a spanning tree would contain, or

(d) state how many edges a spanning tree would contain, or

(e) state the degree of a selected (randomly chosen) 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.

Students are given the bearings and distances of 2 consecutive straight line walks. They are asked to find the distance from the starting point to the endpoint. They are given a diagram to assist them.

The bearings and distances are randomised (any bearing, distances between 1.1 and 5.). Bearings can be given as either compass bearings or true bearings.

Students are given the bearings and distances of 2 consecutive straight line walks. They are asked to find the distance from the starting point to the endpoint. They are given a diagram to assist them.

The bearings and distances are randomised (any bearing, distances between 1.1 and 5.). Bearings can be given as either compass bearings or true bearings.

Students are shown one of 5 different radial surveys and asked to answer one of 8 questions about it.

2 questions ask for the length of a side.

2 questions ask for the value of an angle.

2 questions ask for the area of a triangle.

1 question asks for the land area, and 1 question asks for the land perimeter.

The values are hard coded. In cases where your choice of precision affects your answer, a range of answers is accepted, and a comment is made in the advice to that effect.

Students are shown a random bearing from A to B and asked to give the bearing from B to A as either a compass bearing or a true bearing.

Students are shown a random bearing and given its value as a compass bearing.

They are asked to give its value as a true bearing.

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.

Students are shown a right angled triangle and asked to find the value of an angle using a trig identity.

The triangle is a fixed image, but the angles and side lengths are randomly selected.

The angle is to be given in degrees and minutes.

There are 4 orientations of the triangle in the diagram. The orientation is randomly chosen.

Students are shown a right angled triangle and asked to compute a side length using a trig identity.

The triangle is a fixed image, but the angles and side lengths are randomly selected.

The angle is given in degrees and minutes, and students are asked for the side length correct to 1 decimal place.

There are 4 different triangle orientations that can display.

Students are shown a line graph and asked to write the line equation.

The line is drawn in geogebra. m and b are randomised. 

The line equation is given as a fill-in-the-gaps, y = <gap>x + <gap>

Students are shown a graph of the value of a machine over time. The line equation is randomised.

They are asked to evaluate value at a given time, and the time at which a given value is reached. They are asked when the machine has no value, and the range of times over which the model is valid. They are also asked to explain the physical meaning of the gradient.