Merryn Horrocks

Remove the brackets from (na)^k, or from n(a)^kwhere n is a number and a is a variable.

Part of HELM Book 1.2

Use the index laws to simplify 3 simple expressions;

n^a*n^b, n^a/n^b, (n^a)^b, where n is a randomised variable or number, and a and b are randomised nonzero integers.

Part of HELM Book 1.2

Evaluate a simple fraction squared or cubed. Part of HELM Book 1.2

Students are given three expanded products and asked to write them in index notation. Part of HELM Book 1.2

Asks students to compute (base)^index without a calculator for two simple questions. Part of HELM Book 1.2

Part of HELM Book 1.2

Part of HELM Book 1.2

Expand (x+a)(x+b)(x+c), where x is a randomised variable, and a,b,c are randomised integers.

Note that the pattern restriction in the marking checks that there are no brackets and that the expression is simplified to at most a single x^3, x^2, x and constant term; but it will let you get away with an additional -x^2 and/or -x term. (e.g., you could write 3x as 4x -x and the marking would accept this. This was to stop the pattern matching getting too complicated.

Part of HELM Book 1.3

Part of HELM Book 1.3

HELM Book 1.2

Add, subtract and multiply indices. Part of HELM Book 1.2

HELM Book 1.1 in NUMBAS

A normal curve is displayed. Mean and standard deviation can be set by sliders.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

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 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 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.