This question ensures that students understand that the fraction line means divide. There are 3 versions of the question, for denominators 10, 100 and 1000.

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

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors. 

Given a generating matrix for a linear code, give a parity check matrix

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are not given in the question and must be calculated.

Given a generating matrix for a binary linear code, construct a parity check matrix, list all the codewords, list all the words in a given coset, give coset leaders, calculate syndromes for each coset, correct a codeword with one error.

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Match up equations with the corresponding lines on a graph.

Es werden grundlegenden Ableitungsregeln geübt.

Die Reihenfolge der Summanden ist auch randomisiert.

Solve a Differential equation with 3 simple linear factors

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This question asks the student to calculate three points of a given linear function then plot these points in a JSXGraph item and find the x and y intercepts of the line.

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Find the equation of a line given a point and a parallel line.

Calculating gradient and finding intercept from a geogebra graph.

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Find the equation of a line given a point and a parallel or perpendicular line.

Using geogebra to draw lines tangent to a curve and calculate their gradient.

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A function $f(x) = cln(ax^2+bx) -x$ is sketched and tangent is also drawn. The equation of the tangent line is asked for and $x$-coordinate for horizontal tangent is asked for. Calculator.

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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.

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.

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 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>