Parametric form of a curve, cartesian points, tangent vector, and speed.

Parametric form of a curve, cartesian points, tangent vector, and speed.

Intersection points, tangent vectors, angles between pairs of curves, given in parametric form.

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.

A right-angled triangle is displayed either pointing left or right with one of the other angles and one of the sides given. Use SOH CAH TOA to find the side indicated with an x.

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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.

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

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

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 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 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 given a parabola equation and 4 points. They need to determine which point lies on the parabola.

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

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.

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.

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$

Given the coordinates of three 2-dimensional points $A$, $B$ and $C$, find the vectors $\vec{AB}$, $\vec{AC}$ and $\vec{CB}$.

Given the polar coordinates of a point $P$, calculate the equivalent cartesian coordinates

Give the cartesian coordinates of a point $P$, find the equivalent polar coordinates

Drag points on an axis to plot a linear graph (integer gradient and intercept only)

Calculate the length of a line segment given two points

Find the gradient of the line that passes through the points 

Drag points on an axis to plot a linear graph (rational gradient and intercept)

Calculating the area enclosed between a cosine function and a quadratic function by integration. The limits (points of intersection) are given in the question.

Finding the stationary points of a cubic equation and determining their nature.

Finding the stationary point of a function of the form $\frac{a \ln(x)}{x}$ and determining its nature.