A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.

State if a function is increasing at given points or on given intervals

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

Recovering original function given some information such as derivative and value at some point.

Finding the coordinates and determining the nature of the stationary points on a polynomial function

A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.

This question demonstrates how to use GeoGebra applets in explore mode.

The student must construct a polygon by adding points one at a time. At any point, they can answer the question, "Is the centroid inside the polygon?"

GeoGebra's IsInRegion command is used to decide if the centroid is inside the polygon.

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.

No description given

No description given

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

(a) Equation given, and five coordinates. Student should select those coordinates which lie on the line. (b) Gradient and a point on line is given. Student is to calculate coordinates of other points on the line.