Given a piecewise function determine whether the limit exists at two points. Part of HELM Book 2.4.1.

Draw a graph of y=x^3 by plotting points. Part of HELM book 2.2.1

Graph the function y=x^2+2 on [-3,3] by plotting points. State the domain and range. This is part of HELM Book 2.2.1.

Student is asked to find the distance from a given point, A, to a house, given the distance between A and another point B, and the angles at A and B. Requires use of the sine rule. Distance and angles are randomised.

Student is asked to find the distance from a given point, B, to a house, given the distance between B and another point A, and the angles at A and B. Requires use of the sine rule. Distance and angles are randomised.

Finding the stationary point (maximum) of a quadratic equation in a contextualised problem. 

Calculating the gradient of a quadratic equation at a specific point and finding the stationary point (maximum) in a contextualised problem. 

Estimating the proportion of sodium carbonate in a solutionat a specific timepoint and vice versa, depicted as a quadratic graph.

Interpreting line graphs depicting the decrease of temperature in a mixture over time. Estimating the temperature of the mixture at a given time point and vice versa.

The student is given a quadratic formula and asked to fill in a table of values of $f(x)$ for a given range of $x$.

There is also a plot of the points, which updates when the table is filled in, or the student can move the points to fill in the table.

The table uses the spreadsheet and JSXgraph extensions.

A random proper fraction $a/b$ with denominator in the range 2 to 30 is picked, and the student must write $\frac{a}{b} \pi$.

The point of this question is to demonstrate that the correct answer is shown as a multiple of $\pi$ rather than a decimal.

Student estimates, then calculates exactly and symbolically the value of $k$ for a parabola $y = k x^2$ which passes through a given point.

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

Turning points of a cubic function

Replace two forces with a equivalent force-couple system at a specified point.

Student is given two points defined symbolically, and must find the equation of the line they define, then use integration to find an equation for the area under the line, bounded by the x-axis and vertical lines through the two points.   

Given 32 datapoints in a table find their minimum, lower quartile, median, upper quartile, and maximum.

Drag points on a graph to the given Cartesian coordinates. There are points in each of the four quadrants and on each axis.

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

Students enter equation and turning 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.

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.