Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

Compute a table of values for a quadratic function. A JSXgraph plot shows the curve going through the entered values.

Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

Compute a table of values for a quadratic function. The student input is now disconnected from the graph so that they slide the points on the graph after they input the values and the answer fields are not updated. Now includes a graph in advice.

Compute a table of values for a quadratic function. A JSXgraph plot shows the curve going through the entered values.

Given an ODE solution: $y=  b x^n + cx$

Use a condition: $y(1)=a$ to find the particular solution and hence the value of $y(d)$.

Useful for students' revision. Assesses ability to apply the algorithms correctly. Question has randomised values.

Prove (by induction) that every value $\ge$ 44ct can be combined by using 5ct and 12ct stamps.

Idea seen in collection of exercises for preparing for the Putnam contest.

Given $\rho(t)=\rho_0e^{kt}$, and values for $\rho(t)$ for $t=t_1$ and a value for $\rho_0$, find $k$. (Two examples).

Given $\rho(t)=\rho_0e^{kt}$, and values for $\rho(t)$ for $t=t_1$ and a value for $\rho_0$, find $k$. (Two examples).

Apply and combine logarithm laws in a given equation to find the value of $x$.

Two trains arrive at the same platform with different periods. Compute the LCM of the two periods to find the time they clash.

This is a context question testing the student's ability to identify the lowest common multiple of two integer values which are not multiples of each other. 

Simple inequalities - finding values of x

Semi-worked example of solving simultaneous equations using matrices. Equation values are randomly generated. The student is walked through the steps needed to solve the equations.

Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four version of this question: I: cubic, II: linear, III: quadratic, IV: sinusoisal.

Students are given a word problem with the distance travelled and the time taken by a cyclist. They need to choose the correct form for the linear equation, compute the gradient, and plot the line.

The distance travelled and time taken are randomised.

Speed, distance and time are all integer values.

Students need to substitute a value into an equation and solve it. The equation constant (gravity) and the value (time) are both randomised.

This question demonstrates sending commands to geogebra and getting geogebra values and using them as part of a marking algorithm.

Students are shown a graph that simultaneously plots cost and revenue lines. They are asked to identify the break-even point.

They are asked to give the x- and y- coordinate values.

The graph is randomised, but it is set up so that the point of intersection lies on gridlines.

This question is a simple example to show how to input value from numbas to geogebra applet, and get a value back from geogebra to numbas for marking.

Students are given a formula and asked to evaluate it for a given input value, which is randomised.

Substitute values into formulae for the area or volume of various geometric objects.

Exercise using a given uniform distribution $X$, calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$.

Find a regression equation.

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Find eigenvalues and eigenvectors of $A$ $2 \times 2$ matrix.