Asking users to input coefficients of a system of diff equations so that the phase space is a saddle. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$

Find a regression equation.

Now includes a graph of the regression line and another interactive graph gives users the opportunity to move the regression line around. Could be used for allowing users to experiment with what they think the line should be and see how this compares with the calculated line.

Also includes an updated SSE to see how the sum of the squares of the residuals varies with the regression line.

Find a regression equation given 12 months data on temperature and sales of a drink. Includes an interactive diagram for experimenting with fitting a regression line.

rebelmaths

Given a linear programming problem in standard form, write down the dual problem.

Given a linear programming problem in standard form, write down the dual problem.

This question uses the vis.js library to plot 3D functions and data sets.

As well as JME functions to make plots, you can use javascript functions to get more control over how the plots are rendered.

Find a regression equation given 12 months data on temperature and sales of a drink. Includes an interactive diagram for experimenting with fitting a regression line.

rebelmaths

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.

Find a regression equation.

Now includes a graph of the regression line and another interactive graph gives users the opportunity to move the regression line around. Could be used for allowing users to experiment with what they think the line should be and see how this compares with the calculated line.

Also includes an updated SSE to see how the sum of the squares of the residuals varies with the regression line.

Simple counting exercise, with combinations

Introduction to counting with permutations and combinations

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown a bar chart with error bars and asked one of five possible questions.

Compare two savings accounts with different interest rates.

rebelmaths

Three lines given with different information provided. Equation of the line is asked for.

Questions around the notion of map, with underlying topic the statement of Goldbach's conjecture. The student has to write the conjecture (by filling in some gaps) as a surjectivity statement for a map, and compute some preimages of elements.

(In German)

More work on differentiation with trigonometric functions

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Rationalise the denominator with increasingly difficult examples involving compound denominators. 

Translated to German, made some minor changes to Advice section.

Original: https://numbas.mathcentre.ac.uk/question/22555/rationalising-the-denominator-surds/ by Lauren Richards

A set of Numbas exercises for students transitioning from school to University. Designed to help students gain familiarity with using Numbas to enter mathematics, and as revision for algebra, geometry and calculus. 

Solve for $x$ each of the following equations: $n^{ax+b}=m^{cx}$ and $p^{rx^2}=q^{sx}$.

Separable 1st order ODE with exponentials

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. 

Integrate Paris Law equation to estimate life to failure.

Exercises in solving simultaneous equations with 2 variables.

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

This question is the one described in method 1 of the example "Apply a standard integral" in the Numbas documentation.

The student is shown a randomly chosen function to integrate. The function is one of $e^{kx}$, $x^k$, $\cos(kx)$, $\sin(kx)$, with $k$ a randomly chosen integer.

An example of using the GeoGebra extension to ask the student to create a geometric construction, with marking and steps.

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.

This is a very simple question with no randomisation.

Students are asked to identify an inverse relationship equation.