Use the excellent Desmos graphing calculator to explore the gradient of a straight line. Select the image then you can change the sliders for m and c to change the line and drag the points so you can verify the gradient of the line.

To solve a quadratic inequality such as x^{2}-6x+8>0 the best approach is to find the critical values of x which make the value of the function 0 and sketch the graph. Here we can factorise so we see that we require (x-2)(x-4)>0 We are looking for values of x to make x^{2}-6x+8 positive. We see that y is positive when x>4 and when x<2.

Note the link to another Desmos page where you can look at further quadratic functions.

Select image to experiment

If you wish to see some worked examples and try some exercises you could check The Maths Teacher – See Algebra AS Level – Inequalities: Linear and Quadratic. Note the choice of video / transcript or go straight to the exercise with worked solutions. You may find other useful resources here too.

You could of course use WolframAlpha to check the solution to any inequalities and generate as many examples as you want. Simply type in the inequality and plot as well as the he solutions will be returned.

Students of all ages, how are your coding skills? Why not try the challenges on CodeMonkey? This is a great way to learn to code if you have little experience – and still fun if you do have some coding skills already.

Can you help the monkey get all his bananas? Look at this simple example – challenge#8; click on the image to see this solution. Note that you learn about loops in later challenges.

Select the image to see the solution

After each challenge is successfully completed, you will receive a number of stars, note the meaning of each. Did you get all the bananas? Did you use what you learned and were you efficient in your coding?

Research UK university courses with SACU. The site is useful for students of any subject anywhere however as you can take the Spartan Test to help you find the right course; the test is quick and fun to do – select images which best describe you!

You can use the Research Tools (all free to use) to take the Spartan Test, explore subjects, courses, the UK map and Apprenticeships; You can also look at possible careers. The gallery below will give you an idea of the wealth of information available and different ways to explore it. The site is intuitive to use and very well designed.

There are many sites where you can explore Mathematics beyond your school syllabus – try some of these:

Maths Careers this site, managed and maintained by the Institute of Mathematics and its Applications has extensive information on careers in Mathematics and applications of Mathematics in everyday life. Note the various tabs such as Science and Engineering at the top of the page and pages for various age groups, see 11-14 for example.

Perhaps you are revising for end of year exams. If you want some basic practice then David Watkins has an extensive collection of spreadsheets so you can try as many questions as you like on many topics at your chosen difficulty level and then check your answers. The spreadsheets can all be found on his Dynamic maths site.

Search Dynamic Maths

Start by searching for the topic you want; let’s suppose you want to look at adding and subtracting directed numbers. Select the down arrow in the search box and select the topic you want; here we need integers. You will then see a selection of Dynamic Worksheets which are all Excel files. If you want to add and subtract integers then choose Integers-01 and download it. Once you have your Excel file you can practise as much as you want as you can generate as many questions as you like.

You will need macros enabled.

Dynamic Maths – Integers

Note that you have several choices, you can show answers when you are ready to check; you can choose the number and type of questions and so on.

For more sites with lots of questions see this postwhich includes questions for older students too.

From the Centre for Innovation in Mathematics Teaching see section 10.13 of this chapter on equations for examples and exercises with algebraic fractions. You could check answers to the exercises on Wolfram Alpha. For example :

I have checked all links are working and made some happy discoveries along the way where tools have been improved. There are many calculators here from basic to rather more advanced. I will keep these pages regularly updated.

On Decision Mathematics for example, check the excellent Linear Programming grapher from zweigmedia.com:

Linear Programming Grapher – zweigmedia.com

And look at the calculator from zweigmedia for normal distribution probabilities on the Statistics 16+ page, not only are probabilities calculated but a very clear diagram illustrating those probabilities is also provided.

Normal Distribution Calculator – Random Science Tools and Calculators

The Graphs section has also had a major update with all the Desmos resources gathered together