Around this time of year, many UK schools will have taster sessions as part of a Sixth Form Welcome Event. What to do for such lessons?

I can never resist starting by asking students to do a graph sketch.

We’ll see who is immediately familiar with my 11th Commandment!

Graph plotters cannot usually cope with graphs with holes, ask **WolframAlpha for a plot** for example and we see

However, we can force WolframAlpha to **show the point discontinuity**…

See this cK-12 resource – **Holes in Rational Functions** for many examples.

Another possible graph sketch, **y ^{2 }= x**

^{2 }which could lead to futher discussion on line pairs. Graph sketching is of course ideal for illustrating how technology can help, something we should be doing as a natural part of A Level courses.

A very useful source of ideas for such lessons is **Underground Maths. **In fact it was **Straight Lines** from Underground Maths which led to my investigation of line pairs with a group of Level 2 Further Mathematicians, perfect since they are required to be able to factorise expressions such as 12x^{2} + xy − y^{2} .

Underground Maths is very helpful for teachers of A Level, I particularly like the Resource suggestions (scroll down the page) for the A Level specification.

For each content statement, Underground Maths have suggested up to three rich resources and up to three Review questions. Each suggestion is hyperlinked to take you directly to the resource on the Underground Mathematics site. Resources that are particularly good at supporting the overarching theme of *Mathematical modelling* have been highlighted.

I find the Review Questions can be excellent for either introducing ideas or for review and have created a spreadsheet of my own for just Review Questions which lists the questions by title rather than by number. I keep the latest version of the spreadsheet on this page. Excel File: **Underground Maths Mapping Review Questions August 19** or the same file in pdf format: **Underground Maths Mapping Review Questions August 19**

I have found the Review questions a valuable source of tasks for Year 11, 12 and 13. You can browse **all the Review questions **or narrow your search by question type; note the **O/AO-level questions** which are questions from old papers, definitely a useful source of resources for planning taster sessions for new Sixth Form Students. One can also search by line ( Number, Geometry, Algebra, Functions or Calcuus) and by Station. Try **When is 6 × 7 = 42 a counter-example**?

Working on these problems is ideal for students aiming for the highest grades and they are indeed appropriate for the more demanding A Level questions. Note the **many Underground Mathematics Resource Types**.

Review Questions in the words of the Underground Maths Team:

These are questions designed to test students’ understanding of one or more topics and to exercise their problem-solving skills. In many cases they can also be used as a classroom resource to help teach concepts and methods. They are mostly drawn from past examination questions and have been chosen as ones that are interesting in nature and require non-routine thinking. The hints and solutions are designed to explain the reasoning and highlight connections as well as giving the answer. In many cases, alternative methods or solutions are presented.

Read about the **use of Review questions in the classroom** on this Teacher Support page.

If you create an account you can easily save and organise your favourite resources. This list of favourites can be easily downloaded as a csv file.

I have so many favourites on Underground Maths, here’s one – **Scary Sum**!

To further organise your favourites you can create subcollections.