Mathematics Challenges

UK Maths Challenges
You can practice for the UK Maths Challenges with these past papers. Questions and full solutions are provided.

You could generate a random quiz, using Mathster’s UKMT Mathematics Challenge Online Quiz. Choose Junior, Intermediate or Senior and one of three difficulty levels; you can also choose the number of questions, a time limit and the order the questions are presented in – random or in order of difficulty.

Note Geoff Smith’s advice for young mathematicans and as he says you will find thousands of questions are available at all levels on the Art of Problem Solving site.

Nrich have a series of short problems based on the UK Junior and Intermediate Challenges.Nrich Short Problems


Nrich publish new problems every month. Why not try and get a solution published on their website? There is a menu specifically for studentsYou can sign up for an Nrich student newsletter if you want to be notified of new developments on the site.

If you have not tried Nrich problems before you may find their recommended starter problems good to try. You can search for problems by topic if you wish.

If you have not tried Nrich problems before you may find their recommended starter problems good to try. You can search for problems by topic if you wish

Brilliant
Brilliant problem

Signing up to Brilliant (including an easy option for sign in for Facebook users) will allow you to join an international community and try numerous.questions at various levels.

MadAsMaths

A great source of questions and full solutions for the Pure Maths content of A Level exams.

Mathematics, Learning and Technology

MadAsMaths MadAsMaths

One of my students told me recently about MadAsMaths by Dr Trifon Madas. She likes the Practice Papers, particularly the way the papers are rated according to their difficulty, see C1 for example. All papers come with full solutions.

MadAsMaths question & solution MadAsMaths question & solution

Not only do all the questions come with full solutions but most have very clear mark schemes too.

MadAsMaths mark scheme example MadAsMaths mark scheme example

MenuThe papers cover the Pure Mathematics content of the UK A Level course. Note the Special Papers designed for extremely able students; ideal for students capable of the top grades. This is a really valuable collection of questions.

There are further questions and solutions available in the large collection of booklets, originally samples they are free to use. These are pdf files, if you zoom you will see a clear solution as illustrated in the image here. Some of these booklets are aimed…

View original post 3 more words

Polar Curve Plotter

Polar & Cartesian PlotterFor a really clear plotter showing the connection between the Cartesian graph of r=f(θ) and the graph in polar coordinates try this Polar Curves and Cartesian Graphs applet. Watch the display carefully as you move the slider; you can easily see when r is negative for example.

For more on Polar Curves – including notes and the use of Desmos, see this post.

Free Mathematics Books

Some books that might be useful for you:

GCSE Text
Complete GCSE Maths Revision text from CLCnet. Don’t be put off by the 2007 date – this is still useful. The text includes numerous set of questions for each topic by grade with solutions for all the examples.


The Maths E-Book of Notes and ExamplesCraig Barton’s E-Book of Notes and Examples is a comprehensive set of notes with very clear worked examples; this is extremely useful for students age 11 to 16 and for any older students who need a refresher.

 


aqa-further-maths-text

AQA Further Maths Text

For Further Mathematics A Level (age 16-18) AQA have provided a set of three textbooks.
(Scroll down to Resources for students).
AQA-MFP2-TEXTBOOK   AQA-MFP3-TEXTBOOK   AQA-MFP4-TEXTBOOK


street-fighting-mathematicsStreet Fighting Mathematics‘ by Sanjoy Mahajan, with the excellent sub-title ‘The Art of Educated Guessing and Opportunistic Problem Solving’ (note the link on the left to the free Creative Commons edition under Essential Info).

 

 

 


Check Amazon for Kindle books, a small number of which are free or very low cost. Now you don’t have to own a Kindle to read Kindle books as the Kindle app is free to download for any device you may own: PC, phone or tablet. It is possible to search Kindle books by price, so a search on Mathematics books by price from lowest to highest will give all the free entries; there are lots of toddler books and samples there but the odd useful book is  available. A very useful search for low cost books is a search on popular Mathematics books, price low to high. which returns popular Mathematics and Science books for as little as 99p.

Try Henry Ernest Dudeney’s – Amusements in Mathematics a puzzle collection (with solutions). The first set of puzzles offers a little History, money – pre-decimal! There are several categories of puzzles available. Or try Edwin Abbott’s Flatand the tale of a two-dimensional world occupied by geometric figures.


Project Gutenberg  includes numerous Mathematics books, including classics such as Flatland(Mark Twain’s comment on “Classic’ – a book which people praise and don’t read.” always amuses me!)


You could even write your own book! If publishing your own Kindle eBook feels a little too much right now – you could try something simpler using Storybird – click the image to see this story on StorybirdStorybird Sequences

..and finally, I must mention John & Betty’s Journey Into Complex Numbers!
John and Betty

 

Valentines day is coming

Desmos Valentine

Click on the image and then on the slider!

Desmos Valentine instructions

Why not send your mathematical friends (or anybody else!) a Desmos ValentineThe wonderful team at Desmos have made their brilliant math-o-grams available earlier this year….and watch out for new designs coming soon.

The math-o-grams are really easy to create; why not give it a try? Just select your design, add your message and share!

Mathematical Handwriting

Handwriting

John Kerl – Tips for mathematical handwriting

Is your writing legible? Is that a 5 or an s, a 2 or a z? Included on the Study Tips page see John Kerl’s Tips for mathematical handwriting.

Dr Kevin Lee - A Guide to Writing Mathematics

Dr Kevin Lee – A Guide to Writing Mathematics

Is your writing clear and well structured? Easy to read and follow?
You will find some excellent examples from Dr Kevin Lee in his Guide to Writing Mathematics.

See also Ten Simple Rules for Mathematical Writing from Dimitri Bertsekas.

Algebra Examples & Exercises

These sites are mentioned elsewhere on this site but these all include notes and exercises on Algebra. Answers are included in these resources and of course you can check answers on WolframAlpha.

Note there are resources for older students further down the page.

For younger students (age 11-16) try the Interactive Tutorials from The Centre for Innovation in Mathematics Teaching, (CIMT).
Fundamental Skills   Function Machines   Linear Equations   Basic Factorising
Expansion – Single Brackets  Linear Equations with Brackets
Factorising Expressions 
Substitution into Formulae 1     Substitution into Formulae 2
Linear Equations 1   Linear Equations 2
Coordinates   Plotting Straight Lines   Graphs and Gradients
Laws of Indices   Negative Indices   Fractional Indices
Straight Line Graphs   Linear Equations   Parallel and Perpendicular Lines
Simultaneous Equations   Equations in Context
Equations, Formulae and Identities   Simplifying Expressions   Factorising  Using Formulae
Quadratic Equations: Factorisation  
and by Completing the Square

The following example – note the colours shows how to expand three brackets.
You could check your answers on WolframAlpha and change the query to make up your own examples.
Expand Brackets Colleen Young

The Maths Teacher (age 11-17)
David Smith’s site, The Maths Teacher has an extensive collection of videos to help you study Mathematics. GCSE (age 14-16, though many of these resources would be helpful for younger students also) and A-Level (age 16-18) lessons are available. For each topic not only is a video available but also a transcript and exercises with worked solutions. This makes the site ideal for revision – you have the choice of perhaps just trying the exercises or if you feel you need more help you can watch the video – whatever is right for you.

Trinity school (age 11-16)
Trinity School have very helpful Mathematics resources – many examples for you to try (answers included) including Algebra.
Trinity School Nottingham - numerous questions and answers

Trinity School Nottingham – numerous questions and answers

For older students who have already studied many topics in Algebra, CIMT’s Step Up to A Level Maths includes notes and examples on Basic Algebra, Quadratic Functions and Equations and Inequalities. These exercises could also be used by GCSE students aiming for the highest grades. Another very useful publication is the Algebra Refresher from The Mathcentre which has many questions with the answers provided at the end of the document. Also from the Mathcentre you can view all the topics available – several different resource types such as notes and videos are available for each topic.

Sections 1 (Basic Algebra) & 3 (Equations, Inequalities and Partial Fractions) of the very helpful Helm Workbooks include worked examples and exercises (with answers).

Plymouth University Algebraic Fractions

Plymouth University Support Materials

Plymouth University have some very clear workbooks, try Basic Algebra – Brackets for example or Algebraic Fractions.

For videos try the following sites:
Corbettmaths

Exam Solutions GCSE Maths     

Exam Solutions A Level Maths (select your exam board from A Level Maths tab)

Hegarty Maths GCSE      A Level  and KS3 for younger students (11-14)

and note The Mathcentre, already mentioned above.

 

Happy New Year

Math Forum @Drexel 2016 Year Game

Math Forum @Drexel 2016 Year Game

If you want a little something to do then try the Math Forum Year Game. How many numbers from 1 to 100 can you generate using the digits of 2016? Unlike Countdown which uses only the four operations and brackets, additional operations are allowed – see the detailed rules.

And did you know 2016 is an evil number!

Perhaps a good time to remind you of some resolutions I suggested for the New Academic Year:

Firstly – remember the 10 11 Commandments…

or as a poster: 11 commandments

To elaborate a little more on some of these:

5 – looking it up – there are several excellent resources online for you to look up definitions or find extra examples. Never rely on just one source if you are finding a topic tricky, it can be helpful to see explanations written by different authors.

6 – To learn Mathematics you need to do Mathematics. You can never do enough examples! There are plenty of questions here (with answers included). Have you looked at the problems on Brilliant? New problems are published regularly and are suitable for younger school students all the way through to university students.

9 – if you want to practise your arithmetic you could play some games! If you enjoy Maths games there are many excellent free resources available.

10 – on writing the language of mathematics correctly – see  this clear guide to writing Mathematics from Dr Kevin P Lee and from John Kerl some excellent tips for mathematical handwriting, many of these tips these apply to students of all ages – do you distinguish carefully between a 1 and a 7 for example? Perhaps it is hard to tell whether you have written a 2 or a z or perhaps your 5s look a bit like a letter s?


Have a look at Peter Alfeld’s  guide to Understanding Mathematics which he wrote for his students at Utah University.

Are you familiar with all the excellent (free) resources online to help your studies? Have you tried the brilliant Desmos graphing calculator for example, or used WolframAlpha to check your work? Do you have the GeoGebra app on your phone?

GeoGebra AppGeoGebra announced the release of their GeoGebra Graphing Calculator earlier this month; currently available for Android, the app will also be available for iPhone and Windows – watch for announcements.

For all the information you need to learn how to use this outstanding app for Mathematics see “What is the GeoGebra Graphing calculator?” and all the Tutorials available.

Having downloaded the app to my phone I can confirm it works really well and i was easily able to follow the instructions given in the links here.

I very quickly created the diagram in the screenshot from my phone below. Using a finger one can drag point D around and note the angle at the circumference. With an account you can also save your files which are standard GeoGebra files.

GeoGebra App

GeoGebra App

Follow GeoGebra on Twitter or Facebook

Some more thoughts for you.

If you are trying to get organised generally then some of the resources on this page might be useful. I recommend Evernote highly (it’s free).

Wishing you all a very happy and productive new year!

Christmas 2015

Plus 2015 Advent

Plus Advent 2015

So, time to relax and what better way to relax than with a puzzle or two?!

On Nrich you’ll find a collection of advent calendars a Sudoku for each day perhaps? (Solutions are supplied if you want them). Or a tangram? Maybe you want to play a game? (Clearly the year doesn’t matter for an Advent Calendar!)

Plus Magazine also have an Advent Calendar which this year has puzzles and articles designed with your creativity in mind.

For many more games and puzzles, see this collection including a challenging logic puzzle from Coolmath Games – can you set the circuits to light up that Christmas tree?!  If any of you have any little relatives they might enjoy Top Marks’ collection of their favourite Christmas Activities.

Perhaps you could make your Mathematical friends some cards! Why not put a Desmos tree on theDesmos Christmas tree cover?! Note this is simply a collection of lines and circles, as you can see from the syntax it is very easy to restrict x or y values. (For more on getting creative with Desmos, see Graph Art).

Staying with the subject of cards you can practise your coding skills with this Scratch project.
Scratch card

Turn the sound on!

If you are feeling creative you might like these Christmas fonts.

Wishing students everywhere a great Christmas.