University Mathematics Preparation

STEP (Sixth Term Examination Paper) Mathematics is a well-established mathematics examination designed to test candidates on questions that are similar in style to undergraduate mathematics. For students studying for STEP papers try this excellent portal from stepmaths.co.uk which has (all free) access to STEP questions and solutions. Create an account, login and you have access to a complete library of resources.

The resources are very clearly presented. For each question you have access to a pdf with the question, Examiners’ Report and both an Official and thanks to Peter Mitchell a fully worked handwritten solution.

Note that you can also download a copy of  Stephen Siklos’ Advanced Problems in Mathematics and Core MathematicsAdvanced Problems in Mathematics is excellent preparation for ANY undergraduate Mathematics course.

Following each question, you will find a discussion and a full solution. The clear Contents page lists all 43 problems. Each problem has been given a title and a rough indication of the mathematical content which means you can pick out questions by topic.

Stephen Siklos Advanced Problems in Mathematics and Core Mathematics

See also, from Cambridge University, their STEP Support Programme.
STEP CU

And from Nrich, Prepare for University.

Projectiles

demos-pagesA project – note the new tab Demos – a place for some favourite demonstrations / simulations. Currently just two pages but note the numerous PhET simulations for a variety of subjects to explore.

The most recent addition is the PhET Projectiles Simulation.

 

projectiles

Use this excellent PhET simulation to explore the path of a projectile. Try changing the angle to investigate the relationship between the angle of projection and the horizontal distance (range) travelled.

Have a look at these problems on Underground Maths to extend your thinking:
Where did it land? and Maximum Angle Throw. Note the questions given on these problems and things you might have noticed.
projectilesFor amusement try projectiles of different types!

You will find some very useful notes on Mechanics on Mr Barton’s website.

There are numerous PhET simulations covering Physics, Biology, Chemistry, Earth Science and Mathematics. Note the growing collection of HTML5 versions which will work across all platforms and devices. The Projectiles simulation here is currently a Flash resource.

You can download an app for iOS also for Android.
PhET Balancing Act working nicely on my phone!
balancing-act

Mathematics Challenges

UK Maths Challenges
You can practice for the UK Maths Challenges with these past papers. Questions and full solutions are provided. You can find British Mathematical Olympiad papers here.

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.

Circles & Teddy Bears

teddy-bear-desmos

Have a look at the teddy bear – can you identify all the equations from this list?
This problem comes from the excellent Underground Maths site.
You can view the Teddy Bear on Desmos by selecting the image above.

desmos-toggleNote that on Desmos you can choose to display or hide a graph.

As with all problems on the site you can see the question and a very full solution with all reasoning explained.

For further notes on the equation of a circle, check these Helm Project notes and exercises on the circle.

Top Tools for Learning 2016

The Top Tools for Learning 2016, inlcuding top tools for Education. This is what the educators think. Students what do you think? What are your favourite tools for learning?

Mathematics, Learning and Technology

Jane Hart is the Founder of the Centre for Learning & Performance Technologies and 2016 marks the 10th year of her annual Top 100 Tools for Learning list. Jane has put together all the presentation slidesets as well as an alphabetical list of ALL the tools which have appeared on any of the lists.

The 2016 slideset is shown here.

Note from Jane’s overview she has done a finer analysis for 2016 including the Top 100 Tools For Education (for use in primary and secondary (K12) schools, colleges, universities and adult education.)

Back in April, I wroye about my own choices for 2016 and I am always interested to see where my own choices are in Jane’s list.

CY 2016 votes Education Personal Learning & Productivity Place in Top 200 2016  Place in Top 100 Tools for Education 2016
Evernote x x  17  27
WordPress x x  9

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Mathematical Advent Calendars

Students try an alternative to chocolate – mathematical Advent calendars up to Advanced Level, and note the Primary calendars from Nrich if you have little siblings!

Mathematics, Learning and Technology

It’s that time of year again…!

Nrich Advent Calendars Nrich Advent Calendars

December means Advent Calendars and Nrich have published two Advent Calendars, one for Primary and one for Secondary each containing twenty-four problem-solving activities, one for each day in the run-up to Christmas. The primary Calendar tasks focus on encouraging mathematical habits of mind and the Secondary tasks have been chosen to encourage mathematical creativity.

You can in fact find a whole collection of advent calendars on Nrich and clearly the year doesn’t matter! Note the different themes available – a Sudoku for each day perhaps? Or a tangram? Maybe you want to play a game? 

Advent calendar Alex Pett Advent Calendar by Alex Pett

Alex Pett created his advent calendar complete with history and problems for each day. Alex has provided a pdf version or use as aGoogle document. For an Activeinspire resource this version also has sound.

revision-calendarAlternatively how about this

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GCSE Revision Resources

For some excellent GCSE (UK age 15-16) revision resources explore this collection. Thank you so much to the teachers who create these resources and make them freely available.

gcse-question-example

Jonathan Hall has a bank of GCSE questions. on his site; note that you can show solutions for these questions. Also on this site – you can create a practice paper with your chosen topics and the number of questions you want. If you would like a random collection you could also try his Revision Grid.

mathsbot-revision-grid

Mathsbot Revision Grid – Jonathan Hall


9-1-revision-book

From Steve Blades, have a look at his very helpful 9-1 GCSE Help Book. Note that you can download the book (52 pages) free.

For more resources see Steve Blades’ site www.m4ths.com;on the GCSE page Steve has a section (near the end of the page) of eBooks, and one of those is on GCSE Higher wordy questions. See also Steve’s Think like a problem solver and mathematician book.
m4ths


mr-carter-mathsMr Carter Maths – for lots of practice questions. Select Differentiated Topics to see the selection available. If you want to practise this new topic – Iteration; this is the direct link.iteration-mr-carter-maths


flashcardsOn Tanner Maths you will find Flashcards for the new specification – choose A4 or A5.


Many of these resources are also very useful. Check with your teacher the detailed content for your specification.


Underground Mathematics

exponentials
For many challenging questions to really get you thinking, try the brilliant Underground Mathematics site. You can follow them on Facebook or Twitter too.

underground-mathematics

thinkig-about-algebraYou can search by Station, suppose you want to practise your Algebra – try the Thinking About Algebra Station for example where you will find everything from Equation Sudoku to some challenging Surd manipulations.
nested-surds

On the subject of surds – try Scary Sum!
scary-sum

If you create a (free) account you can save and categorise your favourite resources.

There are many Underground Mathematics Resource Types. Try the Review Questions for example, which 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.

review-question-types

Note the various question types available; these include very challenging questions for students age 16+.

oxford-mat-example

Select image for question & solution


The Oxford MAT collection includes an extensive selection of Multiple Choice Questions.

O/AO-level questions are included. These questions provide excellent challenge for sudents aspiring to the top grades for examinations taken at age 15-16 and beyond..

Can we fully factorise x4+4y4?
Starts with a Show that….
We could get very sophisticated and look at those quadratic factors too; useful for those studying the Level 2 Further Mathematics Qualification.

Can we simplify these algebraic fractions?
Review algebraic fractions

Can we simplify these simultaneous equations of degree 1 and 2?
Solve simultaneous equations. We will need to factorise a quadratic in this problem with a coefficient which is not 1 for the square term. My students and I are fans of the Box Method where a factorisation cannot easily be done by inspection.