KS5 Mathematics

St. Philomena's Catholic High School for Girls

A Post-16 Subject Guide

Contents

Welcome .................................................................................................... 2

Entry Requirements for the Course ............................................................ 2 Mathematics ............................................................................................... 2

What will I learn on this course? ................................................................. 2 Pure Maths ................................................................................................. 3

Mechanics .................................................................................................. 3 Statistics ..................................................................................................... 3 Decision ..................................................................................................... 3

Specification Summary – A Level Mathematics ......................................... 4 How to Succeed ......................................................................................... 5

Textbooks................................................................................................... 6 Calculators ................................................................................................. 7 Further Reading ......................................................................................... 8

Online Material ......................................................................................... 11 Podcasts .................................................................................................. 12 Bridging the Gap ...................................................................................... 13 Diagnostic Test ........................................................................................ 13

Assessments ............................................................................................ 13 Intervention and Support .......................................................................... 13 Independent Study ................................................................................... 14 Should I study Further Mathematics? ....................................................... 15 Specification Summary – Further Mathematics ........................................ 16

Useful Resources ..................................................................................... 17 Enrichment ............................................................................................... 17

Websites .................................................................................................. 17

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Welcome Welcome to A Level Mathematics. This short guide will hopefully give you a taste of what to expect from this much sought-after qualification which is challenging but highly rewarding.

Entry Requirements for the Course

To study mathematics at St. Philomena's you must look carefully at the entrance requirements that are published. The most common method of entry is to achieve the following:

7 or above at GCSE Higher Mathematics

Pass the Diagnostic Test in September (details below)

You must pass this test to continue with the course! However, the most important thing is to have a lively enquiring mind together with an enjoyment of the subject and determination. In return you will gain a great depth of knowledge and excellent training in a wide range of skills.

Mathematics The A Level course is a linear one covering a range of elements of mathematics. You will be enhancing your knowledge and understanding of topics covered in GCSE in Algebra, Trigonometry and Graphs and extending these ideas into new areas. In the Statistics, Mechanics or Decision topics you will be applying these ideas in a real life context. Mathematics is also the only subject that offers two (in fact three!) A Levels in the same subject.

What will I learn on this course?

Mathematics at A Level is a course worth studying not only as a supporting subject for the physical and social sciences, but in its own right. It is the most facilitating subject you can take and is highly sought after by employers and universities alike, no matter what field of employment or study you seek to take. While studying mathematics you will be expected to:

Use mathematical skills and knowledge to solve problems

Solve quite complicated problems by using mathematical arguments and logic. You will also have to understand and demonstrate what is meant by proof in mathematics

Simplify real-life situations so that you can use mathematics to show what is happening and what might happen in different circumstances

Use calculator technology and other resources effectively and appropriately; understand calculator limitations and when it is inappropriate to use such technology

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Pure Maths

Pure Maths at A Level is the cornerstone on which the foundations for further study are laid. In addition to developing your command of algebra, geometry and trigonometry, there is a whole range of new topics to grapple with: differential and integral calculus, numerical methods, series etc. If you enjoyed the challenge of problem solving at GCSE using such mathematical techniques, then you should find the prospect of this course very appealing. This wealth of new material results in a need for a more rigorous, logical approach to the subject. This is bound to take some getting used to but once the adaptation is made, there can be a sudden, dramatic increase in the level of your understanding and enjoyment of the subject

Mechanics

When you study mechanics you will learn how to describe mathematically the motion of objects and how they respond to forces acting upon them, from cars in the street to satellites revolving around a planet. You will learn the technique of mathematical modelling; that is, of turning a complicated physical problem into a simpler one that can be analysed and solved using mathematical methods. Many of the ideas you will meet in the course form an almost essential introduction to such important modern fields of study as cybernetics, robotics, biomechanics and sport science, as well as the more traditional areas of engineering and physics.

Statistics

When you study statistics you will learn how to analyse and summarise numerical data in order to arrive at conclusions about it. You will extend the range of probability problems that you started for GCSE by using the new mathematical techniques studied on the pure mathematics course. Many of the ideas you will meet in this course have applications in a wide range of other fields – from assessing what your car insurance is going to cost to how likely the earth is going to be hit by a comet in the next few years.

Decision Studying decision mathematics enables you to analyse complex problems that are applicable to everyday life and are vital to the success of the modern world. You will look at optimising routes for delivery of items, finding the quickest and most efficient ways to process a task.. You can look at how best to play a game and win much more. Many of these ideas are very different to what you would have studied at GCSE and they give a valuable insight into whole new branches of mathematics you have not studied before, such as Graph Theory and Game Theory.

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Specification Summary – A Level Mathematics A Level Mathematics is now a linear course. This means you will study a variety of topics over two years in Year 12 and Year 13. You will take all your exams at the end of Year 13. Mathematics has only just recently been accredited and the specification approved. All exam boards will be following the same specification for A Level Mathematics. More content has been added compared to previous years and there may be more emphasis on problem solving and using data sets and technology. The full specification, details on the changes and more can be found at:

https://www.gov.uk/government/publications/gce-as-and-a-level-mathematics http://furthermaths.org.uk/2017 https://qualifications.pearson.com/en/qualifications/edexcel-a-levels/mathematics-2017.html

KS5 Mathematics

St. Philomena's Catholic High School for Girls

How to Succeed

You must get to grips with:

Algebra. This is the language that is used to make mathematical statements. You must be very sharp at writing and manipulating algebra.

Interpretation. Making sense of the question. What is it asking you? What do you have to do? What facts and methods do you need to call on? Can you draw a diagram that contains all of the significant details?

Proof. Constructing that mathematical argument. Making sure that one step follows the other and being able to explain why.

Accurate calculation. One tiny slip with a negative sign or a decimal point in the wrong place and your solution will go wildly off beam. You must be able to calculate accurately and to check your work with great care.

Memory. At GCSE level there isn't too much in maths that needs to be memorised. At this level, there's a whole host of formulae, methods and facts that you just have to store away where you can get at them.

Understanding. Having said that there's a lot to remember, at this level it is impossible if you don't really understand what you're doing and difficult to move on to new things.

Enjoyment. One of the good things about doing maths is that you can feel chuffed when you've got there - enjoy it!

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Textbooks

The specification for the new Linear A Levels in Mathematics and Further Mathematics have only recently been approved. Currently we are considering a range of textbooks for purchase. At this present time (June 2017) we are not recommending a particular book but here are some of the textbooks we are looking at to give you a feel for what is available.

Collins https://collins.co.uk/category/Secondary/Maths A single textbook for Year 12 for A Level Maths

Pearson http://www.pearsonschoolsandfecolleges.co.uk/Secondary/Mathematics/16plus/EdexcelASandAlevelMathematics2017/ Two textbooks (one Pure, one Applied) for Year 12 for A Level maths

Hodder https://www.hoddereducation.co.uk/alevelmaths/edexcel A single textbook for Year 12 for A Level Maths

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Calculators

The new A Level puts more emphasis on certain techniques and skills that can be best served on a calculator rather than using tables from a printed sheet. As such it may be useful to consider a calculator that is designed with these functions in mind. However, if you had a good quality calculator that served you well at GCSE there should be no real issue.

Casio fx-991EX https://edu.casio.com/products/cwiz/fx991ex/ This will serve you extremely well in A Level Maths and Further Maths and is not considerably different in price to the calculator you may have used at GCSE If you are looking to upgrade or replace this comes highly recommended. Does your calculator have binomial tables? Spreadsheet functions? Matrices? List display for statistics? Simultaneous equations? Quartics? Riemann integrals? Vectors? Inequalities?

Casio FX-CG50 We are not recommending or asking that students purchase this. This is a much more expensive model. The purpose here is to demonstrate that these calculators are designed with the exam in mind and are allowed.

Rules There are certain rules set by JCQ for all examinations with regards to calculators

http://www.jcq.org.uk/exams-office/ice---instructions-for-conducting-examinations

Calculators must not: • be designed or adapted to offer any of these

facilities: language translators, symbolic algebra manipulation, symbolic differentiation or integration, communication with other machines or the internet

• have retrievable information stored in them - this includes: databanks, dictionaries, mathematical formulas, text.

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Further Reading

What the Numbers Say: A Field Guide to Mastering Our Numerical World (Derrick Niederman and David Boyum)

The Man Who Knew Infinity: Life of the Genius Ramanujan by Robert Kanigel

My Brain is Open: The Mathematical Journeys of Paul Erdos by Bruce Schechter

The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth Paperback by Paul Hoffman

KS5 Mathematics

St. Philomena's Catholic High School for Girls

"e": The Story of a Number (Princeton Science Library) by Eli Maor

Brief History of Infinity: The Quest to Think the Unthinkable by Brian Clegg

Does God Play Dice?: The Mathematics of Chaos by Ian Stewart

Alex's Adventures in Numberland (Alex Bellos)

Why Do Buses Come in Threes? The Hidden Mathematics of Everyday Life By Rob Eastaway and Jeremy Wyndham

KS5 Mathematics

St. Philomena's Catholic High School for Girls

The Number Devil By Hans-Magnus Enzensberger

Fermat’s Last Theorem by Simon Singh

Professor Stewart's Cabinet of Mathematical Curiosities by Ian Stewart

A History of Pi by Petr Beckmann

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Online Material Should I study AS/A Level Further Maths? www.furthermaths.org.uk/student_area/shouldistudyfm.php

Cambridge Recommended Reading List

https://www.maths.cam.ac.uk/sites/www.maths.cam.ac.uk/files/pre2014/undergrad/ad

missions/readinglist.pdf

Oxford Recommended Reading List

https://www.maths.ox.ac.uk/system/files/attachments/introbook17.pdf

MEI Recommended Reading List

http://mei.org.uk/books2

You’re saying you don’t know who M C Escher is? http://www.mcescher.com

NRICH – the online maths magazine http://nrich.maths.org/public/

How maths can make you rich and famous http://plus.maths.org/issue24/features/budd/index.html

First Career destinations, the University of Liverpool http://www.liv.ac.uk/maths/Prosp_Student/Careers/

Brief introduction to advanced algebra (post 16) http://www.mathsisfun.com/algebra/index-college.html

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Podcasts

Relatively Prime

http://relprime.com/

Travels in a Mathematical World

http://www.travelsinamathematicalworld.co.uk/

Plus

http://plus.maths.org/content/Podcast

All Squared

http://aperiodical.com/category/main/podcasts/all-squared/

A Brief History of Maths

http://www.bbc.co.uk/programmes/b00srz5b

Math Mutation

http://mathmutation.blogspot.co.uk/

The Secrets of Mathematics

https://podcasts.ox.ac.uk/series/secrets-mathematics

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Bridging the Gap

In order to help you bridge the gap from GCSE to A Level there is a pack of resources available from the department. These provide a wealth of material on the key skills that are required at A Level, especially for the first few modules you will be studying. This will also help you prepare for the Diagnostic Test you will be taking in September, which you will need to pass if you are to remain on the course. Topics include (but may not be limited to): Factorising quadratics, completing the square, sine and cosine graphs, solving equations, manipulating surds and fractions and more. We have also provided a list of useful websites and resources so that when you turn up for your first lesson you can be one step ahead!

Diagnostic Test

There will be a Diagnostic Test very early in September. This will consist of nothing but GCSE Higher Exam questions (often at Grade 7, 8 or 9 standard) on the topics that are most useful and most vital for studying mathematics at A Level.

You must pass this test to continue with the course! Preparation, practice and example tests are all available for study and practice over the summer. The skills tested here are vital to success at A Level and students who in the past achieved a grade 7 at GCSE but NOT mastered these skills have been proven to struggle greatly at A Level.

Assessments

Assessments will be set for every chapter. Students who score below 50% in an assessment have to resit. Assessments that have previously been set throughout the year are available online to aid revision. The results of assessments and exam papers can also be found in the detailed spreadsheets. This will form a very useful source of revision as students can highlight their weak areas using the spreadsheets.

Intervention and Support

Progress and results are monitored throughout the year and intervention techniques such as extended tutoring, extra support, further differentiation or resources will be offered to those students who require it. Targeted revision lessons will be offered at a set time outside of normal lessons. These include direct help, exam questions, exam technique and worked solutions. These sessions are reserved for KS5 students.

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Independent Study

Independent Study is a vital skill to learn in order to progress through any A Level course, most especially in Mathematics. Here are some key points;

To be able to understand and learn maths fully, you need to do plenty of extra questions from either your text book, exam papers or material provided.

Do lots of practise papers. The more you do, the more you start to realise what the questions are asking you to do.

Remember: the more you practise, the more likely you will remember how to work out questions.

Help each other. Explain to your class mates how to solve questions. This will help you too as you are more likely to remember how to solve questions.

When you get stuck, go to your teacher! They are there to help you! Use them! The standard homework expectation for all modules is for 2 or 3 hours per module per week. This should be in two or three different one hour sessions spaced strategically through the week so that topics are mastered and maths is practised regularly.

When revising for tests and exams, 5 or 6 hours per week may be needed and maths

should be practised more frequently, maybe every day, in sessions of up to 2 hours.

Parents can help to monitor that students are allocating the full amount of time to maths modules.

Initially modules are taught topic by topic. Each topic must be mastered by the student using some class time and the 2 or 3 hours of homework. A student has mastered a topic when they can quickly lay out the working and arrive at correct answers for exam questions at the end of each exercise. Further work can be found on the list of resources. Students should note which formulas they need to learn for each topic.

If a topic is not understood, the student must take the next opportunity to raise the

problem with their class teacher and maybe attend a workshop session to get the topic sorted out.

When preparing for tests on chapters students should sample exercises to ensure that they can complete exam questions at a speed of 1 mark per minute.

Exam preparation requires all chapters to be mastered and the use of practice papers

to ensure that questions on all topics can be answered at a rate of 1 mark per minute. As much practice and repetition as possible is required at this stage to ensure the required speed of performance.

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Should I study Further Mathematics?

Further Mathematics is a full A Level, above, beyond and in addition to the standard A Level Mathematics. Typically this would be taken by those students who are confident in their mathematics and very interested in the subject or a related subject, especially looking towards their later careers or studies at university. It is a demanding and yet very rewarding A Level. It must be remembered that it is a fully fledged A Level (and perhaps the most demanding one you can take out of all the subjects) so careful consideration must be given to self discipline and self motivation. However it will always be an excellent choice that is a highly respected qualification around the world and will serve to gain you entrance to any career or later study at university.

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Specification Summary – Further Mathematics A Level Further Mathematics is now a linear course. This means you will study a variety of topics over two years in Year 12 and Year 13. You will take all your exams at the end of Year 13. Further Mathematics has only just recently been accredited and the specification approved. Further Mathematics has now been decoupled from A Level Mathematics. This means that in theory you can sit Further Mathematics with a different exam board to what you sit Mathematics. It also implies there will be little or no overlap between content. Further Mathematics also only has half the course prescribed. So for half the course everyone with every exam board will cover the same material (in pure maths). For the other half there will be an element of choice. For the second half of the course content in Further Mathematics there is a choice. Often this choice will be made by schools due to timetabling and teaching constraints. Currently our intention is to offer the same broad range of topics we have always covered here at St. Phil’s in Further Mathematics. Namely Pure Maths, Decision Maths and Further Mechanics and/or Further Statistics.

The full specification, details on the changes and more can be found at:

https://www.gov.uk/government/publications/gce-as-and-a-level-mathematics http://furthermaths.org.uk/2017 https://qualifications.pearson.com/en/qualifications/edexcel-a-levels/mathematics-2017.html

KS5 Mathematics

St. Philomena's Catholic High School for Girls

Useful Resources

During your time at St. Philomena's you will be provided with a wealth of resources to help you in your studies of mathematics. These include resources available include, for each and every chapter: Introduction Study Guide Glossary Additional Exercises Multiple Choice Test Practice Assessments Further resources on all topics are available on request and an extensive collection of useful websites and ‘bookmarks’ are available on the website and discussed and used in class. Other important resources include additional worksheets, the “Big 50” lists, the personalised learning tool from PiXL and various self-assessment sheets. Details of how to revise will be discussed and given as well as forming an integral part of the whole course. It is expected that students are undergoing a well-planned and thorough programme of revision. Extra revision material, revision booklets and exam papers are provided.

Enrichment

Enrichment opportunities will be offered throughout the year. These may include the Senior Maths Challenge, Senior Team Maths Challenge, Maths Circle Lectures, visit from QMW Staff, Oxbridge applications and more.

Websites https://sites.google.com/stphils.org.uk/maths

http://www.cut-the-knot.org/content.shtml https://www.wolframalpha.com/

https://www.desmos.com/

Mr Dowling KS5 Coordinator for Mathematics