A-level Maths, from the right angle AS and A-level Maths and Further Maths – a companion guide to our new qualifications

Find out more at aqa.org.uk/rightangle

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AS and A-level Maths and Further Maths

Welcome to your companion guide for our new draft AS and A-level Maths and Further Maths qualifications. It contains everything you need to know about the Government’s changes, details of our new specifications and the support and resources available for you. The changes to A-level Maths qualifications represent the biggest in a generation and have given us the opportunity to stand back, look at our research and work with teachers and assessment experts to design new qualifications to give your students the best chance to realise their potential.

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A-level Maths qualifications are changing… A-levels in England are being reformed by the Department for Education and Ofqual. Here are the key changes affecting A-level Maths qualifications. • AS and A-level Maths content is 100% prescribed, containing both pure and applied maths. • The applied content for AS and A-level Maths is drawn from statistics and mechanics. There is no decision maths included.

as part of the AS and A-level Maths specifications. Some exam questions will be based on this data set so students need to be familiar with it. These changes will apply to all exam boards.

• A-level Further Maths content contains a proportion of optional content, defined by exam boards. • Exams will be linear, not modular – this means that all exams must be taken at the end of the course, in the summer exam series. • AS will be decoupled from A-level – AS results will no longer count towards the final A-level grades. • Overarching themes of mathematical argument, language and proof, problem solving and mathematical modelling underpin all parts of the qualifications. • The use of technology in the classroom is encouraged, so a large data set will be provided for students to analyse

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The new qualifications will be ready for first teaching in September 2017.

AS and A-level Maths and Further Maths

Our route to the new specifications The AQA philosophy Maths is for everyone, and we design qualifications and support to enable students to engage with, explore, enjoy and succeed in maths. Diverse and engaging, maths is essential in equipping students with the right skills to reach their future destination – whatever that may be. The specifications you’ll see from us are a new direction for A-level Maths. Through testing with students, extensive feedback from teachers and collaboration with assessment experts, higher education and the maths community, we believe this is A-level Maths from the right angle.

A specification with freedom… We want students to see the intrinsic links between the different areas of mathematics, and to be able to apply their mathematical skills across all content areas. That’s why the assessment structure we’ve designed doesn’t constrain how you teach the mathematics.

...and assessment design that rewards understanding Consistent assessments are essential, so we’ve made sure our papers are as clear as possible, to fairly reward students for their skills and knowledge of mathematics. No matter which route your students enter for, our qualifications are co-teachable and there are marks accessible to the full cohort – with some to stretch the most able students.

These design principles are central to our qualifications and ultimately will create better mathematicians.

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“AQA’s new A-levels offer the best progress opportunities because they provide a broad base for students wishing to go onto any degree programme at university, which requires a Mathematics A-level. They also provide opportunities for students to study mathematics because they love the subject, which may help them follow other career paths.” Aileen MacGregor, Lecturer at University of Exeter

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AS and A-level Maths and Further Maths

With such big changes to A-level Maths, we couldn’t just rework the existing qualification we needed a new solution. We also wanted to make sure we were creating qualifications to help every student realise their potential. As you explore our specifications, these are some of the new features you’ll see. 1

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Focus on pure maths

Question papers in sections

In both Maths and Further Maths, any of the pure content can be tested on any paper. So, we are encouraging students to see and make the connections in mathematics, a skill that is highly valued by universities.

To make the exam experience better for the student, where applications are assessed, we have divided the papers into sections so that the content being assessed is not constrained, but the structure is more logical for the student, enabling them to pick which section they do first.

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Question styles A variety of question types gives us the opportunity to test the full range of skills across the full range of ability. For example, most papers will start with multiple choice or short answer questions to settle students into the exam before ramping to longer, often less structured problems.

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Question and answer space Echoing our style at GCSE, we've put the answer space directly beneath the question so our papers look consistent and familiar.

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Our new qualifications are co-teachable No matter which route your students enter for, we’ve designed our new AS qualifications to be fully co-teachable with our new A-levels.

(consecutive)

(combined)

All AS Maths content covered

(in-parallel)

A-level Maths and A-level Further Maths

A-level Maths

Year 1

Summer 2018

Sit AS Maths exams

Year 2 All A-level Maths content covered (with recap of AS content)

Sit A-level Maths exams

Sit A-level Maths exams

All AS and A-level Maths and all AS and A-level Further Maths content covered

All AS and A-level Maths content covered

All AS Maths and AS Further Maths content covered

Sit A-level Maths exams

Sit AS Maths exams

Sit AS Further Maths exams

All AS and A-level Further Maths content covered

All A-level Maths and A-level Further Maths content covered (with recap of AS content)

Teaching starts September 2017 These are only suggested routes through the qualifications.

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Summer 2019

Sit A-level Further Maths exams

Sit A-level Further Maths exams

Sit A-level Maths exams

Sit A-level Further Maths exams

Optional exams

AS and A-level Maths and Further Maths

A-level Maths takes you places A-level Maths is the biggest facilitating subject – it is one of the most important subjects your students will study, and essential to so many future destinations. So we made sure that we worked closely with higher education to give your students the best progression opportunities. • We brought higher education representatives and teachers together at the start of development for a truly collaborative process that puts students at the heart of our qualifications. • Higher education partners told us that they value a solid understanding of pure mathematics, which is why we decided to include more pure content in our Further Maths qualifications.

• We worked with a range of universities – and not just maths departments, so that our qualifications work for all students.

Did you know? The UCAS tariff has changed so that an AS is now worth approximately 40% of an A-level.

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Specification at a glance AS Maths AS Maths assessment objectives Assessment objective

Weighting

AO1: Use and apply standard techniques

60%

AO2: Reason, interpret and communicate mathematically

20%

AO3: Solve problems within mathematics and in other contexts

20%

AS Maths papers Paper 1

Paper 2

Time

1 hour 30 minutes

1 hour 30 minutes

Marks

80 (two unequal sections of 53 and 27 marks)

80 (two unequal sections of 53 and 27 marks)

Content from

Assesses the following content only:

Assesses the following content only:

• • • • • • • •

Proof Algebra and functions Coordinate geometry Sequences and series Trigonometry Exponentials and logarithms Differentiation Integration.

• • • • • • • •

Proof Algebra and functions Coordinate geometry Sequences and series Trigonometry Exponentials and logarithms Differentiation Integration.

• • • •

Vectors Quantities and units in mechanics Kinematics Forces and Newton’s laws.

• • • • •

Statistical sampling Data presentation and interpretation Probability Statistical distributions Statistical hypothesis testing.

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AS and A-level Maths and Further Maths

Specification at a glance A-level Maths

Both AS and A-level Maths will be available for first assessment in summer 2018. This additional assessment opportunity has been provided by the DfE to cater for those students who hope to complete the new A-level Maths in one year.

A-level Maths assessment objectives Assessment objective

Weighting

AO1: Use and apply standard techniques

50%

AO2: Reason, interpret and communicate mathematically

25%

AO3: Solve problems within mathematics and in other contexts

25%

A-level Maths papers Paper 1

Paper 2

Paper 3

Time

2 hours

2 hours

2 hours

Marks

100

100 (two sections of 50 marks)

100 (two sections of 50 marks)

Content from

Assesses the following content only:

May assess any content from paper 1.

May assess any content from paper 1.

• • • • • •

Will assess the following:

Will assess the following:

• Vectors • Quantities and units in mechanics • Kinematics • Forces and Newton’s law • Moments.

• Statistical sampling • Data presentation and interpretation • Probability • Statistical distributions • Statistical hypothesis testing.

Proof Algebra and functions Coordinate geometry Sequences and series Trigonometry Exponentials and logarithms • Differentiation • Integration • Numerical methods.

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Specification at a glance AS Further Maths AS Further Maths assessment objectives Assessment objective

Weighting

AO1: Use and apply standard techniques

60%

AO2: Reason, interpret and communicate mathematically

At least 10%

AO3: Solve problems within mathematics and in other contexts

At least 10%

AS Further Maths papers Paper 1

Paper 2: Choose one of the following routes: • Discrete and Statistics • Statistics and Mechanics • Mechanics and Discrete.

Time

1 hour 30 minutes

1 hour 30 minutes

Marks

80

80 (two sections of 40 marks)

Content from

• • • • • • •

Complex numbers Matrices Further algebra and functions Further calculus Further vectors Polar coordinates Hyperbolic functions.

Mechanics • • • •

Dimensional analysis Momentum and collisions Work, energy and power Circular motion.

Statistics • • • •

Discrete random variables Poisson distribution Type I and II errors and power of a test Continuous random variables.

Discrete • • • • • • •

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AS and A-level Maths and Further Maths

Graphs Networks Network Flow Linear programming Critical path analysis Game theory for zero sum games Binary operations and group theory.

Specification at a glance A-level Further Maths A-level Further Maths assessment objectives Assessment objective

Weighting

AO1: Use and apply standard techniques

50%

AO2: Reason, interpret and communicate mathematically

At least 15%

AO3: Solve problems within mathematics and in other contexts

At least 15%

A-level Further Maths papers Paper 1

Paper 2

Paper 3: Choose one of the following routes: • Discrete and Statistics • Statistics and Mechanics • Mechanics and Discrete.

Time

2 hours

2 hours

2 hours

Marks

100

100

100 (two sections of 50 marks)

Content from

• • • •

• • • •

Mechanics • Dimensional analysis • Momentum and collisions • Work, energy and power • Circular motion.

• • • • • • • •

Proof Complex numbers Matrices Further algebra and functions Further calculus Further vectors Polar coordinates Hyperbolic functions Differential equations Trigonometry Numerical methods Coordinate geometry.

• • • • • • • •

Proof Complex numbers Matrices Further algebra and functions Further calculus Further vectors Polar coordinates Hyperbolic functions Differential equations Trigonometry Numerical methods Coordinate geometry.

Statistics • Discrete random variables • Poisson distribution • Type I and II errors and power of a test • Continuous random variables • Exponential distribution • Inference. Discrete • Graphs • Networks • Network Flow • Linear programming • Critical path analysis • Game theory for zero sum games • Binary operations and group theory. 13

Resources and support We’ll help you get to grips with the new specifications with our free resources and support to help you plan, teach and assess. Teaching Guidance

e-library

The Teaching Guidance is a new resource for A-level. It clarifies how we have interpreted content of the specification and includes example questions of how content may be assessed. Each Teaching Guidance document accompanies the specification and is a powerful and essential planning tool.

Our e-library contains links to interesting and useful maths resources. Using our e-library will save you time searching for resources to help you teach the specifications.

Available after accreditation Route Maps Our Route Maps are interactive schemes of work – fully customisable to help you plan your teaching. Drag and drop the topics into the order that suits you and then click through to access the resources for that topic.

Available after accreditation Get the PowerPoint version of the Route Map for A-level Maths over 2 years (AS Maths after 1 year) on our website. aqa.org.uk/routemap

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Available after accreditation and updated annually Brand new textbooks AQA approved A-level Maths and Further Maths textbooks, completely aligned with the new specifications will be available from Cambridge University Press, Hodder and Oxford University Press.

Visit our website to keep up to date: aqa.org.uk/mathstextbooks

AS and A-level Maths and Further Maths

Additional specimen papers

Topic tests covering all content

We know the greatest challenge of exam change is having enough material to use to get your students ready. So we’ll give you two sets of papers, which will give you plenty to draw on, showing the improvements we’ve made and consistency of our standards.

Student progress is going to be even more of a focus with the new A-levels. That’s why we’re giving you a range of topic tests, to help you track progression and intervention that might be needed.

Set one will be available after accreditation. Set two available in January 2018

Our topic tests will cover each topic on our Route Map and will exemplify the type and style of questions students can expect to see in the live exams. Use them on their own or combine a few to make a longer test.

The tests will be available in a phased approach after accreditation Question commentaries and mark schemes extract These commentaries and their mark schemes highlight some of the key aspects of our draft specimen papers and show the strategy behind our clean and clear approach to assessment – to help every student realise their potential.

Download your copy now aqa.org.uk/commentaries Exemplar student responses A number of students sat our new papers in 2016. We’ve collated their responses and will provide you with the data so you can see our new approach in action and see how students responded.

Available after accreditation

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The team behind the specifications We work with experts to make sure our specifications are right for you and your students.

Christine Andrews Chair and Lead Developer As AQA’s Chair of Maths, Christine leads teams of examiners responsible for both setting and marking AS and A-levels in Maths, Further Maths, Use of Maths and Statistics. Christine is currently leading the development of reformed AS and A-levels in Maths and Further Maths.

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Coming from a maths and philosophy background, Christine has worked in the field of education and learning for over 30 years. During that time she has taught in state and independent schools as well as in further education. She has examined and moderated for AQA since 2002.

AS and A-level Maths and Further Maths

Examining team Our wider examining team are all current classroom practitioners, ex-teachers and other educational experts. They are the people writing the papers. They’re vastly experienced, particularly in testing the key mathematical skills of problem solving and reasoning in a way that is appropriate for all students.

Centre for Education Research and Practice (CERP)

Andrew Taylor Head of Maths Andrew is responsible for the development and delivery of all of our mathematics qualifications from Entry Level through to our GCSEs and A-levels. Currently, he is heavily involved in the reform of AS and A-levels in Maths and Further Maths. Before joining AQA, Andrew taught mathematics for 17 years and was Head of Faculty in large comprehensive schools in Cambridgeshire and Manchester.

Our Centre for Education Research and Practice provides statistics and research evidence to make sure we assess and mark your students’ work fairly. Find out more about their research cerp.aqa.org.uk

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Need help? Any questions? Get in touch Get in touch with us if you have any questions about the new specifications. Call us on 0161 957 3852, email us at [email protected] or tweet us @AQAMaths.

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AS and A-level Maths and Further Maths

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To receive regular updates about A-level Maths, register with us at: A-level Maths takes you places aqa.org.uk/updatemaths For more information visit: www.aqa.org.uk/a-level-maths

The information in this guide is based on the draft specifications submitted to Ofqual in June 2016 and is subject to change. We will publish the accredited specification and specimen question papers as soon as we receive Ofqual accreditation. Copyright © 2016 AQA and its licensors. All rights reserved. AQA Education (AQA) is a registered charity (registered charity number 1073334) and a company limited by guarantee registered in England and Wales (company number 3644723). Registered address: AQA, Devas Street, Manchester M15 6EX. June 2016. 20