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T DRAFT 7356 Specification For teaching from September 2017 onwards For AS exams in 2018 onwards R AF DRAFT SPECIFICATION AS MATHEMATICS D Version 0.1 June 2016 DRAFT SPECIFICATION T R AF D AS Mathematics DRAFT 7356 AS exams June 2018 onwards Version 0.1 June 2016 Contents Introduction 2.1 Subject content 2.2 Assessments 7 Subject content 11 3.1 Overarching themes 3.2 A: Proof 3.3 B: Algebra and functions 3.4 C: Coordinate geometry in the (x,y) plane 3.5 D: Sequences and series 3.6 E: Trigonometry 3.7 F: Exponentials and logarithms 3.8 G: Differentiation 3.9 H: Integration 3.10 J: Vectors 3.11 K: Statistical sampling 3.12 L: Data presentation and interpretation 3.13 M: Probability 3.14 N: Statistical distributions 3.15 O: Statistical hypothesis testing 3.16 P: Quantities and units in mechanics 3.17 Q: Kinematics 3.18 R: Forces and Newton’s laws 3.19 Use of data in statistics 11 12 12 13 14 14 15 16 16 16 17 17 18 18 19 19 19 20 20 R AF DRAFT SPECIFICATION Specification at a glance 5 T 1.1 Why choose AQA for AS Mathematics 1.2 Support and resources to help you teach 1.3 Draft specification D Scheme of assessment 4.1 Aims 4.2 Assessment objectives 4.3 Assessment weightings General administration 5.1 Entries and codes 5.2 Overlaps with other qualifications 5.3 Awarding grades and reporting results 5.4 Re-sits and shelf life 5.5 Previous learning and prerequisites 5.6 Access to assessment: diversity and inclusion 23 23 24 25 27 27 27 27 27 28 28 Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration R AF D Are you using the latest version of this specification? • • You will always find the most up-to-date version of this specification on our website at aqa.org.uk/7356 We will write to you if there are significant changes to the specification Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION 28 29 29 T 5.7 Working with AQA for the first time 5.8 Private candidates 5.9 Use of calculators AS Mathematics DRAFT 7356 AS exams June 2018 onwards Version 0.1 June 2016 Introduction 1.1 Why choose AQA for AS Mathematics T Maths is one of the biggest facilitating subjects and it’s essential for many higher education courses and careers We’ve worked closely with higher education to ensure these qualifications give your students the best possible chance to progress A specification with freedom – assessment design that rewards understanding R AF DRAFT SPECIFICATION The changes to AS and A-level Maths qualifications represent the biggest in a generation They’ve also given us the chance to design new qualifications, with even more opportunity for your students to realise their potential We want students to see the links between different areas of maths and to apply their maths skills across all areas That’s why our assessment structure gives you the freedom to teach maths your way Consistent assessments are essential, which is why we’ve worked hard to ensure our papers are clear and reward your students for their mathematical skills and knowledge You can find out about all our Mathematics qualifications at aqa.org.uk/maths 1.2 Support and resources to help you teach We’ve worked with experienced teachers to provide you with a range of resources that will help you confidently plan, teach and prepare for exams Teaching resources Visit aqa.org.uk/7356 to see all our teaching resources They include: D • route maps to allow you to plan how to deliver the specification in the way that will best suit you and your students • teaching guidance to outline clearly the possible scope of teaching and learning • textbooks approved by AQA • training courses to help you deliver AQA mathematics qualifications • subject expertise courses for all teachers, from newly qualified teachers who are just getting started, to experienced teachers looking for fresh inspiration Preparing for exams Visit aqa.org.uk/7356 for everything you need to prepare for our exams, including: • • • • past papers, mark schemes and examiners’ reports specimen papers and mark schemes for new courses Exampro: a searchable bank of past AQA exam questions example student answers with examiner commentaries Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration Analyse your students' results with Enhanced Results Analysis (ERA) Find out which questions were the most challenging, how the results compare to previous years and where your students need to improve ERA, our free online results analysis tool, will help you see where to focus your teaching Register at aqa.org.uk/era For information about results, including maintaining standards over time, grade boundaries and our post-results services, visit aqa.org.uk/results Keep your skills up-to-date with professional development T • Improve your teaching skills in areas including differentiation, teaching literacy and meeting Ofsted requirements • Prepare for a new role with our leadership and management courses You can attend a course at venues around the country, in your school or online – whatever suits your needs and availability Find out more at coursesandevents.aqa.org.uk R AF Help and support Visit our website for information, guidance, support and resources at aqa.org.uk/7356 If you'd like us to share news and information about this qualification, sign up for emails and updates at aqa.org.uk/from-2017 Alternatively, you can call or email our subject team direct E: maths@aqa.org.uk T: 0161 957 3852 1.3 Draft specification D This draft qualification has not yet been accredited by Ofqual It is published to enable teachers to have early sight of our proposed approach to AS Mathematics Further changes may be required and no assurance can be given that this proposed qualification will be made available in its current form, or that it will be accredited in time for first teaching in September 2017 and first award in August 2018 Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION Wherever you are in your career, there’s always something new to learn As well as subject specific training, we offer a range of courses to help boost your skills AS Mathematics DRAFT 7356 AS exams June 2018 onwards Version 0.1 June 2016 Specification at a glance This qualification is linear Linear means that students will sit all their exams at the end of the course 2.1 Subject content OT1: Mathematical argument, language and proof (page 11) OT2: Mathematical problem solving (page 11) OT3: Mathematical modelling (page 12) A: Proof (page 12) B: Algebra and functions (page 12) C: Coordinate geometry in the (x,y) plane (page 13) D: Sequences and series (page 14) E: Trigonometry (page 14) F: Exponentials and logarithms (page 15) G: Differentiation (page 16) H: Integration (page 16) J: Vectors (page 16) K: Statistical sampling (page 17) L: Data presentation and interpretation (page 17) M: Probability (page 18) N: Statistical distributions (page 18) O: Statistical hypothesis testing (page 19) P: Quantities and units in mechanics (page 19) Q: Kinematics (page 19) R: Forces and Newton’s laws (page 20) T • • • • • • • • • • • • • • • • • • • • D R AF DRAFT SPECIFICATION Core content Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration 2.2 Assessments Paper What's assessed How it's assessed • Written exam: hour 30 minutes • 80 marks • 50% of AS Questions D A mix of question styles, from short, single-mark questions to multi-step problems Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION A: Proof B: Algebra and functions C: Coordinate geometry D: Sequences and series E: Trigonometry F: Exponentials and logarithms G: Differentiation H: Integration J: Vectors P: Quantities and units in mechanics Q: Kinematics R: Forces and Newton’s laws R AF • • • • • • • • • • • • T Content from the following sections: AS Mathematics DRAFT 7356 AS exams June 2018 onwards Version 0.1 June 2016 Paper What's assessed A: Proof B: Algebra and functions C: Coordinate geometry D: Sequences and series E: Trigonometry F: Exponentials and logarithms G: Differentiation H: Integration K: Statistical sampling L: Data presentation and interpretation M: Probability N: Statistical distributions O: Statistical hypothesis testing T • • • • • • • • • • • • • R AF DRAFT SPECIFICATION Content from the following sections: How it's assessed • Written exam: hour 30 minutes • 80 marks • 50% of AS Questions D A mix of question styles, from short, single-mark questions to multi-step problems Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION T R AF D 10 Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration 3.8 G: Differentiation Content Content G2 n Differentiate x , for rational values of n, and related constant multiples, sums and differences R AF Content G3 • Apply differentiation to find gradients, tangents and normals, maxima and minima and stationary points • Identify where functions are increasing or decreasing 3.9 H: Integration Content H1 Know and use the Fundamental Theorem of Calculus Content H2 n Integrate x (excluding n = -1), and related sums, differences and constant multiples D Content H3 Evaluate definite integrals; use a definite integral to find the area under a curve 3.10 J: Vectors Content J1 Use vectors in two dimensions 16 Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION • Understand and use the derivative of f x as the gradient of the tangent to the graph of y = f x at a general point (x, y); the gradient of the tangent as a limit; interpretation as a rate of change; sketching the gradient function for a given curve; second derivatives; differentiation from first principles for small positive integer powers of x • Understand and use the second derivative as the rate of change of gradient T G1 AS Mathematics DRAFT 7356 AS exams June 2018 onwards Version 0.1 June 2016 Content J2 Calculate the magnitude and direction of a vector and convert between component form and magnitude/direction form Content J3 Add vectors diagrammatically and perform the algebraic operations of vector addition and multiplication by scalars, and understand their geometrical interpretations Understand and use position vectors; calculate the distance between two points represented by position vectors Knowledge/skill J5 T J4 Use vectors to solve problems in pure mathematics and in context, including forces R AF DRAFT SPECIFICATION Knowledge/skill 3.11 K: Statistical sampling For sections K to O students must demonstrate the ability to use calculator technology to compute summary statistics and access probabilities from standard statistical distributions Content • Understand and use the terms ‘population’ and ‘sample’ • Use samples to make informal inferences about the population • Understand and use sampling techniques, including simple random sampling and opportunity sampling • Select or critique sampling techniques in the context of solving a statistical problem, including understanding that different samples can lead to different conclusions about the population D K1 3.12 L: Data presentation and interpretation Content L1 • Interpret diagrams for single-variable data, including understanding that area in a histogram represents frequency • Connect to probability distributions Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration 17 Content L2 • Interpret scatter diagrams and regression lines for bivariate data, including recognition of scatter diagrams which include distinct sections of the population (calculations involving regression lines are excluded) • Understand informal interpretation of correlation • Understand that correlation does not imply causation Content Content • Recognise and interpret possible outliers in data sets and statistical diagrams • Select or critique data presentation techniques in the context of a statistical problem • Be able to clean data, including dealing with missing data, errors and outliers R AF L4 3.13 M: Probability Content M1 • Understand and use mutually exclusive and independent events when calculating probabilities • Link to discrete and continuous distributions 3.14 N: Statistical distributions Content Understand and use simple, discrete probability distributions (calculation of mean and variance of discrete random variables is excluded), including the binomial distribution, as a model; calculate probabilities using the binomial distribution D N1 Content N3 Select an appropriate probability distribution for a context, with appropriate reasoning, including recognising when the binomial or Normal model may not be appropriate 18 Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION • Interpret measures of central tendency and variation, extending to standard deviation • Be able to calculate standard deviation, including from summary statistics T L3 AS Mathematics DRAFT 7356 AS exams June 2018 onwards Version 0.1 June 2016 3.15 O: Statistical hypothesis testing Content • • • • • • • • • • null hypothesis alternative hypothesis significance level test statistic 1-tail test 2-tail test critical value critical region acceptance region p-value T Understand and apply the language of statistical hypothesis testing, developed through a binomial model: R AF DRAFT SPECIFICATION O1 Content O2 • Conduct a statistical hypothesis test for the proportion in the binomial distribution and interpret the results in context • Understand that a sample is being used to make an inference about the population and appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis 3.16 P: Quantities and units in mechanics Content • Understand and use fundamental quantities and units in the S.I system: length, time, mass • Understand and use derived quantities and units: velocity, acceleration, force, weight D P1 3.17 Q: Kinematics Content Q1 Understand and use the language of kinematics: • • • • • • position displacement distance travelled velocity speed acceleration Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration 19 Content Q2 Understand, use and interpret graphs in kinematics for motion in a straight line: • displacement against time and interpretation of gradient • velocity against time and interpretation of gradient and area under the graph Content Content Q4 Use calculus in kinematics for motion in a straight line: dr , dt a= dv dt = d 2r , dt2 r = ∫ v dt,v = ∫ a dt R AF v= 3.18 R: Forces and Newton’s laws Content R1 Understand the concept of a force; understand and use Newton’s first law Content R2 Understand and use Newton’s second law for motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2D vectors Content Understand and use weight and motion in a straight line under gravity; gravitational acceleration, g, and its value in S.I units to varying degrees of accuracy (The inverse square law for gravitation is not required and g may be assumed to be constant, but students should be aware that g is not a universal constant but depends on location) D R3 Content R4 Understand and use Newton’s third law; equilibrium of forces on a particle and motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2D vectors); application to problems involving smooth pulleys and connected particles 3.19 Use of data in statistics As set out in the Department for Education’s Mathematics: AS and A-level content document, students studying AS Mathematics must: 20 Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION Understand, use and derive the formulae for constant acceleration for motion in a straight line T Q3 AS Mathematics DRAFT 7356 AS exams June 2018 onwards Version 0.1 June 2016 • become familiar with one or more specific large data set(s) in advance of the final assessment (these data must be real and sufficiently rich to enable the concepts and skills of data presentation and interpretation in the specification to be explored) • use technology such as spreadsheets or specialist statistical packages to explore the data set(s) • interpret real data presented in summary or graphical form • use data to investigate questions arising in real contexts This requirement is common to all exam boards 3.19.1 Data set T The data set must be used in teaching to allow students to perform tasks that build familiarity with the contexts, the main features of the data and the ways in which technology can help explore the data Students should also be able to demonstrate the ability to analyse a subset or features of the data using a calculator with standard statistical functions For information on the data set students should be familiar with and supporting resources, visit aqa.org.uk/7356 D R AF DRAFT SPECIFICATION We have selected one data set that will feature in statistics questions throughout the lifetime of this specification Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration 21 DRAFT SPECIFICATION T R AF D 22 Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration AS Mathematics DRAFT 7356 AS exams June 2018 onwards Version 0.1 June 2016 Scheme of assessment Find past papers and mark schemes, and specimen papers for new courses, on our website at aqa.org.uk/pastpapers This specification is designed to be taken over one or two years This is a linear qualification In order to achieve the award, students must complete all assessments at the end of the course and in the same series T All materials are available in English only Our AS exams in Mathematics include questions that allow students to demonstrate their ability to: • recall information • draw together information from different areas of the specification • apply their knowledge and understanding in practical and theoretical contexts R AF DRAFT SPECIFICATION AS exams and certification for this specification are available for the first time in May/June 2018 and then every May/June for the life of the specification 4.1 Aims Courses based on this specification should encourage students to: D • understand mathematics and mathematical processes in a way that promotes confidence, fosters enjoyment and provides a strong foundation for progress to further study • extend their range of mathematical skills and techniques • understand coherence and progression in mathematics and how different areas of mathematics are connected • apply mathematics in other fields of study and be aware of the relevance of mathematics to the world of work and to situations in society in general • use their mathematical knowledge to make logical and reasoned decisions in solving problems both within pure mathematics and in a variety of contexts, and communicate the mathematical rationale for these decisions clearly • reason logically and recognise incorrect reasoning • generalise mathematically • construct mathematical proofs • use mathematical skills and techniques to solve challenging problems which require them to decide on the solution strategy • recognise when mathematics can be used to analyse and solve a problem in context • represent situations mathematically and understand the relationship between problems in context and mathematical models that may be applied to solve them • draw diagrams and sketch graphs to help explore mathematical situations and interpret solutions • make deductions and inferences and draw conclusions by using mathematical reasoning • interpret solutions and communicate their interpretation effectively in the context of the problem • read and comprehend mathematical arguments, including justifications of methods and formulae, and communicate their understanding Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration 23 • read and comprehend articles concerning applications of mathematics and communicate their understanding • use technology such as calculators and computers effectively and recognise when such use may be inappropriate • take increasing responsibility for their own learning and the evaluation of their own mathematical development 4.2 Assessment objectives Assessment objectives (AOs) are set by Ofqual and are the same across all AS Mathematics specifications and all exam boards R AF • AO1: Use and apply standard techniques Learners should be able to: • select and correctly carry out routine procedures • accurately recall facts, terminology and definitions • AO2: Reason, interpret and communicate mathematically Learners should be able to: • construct rigorous mathematical arguments (including proofs) • make deductions and inferences • assess the validity of mathematical arguments • explain their reasoning • use mathematical language and notation correctly • AO3: Solve problems within mathematics and in other contexts Learners should be able to: • translate problems in mathematical and non-mathematical contexts into mathematical processes • interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations • translate situations in context into mathematical models • use mathematical models • evaluate the outcomes of modelling in context, recognise the limitations of models and, where appropriate, explain how to refine them 4.2.1 Assessment objective weightings for AS Mathematics Assessment objectives (AOs) Component weightings (approx Overall weighting (approx %) %) Paper AO1 60 60 60 AO2 20 20 20 AO3 20 20 20 Overall weighting of components 50 50 100 D Paper 24 Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION T The exams will measure how students have achieved the following assessment objectives AS Mathematics DRAFT 7356 AS exams June 2018 onwards Version 0.1 June 2016 4.3 Assessment weightings The marks awarded on the papers will be scaled to meet the weighting of the components Students’ final marks will be calculated by adding together the scaled marks for each component Grade boundaries will be set using this total scaled mark The scaling and total scaled marks are shown in the table below Component Maximum raw mark Scaling factor Maximum scaled mark Paper 80 x1 80 Paper 80 x1 80 T D R AF DRAFT SPECIFICATION Total scaled mark: 160 Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration 25 DRAFT SPECIFICATION T R AF D 26 Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration AS Mathematics DRAFT 7356 AS exams June 2018 onwards Version 0.1 June 2016 General administration You can find information about all aspects of administration, as well as all the forms you need, at aqa.org.uk/examsadmin 5.1 Entries and codes T Every specification is given a national discount (classification) code by the Department for Education (DfE), which indicates its subject area If a student takes two specifications with the same discount code, further and higher education providers are likely to take the view that they have only achieved one of the two qualifications Please check this before your students start their course R AF DRAFT SPECIFICATION You only need to make one entry for each qualification – this will cover all the question papers, non-exam assessment and certification Qualification title AQA entry code DfE discount code AQA Advanced Subsidiary GCE in Mathematics 7356 TBC This specification complies with: • • • • Ofqual General conditions of recognition that apply to all regulated qualifications Ofqual GCE qualification level conditions that apply to all GCEs Ofqual GCE subject level conditions that apply to all GCEs in this subject all other relevant regulatory documents The Ofqual qualification accreditation number (QAN) is TBC 5.2 Overlaps with other qualifications There is overlapping content in the AS and A-level Mathematics specifications This helps you teach the AS and A-level together D 5.3 Awarding grades and reporting results The AS qualification will be graded on a five-point scale: A, B, C, D and E Students who fail to reach the minimum standard for grade E will be recorded as U (unclassified) and will not receive a qualification certificate 5.4 Re-sits and shelf life Students can resit the qualification as many times as they wish, within the shelf life of the qualification Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration 27 5.5 Previous learning and prerequisites There are no previous learning requirements Any requirements for entry to a course based on this specification are at the discretion of schools and colleges However, we recommend that students should have the skills and knowledge associated with a GCSE Mathematics or equivalent 5.6 Access to assessment: diversity and inclusion The subject criteria have been assessed to see if any of the skills or knowledge required present any possible difficulty to any students, whatever their ethnic background, religion, sex, age, disability or sexuality Tests of specific competences were only included if they were important to the subject R AF As members of the Joint Council for Qualifications (JCQ) we participate in the production of the JCQ document Access Arrangements and Reasonable Adjustments: General and Vocational qualifications We follow these guidelines when assessing the needs of individual students who may require an access arrangement or reasonable adjustment This document is published at jcq.org.uk 5.6.1 Students with disabilities and special needs We're required by the Equality Act 2010 to make reasonable adjustments to remove or lessen any disadvantage that affects a disabled student We can make arrangements for disabled students and students with special needs to help them access the assessments, as long as the competences being tested aren't changed Access arrangements must be agreed before the assessment For example, a Braille paper would be a reasonable adjustment for a Braille reader To arrange access arrangements or reasonable adjustments, you can apply using the online service at aqa.org.uk/eaqa 5.6.2 Special consideration D We can give special consideration to students who have been disadvantaged at the time of the assessment through no fault of their own – for example a temporary illness, injury or serious problem such as family bereavement We can only this after the assessment Your exams officer should apply online for special consideration at aqa.org.uk/eaqa For more information and advice visit aqa.org.uk/access or email accessarrangementsqueries@aqa.org.uk 5.7 Working with AQA for the first time If your school or college hasn't previously offered our specifications, you need to register as an AQA centre Find out how at aqa.org.uk/becomeacentre 28 Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION T General qualifications are designed to prepare students for a wide range of occupations and further study Therefore our qualifications must assess a wide range of competences AS Mathematics DRAFT 7356 AS exams June 2018 onwards Version 0.1 June 2016 5.8 Private candidates This specification is available to private candidates A private candidate is someone who enters for exams through an AQA approved school or college but is not enrolled as a student there A private candidate may be self-taught, home schooled or have private tuition, either with a tutor or through a distance learning organisation They must be based in the UK 5.9 Use of calculators T • speak to the exams officer at the school or college where you intend to take your exams • visit our website at aqa.org.uk/privatecandidates • email privatecandidates@aqa.org.uk A calculator is required for use in all assessments in this specification Details of the requirements for calculators can be found in the Joint Council for General Qualifications document Instructions for conducting examinations R AF DRAFT SPECIFICATION If you have any queries as a private candidate, you can: For AS Mathematics exams, calculators should have the following as a required minimum: • an iterative function • the ability to compute summary statistics and access probabilities from standard statistical distributions D For the purposes of this specification, a ‘calculator’ is any electronic or mechanical device which may be used for the performance of mathematical computations However, only those permissible in the guidance in the Instructions for conducting examinations are allowed in the AS Mathematics exams Visit aqa.org.uk/7356 for the most up-to-date specification, resources, support and administration 29 Get help and support Visit our website for information, guidance, support and resources at aqa.org.uk/7356 You can talk directly to the Mathematics subject team: E: maths@aqa.org.uk aqa.org.uk Copyright © 2015 AQA and its licensors All rights reserved AQA retains the copyright on all its publications, including the specifications However, schools and colleges registered with AQA are permitted to copy material from this specification for their own internal use AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (company number 3644723) Our registered address is AQA, Devas Street, Manchester M15 6EX DRAFT SPECIFICATION D R AF T T: 0161 957 3852