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• 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 pa

DRAFT 7357

Specification

For teaching from September 2017 onwards

For A-level exams in 2018 onwards

Version 0.1 9 June 2016

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DRAFT SPECIFICA

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1.1 Why choose AQA for A-level Mathematics 5

1.2 Support and resources to help you teach 5

3.4 C: Coordinate geometry in the (x,y) plane 14

3.16 O: Statistical hypothesis testing 23

3.17 P: Quantities and units in mechanics 23

5.2 Overlaps with other qualifications 31

5.3 Awarding grades and reporting results 31

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5.5 Previous learning and prerequisites 32

5.6 Access to assessment: diversity and inclusion 32

5.7 Working with AQA for the first time 32

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

1 Introduction

1.1 Why choose AQA for A-level Mathematics

The changes to 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

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

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/7357 to see all our teaching resources They include:

• route maps to allow you to plan how to deliver the specification in the way that will best suit youand your students

• teaching guidance to outline clearly the possible scope of teaching and learning

• textbooks that are 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/7357 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

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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

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

• 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

Help and support

Visit our website for information, guidance, support and resources at aqa.org.uk/7357

If you'd like us to share news and information about this qualification, sign up for emails and

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 A-level 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

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• 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 13)

• C: Coordinate geometry in the (x,y) plane (page 14)

• D: Sequences and series (page 15)

• K: Statistical sampling (page 21)

• L: Data presentation and interpretation (page 21)

• M: Probability (page 22)

• N: Statistical distributions (page 22)

• O: Statistical hypothesis testing (page 23)

• P: Quantities and units in mechanics (page 23)

How it's assessed

• Written exam: 2 hours

How it's assessed

• Written exam: 2 hours

• O: Statistical hypothesis testing

How it's assessed

• Written exam: 2 hours

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3 Subject content

The subject content for A-level Mathematics is set out by the Department for Education (DfE) and

is common across all exam boards The content set out in this specification covers the complete level course of study

A-3.1 Overarching themes

A-level specifications in mathematics must require students to demonstrate the overarching

knowledge and skills contained in sections OT1, OT2 and OT3 These must be applied, along with

associated mathematical thinking and understanding, across the whole of the detailed content set

OT1.1 Construct and present mathematical arguments through appropriate use of

diagrams; sketching graphs; logical deduction; precise statements involvingcorrect use of symbols and connecting language, including: constant, coefficient,expression, equation, function, identity, index, term, variable

OT1.2 Understand and use mathematical language and syntax as set out in the content.

OT1.3 Understand and use language and symbols associated with set theory, as set out

in the content

Apply to solutions of inequalities and probability

OT1.4 Understand and use the definition of a function; domain and range of functions.

OT1.5 Comprehend and critique mathematical arguments, proofs and justifications of

methods and formulae, including those relating to applications of mathematics

3.1.2 OT2: Mathematical problem solving

Content

OT2.1 Recognise the underlying mathematical structure in a situation and simplify and

abstract appropriately to enable problems to be solved

OT2.2 Construct extended arguments to solve problems presented in an unstructured

form, including problems in context

OT2.3 Interpret and communicate solutions in the context of the original problem.

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OT2.4 Understand that many mathematical problems cannot be solved analytically, but

numerical methods permit solution to a required level of accuracy

OT2.5 Evaluate, including by making reasoned estimates, the accuracy or limitations of

solutions, including those obtained using numerical methods

OT2.6 Understand the concept of a mathematical problem solving cycle, including

specifying the problem, collecting information, processing and representinginformation and interpreting results, which may identify the need to repeat thecycle

OT2.7 Understand, interpret and extract information from diagrams and construct

mathematical diagrams to solve problems, including in mechanics

3.1.3 OT3: Mathematical modelling

Content

OT3.1 Translate a situation in context into a mathematical model, making simplifying

assumptions

OT3.2 Use a mathematical model with suitable inputs to engage with and explore

situations (for a given model or a model constructed or selected by the student)

OT3.3 Interpret the outputs of a mathematical model in the context of the original

situation (for a given model or a model constructed or selected by the student)

OT3.4 Understand that a mathematical model can be refined by considering its outputs

and simplifying assumptions; evaluate whether the model is appropriate

OT3.5 Understand and use modelling assumptions.

3.2 A: Proof

Content

A1 • Understand and use the structure of mathematical proof, proceeding from

given assumptions through a series of logical steps to a conclusion; usemethods of proof, including proof by deduction, proof by exhaustion

• Disproof by counter example

• Proof by contradiction (including proof of the irrationality of √2 and the infinity ofprimes, and application to unfamiliar proofs)

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B3 Work with quadratic functions and their graphs; the discriminant of a quadratic

function, including the conditions for real and repeated roots; completing thesquare; solution of quadratic equations including solving quadratic equations in afunction of the unknown

Content

B4 Solve simultaneous equations in two variables by elimination and by substitution,

including one linear and one quadratic equation

Content

B5 • Solve linear and quadratic inequalities in a single variable and interpret such

inequalities graphically, including inequalities with brackets and fractions

• Express solutions through correct use of ‘and’ and ‘or’, or through set notation

• Represent linear and quadratic inequalities such as y>x+ 1 and

y>ax2+bx+c graphically

Content

B6 • Manipulate polynomials algebraically, including expanding brackets and

collecting like terms, factorisation and simple algebraic division; use of thefactor theorem

• Simplify rational expressions including by factorising and cancelling, andalgebraic division (by linear expressions only)

Content

B7 • Understand and use graphs of functions; sketch curves defined by simple

equations including polynomials, the modulus of a linear function, y= a x and

y= x a2 (including their vertical and horizontal asymptotes); interpret algebraicsolution of equations graphically; use intersection points of graphs to solveequations

• Understand and use proportional relationships and their graphs

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B8 Understand and use composite functions; inverse functions and their graphs.

Content

B9 Understand the effect of simple transformations on the graph of y= f x including

sketching associated graphs:

y=a f x , y= f x +a,y= f x+a, y= f ax , and combinations of thesetransformations

Content

B10 Decompose rational functions into partial fractions (denominators not more

complicated than squared linear terms and with no more than 3 terms, numeratorsconstant or linear)

Content

B11 Use of functions in modelling, including consideration of limitations and

refinements of the models

3.4 C: Coordinate geometry in the (x,y) plane

Content

C1 • Understand and use the equation of a straight line, including the forms:

y−y1=m x−x1 and ax+by+c= 0 ; gradient conditions for two straightlines to be parallel or perpendicular

• Be able to use straight line models in a variety of contexts

Content

C2 Understand and use the coordinate geometry of the circle including using the

equation of a circle in the form x−a 2+ y−b 2=r2 ; completing the square tofind the centre and radius of a circle; use of the following properties:

• the angle in a semicircle is a right angle

• the perpendicular from the centre to a chord bisects the chord

• the radius of a circle at a given point on its circumference is perpendicular tothe tangent to the circle at that point

Content

C3 Understand and use the parametric equations of curves and conversion between

Cartesian and parametric forms

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Use parametric equations in modelling in a variety of contexts.

3.5 D: Sequences and series

Content

D1 • Understand and use the binomial expansion of a+bxn for positive integer n;

the notations n! and nCr; link to binomial probabilities.

• Extend to any rational n, including its use for approximation; be aware that theexpansion is valid for bx a < 1 (proof not required)

Content

D2 Work with sequences including those given by a formula for the nth term and

those generated by a simple relation of the form xn+1 = f(xn); increasingsequences; decreasing sequences; periodic sequences

Content

D3 Understand and use sigma notation for sums of series.

Content

D4 Understand and work with arithmetic sequences and series, including the

formulae for nth term and the sum to n terms.

Content

D5 Understand and work with geometric sequences and series including the formulae

for the nth term and the sum of a finite geometric series; the sum to infinity of a convergent geometric series, including the use of |r | < 1; modulus notation.

Content

D6 Use sequences and series in modelling.

3.6 E: Trigonometry

Content

E1 • Understand and use the definitions of sine, cosine and tangent for all

arguments; the sine and cosine rules; the area of a triangle in the form1

E2 Understand and use the standard small angle approximations of sine, cosine and

tangentsinθ ≈θ, cosθ ≈ 1 −θ22, tanθ≈θ where θ is in radians

Content

E3 • Understand and use the sine, cosine and tangent functions; their graphs,

symmetries and periodicity

• Know and use exact values of sin and cos for 0, π

6,π4,π3,π2, π and multiplesthereof, and exact values of tan for 0, π6,π4,π3,π and multiples thereof

Content

E4 Understand and use the definitions of secant, cosecant and cotangent and of

arcsin, arccos and arctan; their relationships to sine, cosine and tangent;

understanding of their graphs; their ranges and domains

Content

E5 • Understand and use tanθ= cossinθ θ

• Understand and use sin2θ+cos2θ = 1 ; sec2θ = 1 +tan2θ and

cosec2θ = 1 +cot2θ

Content

E6 • Understand and use double angle formulae; use of formulae for

sin A±B, cos A±Band tan A±B ; understand geometrical proofs of theseformulae

• Understand and use expressions for a cosθ+ b sinθ in the equivalent forms of

rcosθ±α or rsin θ±α

Content

E7 Solve simple trigonometric equations in a given interval, including quadratic

equations in sin, cos and tan and equations involving multiples of the unknownangle

Use trigonometric functions to solve problems in context, including problemsinvolving vectors, kinematics and forces.

3.7 F: Exponentials and logarithms

Content

F1 • Know and use the function ax and its graph, where a is positive

• Know and use the function ex and its graph

• Know and use the function lnx and its graph

• Know and use lnx as the inverse function of ex

Content

F4 Understand and use the laws of logarithms:

logax+ logay= loga xy ; logax− logay= loga x y ; klogax= logaxk

(including, for example, k= − 1 and k= − 12 )

Use logarithmic graphs to estimate parameters in relationships of the form y=axn

and y=kbx , given data for x and y

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F7 Understand and use exponential growth and decay; use in modelling (examples

may include the use of e in continuous compound interest, radioactive decay, drugconcentration decay, exponential growth as a model for population growth);

consideration of limitations and refinements of exponential models

3.8 G: Differentiation

Content

G1 • 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 givencurve; second derivatives; differentiation from first principles for small positive

integer powers of x and for sinx and cosx

• Understand and use the second derivative as the rate of change of gradient;

connection to convex and concave sections of curves and points of inflection

G3 • Apply differentiation to find gradients, tangents and normals, maxima and

minima and stationary points, points of inflection

• Identify where functions are increasing or decreasing

Content

G4 Differentiate using the product rule, the quotient rule and the chain rule, including

problems involving connected rates of change and inverse functions

Content

G5 Differentiate simple functions and relations defined implicitly or parametrically, for

first derivative only

Content

G6 Construct simple differential equations in pure mathematics and in context,

(contexts may include kinematics, population growth and modelling the

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