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DRAFT 7356

Specification
For teaching from September 2017 onwards
For AS exams in 2018 onwards

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DRAFT SPECIFICATION

AS
MATHEMATICS

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Version 0.1 9 June 2016


DRAFT SPECIFICATION

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AS Mathematics DRAFT 7356. AS exams June 2018 onwards. Version 0.1 9 June 2016

Contents
1 Introduction

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2.1 Subject content
2.2 Assessments

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3 Subject content

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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

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2 Specification at a glance

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1.1 Why choose AQA for AS Mathematics
1.2 Support and resources to help you teach
1.3 Draft specification

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4 Scheme of assessment
4.1 Aims
4.2 Assessment objectives
4.3 Assessment weightings

5 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

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Are you using the latest version of this specification?
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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.

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DRAFT SPECIFICATION

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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 9 June 2016

1 Introduction
1.1 Why choose AQA for AS Mathematics

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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

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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:

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• 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:
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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

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• 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

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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:
T: 0161 957 3852

1.3 Draft specification

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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.

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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 9 June 2016

2 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)

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Core content

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2.2 Assessments
Paper 1
What's assessed

How it's assessed

• Written exam: 1 hour 30 minutes
• 80 marks
• 50% of AS
Questions

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A mix of question styles, from short, single-mark questions to multi-step problems.

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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

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Content from the following sections:


AS Mathematics DRAFT 7356. AS exams June 2018 onwards. Version 0.1 9 June 2016

Paper 2
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

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Content from the following sections:

How it's assessed

• Written exam: 1 hour 30 minutes
• 80 marks
• 50% of AS
Questions

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A mix of question styles, from short, single-mark questions to multi-step problems.

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DRAFT SPECIFICATION

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AS Mathematics DRAFT 7356. AS exams June 2018 onwards. Version 0.1 9 June 2016

3 Subject content
The subject content for AS 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 AS
course of study.

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AS 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 out in
sections A to S.

Students must use the mathematical notation and must be able to recall the mathematical formulae
and identities set out in the DfE subject content.

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3.1 Overarching themes

3.1.1 OT1: Mathematical argument, language and proof
Content

OT1.1

Construct and present mathematical arguments through appropriate use of
diagrams; sketching graphs; logical deduction; precise statements involving
correct 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.

OT1.5

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

Recognise the underlying mathematical structure in a situation and simplify and
abstract appropriately to enable problems to be solved.

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OT2.1

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.

OT2.5

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

OT2.6

Understand the concept of a mathematical problem solving cycle, including
specifying the problem, collecting information, processing and representing
information and interpreting results, which may identify the need to repeat the
cycle.

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Content
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
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.

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OT3.1

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. Use
methods of proof, including proof by deduction, proof by exhaustion.
• Disproof by counter example.

3.3 B: Algebra and functions

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Content

B1

Understand and use the laws of indices for all rational exponents.
Content

B2

Use and manipulate surds, including rationalising the denominator.
Content

B3

Work with quadratic functions and their graphs: the discriminant of a quadratic
function, including the conditions for real and repeated roots; completing the
square; solution of quadratic equations including solving quadratic equations in a
function of the unknown.

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Content


AS Mathematics DRAFT 7356. AS exams June 2018 onwards. Version 0.1 9 June 2016

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

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Content
B6

Manipulate polynomials algebraically, including expanding brackets and collecting
like terms, factorisation and simple algebraic division. Use of the factor theorem.

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y > ax2 + bx + c graphically.

Content

B7

• Understand and use graphs of functions. Sketch curves defined by simple
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equations including polynomials, the modulus of a linear function, y = x and

y=

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x2

(including their vertical and horizontal asymptotes). Interpret algebraic

solution of equations graphically. Use intersection points of graphs to solve
equations.
• Understand and use proportional relationships 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

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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 straight
lines to be parallel or perpendicular.
• Be able to use straight line models in a variety of contexts.

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Content
C2

Understand and use the coordinate geometry of the circle including using the
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equation of a circle in the form x − a + y − b = r ; completing the square to
find the centre and radius of a circle. Use of the following properties:

Content

Understand and use the binomial expansion of a + bx
notations n! and nCr; link to binomial probabilities.

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for positive integer n; the

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3.6 E: Trigonometry
Content

E1

Understand and use the definitions of sine, cosine and tangent for all arguments;
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the sine and cosine rules; the area of a triangle in the form 2 absin C

Content

E3

Understand and use the sine, cosine and tangent functions; their graphs,
symmetries and periodicity.

Content

E5

• Understand and use tan θ =

sinθ
cosθ

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• Understand and use sin2θ + cos2θ = 1
Content

E7

Solve simple trigonometric equations in a given interval, including quadratic
equations in sin, cos and tan and equations involving multiples of the unknown
angle.

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3.5 D: Sequences and series

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• 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 to
the tangent to the circle at that point.


AS Mathematics DRAFT 7356. AS exams June 2018 onwards. Version 0.1 9 June 2016

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.
Content
kx

kx

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Know that the gradient of e is equal to ke and hence understand why the
exponential model is suitable in many applications.
Content

F3

• Know and use the definition of log x as the inverse of ax , where a is positive
a
and x ≥ 0

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F2

• Know and use the function ln x and its graph.
• Know and use ln x as the inverse function of ex

Content

F4

Understand and use the laws of logarithms:

x

k

loga x+ loga y = loga xy ; loga x− loga y = loga y ; k loga x = loga x
(including, for example, k = − 1 and k = −

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F5

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Solve equations of the form a = b

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

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F6

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and y = kb , given data for x and y.

Content

F7

Understand and use exponential growth and decay; use in modelling (examples
may include the use of e in continuous compound interest, radioactive decay, drug
concentration decay, exponential growth as a model for population growth);
consideration of limitations and refinements of exponential models.

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3.8 G: Differentiation
Content

Content
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Differentiate x , for rational values of n, and related constant multiples, sums and
differences.

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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

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Integrate x (excluding n = -1), and related sums, differences and constant
multiples.

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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.

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• 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.

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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

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J4

Use vectors to solve problems in pure mathematics and in context, including
forces.

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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.

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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.

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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.

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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.

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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.

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• Interpret measures of central tendency and variation, extending to standard
deviation.
• Be able to calculate standard deviation, including from summary statistics.

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AS Mathematics DRAFT 7356. AS exams June 2018 onwards. Version 0.1 9 June 2016

3.15 O: Statistical hypothesis testing
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null hypothesis
alternative hypothesis
significance level
test statistic
1-tail test
2-tail test
critical value
critical region
acceptance region
p-value.

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Understand and apply the language of statistical hypothesis testing, developed
through a binomial model:

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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.

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3.17 Q: Kinematics
Content

Q1

Understand and use the language of kinematics:

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position
displacement
distance travelled
velocity
speed
acceleration.

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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
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dt

a=

dv
dt

=

d 2r
,
dt2

r = ∫ v dt,v = ∫ a dt

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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).

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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:

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Understand, use and derive the formulae for constant acceleration for motion in a
straight line.

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AS Mathematics DRAFT 7356. AS exams June 2018 onwards. Version 0.1 9 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

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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

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We have selected one data set that will feature in statistics questions throughout the lifetime of this
specification.

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AS Mathematics DRAFT 7356. AS exams June 2018 onwards. Version 0.1 9 June 2016

4 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.

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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.

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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:

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• 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

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• 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 2

AO1

60

60

60

AO2

20

20

20

AO3

20

20

20

Overall weighting of
components

50

50

100

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Paper 1

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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 9 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 1

80

x1

80

Paper 2

80

x1

80

T

D

R
AF

DRAFT SPECIFICATION

Total scaled mark: 160

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