EDEXEL INTERNATIONAL ADVANCED LEVEL
MATHEMATICS/ FURTHER MATHEMATICS/ PURE
MATHEMATICS SPECIFICATIONSPECIFICATION
Edexcel International GCSE in Economics (9-1) (4ET0)
First examination June
ECONOMICS
INTERNATIONAL
...
EDEXEL INTERNATIONAL ADVANCED LEVEL
MATHEMATICS/ FURTHER MATHEMATICS/ PURE
MATHEMATICS SPECIFICATIONSPECIFICATION
Edexcel International GCSE in Economics (9-1) (4ET0)
First examination June
ECONOMICS
INTERNATIONAL ADVANCED LEVEL EDEXCEL INTERNATIONAL GCSE
MATHEMATICS/
FURTHER MATHEMATICS/
PURE MATHEMATICS
SPECIFICATION
Pearson Edexcel International Advanced Subsidiary in Mathematics (XMA01)
Pearson Edexcel International Advanced Subsidiary in Further Mathematics (XFM01)
Pearson Edexcel International Advanced Subsidiary in Pure Mathematics (XPM01)
Pearson Edexcel International Advanced Level in Mathematics (YMA01)
Pearson Edexcel International Advanced Level in Further Mathematics (YFM01)
Pearson Edexcel International Advanced Level in Pure Mathematics (YPM01)
First teaching September 2018
First examination from January 2019
First certification from August 2019 (International Advanced Subsidiary) and August 2020
(International Advanced Level)
Issue 3Edexcel, BTEC and LCCI qualifications
Edexcel, BTEC and LCCI qualifications are awarded by Pearson, the UK’s largest awarding
body offering academic and vocational qualifications that are globally recognised and
benchmarked. For further information, please visit our qualification website at
qualifications.pearson.com. Alternatively, you can get in touch with us using the details on
our contact us page at qualifications.pearson.com/contactus
About Pearson
Pearson is the world's leading learning company, with 35,000 employees in more than
70 countries working to help people of all ages to make measurable progress in their lives
through learning. We put the learner at the centre of everything we do, because wherever
learning flourishes, so do people. Find out more about how we can help you and your
learners at qualifications.pearson.com
Acknowledgements
This specification has been produced by Pearson on the basis of consultation with teachers,
examiners, consultants and other interested parties. Pearson would like to thank all those
who contributed their time and expertise to the specification’s development.
References to third party material made in this specification are made in good faith. Pearson
does not endorse, approve or accept responsibility for the content of materials, which may
be subject to change, or any opinions expressed therein. (Material may include textbooks,
journals, magazines and other publications and websites.)
All information in this specification is correct at time of going to publication.
ISBN 978 1 446 94981 8
All the material in this publication is copyright
© Pearson Education Limited 2019Summary of Pearson Edexcel International Advanced
Subsidiary/Advanced Level in Mathematics, Further
Mathematics and Pure Mathematics Specification
Issue 3 changes
Summary of changes made between previous issue and this current
issue
Page
number
In section Notation and formulae, Integration, the equation for ax now reads as
follows:
ax
ln
x
a
a
+ c
22
In Unit P4.3, the following section 6.5 has been added for clarification:
6.5 Use integration to find the area
under a curve given its parametric
equations.
Students should be able to find the area
under a curve given its parametric
equations. Students will not be expected
to sketch a curve from its parametric
equations.
28
Earlier issues show previous changes.
If you need further information on these changes or what they mean, contact us via our
website at: qualifications.pearson.com/en/support/contact-us.html.Contents
About this specification 1
Why choose Edexcel qualifications? 3
Why choose Pearson Edexcel International Advanced
Subsidiary/Advanced Level qualifications in Mathematics, Further
Mathematics and Pure Mathematics? 4
Supporting you in planning and implementing these qualifications 5
Qualification at a glance 6
Mathematics, Further Mathematics and Pure
Mathematics content 11
Unit P1: Pure Mathematics 1 12
Unit P2: Pure Mathematics 2 17
Unit P3: Pure Mathematics 3 21
Unit P4: Pure Mathematics 4 26
Unit FP1: Further Pure Mathematics 1 30
Unit FP2: Further Pure Mathematics 2 36
Unit FP3: Further Pure Mathematics 3 40
Unit M1: Mechanics 1 44
Unit M2: Mechanics 2 47
Unit M3: Mechanics 3 50
Unit S1: Statistics 1 53
Unit S2: Statistics 2 57
Unit S3: Statistics 3 60
Unit D1: Decision Mathematics 1 63
Assessment information 67
Administration and general information 71
Entries and resitting of units 71
Access arrangements, reasonable adjustments, special
consideration and malpractice 71
Awarding and reporting 73
Student recruitment and progression 75Appendices 77
Appendix 1: Codes 78
Appendix 2: Pearson World Class Qualification design principles 79
Appendix 3: Transferable skills 81
Appendix 4: Level 3 Extended Project qualification 82
Appendix 5: Glossary 85
Appendix 6: Use of calculators 86
Appendix 7: Notation 87Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
1
About this specification
The Pearson Edexcel International Advanced Subsidiary in Mathematics, Further
Mathematics and Pure Mathematics and the Pearson Edexcel International Advanced Level in
Mathematics, Further Mathematics and Pure Mathematics and are part of a suite of
International Advanced Level qualifications offered by Pearson.
These qualifications are not accredited or regulated by any UK regulatory body.
Key features
This specification includes the following key features.
Structure
The Pearson Edexcel International Advanced Subsidiary in Mathematics, Further
Mathematics and Pure Mathematics and the Pearson Edexcel International Advanced Level in
Mathematics, Further Mathematics and Pure Mathematics are modular qualifications.
The Advanced Subsidiary and Advanced Level qualifications can be claimed on completion of
the required units, as detailed in the Qualification overview section.
Content
• A variety of 14 equally weighted units allowing many different combinations, resulting in
flexible delivery options.
• Core mathematics content separated into four Pure Mathematics units.
• From the legacy qualification:
o Decision Mathematics 1 has been updated for a more balanced approach to content.
o The Further, Mechanics and Statistics units have not changed.
Assessment
• Fourteen units tested by written examination.
• Pathways leading to International Advanced Subsidiary Level and International Advanced
Level in Mathematics, Further Mathematics and Pure Mathematics.
Approach
Students will be encouraged to take responsibility for their own learning and mathematical
development. They will use their knowledge and skills to apply mathematics to real-life
situations, solve unstructured problems and use mathematics as an effective means of
communication.
Specification updates
This specification is Issue 3 and is valid for first teaching from September 2018. If there are
any significant changes to the specification, we will inform centres in writing. Changes will
also be posted on our website.
For more information please visit qualifications.pearson.comPearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
2
Using this specification
This specification gives teachers guidance and encourages effective delivery. The following
information will help teachers to get the most out of the content and guidance.
Compulsory content: as a minimum, all the bullet points in the content must be taught.
The word ‘including’ in content specifies the detail of what must be covered.
Examples: throughout the content, we have included examples of what could be covered or
what might support teaching and learning. It is important to note that examples are for
illustrative purposes only and that centres can use other examples. We have included
examples that are easily understood and recognised by international centres.
Assessments: use a range of material and are not limited to the examples given. Teachers
should deliver these qualifications using a good range of examples to support the
assessment of the content.
Depth and breadth of content: teachers should use the full range of content and all the
assessment objectives given in the subject content section.
Qualification aims and objectives
The aims and objectives of these qualifications are to enable students to:
• develop their understanding of mathematics and mathematical processes in a way that
promotes confidence and fosters enjoyment
• develop abilities to reason logically and recognise incorrect reasoning, to generalise and
to construct mathematical proofs
• extend their range of mathematical skills and techniques and use them in more difficult,
unstructured problems
• develop an understanding of coherence and progression in mathematics and of how
different areas of mathematics can be connected
• recognise how a situation may be represented mathematically and understand the
relationship between ‘real-world’ problems and standard and other mathematical models
and how these can be refined and improved
• use mathematics as an effective means of communication
• read and comprehend mathematical arguments and articles concerning applications of
mathematics
• acquire the skills needed to use technology such as calculators and computers effectively,
recognise when such use may be inappropriate and be aware of limitations
• develop an awareness of the relevance of mathematics to other fields of study, to the
world of work and to society in general
• take increasing responsibility for their own learning and the evaluation of their own
mathematical development.
Qualification abbreviations used in this specification
The following abbreviations appear in this specification:
International Advanced Subsidiary – IAS
International A2 – IA2
International Advanced Level – IALPearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
3
Why choose Edexcel qualifications?
Pearson – the world’s largest education company
Edexcel academic qualifications are from Pearson, the UK’s largest awarding organisation.
With over 3.4 million students studying our academic and vocational qualifications
worldwide, we offer internationally recognised qualifications to schools, colleges and
employers globally.
Pearson is recognised as the world’s largest education company, allowing us to drive
innovation and provide comprehensive support for Edexcel students to acquire the
knowledge and skills they need for progression in study, work and life.
A heritage you can trust
The background to Pearson becoming the UK’s largest awarding organisation began in 1836,
when a royal charter gave the University of London its first powers to conduct exams and
confer degrees on its students. With over 150 years of international education experience,
Edexcel qualifications have a firm academic foundation, built on the traditions and rigour
associated with Britain’s educational system.
To find out more about our Edexcel heritage please visit our website:
qualifications.pearson.com/en/about-us/about-pearson/our-history
Results you can trust
Pearson’s leading online marking technology has been shown to produce exceptionally
reliable results, demonstrating that at every stage, Edexcel qualifications maintain the
highest standards.
Developed to Pearson’s world-class qualifications standards
Pearson’s world-class standards mean that all Edexcel qualifications are developed to be
rigorous, demanding, inclusive and empowering. We work collaboratively with a panel of
educational thought-leaders and assessment experts to ensure that Edexcel qualifications
are globally relevant, represent world-class best practice and maintain a consistent
standard.
For more information on the world-class qualification process and principles please go to
Appendix 2: Pearson World Class Qualification design principles or visit our website:
uk.pearson.com/world-class-qualifications.Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
4
Why choose Pearson Edexcel International
Advanced Subsidiary/Advanced Level qualifications
in Mathematics, Further Mathematics and Pure
Mathematics?
We have listened to feedback from all parts of the international school subject community,
including a large number of teachers. We have made changes that will engage international
learners and give them skills that will support their progression to further study of
mathematics and to a wide range of other subjects.
Key qualification features – Unitised structure with all units equally weighted, allowing
many different combinations of units and greater flexibility. Three exam series per year
means students can sit unit exams when they are ready.
Clear and straightforward question papers – our question papers are clear and
accessible for students of all ability ranges. Our mark schemes are straightforward so that
the assessment requirements are clear.
Broad and deep development of learners’ skills – we designed the International
Advanced Level qualifications to:
• develop their understanding of mathematics and mathematical processes in a way that
promotes confidence and fosters enjoyment
• develop abilities to reason logically and recognise incorrect reasoning, to generalise and
to construct mathematical proofs
• extend their range of mathematical skills and techniques and use them in more difficult,
unstructured problems
• develop an understanding of coherence and progression in mathematics and of how
different areas of mathematics can be connected
• recognise how a situation may be represented mathematically and understand the
relationship between ‘real-world’ problems and standard and other mathematical models
and how these can be refined and improved
• use mathematics as an effective means of communication
• read and comprehend mathematical arguments and articles concerning applications of
mathematics
• acquire the skills needed to use technology such as calculators and computers effectively,
recognise when such use may be inappropriate and be aware of limitations
• develop an awareness of the relevance of mathematics to other fields of study, to the
world of work and to society in general
• take increasing responsibility for their own learning and the evaluation of their own
mathematical development.
Progression – International Advanced Level qualifications enable successful progression to
H.E. courses in mathematics and many other subjects and to employment. Through our
world-class qualification development process we have consulted with higher education to
validate the appropriateness of these qualifications, including content, skills and assessment
structure.
More information can be found on our website (qualifications.pearson.com) on the
Edexcel International Advanced Level pages.Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
5
Supporting you in planning and implementing
these qualifications
Planning
• Our Getting Started Guide gives you an overview of the Pearson Edexcel International
Advanced Subsidiary/Advanced Level in Mathematics qualifications to help you
understand the changes to content and assessment, and what these changes mean for
you and your students.
• We will provide you with an editable course planner and scheme of work.
• Our mapping documents highlight key differences between the new and
legacy qualifications.
Teaching and learning
• Print and digital learning and teaching resources – promote any time, any place learning
to improve student motivation and encourage new ways of working.
Preparing for exams
We will also provide a range of resources to help you prepare your students for the
assessments, including:
• specimen papers to support formative assessments and mock exams
• examiner commentaries following each examination series.
ResultsPlus
ResultsPlus provides the most detailed analysis available of your students’ examination
performance. It can help you identify the topics and skills where further learning would
benefit your students.
examWizard
A free online resource designed to support students and teachers with examination
preparation and assessment.
Training events
In addition to online training, we host a series of training events each year for teachers to
deepen their understanding of our qualifications.
Get help and support
Our subject advisor service will ensure that you receive help and guidance from us. You can
sign up to receive email updates from Graham Cumming’s famous maths emporium for
qualification updates and product and service news.
Just email
[email protected] and ask to be included in the email updates.Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
6
Qualification at a glance
Qualification overview
This specification contains the units for the following qualifications:
• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics
• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Further
Mathematics
• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Pure Mathematics
Course of study
The structure of these qualifications allows teachers to construct a course of study that can
be taught and assessed as either:
• distinct units of teaching and learning with related assessments taken at appropriate
stages during the course; or
• a linear course assessed in its entirety at the end.
Students study a variety of units, following pathways to their desired qualification.
Calculators may be used in the examination. Please see Appendix 6: Use of calculators.Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
7
Content and assessment overview
Each unit:
• is externally assessed
• has a written examination of 1 hour and 30 minutes
• has 75 marks.
Unit *Unit
code:
Availability First
assessment
IAS
weighting
IAL
weighting
Content overview
Pure Mathematics units
P1: Pure
Mathematics 1
WMA11/01 January,
June and
October
January
2019
33⅓ % 16⅔ % Algebra and functions; coordinate geometry in the
(x, y); trigonometry; differentiation; integration.
P2: Pure
Mathematics 2
WMA12/01 January,
June and
October
June 2019 33⅓ % 16⅔ % Proof; algebra and functions; coordinate geometry
in the (x, y) plane; sequences and series;
exponentials and logarithms; trigonometry;
differentiation; integration.
P3: Pure
Mathematics 3
WMA13/01 January,
June and
October
January
2020
N/A 16⅔ % Algebra and functions; trigonometry; exponentials
and logarithms; differentiation; integration;
numerical methods.
P4: Pure
Mathematics 4
WMA14/01 January,
June and
October
June 2020 N/A 16⅔ % Proof; algebra and functions; coordinate geometry
in the (x, y) plane; binomial expansion;
differentiation; integration; vectors.
FP1:
Further Pure
Mathematics 1
WFM01/01 January and
June
June 2019 33⅓ % 16⅔ % Complex numbers; roots of quadratic equations;
numerical solution of equations; coordinate
systems; matrix algebra; transformations using
matrices; series; proof.Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
8
Unit *Unit
code:
Availability First
assessment
IAS
weighting
IAL
weighting
Content overview
FP2:
Further Pure
Mathematics 2
WFM02/01 January and
June
June 2020 33⅓ % 16⅔ % Inequalities; series; further complex numbers; first
order differential equations; second order
differential equations; Maclaurin and Taylor series;
Polar coordinates.
FP3:
Further Pure
Mathematics 3
WFM03/01 January and
June
June 2020 33⅓ % 16⅔ % Hyperbolic functions; further coordinate systems;
differentiation; integration; vectors; further matrix
algebra.
Applications units
M1:
Mechanics 1
WME01/01 January,
June and
October
June 2019 33⅓ % 16⅔ % Mathematical models in mechanics; vectors in
mechanics; kinematics of a particle moving in a
straight line; dynamics of a particle moving in a
straight line or plane; statics of a particle;
moments.
M2:
Mechanics 2
WME02/01 January,
June and
October
June 2020 33⅓ % 16⅔ % Kinematics of a particle moving in a straight line or
plane; centres of mass; work and energy; collisions;
statics of rigid bodies.
M3:
Mechanics 3
WME03/01 January and
June
June 2020 33⅓ % 16⅔ % Further kinematics; elastic strings and springs;
further dynamics; motion in a circle; statics of rigid
bodies.
S1:
Statistics 1
WST01/01 January,
June and
October
June 2019 33⅓ % 16⅔ % Mathematical models in probability and statistics;
representation and summary of data; probability;
correlation and regression; discrete random
variables; discrete distributions; the Normal
distribution.
S2:
Statistics 2
WST02/01 January,
June and
October
June 2020 33⅓ % 16⅔ % The Binomial and Poisson distributions; continuous
random variables; continuous distributions;
samples; hypothesis tests.Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
9
Unit *Unit
code:
Availability First
assessment
IAS
weighting
IAL
weighting
Content overview
S3:
Statistics 3
WST03/01 January and
June
June 2020 33⅓ % 16⅔ % Combinations of random variables; sampling;
estimation, confidence intervals and tests; goodness
of fit and contingency tables; regression and
correlation.
D1: Decision
Mathematics 1
WDM11/01 January and
June
June 2019 33⅓ % 16⅔ % Algorithms; algorithms on graphs; algorithms on
graphs II; critical path analysis; linear
programming.
*See Appendix 1: Codes for a description of this code and all other codes relevant to these qualifications.Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
10
Qualification overview
Pearson Edexcel International Advanced Subsidiary
The International Advanced Subsidiary in Mathematics, Further Mathematics and Pure
Mathematics qualifications each consist of three externally-examined units:
Qualification Compulsory units Optional units
International Advanced Subsidiary in
Mathematics
P1, P2 M1, S1, D1
International Advanced Subsidiary in
Further Mathematics
FP1 FP2, FP3, M1, M2, M3,
S1, S2, S3, D1
International Advanced Subsidiary in
Pure Mathematics
P1, P2, FP1
Pearson Edexcel International Advanced Level
The International Advanced Level in Mathematics, Further Mathematics and Pure
Mathematics qualifications each consist of six externally-examined units:
Qualification Compulsory units Optional units
International Advanced Level in
Mathematics
P1, P2, P3, P4 M1 and S1 or
M1 and D1 or
M1 and M2 or
S1 and D1 or
S1 and S2
International Advanced Level in Further
Mathematics
FP1 and either FP2 or
FP3
FP2, FP3, M1, M2, M3,
S1, S2, S3, D1
International Advanced Level in Pure
Mathematics
P1, P2, P3, P4, FP1 FP2 or FP3
The certification of each qualification requires different contributing units. For example,
students who are awarded certificates in both International Advanced Level Mathematics and
International Advanced Level Further Mathematics must use unit results from 12 different
units, i.e. once a unit result has been used to cash in for a qualification, it cannot be re-used
to cash in for another qualification.
Calculators
Calculators may be used in the examinations. Please see Appendix 6: Use of calculators.Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
11
Mathematics, Further Mathematics and Pure
Mathematics content
Unit P1: Pure Mathematics 1 12
Unit P2: Pure Mathematics 2 17
Unit P3: Pure Mathematics 3 21
Unit P4: Pue Mathematics 4 26
Unit FP1: Further Pure Mathematics 1 30
Unit FP2: Further Pure Mathematics 2 36
Unit FP3: Further Pure Mathematics 3 40
Unit M1: Mechanics 1 44
Unit M2: Mechanics 2 47
Unit M3: Mechanics 3 50
Unit S1: Statistics 1 53
Unit S2: Statistics 2 57
Unit S3: Statistics 3 60
Unit D1: Decision Mathematics 1 63Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
12
Unit P1: Pure Mathematics 1
Compulsory unit for IAS Mathematics and Pure Mathematics
Compulsory unit for IAL Mathematics and Pure Mathematics
Externally assessed
P1.1 Unit description
Algebra and functions; coordinate geometry in the (x,y); trigonometry;
differentiation; integration.
P1.2 Assessment information
1. Examination • First assessment: January 2019.
• The assessment is 1 hour and 30 minutes.
• The assessment is out of 75 marks.
• Students must answer all questions.
• Calculators may be used in the examination. Please see
Appendix 6: Use of calculators.
• The booklet Mathematical Formulae and Statistical Tables will be
provided for use in the assessments.
2. Notation and formulae Students will be expected to understand the symbols outlined in
Appendix 7: Notation.
Formulae that students are expected to know are given below and will not
appear in the booklet; Mathematical Formulae and Statistical Tables. This
booklet will be provided for use with the paper. Questions will be set in SI
units and other units in common usage.
Quadratic equations
ax2 + bx + c = 0 has roots
2
4
2
b b ac
a
− ± −
Trigonometry
In the triangle ABC,
sin
a
A
=
sin
b
B
=
sin
c
C
area = 1
2 ab sin C
arc length = rθ
area of sector = 1
2 r2θPearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
13
2. Notation and formulae
continued
Differentiation
f(x) f ′(x)
xn nxn − 1
Integration
f(x) ∫ f( ) d x x
xn 1
1
1
+
+
n
x
n
+ c, n ≠ −1Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
14
P1.3 Unit content
What students need to learn: Guidance
1. Algebra and functions
1.1 Laws of indices for all rational
exponents.
am × an = am + n, am ÷ an = am − n, (am)n = amn
The equivalence of
mn
a and n am should be known.
1.2 Use and manipulation of surds. Students should be able to rationalise denominators.
1.3 Quadratic functions and their
graphs.
1.4 The discriminant of a quadratic
function.
Need to know and to use
b2 − 4ac > 0, b2 − 4ac = 0 and b2 − 4ac < 0
1.5 Completing the square. Solution of
quadratic equations.
Solution of quadratic equations by factorisation, use of the
formula, use of a calculator and completing the square.
ax2 + bx + c =
2 2
2 4
b b
a x c
a a
+ −
+
1.6 Solve simultaneous equations;
analytical solution by substitution.
1.7 Interpret linear and quadratic
inequalities graphically.
For example,
ax + b > cx + d, px2 + qx + r 0, px2 + qx + r < ax + b.
Interpreting the third inequality as the range of x for which
the curve
y = px2 + qx + r is below the line with equation y = ax + b.
Including inequalities with brackets and fractions. These
would be reducible to linear or quadratic inequalities,
e.g.
a x
< b becomes ax < bx2, x ≠ 0.
1.8 Represent linear and quadratic
inequalities graphically.
Represent linear and quadratic inequalities such as y > x + r
and y > ax2 + bx + c graphically.
Shading and use of dotted and solid line convention is
required.
1.9 Solutions of linear and quadratic
inequalities.
For example,
solving ax + b > cx + d, px2 + qx + r 0,
px2 + qx + r < ax + b.
1.10 Algebraic manipulation of
polynomials, including expanding
brackets and collecting like terms,
factorisation.
Students should be able to use brackets. Factorisation of
polynomials of degree n, n 3, e.g. x3 + 4x2 + 3x. The
notation f(x) may be used.Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
15
What students need to learn: Guidance
1. Algebra and functions continued
1.11 Graphs of functions; sketching
curves defined by simple equations.
Geometrical interpretation of
algebraic solution of equations. Use
of intersection points of graphs of
functions to solve equations.
Functions to include simple cubic functions and the
reciprocal functions
y =
k x
and y = k2
x
with x ≠ 0.
Knowledge of the term asymptote is expected.
Also, trigonometric graphs.
1.12 Knowledge of the effect of simple
transformations on the graph of
y = f(x) as represented by y = af(x),
y = f(x) + a, y = f(x + a), y = f(ax).
Students should be able to apply one of these
transformations to any of the above functions (quadratics,
cubics, reciprocals, sine, cosine, and tangent) and sketch the
resulting graphs.
Given the graph of any function y = f(x), students should be
able to sketch the graph resulting from one of these
transformations.
2. Coordinate geometry in the (x, y) plane
2.1 Equation of a straight line,
including the forms
y − y1 = m(x − x1) and
ax + by + c = 0.
To include:
(i) the equation of a line through two given points
(ii) the equation of a line parallel (or perpendicular) to a
given line through a given point. For example, the line
perpendicular to the line
3x + 4y = 18 through the point (2, 3) has equation
y − 3 = 4 3 (x − 2).
2.2 Conditions for two straight lines to
be parallel or perpendicular to each
other.
3. Trigonometry
3.1 The sine and cosine rules, and the
area of a triangle in the form
12
ab sin C.
Including the ambiguous case of the sine rule.
3.2 Radian measure, including use for
arc length and area of sector.
Use of the formulae s = rθ and A = 1
2 r2θ.
3.3 Sine, cosine and tangent functions.
Their graphs, symmetries and
periodicity.
Knowledge of graphs of curves with equations such as
y = 3 sin x, y = sin
6
x
π +
, y = sin 2x is expected.Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
16
What students need to learn: Guidance
4. Differentiation
4.1 The derivative of f(x) as the
gradient of the tangent to the graph
of y = f(x) at a point; the gradient of
the tangent as a limit; interpretation
as a rate of change; second order
derivatives.
For example, knowledge that d
ydx
is the rate of change of y
with respect to x. Knowledge of the chain rule is not
required.
The notation f ′(x) and f ′′(x) may be used.
4.2 Differentiation of xn, and related
sums, differences and constant
multiples.
The ability to differentiate expressions such as
(2x + 5)(x − 1) and
2 5 3
3
x x
x
+ −
is expected.
4.3 Applications of differentiation to
gradients, tangents and normals.
Use of differentiation to find equations of tangents and
normals at specific points on a curve.
5. Integration
5.1 Indefinite integration as the reverse
of differentiation.
Students should know that a constant of integration is
required.
5.2 Integration of xn and related sums,
differences and constant multiples.
(Excluding n = −1 and related sums, differences and
multiples).
For example, the ability to integrate expressions such as
12
1 2
2 x x −3 − and
( 2) x 2
x
+
is expected.
Given f ′(x) and a point on the curve, students should be
able to find an equation of the curve in the form y = f(x).Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics
and Pure Mathematics – Specification – Issue 3 – April 2019 © Pearson Education Limited 2019
17
Unit P2: Pure Mathematics 2
Compulsory unit for IAS Mathematics and Pure Mathematics
Compulsory unit for IAL Mathematics and Pure Mathematics
Externally assessed
P2.1 Unit description
Proof; algebra and functions; coordinate geometry in the (x, y) plane;
sequences and series; exponentials and logarithms; trigonometry;
differentiation; integration.
P2.2 Assessment information
1. Prerequisites A knowledge of the specification for P1 and its associated formulae is assumed
and may be tested.
2. Examination • First assessment: June 2019.
• The assessment is 1 hour and 30 minutes.
• The assessment is out of 75 marks.
• Students must answer all questions.
• Calculators may be used in the examination. Please see
Appendix 6: Use of calculators.
• The booklet Mathematical Formulae and Statistical Tables will be
provided for use in the assessments.
2. Notation and formulae Students will be expected to understand the symbols outlined in
Appendix 7: Notation.
Formulae that students are expected to know are given below and will not
appear in the booklet; Mathematical Formulae and Statistical Tables, which
will be provided for use with the paper. Questions will be set in SI units and
other units in common usage.
Laws of logarithms
loga x + loga y ≡ loga (xy)
loga x − loga y ≡ loga x
y
k logax ≡ loga(xk)
Trigonometry
sin2 A + cos2 A ≡ 1
tan θ ≡
sin
cos
θ
θ
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
 2e Peter Olver, Chehrzad Shakiban.png)
