Cambridge International AS and A Level Mathematics (9709)
SyllabuS
Cambridge International aS & a level
Mathematics
9709
For examination in June and November 2019.
Also available for examination in March 2019 for India only.
Cambridge advanced
Version 1
Changes to the syllabus for 2019
The latest syllabus is version 1, published September 2016
There are no signiicant changes which affect teaching.
you are strongly advised to read the whole syllabus before planning your teaching programme.
any textbooks endorsed to support the syllabus for examination from 2002 are still suitable for
use with this syllabus.
Cambridge International Examinations retains the copyright on all its publications. Registered Centres are
permitted to copy material from this booklet for their own internal use. However, we cannot give permission
to Centres to photocopy any material that is acknowledged to a third party even for internal use within a
Centre.
® IGCSE is the registered trademark of Cambridge International Examinations
© Cambridge International Examinations 2016
Contents
Introduction .......................................................................................................................... 2
Why choose Cambridge International Examinations?
Why Cambridge International AS & A Levels?
Why Cambridge International AS & A Level Mathematics?
Teacher support
1
Assessment at a glance ................................................................................................. 7
2
Syllabus aims and assessment objectives ................................................................... 10
2.1 Syllabus aims
2.2 Assessment objectives
3
Syllabus content ........................................................................................................... 11
4
List of formulae and tables of the normal distribution (MF9) ....................................... 28
5
Mathematical notation .................................................................................................. 33
6
Other information ......................................................................................................... 37
Equality and inclusion
Language
Grading and reporting
Entry option codes
Cambridge International aS & a level Mathematics 9709 syllabus. Introduction
Syllabus for examination in 2019.
Why choose Cambridge International Examinations?
Cambridge International Examinations prepares school students for life, helping them develop an
informed curiosity and a lasting passion for learning. We are part of Cambridge Assessment, a
department of the University of Cambridge.
Our international qualiications are recognised by the world’s best universities and employers,
giving students a wide range of options in their education and career. As a not-for-proit
organisation, we devote our resources to delivering high-quality educational programmes that can
unlock learners’ potential.
Our programmes and qualiications set the global standard for international education. They are created
by subject experts, rooted in academic rigour and relect the latest educational research. They provide a
strong platform for learners to progress from one stage to the next, and are well supported by teaching and
learning resources.
Every year, nearly a million Cambridge learners from 10 000 schools in 160 countries prepare for their future
with an international education from Cambridge.
Cambridge learners
Our mission is to provide educational beneit through provision of international programmes and
qualiications for school education and to be the world leader in this ield. Together with schools, we
develop Cambridge learners who are:
• conident in working with information and ideas – their own and those of others
• responsible for themselves, responsive to and respectful of others
• relective as learners, developing their ability to learn
• innovative and equipped for new and future challenges
• engaged intellectually and socially ready to make a difference.
Responsible
Coni dent
Relective
Cambridge
learners
Engaged
Innovative
learn more about the Cambridge learner attributes in Chapter 2 of our Implementing the curriculum
with Cambridge guide at www.cie.org.uk/curriculumguide
2
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Cambridge International aS & a level Mathematics 9709 syllabus. Introduction
Syllabus for examination in 2019.
Why Cambridge International AS & A Levels?
Cambridge International AS & A Levels are international in outlook, but retain a local relevance.
The syllabuses provide opportunities for contextualised learning and the content has been created
to suit a wide variety of schools, avoid cultural bias and develop essential lifelong skills, including
creative thinking and problem-solving.
Our aim is to balance knowledge, understanding and skills in our qualiications to enable students to become
effective learners and to provide a solid foundation for their continuing educational journey. Cambridge
International AS & A Levels give learners building blocks for an individualised curriculum that develops their
knowledge, understanding and skills.
Cambridge International AS & A Level curricula are lexible. It is possible to offer almost any combination
from a wide range of subjects. Cambridge International A Level is typically a two-year course, and
Cambridge International AS Level is typically one year. Some subjects can be started as a Cambridge
International AS Level and extended to a Cambridge International A Level.
There are three possible assessment approaches for Cambridge International AS & A Level:
Option two
Option three
(remainder of A Level)
Cambridge International
aS level
Cambridge International
aS level
(standalone AS)
(AS is irst half of A Level)
Learners take the Cambridge
International AS Level only. The
syllabus content for Cambridge
International AS Level is half
of a Cambridge International
A Level programme.
Learners take the Cambridge
International AS Level in Year 1 and
in Year 2 complete the Cambridge
International A Level.
Cambridge
International
a level
Year 1
Option one
Year 2
Cambridge International
a level
Learners take all papers of the
Cambridge International A Level course
in the same examination series, usually
at the end of the second year of study.
Every year thousands of learners with Cambridge International AS & A Levels gain places at leading
universities worldwide. Cambridge International AS & A Levels are accepted and valued by top
universities around the world including those in the UK, US (including Ivy League universities), European
nations, Australia, Canada and New Zealand. Learners should check the university website for speciic
entry requirements before applying.
Did you know?
In some countries universities accept Cambridge International AS Levels in their own right as
qualiications counting towards entry to courses in the same or other related subjects. Many learners
who take Cambridge International AS Levels also choose to progress to Cambridge International
A Level.
learn more
For more details go to www.cie.org.uk/recognition
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3
Cambridge International aS & a level Mathematics 9709 syllabus. Introduction
Syllabus for examination in 2019.
Why Cambridge International AS & A Level Mathematics?
about the syllabus
Cambridge International AS & A Level Mathematics is accepted by universities and employers as proof of
mathematical knowledge and understanding. Successful candidates gain lifelong skills, including:
• a deeper understanding of mathematical principles
• the further development of mathematical skills including the use of applications of mathematics in the
context of everyday situations and in other subjects that they may be studying
• the ability to analyse problems logically, recognising when and how a situation may be represented
mathematically
• the use of mathematics as a means of communication
• a solid foundation for further study.
The syllabus allows Centres lexibility to choose from three different routes to AS Level Mathematics – Pure
Mathematics only or Pure Mathematics and Mechanics or Pure Mathematics and Probability & Statistics.
Centres can choose from three different routes to Cambridge International A Level Mathematics depending
on the choice of Mechanics, or Probability & Statistics, or both, in the broad area of ‘applications’.
Guided learning hours
Guided learning hours give an indication of the amount of contact time teachers need to have with learners
to deliver a particular course. Our syllabuses are designed around 180 guided learning hours for Cambridge
International AS Level, and around 360 guided learning hours for Cambridge International A Level.
These igures are for guidance only. The number of hours needed to gain the qualiication may vary
depending on local practice and the learners’ previous experience of the subject.
Prior learning
We recommend that learners who are beginning this course should have previously completed a Cambridge
O Level or Cambridge IGCSE® course in Mathematics or the equivalent
Progression
Cambridge International A Level Mathematics provides a suitable foundation for the study of Mathematics
or related courses in higher education.
Cambridge International AS Level Mathematics is the irst half of Cambridge International A Level
Mathematics. Depending on local university entrance requirements, the qualiication may permit or assist
progression directly to university courses in Mathematics or some other subjects.
We recommend learners check the Cambridge recognitions database and the university websites to ind the
most up-to-date entry requirements for courses they wish to study.
4
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Cambridge International aS & a level Mathematics 9709 syllabus. Introduction
Syllabus for examination in 2019.
How can I ind out more?
If you are already a Cambridge school
You can make entries for this qualiication through your usual channels. If you have any questions,
please contact us at info@cie.org.uk
If you are not yet a Cambridge school
Learn more about the beneits of becoming a Cambridge school from our website
at www.cie.org.uk/startcambridge
Email us at info@cie.org.uk to ind out how your organisation can register to become a
Cambridge school.
Cambridge AICE
Cambridge AICE Diploma is the group award of the Cambridge International AS & A Level. It gives schools
the opportunity to beneit from offering a broad and balanced curriculum by recognising the achievements
of candidates who pass examinations from different curriculum groups.
learn more
For more details go to www.cie.org.uk/aice
Our research has shown that students who came to the university with a
Cambridge AICE background performed better than anyone else that came to the
university. That really wasn’t surprising considering the emphasis they have on critical
research and analysis, and that’s what we require at university.
John Barnhill, Assistant Vice President for Enrollment Management, Florida State University, USA
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5
Cambridge International aS & a level Mathematics 9709 syllabus. Introduction
Syllabus for examination in 2019.
Teacher support
We offer a wide range of practical and innovative support to help teachers plan and deliver our
programmes and qualiications conidently.
The support package for our Cambridge International AS & A Levels gives teachers access to a worldwide
teaching community enabling them to connect with other teachers, swap ideas and share best practice.
Teaching and learning
Exam preparation
• Support materials provide teachers with ideas and
planning resources for their lessons.
• Past question papers and mark schemes so
teachers can give learners the opportunity
to practise answering different questions.
• Endorsed textbooks, ebooks and digital resources
are produced by leading publishers. We have
quality checked these materials to make sure they
provide a high level of support for teachers and
learners.
• Resource lists to help support teaching,
including textbooks and websites.
Professional development
• Example candidate responses help teachers
understand exactly what examiners are looking for.
• Principal examiner reports describing learners’
overall performance on each part of the papers.
The reports give insight into common
misconceptions shown by learners, which teachers
can address in lessons.
Cambridge
International
AS & A Level
support for
teachers
Face-to-face training
We hold workshops around the world to support
teachers in delivering Cambridge syllabuses and
developing their skills.
Online training
We offer self-study and tutor-led online training
courses via our virtual learning environment. A
wide range of syllabus-speciic courses and skills
courses is available. We also offer training via
video conference and webinars.
Qualiications
learn more
Find out more about support for this
syllabus at www.cie.org.uk/alevel
Visit our online resource bank and community
forum at https://teachers.cie.org.uk
useful links
Customer Services
http://linkd.in/cambridgeteacher
LinkedIn
Twitter
www.cie.org.uk/help
@cie_education
Facebook
www.facebook.com/cie.org.uk
We offer a wide range of practice-based qualiications
at Certiicate and Diploma level, providing a
framework for continuing professional development.
6
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Cambridge International aS & a level Mathematics 9709 syllabus. Assessment at a glance
Syllabus for examination in 2019.
1
assessment at a glance
The 7 units in the scheme cover the following subject areas:
• Pure Mathematics (units P1, P2 and P3);
• Mechanics (units M1 and M2);
• Probability & Statistics (units S1 and S2).
Centres and candidates may:
• take all four Advanced (A) Level components in the same examination series for the full Cambridge
International A Level;
• follow a staged assessment route to the Cambridge International A Level by taking two Advanced
Subsidiary (AS) papers (P1 and M1 or P1 and S1) in an earlier examination series;
• take the Advanced Subsidiary (AS) qualiication only.
Cambridge International AS Level candidates take:
Paper 1: Pure Mathematics 1 (P1)
1 hour 45 minutes
About 10 shorter and longer questions
75 marks weighted at 60% of total
plus one of the following papers:
Paper 2: Pure Mathematics
2 (P2)
Paper 4: Mechanics 1 (M1)
Paper 6: Probability &
Statistics 1 (S1)
1 hour 15 minutes
1 hour 15 minutes
1 hour 15 minutes
About 7 shorter and longer
questions
About 7 shorter and longer
questions
About 7 shorter and longer
questions
50 marks weighted at 40%
of total
50 marks weighted at 40%
of total
50 marks weighted at 40%
of total
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Cambridge International aS & a level Mathematics 9709 syllabus. Assessment at a glance
Syllabus for examination in 2019.
Cambridge International A Level candidates take:
Paper 1: Pure Mathematics 1 (P1)
Paper 3: Pure Mathematics 3 (P3)
1 hour 45 minutes
1 hour 45 minutes
About 10 shorter and longer questions
About 10 shorter and longer questions
75 marks weighted at 30% of total
75 marks weighted at 30% of total
plus one of the following combinations of two papers:
Paper 4: Mechanics 1 (M1)
Paper 6: Probability & Statistics 1 (S1)
1 hour 15 minutes
1 hour 15 minutes
About 7 shorter and longer questions
About 7 shorter and longer questions
50 marks weighted at 20% of total
50 marks weighted at 20% of total
Paper 4: Mechanics 1 (M1)
Paper 5: Mechanics 2 (M2)
1 hour 15 minutes
1 hour 15 minutes
About 7 shorter and longer questions
About 7 shorter and longer questions
50 marks weighted at 20% of total
50 marks weighted at 20% of total
Paper 6: Probability & Statistics 1 (S1)
Paper 7: Probability & Statistics 2 (S2)
1 hour 15 minutes
1 hour 15 minutes
About 7 shorter and longer questions
About 7 shorter and longer questions
50 marks weighted at 20% of total
50 marks weighted at 20% of total
or
or
8
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Cambridge International aS & a level Mathematics 9709 syllabus. Assessment at a glance
Syllabus for examination in 2019.
Question papers
There is no choice of questions in any of the question papers and questions will be arranged approximately
in order of increasing mark allocations.
It is expected that candidates will have a calculator with standard ‘scientiic’ functions available for use
for all papers in the examination. Computers, graphical calculators and calculators capable of algebraic
manipulation are not permitted.
A list of formulae and tables of the normal distribution (MF9) is supplied for the use of candidates in the
examination. Details of the items in this list are given for reference in section 4.
Relationships between units
Units P2, M2, S2 are sequential to units P1, M1, S1 respectively, and the later unit in each subject area may
not be used for certiication unless the corresponding earlier unit is being (or has already been) used.
Unit P3 is also sequential to unit P1, and may not be used for certiication unless P1 is being (or has already
been) used. The subject content of unit P2 is a subset of the subject content of unit P3; otherwise, the
subject content for different units does not overlap, although later units in each subject area assume
knowledge of the earlier units.
Availability
This syllabus is examined in the June and November examination series. This syllabus is also available for
examination in March for India only.
This syllabus is available to private candidates.
Detailed timetables are available from www.cie.org.uk/timetables
Combining this with other syllabuses
Candidates can combine this syllabus in an examination series with any other Cambridge syllabus, except:
• syllabuses with the same title at the same level.
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus aims and assessment objectives
Syllabus for examination in 2019.
2
Syllabus aims and assessment objectives
2.1 Syllabus aims
The aims of the syllabus are the same for all students. These are set out below and describe the educational
purposes of any course based on the Mathematics units for the Cambridge International AS & A Level
examinations. The aims are not listed in order of priority.
The aims are to enable candidates to:
• develop their mathematical knowledge and skills in a way which encourages conidence and provides
satisfaction and enjoyment
• develop an understanding of mathematical principles and an appreciation of mathematics as a logical
and coherent subject
• acquire a range of mathematical skills, particularly those which will enable them to use applications of
mathematics in the context of everyday situations and of other subjects they may be studying
• develop the ability to analyse problems logically, recognise when and how a situation may be
represented mathematically, identify and interpret relevant factors and, where necessary, select an
appropriate mathematical method to solve the problem
• use mathematics as a means of communication with emphasis on the use of clear expression
• acquire the mathematical background necessary for further study in this or related subjects.
2.2 Assessment objectives
The abilities assessed in the examinations cover a single area: technique with application.
The examination will test the ability of candidates to:
• understand relevant mathematical concepts, terminology and notation
• recall accurately and use successfully appropriate manipulative techniques
• recognise the appropriate mathematical procedure for a given situation
• apply combinations of mathematical skills and techniques in solving problems
• present mathematical work, and communicate conclusions, in a clear and logical way.
10
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
3
Syllabus content
The mathematical content for each unit in the scheme is detailed below. The order in which topics are listed
is not intended to imply anything about the order in which they might be taught.
As well as demonstrating skill in the appropriate techniques, candidates will be expected to apply their
knowledge in the solution of problems. Individual questions set may involve ideas and methods from more
than one section of the relevant content list.
For all units, knowledge of the content of Cambridge O Level/Cambridge IGCSE Mathematics is assumed.
Candidates will be expected to be familiar with scientiic notation for the expression of compound units,
e.g. 5 m s–1 for 5 metres per second.
unit P1: Pure Mathematics 1 (Paper 1)
Candidates should be able to:
1 Quadratics
• carry out the process of completing the square for a quadratic
polynomial ax 2 + bx + c and use this form, e.g. to locate the vertex of
the graph of y = ax 2 + bx + c or to sketch the graph
• ind the discriminant of a quadratic polynomial ax 2 + bx + c and use
the discriminant, e.g. to determine the number of real roots of the
equation ax 2 + bx + c = 0
• solve quadratic equations, and linear and quadratic inequalities, in one
unknown
• solve by substitution a pair of simultaneous equations of which one is
linear and one is quadratic
• recognise and solve equations in x which are quadratic in some
function of x, e.g. x 4 – 5x 2 + 4 = 0.
2 Functions
• understand the terms function, domain, range, one-one function,
inverse function and composition of functions
• identify the range of a given function in simple cases, and ind the
composition of two given functions
• determine whether or not a given function is one-one, and ind the
inverse of a one-one function in simple cases
• illustrate in graphical terms the relation between a one-one function
and its inverse.
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
3 Coordinate
geometry
• ind the length, gradient and mid-point of a line segment, given the
coordinates of the end-points
• ind the equation of a straight line given suficient information (e.g. the
coordinates of two points on it, or one point on it and its gradient)
• understand and use the relationships between the gradients of parallel
and perpendicular lines
• interpret and use linear equations, particularly the forms y = mx + c
and y – y1 = m(x – x1)
• understand the relationship between a graph and its associated
algebraic equation, and use the relationship between points of
intersection of graphs and solutions of equations (including, in simple
cases, the correspondence between a line being tangent to a curve
and a repeated root of an equation).
4 Circular measure
• understand the deinition of a radian, and use the relationship
between radians and degrees
• use the formulae s = r i and A = 1 r2 i in solving problems concerning
2
the arc length and sector area of a circle.
5 Trigonometry
• sketch and use graphs of the sine, cosine and tangent functions (for
angles of any size, and using either degrees or radians)
• use the exact values of the sine, cosine and tangent of 30°, 45°, 60°,
and related angles, e.g. cos 150° = – 1 3
2
• use the notations sin−1x, cos−1x, tan−1x to denote the principal values of
the inverse trigonometric relations
sin i
• use the identities
/ tan i and sin2 i + cos2 i / 1
cos i
• ind all the solutions of simple trigonometrical equations lying in a
speciied interval (general forms of solution are not included).
6 Vectors
x
• use standard notations for vectors, i.e. , xi + yj,
y
AB , a
x
y , xi + yj + zk,
z
• carry out addition and subtraction of vectors and multiplication of a
vector by a scalar, and interpret these operations in geometrical terms
• use unit vectors, displacement vectors and position vectors
• calculate the magnitude of a vector and the scalar product of two
vectors
• use the scalar product to determine the angle between two directions
and to solve problems concerning perpendicularity of vectors.
12
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
7 Series
• use the expansion of (a + b)n , where n is a positive integer (knowledge
of the greatest term and properties of the coeficients are not
JKn NO
required, but the notations KKr OO and n! should be known)
L P
• recognise arithmetic and geometric progressions
• use the formulae for the nth term and for the sum of the irst n terms
to solve problems involving arithmetic or geometric progressions
• use the condition for the convergence of a geometric progression,
and the formula for the sum to ininity of a convergent geometric
progression.
8 Differentiation
• understand the idea of the gradient of a curve, and use the notations
2
dy
dy
and
(the technique of differentiation from irst
2
dx
dx
principles is not required)
f’(x), f’’(x),
• use the derivative of xn (for any rational n), together with constant
multiples, sums, differences of functions, and of composite functions
using the chain rule
• apply differentiation to gradients, tangents and normals, increasing
and decreasing functions and rates of change (including connected
rates of change)
• locate stationary points, and use information about stationary points
in sketching graphs (the ability to distinguish between maximum
points and minimum points is required, but identiication of points of
inlexion is not included).
9 Integration
• understand integration as the reverse process of differentiation,
and integrate (ax + b)n (for any rational n except –1), together with
constant multiples, sums and differences
• solve problems involving the evaluation of a constant of integration,
e.g. to ind the equation of the curve through (1, –2) for which
dy
= 2x + 1
dx
• evaluate deinite integrals (including simple cases of ‘improper’
integrals, such as
yx
1
0
1
-2
yx
3
d x and
1
-2
d x)
• use deinite integration to ind:
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–
the area of a region bounded by a curve and lines parallel to the
axes, or between two curves
–
a volume of revolution about one of the axes.
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
unit P2: Pure Mathematics 2 (Paper 2)
Knowledge of the content of unit P1 is assumed, and candidates may be required to
demonstrate such knowledge in answering questions.
Candidates should be able to:
1 algebra
• understand the meaning of x, and use relations such as
a = b ⇔ a2 = b2 and x – a < b ⇔ a – b < x < a + b in the
course of solving equations and inequalities
• divide a polynomial, of degree not exceeding 4, by a linear or quadratic
polynomial, and identify the quotient and remainder (which may be
zero)
• use the factor theorem and the remainder theorem, e.g. to ind
factors, solve polynomial equations or evaluate unknown coeficients.
2 logarithmic
and exponential
functions
• understand the relationship between logarithms and indices, and use
the laws of logarithms (excluding change of base)
• understand the deinition and properties of ex and In x, including their
relationship as inverse functions and their graphs
• use logarithms to solve equations of the form ax = b, and similar
inequalities
• use logarithms to transform a given relationship to linear form, and
hence determine unknown constants by considering the gradient
and/or intercept.
3 Trigonometry
• understand the relationship of the secant, cosecant and cotangent
functions to cosine, sine and tangent, and use properties and graphs
of all six trigonometric functions for angles of any magnitude
• use trigonometrical identities for the simpliication and exact
evaluation of expressions and, in the course of solving equations,
select an identity or identities appropriate to the context, showing
familiarity in particular with the use of:
4 Differentiation
–
sec2 i ≡ 1 + tan2 i and cosec2 i ≡ 1 + cot2 i
–
the expansions of sin(A ± B), cos(A ± B) and tan(A ± B)
–
the formulae for sin 2A, cos 2A and tan 2A
–
the expressions of a sin i + b cos i in the forms R sin ^i ! ah and
R cos ^i ! ah .
• use the derivatives of ex, In x, sin x, cos x, tan x, together with constant
multiples, sums, differences and composites
• differentiate products and quotients
• ind and use the irst derivative of a function which is deined
parametrically or implicitly.
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
5 Integration
• extend the idea of ‘reverse differentiation’ to include the integration of
1 , sin(ax + b), cos(ax + b) and sec2 (ax + b) (knowledge of
ax + b
the general method of integration by substitution is not required)
eax + b,
• use trigonometrical relationships (such as double-angle formulae) to
facilitate the integration of functions such as cos2 x
• use the trapezium rule to estimate the value of a deinite integral,
and use sketch graphs in simple cases to determine whether the
trapezium rule gives an over-estimate or an under-estimate.
6 Numerical
solution of
equations
• locate approximately a root of an equation, by means of graphical
considerations and/or searching for a sign change
• understand the idea of, and use the notation for, a sequence of
approximations which converges to a root of an equation
• understand how a given simple iterative formula of the form
xn + 1 = F(xn) relates to the equation being solved, and use a given
iteration, or an iteration based on a given rearrangement of an
equation, to determine a root to a prescribed degree of accuracy
(knowledge of the condition for convergence is not included, but
candidates should understand that an iteration may fail to converge).
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
unit P3: Pure Mathematics 3 (Paper 3)
Knowledge of the content of unit P1 is assumed, and candidates may be required to
demonstrate such knowledge in answering questions.
Candidates should be able to:
1 algebra
• understand the meaning of |x|, and use relations such as
a = b ⇔ a2 = b2 and x – a < b ⇔ a – b < x < a + b in the
course of solving equations and inequalities
• divide a polynomial, of degree not exceeding 4, by a linear or quadratic
polynomial, and identify the quotient and remainder (which may be
zero)
• use the factor theorem and the remainder theorem, e.g. to ind
factors, solve polynomial equations or evaluate unknown coeficients
• recall an appropriate form for expressing rational functions in partial
fractions, and carry out the decomposition, in cases where the
denominator is no more complicated than:
–
(ax + b)(cx + d)(ex + f)
–
(ax + b)(cx + d) 2
–
(ax + b)(x2 + c2)
and where the degree of the numerator does not exceed that of the
denominator
• use the expansion of (1 + x)n, where n is a rational number and |x| x1), or a related probability, given the
values of x1, n, v
–
inding a relationship between x1, n and v given the value of
P(X > x1) or a related probability
• recall conditions under which the normal distribution can be used
as an approximation to the binomial distribution (n large enough to
ensure that np > 5 and nq > 5), and use this approximation, with a
continuity correction, in solving problems.
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
unit S2: Probability & Statistics 2 (Paper 7)
Knowledge of the content of unit S1 is assumed, and candidates may be required to
demonstrate such knowledge in answering questions.
Candidates should be able to:
1 The Poisson
distribution
• calculate probabilities for the distribution Po( n )
• use the fact that if X ~ Po( n ) then the mean and variance of X are
each equal to n
• understand the relevance of the Poisson distribution to the distribution
of random events, and use the Poisson distribution as a model
• use the Poisso
Cambridge International aS & a level
Mathematics
9709
For examination in June and November 2019.
Also available for examination in March 2019 for India only.
Cambridge advanced
Version 1
Changes to the syllabus for 2019
The latest syllabus is version 1, published September 2016
There are no signiicant changes which affect teaching.
you are strongly advised to read the whole syllabus before planning your teaching programme.
any textbooks endorsed to support the syllabus for examination from 2002 are still suitable for
use with this syllabus.
Cambridge International Examinations retains the copyright on all its publications. Registered Centres are
permitted to copy material from this booklet for their own internal use. However, we cannot give permission
to Centres to photocopy any material that is acknowledged to a third party even for internal use within a
Centre.
® IGCSE is the registered trademark of Cambridge International Examinations
© Cambridge International Examinations 2016
Contents
Introduction .......................................................................................................................... 2
Why choose Cambridge International Examinations?
Why Cambridge International AS & A Levels?
Why Cambridge International AS & A Level Mathematics?
Teacher support
1
Assessment at a glance ................................................................................................. 7
2
Syllabus aims and assessment objectives ................................................................... 10
2.1 Syllabus aims
2.2 Assessment objectives
3
Syllabus content ........................................................................................................... 11
4
List of formulae and tables of the normal distribution (MF9) ....................................... 28
5
Mathematical notation .................................................................................................. 33
6
Other information ......................................................................................................... 37
Equality and inclusion
Language
Grading and reporting
Entry option codes
Cambridge International aS & a level Mathematics 9709 syllabus. Introduction
Syllabus for examination in 2019.
Why choose Cambridge International Examinations?
Cambridge International Examinations prepares school students for life, helping them develop an
informed curiosity and a lasting passion for learning. We are part of Cambridge Assessment, a
department of the University of Cambridge.
Our international qualiications are recognised by the world’s best universities and employers,
giving students a wide range of options in their education and career. As a not-for-proit
organisation, we devote our resources to delivering high-quality educational programmes that can
unlock learners’ potential.
Our programmes and qualiications set the global standard for international education. They are created
by subject experts, rooted in academic rigour and relect the latest educational research. They provide a
strong platform for learners to progress from one stage to the next, and are well supported by teaching and
learning resources.
Every year, nearly a million Cambridge learners from 10 000 schools in 160 countries prepare for their future
with an international education from Cambridge.
Cambridge learners
Our mission is to provide educational beneit through provision of international programmes and
qualiications for school education and to be the world leader in this ield. Together with schools, we
develop Cambridge learners who are:
• conident in working with information and ideas – their own and those of others
• responsible for themselves, responsive to and respectful of others
• relective as learners, developing their ability to learn
• innovative and equipped for new and future challenges
• engaged intellectually and socially ready to make a difference.
Responsible
Coni dent
Relective
Cambridge
learners
Engaged
Innovative
learn more about the Cambridge learner attributes in Chapter 2 of our Implementing the curriculum
with Cambridge guide at www.cie.org.uk/curriculumguide
2
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Cambridge International aS & a level Mathematics 9709 syllabus. Introduction
Syllabus for examination in 2019.
Why Cambridge International AS & A Levels?
Cambridge International AS & A Levels are international in outlook, but retain a local relevance.
The syllabuses provide opportunities for contextualised learning and the content has been created
to suit a wide variety of schools, avoid cultural bias and develop essential lifelong skills, including
creative thinking and problem-solving.
Our aim is to balance knowledge, understanding and skills in our qualiications to enable students to become
effective learners and to provide a solid foundation for their continuing educational journey. Cambridge
International AS & A Levels give learners building blocks for an individualised curriculum that develops their
knowledge, understanding and skills.
Cambridge International AS & A Level curricula are lexible. It is possible to offer almost any combination
from a wide range of subjects. Cambridge International A Level is typically a two-year course, and
Cambridge International AS Level is typically one year. Some subjects can be started as a Cambridge
International AS Level and extended to a Cambridge International A Level.
There are three possible assessment approaches for Cambridge International AS & A Level:
Option two
Option three
(remainder of A Level)
Cambridge International
aS level
Cambridge International
aS level
(standalone AS)
(AS is irst half of A Level)
Learners take the Cambridge
International AS Level only. The
syllabus content for Cambridge
International AS Level is half
of a Cambridge International
A Level programme.
Learners take the Cambridge
International AS Level in Year 1 and
in Year 2 complete the Cambridge
International A Level.
Cambridge
International
a level
Year 1
Option one
Year 2
Cambridge International
a level
Learners take all papers of the
Cambridge International A Level course
in the same examination series, usually
at the end of the second year of study.
Every year thousands of learners with Cambridge International AS & A Levels gain places at leading
universities worldwide. Cambridge International AS & A Levels are accepted and valued by top
universities around the world including those in the UK, US (including Ivy League universities), European
nations, Australia, Canada and New Zealand. Learners should check the university website for speciic
entry requirements before applying.
Did you know?
In some countries universities accept Cambridge International AS Levels in their own right as
qualiications counting towards entry to courses in the same or other related subjects. Many learners
who take Cambridge International AS Levels also choose to progress to Cambridge International
A Level.
learn more
For more details go to www.cie.org.uk/recognition
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3
Cambridge International aS & a level Mathematics 9709 syllabus. Introduction
Syllabus for examination in 2019.
Why Cambridge International AS & A Level Mathematics?
about the syllabus
Cambridge International AS & A Level Mathematics is accepted by universities and employers as proof of
mathematical knowledge and understanding. Successful candidates gain lifelong skills, including:
• a deeper understanding of mathematical principles
• the further development of mathematical skills including the use of applications of mathematics in the
context of everyday situations and in other subjects that they may be studying
• the ability to analyse problems logically, recognising when and how a situation may be represented
mathematically
• the use of mathematics as a means of communication
• a solid foundation for further study.
The syllabus allows Centres lexibility to choose from three different routes to AS Level Mathematics – Pure
Mathematics only or Pure Mathematics and Mechanics or Pure Mathematics and Probability & Statistics.
Centres can choose from three different routes to Cambridge International A Level Mathematics depending
on the choice of Mechanics, or Probability & Statistics, or both, in the broad area of ‘applications’.
Guided learning hours
Guided learning hours give an indication of the amount of contact time teachers need to have with learners
to deliver a particular course. Our syllabuses are designed around 180 guided learning hours for Cambridge
International AS Level, and around 360 guided learning hours for Cambridge International A Level.
These igures are for guidance only. The number of hours needed to gain the qualiication may vary
depending on local practice and the learners’ previous experience of the subject.
Prior learning
We recommend that learners who are beginning this course should have previously completed a Cambridge
O Level or Cambridge IGCSE® course in Mathematics or the equivalent
Progression
Cambridge International A Level Mathematics provides a suitable foundation for the study of Mathematics
or related courses in higher education.
Cambridge International AS Level Mathematics is the irst half of Cambridge International A Level
Mathematics. Depending on local university entrance requirements, the qualiication may permit or assist
progression directly to university courses in Mathematics or some other subjects.
We recommend learners check the Cambridge recognitions database and the university websites to ind the
most up-to-date entry requirements for courses they wish to study.
4
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Cambridge International aS & a level Mathematics 9709 syllabus. Introduction
Syllabus for examination in 2019.
How can I ind out more?
If you are already a Cambridge school
You can make entries for this qualiication through your usual channels. If you have any questions,
please contact us at info@cie.org.uk
If you are not yet a Cambridge school
Learn more about the beneits of becoming a Cambridge school from our website
at www.cie.org.uk/startcambridge
Email us at info@cie.org.uk to ind out how your organisation can register to become a
Cambridge school.
Cambridge AICE
Cambridge AICE Diploma is the group award of the Cambridge International AS & A Level. It gives schools
the opportunity to beneit from offering a broad and balanced curriculum by recognising the achievements
of candidates who pass examinations from different curriculum groups.
learn more
For more details go to www.cie.org.uk/aice
Our research has shown that students who came to the university with a
Cambridge AICE background performed better than anyone else that came to the
university. That really wasn’t surprising considering the emphasis they have on critical
research and analysis, and that’s what we require at university.
John Barnhill, Assistant Vice President for Enrollment Management, Florida State University, USA
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5
Cambridge International aS & a level Mathematics 9709 syllabus. Introduction
Syllabus for examination in 2019.
Teacher support
We offer a wide range of practical and innovative support to help teachers plan and deliver our
programmes and qualiications conidently.
The support package for our Cambridge International AS & A Levels gives teachers access to a worldwide
teaching community enabling them to connect with other teachers, swap ideas and share best practice.
Teaching and learning
Exam preparation
• Support materials provide teachers with ideas and
planning resources for their lessons.
• Past question papers and mark schemes so
teachers can give learners the opportunity
to practise answering different questions.
• Endorsed textbooks, ebooks and digital resources
are produced by leading publishers. We have
quality checked these materials to make sure they
provide a high level of support for teachers and
learners.
• Resource lists to help support teaching,
including textbooks and websites.
Professional development
• Example candidate responses help teachers
understand exactly what examiners are looking for.
• Principal examiner reports describing learners’
overall performance on each part of the papers.
The reports give insight into common
misconceptions shown by learners, which teachers
can address in lessons.
Cambridge
International
AS & A Level
support for
teachers
Face-to-face training
We hold workshops around the world to support
teachers in delivering Cambridge syllabuses and
developing their skills.
Online training
We offer self-study and tutor-led online training
courses via our virtual learning environment. A
wide range of syllabus-speciic courses and skills
courses is available. We also offer training via
video conference and webinars.
Qualiications
learn more
Find out more about support for this
syllabus at www.cie.org.uk/alevel
Visit our online resource bank and community
forum at https://teachers.cie.org.uk
useful links
Customer Services
http://linkd.in/cambridgeteacher
www.cie.org.uk/help
@cie_education
www.facebook.com/cie.org.uk
We offer a wide range of practice-based qualiications
at Certiicate and Diploma level, providing a
framework for continuing professional development.
6
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Cambridge International aS & a level Mathematics 9709 syllabus. Assessment at a glance
Syllabus for examination in 2019.
1
assessment at a glance
The 7 units in the scheme cover the following subject areas:
• Pure Mathematics (units P1, P2 and P3);
• Mechanics (units M1 and M2);
• Probability & Statistics (units S1 and S2).
Centres and candidates may:
• take all four Advanced (A) Level components in the same examination series for the full Cambridge
International A Level;
• follow a staged assessment route to the Cambridge International A Level by taking two Advanced
Subsidiary (AS) papers (P1 and M1 or P1 and S1) in an earlier examination series;
• take the Advanced Subsidiary (AS) qualiication only.
Cambridge International AS Level candidates take:
Paper 1: Pure Mathematics 1 (P1)
1 hour 45 minutes
About 10 shorter and longer questions
75 marks weighted at 60% of total
plus one of the following papers:
Paper 2: Pure Mathematics
2 (P2)
Paper 4: Mechanics 1 (M1)
Paper 6: Probability &
Statistics 1 (S1)
1 hour 15 minutes
1 hour 15 minutes
1 hour 15 minutes
About 7 shorter and longer
questions
About 7 shorter and longer
questions
About 7 shorter and longer
questions
50 marks weighted at 40%
of total
50 marks weighted at 40%
of total
50 marks weighted at 40%
of total
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Cambridge International aS & a level Mathematics 9709 syllabus. Assessment at a glance
Syllabus for examination in 2019.
Cambridge International A Level candidates take:
Paper 1: Pure Mathematics 1 (P1)
Paper 3: Pure Mathematics 3 (P3)
1 hour 45 minutes
1 hour 45 minutes
About 10 shorter and longer questions
About 10 shorter and longer questions
75 marks weighted at 30% of total
75 marks weighted at 30% of total
plus one of the following combinations of two papers:
Paper 4: Mechanics 1 (M1)
Paper 6: Probability & Statistics 1 (S1)
1 hour 15 minutes
1 hour 15 minutes
About 7 shorter and longer questions
About 7 shorter and longer questions
50 marks weighted at 20% of total
50 marks weighted at 20% of total
Paper 4: Mechanics 1 (M1)
Paper 5: Mechanics 2 (M2)
1 hour 15 minutes
1 hour 15 minutes
About 7 shorter and longer questions
About 7 shorter and longer questions
50 marks weighted at 20% of total
50 marks weighted at 20% of total
Paper 6: Probability & Statistics 1 (S1)
Paper 7: Probability & Statistics 2 (S2)
1 hour 15 minutes
1 hour 15 minutes
About 7 shorter and longer questions
About 7 shorter and longer questions
50 marks weighted at 20% of total
50 marks weighted at 20% of total
or
or
8
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Cambridge International aS & a level Mathematics 9709 syllabus. Assessment at a glance
Syllabus for examination in 2019.
Question papers
There is no choice of questions in any of the question papers and questions will be arranged approximately
in order of increasing mark allocations.
It is expected that candidates will have a calculator with standard ‘scientiic’ functions available for use
for all papers in the examination. Computers, graphical calculators and calculators capable of algebraic
manipulation are not permitted.
A list of formulae and tables of the normal distribution (MF9) is supplied for the use of candidates in the
examination. Details of the items in this list are given for reference in section 4.
Relationships between units
Units P2, M2, S2 are sequential to units P1, M1, S1 respectively, and the later unit in each subject area may
not be used for certiication unless the corresponding earlier unit is being (or has already been) used.
Unit P3 is also sequential to unit P1, and may not be used for certiication unless P1 is being (or has already
been) used. The subject content of unit P2 is a subset of the subject content of unit P3; otherwise, the
subject content for different units does not overlap, although later units in each subject area assume
knowledge of the earlier units.
Availability
This syllabus is examined in the June and November examination series. This syllabus is also available for
examination in March for India only.
This syllabus is available to private candidates.
Detailed timetables are available from www.cie.org.uk/timetables
Combining this with other syllabuses
Candidates can combine this syllabus in an examination series with any other Cambridge syllabus, except:
• syllabuses with the same title at the same level.
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9
Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus aims and assessment objectives
Syllabus for examination in 2019.
2
Syllabus aims and assessment objectives
2.1 Syllabus aims
The aims of the syllabus are the same for all students. These are set out below and describe the educational
purposes of any course based on the Mathematics units for the Cambridge International AS & A Level
examinations. The aims are not listed in order of priority.
The aims are to enable candidates to:
• develop their mathematical knowledge and skills in a way which encourages conidence and provides
satisfaction and enjoyment
• develop an understanding of mathematical principles and an appreciation of mathematics as a logical
and coherent subject
• acquire a range of mathematical skills, particularly those which will enable them to use applications of
mathematics in the context of everyday situations and of other subjects they may be studying
• develop the ability to analyse problems logically, recognise when and how a situation may be
represented mathematically, identify and interpret relevant factors and, where necessary, select an
appropriate mathematical method to solve the problem
• use mathematics as a means of communication with emphasis on the use of clear expression
• acquire the mathematical background necessary for further study in this or related subjects.
2.2 Assessment objectives
The abilities assessed in the examinations cover a single area: technique with application.
The examination will test the ability of candidates to:
• understand relevant mathematical concepts, terminology and notation
• recall accurately and use successfully appropriate manipulative techniques
• recognise the appropriate mathematical procedure for a given situation
• apply combinations of mathematical skills and techniques in solving problems
• present mathematical work, and communicate conclusions, in a clear and logical way.
10
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
3
Syllabus content
The mathematical content for each unit in the scheme is detailed below. The order in which topics are listed
is not intended to imply anything about the order in which they might be taught.
As well as demonstrating skill in the appropriate techniques, candidates will be expected to apply their
knowledge in the solution of problems. Individual questions set may involve ideas and methods from more
than one section of the relevant content list.
For all units, knowledge of the content of Cambridge O Level/Cambridge IGCSE Mathematics is assumed.
Candidates will be expected to be familiar with scientiic notation for the expression of compound units,
e.g. 5 m s–1 for 5 metres per second.
unit P1: Pure Mathematics 1 (Paper 1)
Candidates should be able to:
1 Quadratics
• carry out the process of completing the square for a quadratic
polynomial ax 2 + bx + c and use this form, e.g. to locate the vertex of
the graph of y = ax 2 + bx + c or to sketch the graph
• ind the discriminant of a quadratic polynomial ax 2 + bx + c and use
the discriminant, e.g. to determine the number of real roots of the
equation ax 2 + bx + c = 0
• solve quadratic equations, and linear and quadratic inequalities, in one
unknown
• solve by substitution a pair of simultaneous equations of which one is
linear and one is quadratic
• recognise and solve equations in x which are quadratic in some
function of x, e.g. x 4 – 5x 2 + 4 = 0.
2 Functions
• understand the terms function, domain, range, one-one function,
inverse function and composition of functions
• identify the range of a given function in simple cases, and ind the
composition of two given functions
• determine whether or not a given function is one-one, and ind the
inverse of a one-one function in simple cases
• illustrate in graphical terms the relation between a one-one function
and its inverse.
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
3 Coordinate
geometry
• ind the length, gradient and mid-point of a line segment, given the
coordinates of the end-points
• ind the equation of a straight line given suficient information (e.g. the
coordinates of two points on it, or one point on it and its gradient)
• understand and use the relationships between the gradients of parallel
and perpendicular lines
• interpret and use linear equations, particularly the forms y = mx + c
and y – y1 = m(x – x1)
• understand the relationship between a graph and its associated
algebraic equation, and use the relationship between points of
intersection of graphs and solutions of equations (including, in simple
cases, the correspondence between a line being tangent to a curve
and a repeated root of an equation).
4 Circular measure
• understand the deinition of a radian, and use the relationship
between radians and degrees
• use the formulae s = r i and A = 1 r2 i in solving problems concerning
2
the arc length and sector area of a circle.
5 Trigonometry
• sketch and use graphs of the sine, cosine and tangent functions (for
angles of any size, and using either degrees or radians)
• use the exact values of the sine, cosine and tangent of 30°, 45°, 60°,
and related angles, e.g. cos 150° = – 1 3
2
• use the notations sin−1x, cos−1x, tan−1x to denote the principal values of
the inverse trigonometric relations
sin i
• use the identities
/ tan i and sin2 i + cos2 i / 1
cos i
• ind all the solutions of simple trigonometrical equations lying in a
speciied interval (general forms of solution are not included).
6 Vectors
x
• use standard notations for vectors, i.e. , xi + yj,
y
AB , a
x
y , xi + yj + zk,
z
• carry out addition and subtraction of vectors and multiplication of a
vector by a scalar, and interpret these operations in geometrical terms
• use unit vectors, displacement vectors and position vectors
• calculate the magnitude of a vector and the scalar product of two
vectors
• use the scalar product to determine the angle between two directions
and to solve problems concerning perpendicularity of vectors.
12
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
7 Series
• use the expansion of (a + b)n , where n is a positive integer (knowledge
of the greatest term and properties of the coeficients are not
JKn NO
required, but the notations KKr OO and n! should be known)
L P
• recognise arithmetic and geometric progressions
• use the formulae for the nth term and for the sum of the irst n terms
to solve problems involving arithmetic or geometric progressions
• use the condition for the convergence of a geometric progression,
and the formula for the sum to ininity of a convergent geometric
progression.
8 Differentiation
• understand the idea of the gradient of a curve, and use the notations
2
dy
dy
and
(the technique of differentiation from irst
2
dx
dx
principles is not required)
f’(x), f’’(x),
• use the derivative of xn (for any rational n), together with constant
multiples, sums, differences of functions, and of composite functions
using the chain rule
• apply differentiation to gradients, tangents and normals, increasing
and decreasing functions and rates of change (including connected
rates of change)
• locate stationary points, and use information about stationary points
in sketching graphs (the ability to distinguish between maximum
points and minimum points is required, but identiication of points of
inlexion is not included).
9 Integration
• understand integration as the reverse process of differentiation,
and integrate (ax + b)n (for any rational n except –1), together with
constant multiples, sums and differences
• solve problems involving the evaluation of a constant of integration,
e.g. to ind the equation of the curve through (1, –2) for which
dy
= 2x + 1
dx
• evaluate deinite integrals (including simple cases of ‘improper’
integrals, such as
yx
1
0
1
-2
yx
3
d x and
1
-2
d x)
• use deinite integration to ind:
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–
the area of a region bounded by a curve and lines parallel to the
axes, or between two curves
–
a volume of revolution about one of the axes.
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
unit P2: Pure Mathematics 2 (Paper 2)
Knowledge of the content of unit P1 is assumed, and candidates may be required to
demonstrate such knowledge in answering questions.
Candidates should be able to:
1 algebra
• understand the meaning of x, and use relations such as
a = b ⇔ a2 = b2 and x – a < b ⇔ a – b < x < a + b in the
course of solving equations and inequalities
• divide a polynomial, of degree not exceeding 4, by a linear or quadratic
polynomial, and identify the quotient and remainder (which may be
zero)
• use the factor theorem and the remainder theorem, e.g. to ind
factors, solve polynomial equations or evaluate unknown coeficients.
2 logarithmic
and exponential
functions
• understand the relationship between logarithms and indices, and use
the laws of logarithms (excluding change of base)
• understand the deinition and properties of ex and In x, including their
relationship as inverse functions and their graphs
• use logarithms to solve equations of the form ax = b, and similar
inequalities
• use logarithms to transform a given relationship to linear form, and
hence determine unknown constants by considering the gradient
and/or intercept.
3 Trigonometry
• understand the relationship of the secant, cosecant and cotangent
functions to cosine, sine and tangent, and use properties and graphs
of all six trigonometric functions for angles of any magnitude
• use trigonometrical identities for the simpliication and exact
evaluation of expressions and, in the course of solving equations,
select an identity or identities appropriate to the context, showing
familiarity in particular with the use of:
4 Differentiation
–
sec2 i ≡ 1 + tan2 i and cosec2 i ≡ 1 + cot2 i
–
the expansions of sin(A ± B), cos(A ± B) and tan(A ± B)
–
the formulae for sin 2A, cos 2A and tan 2A
–
the expressions of a sin i + b cos i in the forms R sin ^i ! ah and
R cos ^i ! ah .
• use the derivatives of ex, In x, sin x, cos x, tan x, together with constant
multiples, sums, differences and composites
• differentiate products and quotients
• ind and use the irst derivative of a function which is deined
parametrically or implicitly.
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
5 Integration
• extend the idea of ‘reverse differentiation’ to include the integration of
1 , sin(ax + b), cos(ax + b) and sec2 (ax + b) (knowledge of
ax + b
the general method of integration by substitution is not required)
eax + b,
• use trigonometrical relationships (such as double-angle formulae) to
facilitate the integration of functions such as cos2 x
• use the trapezium rule to estimate the value of a deinite integral,
and use sketch graphs in simple cases to determine whether the
trapezium rule gives an over-estimate or an under-estimate.
6 Numerical
solution of
equations
• locate approximately a root of an equation, by means of graphical
considerations and/or searching for a sign change
• understand the idea of, and use the notation for, a sequence of
approximations which converges to a root of an equation
• understand how a given simple iterative formula of the form
xn + 1 = F(xn) relates to the equation being solved, and use a given
iteration, or an iteration based on a given rearrangement of an
equation, to determine a root to a prescribed degree of accuracy
(knowledge of the condition for convergence is not included, but
candidates should understand that an iteration may fail to converge).
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
unit P3: Pure Mathematics 3 (Paper 3)
Knowledge of the content of unit P1 is assumed, and candidates may be required to
demonstrate such knowledge in answering questions.
Candidates should be able to:
1 algebra
• understand the meaning of |x|, and use relations such as
a = b ⇔ a2 = b2 and x – a < b ⇔ a – b < x < a + b in the
course of solving equations and inequalities
• divide a polynomial, of degree not exceeding 4, by a linear or quadratic
polynomial, and identify the quotient and remainder (which may be
zero)
• use the factor theorem and the remainder theorem, e.g. to ind
factors, solve polynomial equations or evaluate unknown coeficients
• recall an appropriate form for expressing rational functions in partial
fractions, and carry out the decomposition, in cases where the
denominator is no more complicated than:
–
(ax + b)(cx + d)(ex + f)
–
(ax + b)(cx + d) 2
–
(ax + b)(x2 + c2)
and where the degree of the numerator does not exceed that of the
denominator
• use the expansion of (1 + x)n, where n is a rational number and |x| x1), or a related probability, given the
values of x1, n, v
–
inding a relationship between x1, n and v given the value of
P(X > x1) or a related probability
• recall conditions under which the normal distribution can be used
as an approximation to the binomial distribution (n large enough to
ensure that np > 5 and nq > 5), and use this approximation, with a
continuity correction, in solving problems.
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Cambridge International aS & a level Mathematics 9709 syllabus. Syllabus content
Syllabus for examination in 2019.
unit S2: Probability & Statistics 2 (Paper 7)
Knowledge of the content of unit S1 is assumed, and candidates may be required to
demonstrate such knowledge in answering questions.
Candidates should be able to:
1 The Poisson
distribution
• calculate probabilities for the distribution Po( n )
• use the fact that if X ~ Po( n ) then the mean and variance of X are
each equal to n
• understand the relevance of the Poisson distribution to the distribution
of random events, and use the Poisson distribution as a model
• use the Poisso