ZIMBABWE
MINISTRY OF PRIMARY AND SECONDARY EDUCATION
PURE MATHEMATICS
SYLLABUS
FORMS 3 - 4
2015 - 2022
Curriculum Development and Technical Services
P.O. Box MP 133
Mount Pleasant
Harare
© All Rights Reserved
2015
Pure Mathematics Syllabus Forms 3 - 4
ACKNOWLEDGEMENTS
The Ministry of Primary and Secondary Education wishes to acknowledge the following for their valued
contribution in the development of this syllabus:
•
•
Panellists for Form 3-4 Pure Mathematics
Representatives of the following organizations:
- Zimbabwe School Examinations Council (ZIMSEC)
- Uunited Nations Children’s Fund (UNICEF )
- United Nations Cultural, Scientific and Cultural Organisation (UNESCO)
i
Pure Mathematics Syllabus Forms 3 - 4
CONTENTS
ACKNOWLEDGEMENTS.....................................................................................................i
CONTENTS...........................................................................................................................ii
1.0 PREAMBLE....................................................................................................................1
2.0 PRESENTATION OF SYLLABUS..................................................................................1
3.0 AIMS................................................................................................................................1
4.0 SYLLABUS OBJECTIVES.............................................................................................2
5.0 METHODOLOGY............................................................................................................2
6.0 TOPICS...........................................................................................................................2
7.0 SCOPE AND SEQUENCE..............................................................................................3
8.0 COMPTETNCY MATRIX.................................................................................................7
8.2 FORM 4 COMPETENCY MATRIX..................................................................................13
9.0 ASSESSMENT................................................................................................................20
ii
Pure Mathematics Syllabus Forms 3 - 4
1.0 PREAMBLE
calculus.
1.1 Introduction
1.4 Assumption
In developing the Form 3 - 4 Pure Mathematics syllabus
attention was paid to the need to provide continuity of
mathematical concepts from Form 1through to Form
4 and lay foundations for further studies, focusing
on learners who have the ability and interest. It is
assumed that learners who take this syllabus will take it
concurrently with the Form 1 - 4 Mathematics syllabus.
The syllabus is intended to produce a citizen who is a
critical thinker and problem solver in life.The two year
learning phase will provide learners with opportunities
to apply Mathematical concepts in other subject areas
and enhance Mathematical literacy and numeracy. It also
desires to produce a learner with the ability to communicate effectively.
In learning Pure Mathematics, learners should be helped
to acquire a variety of skills, knowledge and processes,
and develop positive attitude towards the subject and in
life. This will enable them to investigate and interpret numerical and spatial relationships as well as patterns that
exist in the world. The syllabus also caters for learners
with diverse needs to experience Pure Mathematics as
relevant and worthwhile.
1.2 Rationale
Zimbabwe is undergoing a socio-economic transformation where Pure Mathematics is key to development,
therefore it is imperative that learners acquire necessary
mathematical knowledge and skills to enable as many
learners as possible to proceed to Form 5-6 Mathematics
and beyond. The knowledge of Pure Mathematics
enables learners to develop mathematical skills such
as dealing with the abstract, presenting mathematical
arguments, interpreting mathematical information and
solving problems essential in life and for sustainable
development. The importance of Ppure Mmathematics
can be underpinned in inclusivity, human dignity and
enterprise as it plays a pivotal role in careers such as
reserach, actuarial science, materology and engineering
The syllabus assumes that the learner has:
1.4.1 mastered concepts and skills involving number,
algebra and geometry at Form 1 and 2 level
1.4.2 shown interest in pursuing Pure Mathematics
1.4.3 the ability to operate some ICT tools
1.5 Cross Cutting Themes
The following are some of the cross cutting themes in
Pure Mathematics:1.5.1
1.5.2
1.5.3
1.5.4
1.5.5
1.5.6
Financial literacy
Disaster risk management
Collaboration
Environmentalissues
Enterprise skills
Sexuality, HIV & AIDS Education
2.0 PRESENTATION OF
SYLLABUS
The Pure Mathematics syllabus is presented as singledocument covering Form 3 - 4.It contains the preamble,
aims, syllabus objectives, syllabus topics, scope and
sequence and competency matrix. The syllabus also
suggests a list of resources that could be used during
learning and teaching process.
3.0 AIMS
This syllabus is intended to provide a guideline for Form
3 - 4 learners which will enable them to:
3.1
3.2
1.3 Summary of Content (Knowledge,
Skills and Attitudes)
3.3
The syllabus will cover the theoretical and practical
aspects of Pure Mathematics. This two year learning
area will cover: algebra, coordinate geometry and
3.4
1
acquire a firm foundation for further studies
and future careers
use ICT tools for learning and solving mathematical problems
develop an ability to apply Pure Mathematics
in life and other subjects, particularly Science
and Technology
develop a further understanding of mathematical concepts and processes in a way that
Pure Mathematics Syllabus Forms 3 - 4
3.5
3.6
3.7
encourages confidence, enjoyment, interest
and lifelong learning
appreciate Pure Mathematics as a basis for
applying the learning area in a variety of life
situations
develop the ability to solve problems, reason
clearly and logically as well as communicate
mathematical ideas successfully
acquire enterprise skills in an indigenised and
globalised economy through research and
project-based learning
contexts. The teaching and learning of Pure Mathematics
must be learner centred and ICT driven. The following
are suggested methods of the teaching and learning of
Pure Mathematics
•
•
•
•
•
•
•
•
4.0 SYLLABUS OBJECTIVES
5.1 Time Allocation
Six periods of 40 minutes each per week should be
allocated for the adequate coverage of the syllabus
By the end of the two year learning period, the learners
should be able to:
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
Guided discovery
Group work
Interactive e-learning
Games and puzzles
Quiz
Problem solving
Simulation and modelling
Experimentation
6.0 TOPICS
use relevant mathematical symbols, terms and
definitions in problem solving
use formulae and generalisations to solve a
variety of problems in Pure Mathematics and
other related learning areas
formulate problems into mathematical terms
and apply appropriate techniques for solutions
use ICT tools for learning through problem
solving
apply Pure Mathematics concepts and principles in life
demonstrate an appreciation of mathematical
concepts and processes
demonstrate an ability to solve problems systematically, applying mathematical reasoning
communicate mathematical concepts and
principles clearly
explore ways of solving routine and non-routine problems in Pure Mathematics using appropriate formulae, algorithms and strategies
model mathematical information from one form
to another e.g. verbal/words to symbolic form
conduct research projects including those
related to enterprise
The following topics will be covered from Form 3 - 4
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
5.0 METHODOLOGY
It is recommended that teachers use methods and
techniques in which Pure Mathematics is seen as a
process which arouses an interest and confidence
in tackling problems both in familiar and unfamiliar
2
Indices and irrational numbers
Polynomials
Identities, equations and inequalities
Graphs and coordinate geometry
Vectors
Functions
Sequences
Binomial expansions
Trigonometry
Logarithmic and exponential functions
Differentiation
Integration
Numerical methods
3
Polynomials
Surds
Components of polynomials
Addition
Subtraction
Partial fractions





Definition of identity
Unknown coefficients
Equations
Quadratic inequalities
Cubic inequalities
FORM 3
Pure Mathematics Syllabus Form 3 – 4 2016
Inequalities
Identities and equations
SUB TOPIC




Multiplication
Division
Factor Theorem
Solving equations
FORM 4


5
Completing the square
Simultaneous equations
FORM 4
TOPIC 3: IDENTITIES, EQUATIONS AND INEQUALITIES




FORM 3
TOPIC 3: IDENTITIES, EQUATIONS AND INEQUALITIES

SUB TOPIC
TOPIC 2: POLYNOMIALS

Irrational numbers
Laws of indices
Equations involving indices
TOPIC 2: POLYNOMIALS


FORM 3
Indices
SUB TOPIC
FORM 4
TOPIC 1: INDICES AND IRRATIONAL NUMBERS
SCOPE AND SEQUENCE
TOPIC 1: INDICES AND IRRATIONAL NUMBERS
7.0
7.0 SCOPE AND SEQUENCE
Pure Mathematics Syllabus Forms 3 - 4
Straight line graphs
Gradient of a line segment
Distance between two points
Coordinates of the mid-point
• Types of vectors
• Vector operations
Vecors in three dimensions
4
• Definition of a function
• Domain and range
• Composite function
Functions
Pure Mathematics Syllabus Form 3 – 4 2016
FORM 3
SUB TOPIC
TOPIC 6: FUNCTIONS
FORM 3
TOPIC 5: VECTORS




FORM 3
SUB TOPIC
Coordinate geometry
Graphs
SUB TOPIC
Graphs of𝑦𝑦 = 𝑘𝑘𝑥𝑥 𝑛𝑛
Unit vectors
Scalar product
Vector properties of plane shapes
Areas of triangles and parallelogram
8
• One- one funcion
• Inverse of a function
• Graphs of functions
FORM 4
•
•
•
•
FORM 4

FORM 4
TOPIC 4: GRAPHS AND COORDINATE GEOMETRY
TOPIC 4: GRAPHS AND COORDINATE GEOMETRY
Pure Mathematics Syllabus Forms 3 - 4
Definition of a sequence
Examples of sequences
5
• Sine and cosine rules
• Area of a trriangle
• Trigonometrical functions for angles of any size
• Exact values of sine, cosine and tangent of special
angles
Plane Trigonometry
Trigonometric functions
Pure Mathematics Syllabus Form 3 – 4 2016
FORM 3
TOPIC 9: TRIGONOMETRY
FORM 3
TOPIC 8: BINOMIAL EXPANSION


FORM 3
SUB TOPIC
Binomial expansion
SUB TOPIC
Sequences
SUB TOPIC
TOPIC 7: SEQUENCES
TOPIC 7: SEQUENCES
Arithmetic progression
Geometric progression
11
• Equations
• Radians
• Length of an arc
• Area of a sector
• Area of a segment
FORM 4
• Pasdcal’s Triangle
• Exapnsion of (a+b) n where n is a positive integer
FORM 4


FORM 4
Pure Mathematics Syllabus Forms 3 - 4
Laws of logarithms
Logarithms and indices
6
SUB TOPIC
Pure Mathematics Syllabus Form 3 – 4 2016
Numerical methods
FORM 3
TOPIC 13: NUMERICAL METHODS
•
•
•
Integration
14
Indefinite integration as the reverse process
of differentiation
Integration of functions of the formaxn
Integration of a polynomial
FORM 3
TOPIC 12: INTEGRATION
FORM
FORM 33
 Gradient of a curve at a point
 Derived function of the form axn
 Derivative of a sum
TOPIC 11: DIFFERENTIATION


FORM 3
SUB TOPIC
SUB
TOPIC
TOPIC
Differentiation
TOPIC 11: DIFFERENTIATION
Exponential functions
Logarithms
SUB TOPIC
Exponential growth and decay
Natural logarithms
Equations of the form a x = b
Area
Volume
•
•
•
Simple iterative procedures
Newton Reaphson method
Trapezium Rule
FORM 4
•
•
FORM 4
FORM
FORM44
 Application of differentiation to gradients,
tangents and normals, stationary points,
rates of change, velocity and acceleration



FORM 4
TOPIC 10: LOGARITHMIC AND EXPONENTIAL FUNCTIONS
TOPIC 10: LOGARITHMIC AND EXPONENTIAL FUNCTIONS
Pure Mathematics Syllabus Forms 3 - 4







define irrational numbers
reduce a surd to its simplest form
carry out the four operations on
surds
rationalise denominators
state the laws of indices
use laws of indices to simplify
algebraic expressions
solve equations involving indices
Learners should be able to:
OBJECTIVES
Pure Mathematics Syllabus Form 3 – 4 2016
Irrational numbers
Indices
SUB TOPIC



Surds
Laws of indices
Equations involving
indices
CONTENT: {Skills,
Knowledge, Attitudes}
TOPIC 1: INDICES AND IRRATIONAL NUMBERS
COMPETENCY MATRIX: FORM 3 SYLLABUS
FORM THREE
(3) SYLLABUS
FORM 3 COMPTETNCY
MATRIX
TOPIC 1: INDICES AND IRRATIONAL NUMBERS
8.0
8.1
8.0 COMPTETNCY MATRIX
7








18
Distinguishing between rational and
irrational numbers
Deriving and finding ways of
simplifying surds
Expressing surds in simple form
Carrying out the four operations on
surds
Rationalising denominators
Deriving the laws of indices
Simplifying algebraic expressions
Applying laws of indices to solve
problems
SUGGESTED NOTES AND ACTIVITIES




ICT tools
Relevant texts
ICT tools
Relevant texts
SUGGESTED
RESOURCES
Pure Mathematics Syllabus Forms 3 - 4





define polynomials
carry out
operations
of
identify
proper
and improper
addition and subtraction of
fractions
carry
out operations of addition and
polynomials
subtraction
polynomials
express aoffunction
as a sum of
express a function as a sum of
simpler fractions
simpler fractions
fractions
 identify
proper
andto:
improper
Learners
should
be able
OBJECTIVES
 define polynomials


Subtraction
Partial fractions
CONTENT: {Skills,
Knowledge,
Attitudes}
CONTENT:
{Skills, of
 Components
Knowledge,
Attitudes}
polynomials
 Addition
 Components of
 polynomials
Subtraction
 Addition
Partial fractions
Distinguishing between proper
and improper fractions
 Discussing polynomials
Adding and subtracting
 Distinguishing
between proper and
polynomials
improper
fractions
 Adding
and subtracting
polynomials
Decomposing
functions
into
 Decomposing
functions
into
fractions
fractions with linear
with linear denominators
denominators

SUGGESTED
NOTES
AND ACTIVITIES
 Discussing
polynomials
SUGGESTED NOTES AND
ACTIVITIES

Learners should be able to:
OBJECTIVES
8
Pure Mathematics Syllabus Form 3 – 4 2016
distinguish between an identity and
an equation
 use identities to determine
unknown coefficients in
polynomials
 solve cubic equations using Factor
Theorem
Inequalities
 factorise quadratic expressions
 solve quadratic inequalities
Pure Mathematics Syllabus
Formcubic
3 – 4inequalities
2016
 solve
with the
use of Factor Theorem
Identities and
equations
SUB TOPIC
Definition of identity
Unknown coefficients
Equations
Quadratic inequalities
Cubic inequalities





CONTENT: (Skills,
Knowledge, Attitudes)







19
Factorising quadratic expressions
Finding solutions of quadratic
12
inequalities
Exploring ways of solving cubic
inequalities
Using the Factor Theorem to solve
cubic inequalities
Discussing the difference between an
and anequation
equation
identity andan
Finding unknown coefficients using
identities
Using the Factor Theorem to solve
cubic equations
SUGGESTED NOTES AND ACTIVITIES
TOPIC 3: IDENTITIES, EQUATIONS AND INEQUALITIES
TOPIC
3:IDENTITIES,
EQUATIONS
AND INEQUALITIES
TOPIC
3: IDENTITIES,
EQUATIONS
AND INEQUALITIES
Polynomials
Polynomials
SUB
TOPIC
OBJECTIVES
TOPIC 2: POLYNOMIALS
Learners should be able to:
TOPIC 2: POLYNOMIALS
SUB TOPIC
TOPIC 2: POLYNOMIALS
ICT tools
Relevant texts




Relevant texts
ICT tools
ICT tools
Relevant texts
SUGGESTED
RESOURCES


SUGGESTED
 ICT tools
RESOURCES
 Relevant texts
SUGGESTED
RESOURCES
Pure Mathematics Syllabus Forms 3 - 4
9








calculate the distance between two
points given in coordinate form
solve practical problems involving
distance between two points
find the coordinates of the mid-point
of a straight line
sketch straight lines
find the gradient of a line segment
find the equation of a straight line
identify parallel and perpendicular
lines
solve problems involving straight line
graphs
Learners should be able to:
OBJECTIVES
Pure Mathematics Syllabus Form 3 – 4 2016
Coordinate geometry
Graphs
SUB TOPIC
TOPIC 4:GRAPHS AND COORDINATE GEOMETRY




Distance between two
points
Coordinates of the midpoint
Straight line graphs
Gradient of a line
segment
CONTENT: {Skills,
Knowledge, Attitudes}
TOPIC 4: GRAPHS AND COORDINATE GEOMETRY









21
Sketching straight lines given
sufficient information
Exploring how to find equation of a
straight line given two points or the
gradient and a point
Distinguishing between parallel and
perpendicular lines
Solving problems involving straight
line graphs
Identifying examples in life where
linear relationships occur
Carrying out experiments involving
linear relationships
Exploring ways to find distance
between two points
Calculating coordinates of the midpoint of a straight line
Conducting field work to solve
problems involving distance between
two points
SUGGESTED NOTES AND ACTIVITIES






Geo-board
ICT tools
Environment
Geo-board
ICT tools
Environment
SUGGESTED
RESOURCES
Pure Mathematics Syllabus Forms 3 - 4
10
TOPIC 6: FUNCTIONS
determineposition and free vectors
identify parallel vectors and co-linear
points
calculate the modulus of a vector
add and subtract vectors
multiply a vector by a scalar
𝐴𝐴𝐴𝐴
xi+yj+zk,→ , a


define a function
define domain and range of a
function
use functional notation
simplify a composite function
Learners should be able to:


𝑥𝑥
use standard notation of vectors (𝑦𝑦𝑧𝑧),
OBJECTIVES






Learners should be able to:
OBJECTIVES
Pure Mathematics Syllabus Form 3 – 4 2016
Functions
SUB TOPIC
TOPIC 6:FUNCTIONS
Vectors in three
dimensions
SUB TOPIC
TOPIC 5: VECTORS
TOPIC 5: VECTORS
Types of vectors
Vector operations



Definition of a function
Domain and range
Composite function
CONTENT: {Skills,
Knowledge, Attitudes}


CONTENT: {Skills,
Knowledge, Attitudes}
𝐴𝐴𝐴𝐴
xi+yj+zk, → , a
Distinguishing between positionand
free vectors
Interpreting operations in geometrical
terms
Computing the magnitude of vectors
in three dimensions
Adding and subtracting vectors
Finding a product of a vector by a
scalar
Solving problems involving vector
operations
𝑥𝑥
(𝑦𝑦𝑧𝑧),
Using standard notation of vectors




22
Identifying and defining functions
Discussing the domain and the range
Using functional notations
Simplifying composite functions
SUGGESTED NOTES AND ACTIVITIES







SUGGESTED NOTES AND ACTIVITIES
ICT tools
Mathematical
models
Environment
Geo-board
Relevant texts


ICT tools
Relevant texts
SUGGESTED
RESOURCES





SUGGESTED
RESOURCES
Pure Mathematics Syllabus Forms 3 - 4


define a sequence
list the elements of a sequence
Learners should be able to:
OBJECTIVES
Composite function


Definition of a
sequence
Examples of
sequences
CONTENT: {Skills,
Knowledge, Attitudes}

OBJECTIVES
11
Trigonometrical
functions
Plane Trigonometry
SUB TOPIC




find the trigonometrical ratios of
angles of any size
use the exact values of the
trigonometrical ratios of special
angles in a variety of situations
find the area of a triangle
2
use sine and cosine rules to solve
problems
1
use the formula 𝐴𝐴 = 𝑎𝑎𝑎𝑎 sin 𝐶𝐶 to
Learners should be able to:
OBJECTIVES
Pure Mathematics Syllabus Form 3 – 4 2016
TOPIC 9: TRIGONOMETRY
Learners should be able to:
Learners should be able to:
OBJECTIVES
TOPIC 9: TRIGONOMETRY
expansion
Binomial
Binomial
expansion
SUB TOPIC
SUB TOPIC
TOPIC 8:BINOMIAL EXPANSION




Trigonometrical
functions for angles of
any size
Exact values of sine,
cosine and tangent of
special angles
Sine and cosine rules
Area of a triangle
CONTENT: {Skills,
Knowledge, Attitudes}
Attitudes}
Tobe
becovered
covered
in form
To
in form
4
4
CONTENT: {Skills,
CONTENT:
{Skills,
Knowledge,
Knowledge, Attitudes}
TOPIC 8: BINOMIAL EXPANSION
TOPIC 8:BINOMIAL EXPANSION
Sequences
SUB TOPIC
TOPIC 7: SEQUENCES
use functional notation
simplify a composite function
TOPIC 7: SEQUENCES








Deriving formulae for the sine and
cosine rules
Solving problems using the sine and
cosine rules
Deriving the formula for finding area
of a triangle
Solving problems involving area of a
triangle
Computing the trigonometrical ratios
of angles of any size
Calculating the exact values of the
sine, cosine and tangent of 0°, 30°,
45° ,60°, 90° in a variety of situations
15
SUGGESTED NOTES AND ACTIVITIES
SUGGESTED NOTES AND
Discussing sequences
Outlining elements of sequences
SUGGESTED
ACTIVITIESNOTES AND ACTIVITIES


SUGGESTED NOTES AND ACTIVITIES


range
Using functional notations
Simplifying composite
functions




ICT tools
Relevant texts
ICT tools
Relevant texts
SUGGESTED
RESOURCES
SUGGESTED
ICT tools
Relevant texts
SUGGESTED
RESOURCES
RESOURCES


SUGGESTED
RESOURCES
Pure Mathematics Syllabus Forms 3 - 4

Exact values of
sine, cosine and
tangent of special
angles
Learners should be able to:
logarithms and indices
 state the laws of logarithms
 use the laws of logarithms in solving
problems
 identify the relationships between
OBJECTIVES
12

TOPIC 12: INTEGRATION
differentiate a polynomial



recognise indefinite integration as the
reverse process of differentiation
integrate functions of the form axn
where n is rational
integrate polynomials
Learners should be able to:
OBJECTIVES
Pure Mathematics Syllabus Form 3 – 4 2016
Integration
SUB TOPIC


Calculating the exact values of
the sine, cosine and tangent of
0°, 30°, 45° ,60°, 90° in a
variety of situations


Indefinite integration as the
reverse process of
differentiation
Integration of functions of
the form axn
Integration of a polynomial
CONTENT: {Skills,
Knowledge, Attitudes}




and vice versa
Exploring the laws of logarithms
Applying laws of logarithms in solving
problems
Expressing logarithms in index form
SUGGESTED NOTES AND ACTIVITIES




17



Discussing indefinite integration as
the reverse process of
differentiation
Performing integration of functions
of the form axn where n is rational
Computing indefinite integrals of
polynomials
SUGGESTED NOTES AND
ACTIVITIES
Calculating the gradient of a
using
tangents
the gradient
of a in
curve
 Calculating
Discussing
situations
life
at where
a given point
using
tangents
gradients of curves
Discussing situations in life where
are important
gradients of curves are important
 Differentiating
Differentiating
and
linearlinear
and quadratic
quadratic
expressions
from
expressions from first principles
Differentiating
functions of the form
first principles
n using the formula
ax
 Differentiating functions of
the form axn using the
formula

SUGGESTED NOTES AND
curve at a given point
ACTIVITIES
16
CONTENT: {Skills,
SUGGESTED NOTES AND
Knowledge, Attitudes} ACTIVITIES
Laws of logarithms
Logarithms and indices
CONTENT: {Skills,
Knowledge, Attitudes}
find the gradient of a curve at a
 Gradient of a curve
CONTENT: {Skills,
point using the tangent
at a point
Knowledge,
Attitudes}
Learners should be able to:
 differentiate linear and quadratic  Derived function of
n
 find
the gradient of
a curve
a point
 Gradient
of aax
curve
at a
expressions
from
firstatprinciples
the form
using the tangent
point
 find the derivative of functions of  Derivative of a sum
 differentiate linear
and quadratic
 Derived function of the
the form from
axn where
n is a rational
expressions
first principles
form axn
number
 find
the derivative of functions of the
 Derivative of a sum
n
ax where n ais polynomial
a rational number
 form
differentiate

OBJECTIVES
TOPIC 12: INTEGRATION
Differentiation
SUB TOPIC
Differentiation
TOPIC 11: DIFFERENTIATION
Pure Mathematics
Syllabus
Form 3 – 4 2016
SUB
TOPIC
OBJECTIVES
TOPIC 11: DIFFERENTIATION
Learners should be able to:
TOPIC 11: DIFFERENTIATION
Logarithms
SUB TOPIC

TOPIC 10: LOGARITHMIC AND EXPONENTIAL FUNCTIONS
use the exact values of the
trigonometrical ratios of
special angles in a variety of
situations
TOPIC 10: LOGARITHMIC AND EXPONENTIAL FUNCTIONS




ICT tools
Relevant texts
Environment
texts
Environment
ICT tools



ICT tools
Relevant texts
Environment
SUGGESTED
RESOURCES


SUGGESTED
RESOURCES
ICT tools
Relevant texts
SUGGESTED
 Relevant
RESOURCES


SUGGESTED
RESOURCES
Pure Mathematics Syllabus Forms 3 - 4
13
Learners should be able to:
OBJECTIVES
Covered in form 3
CONTENT: {Skills,
Knowledge, Attitudes}
TOPIC 1: INDICES AND IRRATIONAL NUMBERS
Pure Mathematics Syllabus Form 3 – 4 2016
Irrational numbers
Indices
SUB TOPIC
FORM FOUR (4) SYLLABUS
To be covered in form 4
FORM 4COMPETENCY MATRIX
COMPETENCY MATRIX: FORM 4 SYLLABUS
8.2
Learners should be able to:
OBJECTIVES
TOPIC 1: INDICES AND IRRATIONAL NUMBERS
8.0
Iterative methods
SUB TOPIC
SUGGESTED NOTES AND
ACTIVITIES
30
SUGGESTED NOTES AND ACTIVITIES
CONTENT: {Skills, Knowledge,
Attitudes}
TOPIC 13: NUMERICAL METHODS
TOPIC 13: NUMERICAL METHODS
SUGGESTED
RESOURCES
SUGGESTED
RESOURCES
Pure Mathematics Syllabus Forms 3 - 4
Learners
should
be able to:
TOPIC
2: POLYNOMIALS
OBJECTIVES
multiply polynomials
polynomial by
Learners
should be able to:
another
use thepolynomials
Factor Theorem to
 multiply
factorise
polynomials
 divide one polynomial
by another
 use
thecubic
Factorequations
Theorem to using
factorise
solve
polynomials
the Factor Theorem
 solve cubic equations using the
 Factor
use Factor
Theorem to
Theorem
evaluate
 use
Factor unknown
Theorem tocoefficients
evaluate




Division
Factor Theorem
Solving equations
14




express ax2 + bx + c in the form
d(x+e)2+f
derive the quadratic formula
solve quadratic equations by
completing the square
solve simultaneous equations by
substitution
Learners should be able to:
OBJECTIVES
Pure Mathematics Syllabus Form 3 – 4 2016
Pure Mathematics Syllabus Form 3 – 4 2016
Identities and
equations
SUB TOPIC










Completing the square
Simultaneous equations
CONTENT: {Skills,
Knowledge, Attitudes}




32
20
Exploring ways of expressing ax2 +
bx + c in the form d(x+e)2+f
Completing the square to derive the
quadratic formula
Solving quadratic equations by
completing the square
Solving simultaneous equations (one
linear and one implicit) by
substitution
SUGGESTED NOTES AND ACTIVITIES
using the Factor Theorem
texts
ICT tools
Relevant texts
ICT tools


ICT tools
Relevant texts
SUGGESTED
RESOURCES
Usinglong division to find the
quotient and
Determining
theremainder
product of

polynomials
Deriving the Factor theorem

Usinglong
find the quotient
Using thedivision
Factorto Theorem
to
and remainder
factorise polynomials
Deriving the Factor theorem
Solving cubic equations using
Using the Factor Theorem to
the Factor
Theorem
factorise
polynomials
Evaluating
Solving
cubic unknown
equations using the
Factor
Theorem
coefficients
using the Factor
Evaluating
unknown
coefficients
Theorem


Determining the product of
SUGGESTED
 Relevant
RESOURCES
SUGGESTED
RESOURCES

SUGGESTED
NOTES AND ACTIVITIES
polynomials
SUGGESTED NOTES AND
ACTIVITIES
TOPIC 3: IDENTITIES, EQUATIONS AND INEQUALITIES
unknown coefficients
OBJECTIVES
 divide one
CONTENT: {Skills,
Knowledge,
Attitudes}
 Multiplication
CONTENT:
{Skills,
 Division
Knowledge, Attitudes}
 Factor Theorem
Solving equations
 Multiplication
TOPIC 3: IDENTITIES, EQUATIONS AND INEQUALITIES
Polynomials
SUB TOPIC
Polynomials
TOPIC 2: POLYNOMIALS
SUB TOPIC
Pure Mathematics Syllabus Forms 3 - 4
15
TOPIC 5: VECTORS
sketch graphs of the form 𝑦𝑦 = 𝑘𝑘𝑥𝑥 𝑛𝑛
explain the geometrical effect of the
value of k on the shape of the graph
of 𝑦𝑦 = 𝑘𝑘𝑥𝑥 𝑛𝑛






calculate unit vectors
define the scalar product
use the scalar product to determine
the angle between vectors
identify vector properties of
quadrilaterals
solve problems involving
perpendicular vectors
calculate areas of triangles and
parallelograms
Learners should be able to:
OBJECTIVES


Learners should be able to:
OBJECTIVES
Pure Mathematics Syllabus Form 3 – 4 2016
Vectors in three
dimensions
SUB TOPIC
TOPIC 5:VECTORS
Graphs
SUB TOPIC
TOPIC 4:GRAPHS AND COORDINATE GEOMETRY
Graphs of 𝑦𝑦 = 𝑘𝑘𝑥𝑥 𝑛𝑛




Unit vectors
Scalar product
Vector properties of
plane shapes
Areas of triangles and
parallelograms
CONTENT: {Skills,
Knowledge, Attitudes}

CONTENT: {Skills,
Knowledge, Attitudes}
TOPIC 4: GRAPHS AND COORDINATE GEOMETRY
Sketching the standard curves where
n and k are rational
Discussing the geometrical effect of
the value of k on the shape of the
graph for a given value of n






34
Computing unit vectors
Discussing the scalar product
Determining the angle between
vectors
Exploring vector properties of
quadrilaterals
Solving problems involving
perpendicular vectors
Computing areas of triangles and
parallelograms
SUGGESTED NOTES AND ACTIVITIES


SUGGESTED NOTES AND ACTIVITIES
ICT tools
Relevant texts
Geo-board



ICT tools
Mathematical
models
Environment
SUGGESTED
RESOURCES



SUGGESTED
RESOURCES
Pure Mathematics Syllabus Forms 3 - 4






16




derive the formulas for the general
terms of the AP and GP
use the formula for the nth term of an
AP and GP
derive the formula for the sum of the
first n terms of an AP and GP and
use it to solve problems
distinguish between APs and GPs
Learners should be able to:
OBJECTIVES
Pure Mathematics Syllabus Form 3 – 4 2016
Sequences
SUB TOPIC
TOPIC 7: SEQUENCES
define a one-one function
restrict the domain to get a one-one
function
sketch the graph of a function for a given
domain
define the inverse of a function
find the inverse of a given function
illustrate graphically the relationship
between a function and its inverse
Learners should be able to:
OBJECTIVES
TOPIC 7: SEQUENCES
Functions
SUB TOPIC
TOPIC 6: FUNCTIONS
TOPIC 6: FUNCTIONS
One-one function
Inverse of a function
Graphs of functions


Arithmetic progression
Geometric progression
CONTENT: {Skills,
Knowledge, Attitudes}



CONTENT: {Skills,
Knowledge, Attitudes}
Discussing one-one functions
Sketching graphs of functions for a
given domain
Discussing the inverse of a function
Determining the range of functions
Determining the inverse of a given
function excluding inverses of
quadratic functions
Illustrating graphically the
relationship between a function and
its inverse





36
Exploring ways of finding the formula
for the general term of an AP and a
GP
Solving problems using the formula
for the nth term of an AP and a GP
Exploring ways of finding the
formulae of the sum of the first n
terms of an AP and a GP and solving
problems
Differentiating APs from GPs
Discussing applications of APs and
GPs in life
SUGGESTED NOTES AND ACTIVITIES






SUGGESTED NOTES AND
ACTIVITIES
ICT tools
Relevant texts
Geo-board


ICT tools
Relevant texts
SUGGESTED
RESOURCES



SUGGESTED
RESOURCES
Pure Mathematics Syllabus Forms 3 - 4

define a radian
Learners should be able to:
OBJECTIVES
17

convert degrees to radians and
find area of a sector and a segment
solve
defineproblems
a radianinvolving length of
arcs,the
areas
of sectors
andnotation
segments
use
correct
radian
formulae for the area of a
sector and segment
24
Equations
Radians
Length of an arc
Area of a sector
Area of a segment
Pure Mathematics Syllabus Form 3 – 4 2016





Knowledge, Attitudes}
Discussing radians and degrees
and their relationship
 Using the correct radian notation
SUGGESTED
NOTES
 Converting degrees
to AND
radians and
radians to degrees
ACTIVITIES
 Deriving and using the formulae for
length of an arc
 Discussing
radians and
 degrees
Deriving and
using
the formulae for
and
their
the area of a sector and segment
relationship
 Solving problems involving length of
 Using
the correct
radian
arcs, areas
of sectors
and
notation
segments
Discussing the
notationto
sin-1x, tan-1x
 Converting
degrees
-1x
and
cos
radians and radians to
 Finding all the solutions, within a
degrees
specified interval of the equations
 Deriving
usingand
thetan(kx)=c
sin(kx)=c,and
cos(kx)=c
for length of equations
an arc
 formulae
Applying trigonometrical
in
solving
life
problems
 Deriving and using the

SUGGESTED NOTES AND
ACTIVITIES
38
convert degrees to radians and
radians to degrees
 find the length of an arc
-1
use area
the notation
sin-1x, tan
 find
of a sector
andx and
a
cos-1x to solve problems
segment
 Solve trigonometrical equations
 solve problems involving length
of arcs, areas of sectors and
segments





 find the length of an arc
Learners
should be able to:
OBJECTIVES
radians to degrees
 Radians
 Length of an arc
 Area of a sector
CONTENT:
 Area of a {Skills,
segment
CONTENT: {Skills,
Knowledge, Attitudes}
ACTIVITIES
 Constructing Pascal’s Triangle
Making use ofPascal’s
the Pascal’s
Triangle
 Constructing
Triangle
to expand (𝑎𝑎 + 𝑏𝑏)n where n is a
 Making use of the Pascal’s Triangle
positive integer
to expand (𝑎𝑎 + 𝑏𝑏)n where n is a
 positive
Solving problems
integer involving
expansion of (𝑎𝑎 + 𝑏𝑏)n
 Solving problems involving
expansion of (𝑎𝑎 + 𝑏𝑏)n
SUGGESTED NOTES AND
ACTIVITIES
Pure Mathematics Syllabus Form 3 – 4 2016
Trigonometrical
functions
Plane
Trigonometry
SUB TOPIC
TOPIC 9: TRIGONOMETRY
 use the correct radian notation
Plane Trigonometry
SUB TOPIC
integer
Knowledge,
Attitudes}
 Pascal’s Triangle
Expansion
of (𝑎𝑎 +
 Pascal’s
Triangle
𝑏𝑏)nwhere n is a positive
 Expansion of (𝑎𝑎 + 𝑏𝑏)n
integern is a positive
where
TOPIC 9: TRIGONOMETRY
Learners
should
be ableTriangle
to:
 construct
a Pascal’s
n
expand (𝑎𝑎a+Pascal’s
𝑏𝑏) using
Pascal’s
 construct
Triangle
Triangle
n
 expand (𝑎𝑎 + 𝑏𝑏) using Pascal’s
 Triangle
solve problems involving
expansion of (𝑎𝑎 + 𝑏𝑏)n
 solve problems involving
expansion of (𝑎𝑎 + 𝑏𝑏)n
Learners should be able to:
OBJECTIVES
TOPIC 9: TRIGONOMETRY
Binomial expansion
Binomial expansion
SUB TOPIC
CONTENT: {Skills,
Knowledge, Attitudes}
TOPIC 8: BINOMIAL EXPANSION
TOPIC 8: BINOMIAL EXPANSION


Relevant texts
Environment
ICT tools
Relevant texts
Environment
Geo-board
Geometrical
 instruments
ICT tools





SUGGESTED
RESOURCES
ICT tools
 ICT tools
 Relevant texts
 Environment
SUGGESTED
 Geo-board
RESOURCES
 Geometrical
instruments

RESOURCES
 Relevant texts
ICT tools texts
 Relevant
SUGGESTED
RESOURCES
Pure Mathematics Syllabus Forms 3 - 4
18











find the equation of a tangent and a
normal to quadratic and cubic curves
determine stationary points and their
nature
find the rate of change of one
variable with respect to another
solve problems involving rates of
change
Learners should be able to:
OBJECTIVES
Pure Mathematics Syllabus Form 3 – 4 2016
Differentiation
SUB TOPIC











Application of differentiation
to gradients, tangents and
normals, stationary points,
rates of change, velocity and
acceleration
Determining equations of
tangents and normals to
quadratic and cubic curves
 Discussing the nature of, and
solving problems involving,
stationary points
 Calculating the rate of change of
one variable with respect to
another
 Solving problems involving rates
40
of change in life

SUGGESTED NOTES AND
ACTIVITIES
Discussing the concept of
exponential growth and decay
Sketching the graph of the
exponential function and compare
with the logarithmic function
Formulating equations involving
exponential growth and decay
Solving equations involving
exponential growth and decay
Discussing the natural logarithms in
relation to logarithms in general
Sketching the graphs of the form
y=ln(ax+b)
Solving equations of the form a x = b
using logarithms
SUGGESTED NOTES AND
ACTIVITIES
CONTENT: {Skills, Knowledge,
Attitudes}
Exponential growth and
decay
Natural logarithms
Equations of the form
ax= b
CONTENT: {Skills,
Knowledge, Attitudes}
TOPIC 11: DIFFERENTIATION
explain the concept of exponential
growth and decay
sketch the graph of the exponential
function
solve equations involving
exponential growth and decay
formulate equations involving
exponential growth and decay
define the natural logarithm
sketch the graph of the form
y=ln(ax+b)
use logarithms to solve equations of
the form a x = b
Learners should be able to:
OBJECTIVES
TOPIC 11: DIFFERENTIATION
Exponential
functions
Logarithms
SUB TOPIC
TOPIC 10: LOGARITHMIC AND EXPONENTIAL FUNCTIONS
TOPIC 10: LOGARITHMIC AND EXPONENTIAL FUNCTIONS
ICT tools
Relevant texts
Geo-board
ICT tools
Relevant texts
Geo-board



ICT tools
Relevant texts
Environment
SUGGESTED
RESOURCES






SUGGESTED
RESOURCES
Pure Mathematics Syllabus Forms 3 - 4


19
Area
Volume
CONTENT: {Skills, Knowledge,
Attitudes}
• locate
locatethe
theposition
positionofofroots
rootsby
bysign • Simple
Simpleiterative
iterativeprocedures
procedures
sign change
Newton-Raphsonmethod
method
change
• Newton-Raphson

solve
equations
by
the
bisection
TrapeziumRule
Rule
• solve equations by the bisection
• Trapezium
method
method
usesimple
simpleiterative
iterativeprocedures
• use
proceduresand the Newtonand the Newton-Raphson method
Raphson method to solve
toequations
solve equations
• estimate
estimateareas
areasunder
undercurves
curvesusing
the
Trapezium
Rule Rule
using
the Trapezium
Learners should be able to:
OBJECTIVES
Pure Mathematics Syllabus Form 3 – 4 2016
Numerical
Numerical methods
methods
SUB TOPIC


CONTENT: {Skills, Knowledge,
Attitudes}
TOPIC 13: NUMERICAL METHODS
compute area bounded by
acurveand a lineparallel to the
coordinate axes
calculatethe volume of revolution
about one of the axes
Learners should be able to:
OBJECTIVES
TOPIC 13: NUMERICAL METHODS
Integration
SUB TOPIC
TOPIC 12: INTEGRATION
TOPIC 12: INTEGRATION
Exploring ways of finding area
bounded by a curve and a line
parallel to the coordinate axes
Exploring ways of finding the
volume of revolution about one
of the axes
Solving problems involving use
of integration in determining
areas and volumes
ICT tools
Relevant texts
Environment
SUGGESTED
RESOURCES



SUGGESTED
RESOURCES
42
• Determining
• ICT
Determiningthe
theexistence
existenceofof
ICTtools
tools
rootswithin
withinan
aninterval
interval
Relevanttexts
texts
roots
• Relevant

Using
the
bisection
methodto
Environment
• Using the bisection method to
• Environment
solveequations
equationstotoaaspecific
specific
solve
degree of accuracy
degree of accuracy
 Solving equations using simple
• Solving equations using simple
iterative procedures and the
iterative
proceduresmethod
and the
Newton-Raphson
Newton-Raphson
method
 Determiningestimates of area
• Determining
estimates
of area
under curves
and related
areas
under
related Rule
areas in
in lifecurves
by the and
Trapezium
life by the Trapezium Rule
SUGGESTED NOTES AND
ACTIVITIES



SUGGESTED NOTES AND
ACTIVITIES
Pure Mathematics Syllabus Forms 3 - 4
Pure Mathematics Syllabus Forms 3 - 4
9.0 ASSESSMENT
(a) ASSESSMENT OBJECTIVES
The assessment will test candidate’s ability to:•
•
•
•
•
•
•
•
•
•
use Mathematical symbols, terms and definitions correctly in problem solving
sketch graphs accurately
use appropriate formulae,algorithms and strategies, to solve routine and non-routine problems in Pure Mathematics
demonstrate the appropriate and accurate use of ICT tools in problem solving
translate Mathematical information from one form to another accurately
demonstrate an appreciation of Mathematical concepts and processes
demonstrate an ability to solve problems systematically
apply Mathematical reasoning and communicate mathematical ideas clearly
model information from other forms to Mathematical form and vice versa
conduct research projects including those related to enterprise
(b) SCHEME OF ASSESSMENT
The Form 3 - 4Pure Mathematics assessment will be based on 30% Continuous Assessment and 70% Summative
Assessment.
The syllabus’ scheme of assessment caters for all learners and does not condone direct or indirect discrimination.
Arrangements, accommodations and modifications must be visible in both continuous and summative assessments to
enable candidates with special needs to access assessments and receive accurate performance measurement of their
abilities. Access arrangements must neither give these candidates an undue advantage over others nor compromise
the standards being assessed.
Candidates who are unable to access the assessments of any component or part of component due to disability
(transitory or permanent) may be eligible to receive an award based on the assessment they would have taken
Continuous Assessment
Continuous assessment will consists of topic tasks, written tests and end of term examinations:
i) Topic Tasks
These are activities that teachers use in their day to day teaching. These may include projects, assignments and team
work activities.
ii) Written Tests
These are tests set by the teacher to assess the concepts covered during a given period of up to a month. The tests
should consist of short structured questions as well as long structured questions.
iii) End of term examinations
These are comprehensive tests of the whole term’s or year’s work. These can be set at school/district/provincial level.
Summary of Continuous Assessment Tasks
From term one to five, candidates are expected to have done at least the following recorded tasks per term:
• 1 Topic task
• 1 Written test
• 1 End of term test
20
Summary of Continuous Assessment Tasks
From term one to five, candidates are expected to have done at least the following recorded tasks per term:

1 Topic task

1 End of term test
 1
Written test Syllabus Forms 3 - 4
Pure
Mathematics
Detailed Continuous Assessment Tasks Table
Detailed Continuous Assessment Tasks Table
Term
Number
of Topic
Tasks
Number of
Written
Tests
Number of
End Of Term
Tests
1
1
1
1
2
1
1
1
3
1
1
1
4
1
1
1
5
1
1
1
Weighting
25%
25%
50%
100%
Actual Weight
7.5%
7.5%
15%
30%
Comment:
Total
Term 6 is for the National Examination
c)(c)Specification
Grid
Specification Grid
Pure Mathematics Syllabus Form 3 – 4 2016
25
Specification grid for continuous assessment
Component
Skills
Topic Tasks
Written Tests
End of Term
Skill 1
30%
30%
30%
50%
50%
50%
20%
20%
20%
Total
100%
100%
100%
Actual
weighting
7.5%
7.5%
15%
Knowledge
Comprehension
Skill 2
Application
Analysis
Skill 3
Synthesis
Evaluation
Summative Assessment
The examination will consist of 2 papers: paper 1 and paper 2, each to be written in 2½ hours
Pure Mathematics Syllabus Form 3 – 4 2016
26
21
Type of Paper
Approximately 16questions
15 Short
where
Answer
candidates
Questions,
answer any
where
10, each
Pure Mathematics Syllabus
3-4
candidatesForms
question
answer all
carrying 10
questions
marks
Summative Assessment
Marks
100
100
The examination will consist of 2 papers: paper 1 and paper 2, each to be written in 2½ hours
P1
P2
Total
Weighting
50%
50%
100%
Actual weighting
35%
35%
70%
Type of paper
Approximately 15 Short Answer
Questions, where candidates anwer all
questions
16 Questions where
candidates answer
any 10, each question
carrying 10 marks
Marks
100
100
Specification Grid for Summative Assessment
Specification Grid for Summative Assessment
Skill 1
P1
P2
Total
50%
30%
80%
Knowledge
&
Pure Mathematics
Syllabus Form 3 – 4 2016
27
Comprehension
Skill 2
40%
50%
90%
10%
20%
30%
Total
100%
100%
200%
Weighting
50%
50%
100%
Application &
Analysis
Skill 3
Synthesis &
Evaluation
(d) Assessment Model
Learners will be assessed using both continuous and summative assessments.
Assessment of learner performance in Pure Mathematics
100%
Pure Mathematics Syllabus Form 3 – 4 2016
28
22
Pure Mathematics Syllabus Forms 3 - 4
d) Assessment Model
Assessment of learner performance in Pure Mathematics
100%
Summative assessment
70%
Continuous assessment
30%
Profiling
Topic Tasks
7.5%
Written Tests
7.5%
End of term
Tests 15%
Paper 1
35%
Paper 2
35%
Profile
Continuous assessment
30%
Examination Mark 100%
Exit Profile
FINAL MARK 100%
23
Pure Mathematics Syllabus Forms 3 - 4
25
Pure Mathematics Syllabus Forms 3 - 4
26