Recent Scheme of Work on Further Mathematics

Syllabus for Senior Secondary




FIRST TERM
SSS 1 SSS 2 SSS 3
WEEK 1: Revision
WEEK 1: Revision
WEEK 1: Revision
WEEK 2

Theme: Pure Mathematics

Topic: Sets

Sub-Topic:
Content:
1. Definition of set
2. Set notation methods
3. Types of sets :
- Null set
- Singleton set
- Finite and infinite set
- Subsets
- Universal set
- Power set
4. Set operations :
- Union
- Intersection
- Complement - Number of elements in a set
5. Venn diagrams and applications up to 3 set problem
WEEK 2

Theme: Pure Mathematics

Topic: Roots of quadratic equation

Sub-Topic:
Content:
1. Sum and product of roots of quadratic equation α+β = -b/a; αβ = c/a
2. Finding quadratic equation given sum and product of roots x2 – (sum of roots) + (product) = 0
3. Condition for quadratic equation to have
- Equal roots (b2 = 4ac)
- Real roots (b2 > 4ac)
- No roots (b2 < 4ac)
4. Conditions for given line to intersect a curve, be tangent to curve, not intersect a curve.
5. Solution of problems on roots of quadratic equation
WEEK 2

Theme: Pure Mathematics

Topic: Inequalities

Sub-Topic:
Content:
1. Quadratic inequalities
2. Inequalities in two dimensions
WEEK 3

Theme: Pure Mathematics

Topic: Sets (Cont.)

Sub-Topic:
Content:
1. Definition of set
2. Set notation methods
3. Types of sets :
- Null set
- Singleton set
- Finite and infinite set
- Subsets
- Universal set
- Power set
4. Set operations :
- Union
- Intersection
- Complement - Number of elements in a set
5. Venn diagrams and applications up to 3 set problem
WEEK 3

Theme: Pure Mathematics

Topic: Roots of quadratic equation (Cont.)

Sub-Topic:
Content:
1. Sum and product of roots of quadratic equation α+β = -b/a; αβ = c/a
2. Finding quadratic equation given sum and product of roots x2 – (sum of roots) + (product) = 0
3. Condition for quadratic equation to have
- Equal roots (b2 = 4ac)
- Real roots (b2 > 4ac)
- No roots (b2 < 4ac)
4. Conditions for given line to intersect a curve, be tangent to curve, not intersect a curve.
5. Solution of problems on roots of quadratic equation
WEEK 3

Theme: Pure Mathematics

Topic: Matrices & determinants(2x2, 3x3)

Sub-Topic:
Content:
1. Basic definitions
2. Matrices as linear transformations
3. Determinants
4. Solutions of 2 and 3 simultaneous equations.
WEEK 4

Theme: Pure Mathematics

Topic: Binary operation

Sub-Topic:
Content:
1. Definition of binary operation
2. Laws of binary operations :
- Associative law
- Commutative law
- Distributive law
- Laws of complementation as in sets
- Identify elements
- Inverse of an element
3. Multiplication tables of binary operations
WEEK 4

Theme: Pure Mathematics

Topic: Polynomials

Sub-Topic:
Content:
1. Definition of polynomials
2. Division of polynomials by a polynomial of lesser degree
3. Remainder theorem
4. Factorisation of polynomial
5. Roots of cubic equation
- Sum of roots α+β+δ = - b/a
- Sum of products of two roots αβ+αδ+βδ = c/a
- Product of roots αβδ = - d/a
Where ax3 + bx2 + cx + d = 0
WEEK 4

Theme: Pure Mathematics

Topic: Matrices & determinants(2x2, 3x3) (Cont.)

Sub-Topic:
Content:
1. Basic definitions
2. Matrices as linear transformations
3. Determinants
4. Solutions of 2 and 3 simultaneous equations.
WEEK 5

Theme: Pure Mathematics

Topic: Indices

Sub-Topic:
Content:
1. Laws of indices
am x an = am + n
am ÷ an = am – n
(am)n = amn
a0 = 1
a-n = 1/an
1/an = n/a
2. Application of indices
-solution of indicial equations up to quadratic equations
WEEK 5

Theme: Pure Mathematics

Topic: Polynomials (cont.)

Sub-Topic:
Content:
1. Definition of polynomials
2. Division of polynomials by a polynomial of lesser degree
3. Remainder theorem
4. Factorisation of polynomial
5. Roots of cubic equation
- Sum of roots α+β+δ = - b/a
- Sum of products of two roots αβ+αδ+βδ = c/a
- Product of roots αβδ = - d/a
Where ax3 + bx2 + cx + d = 0
WEEK 5

Theme: Pure Mathematics

Topic: Partial fractions

Sub-Topic:
Content:
1. Basic definitions
2. Proper rational functions with denominators as linear factors (distinct and repeated) and others.
WEEK 6

Theme: Pure Mathematics

Topic: Logarithm

Sub-Topic:
Content:
1. Laws of logarithms :
- Loga(xy) = logax + logay
- Loga = logax - logay
- Logaxn = nlogax
- Logaa = 1
- Loga1 = 0
Where a ≠ 1
- Logax = o when x=1
2. Change of base of logarithms i.e
logax = 1/(logxa) = (logxx)/(logxa)
WEEK 6

Theme: Pure Mathematics

Topic: Logical reasoning II

Sub-Topic:
Content:
1. Fundamental issues in intelligent system 2. Fundamental definition
3. Modelling the world
4. Introduction to propositional and predicate logical resolution
5 Introduction to theorem proving
WEEK 6

Theme: Pure Mathematics

Topic: Integration

Sub-Topic:
Content:
1. Understand integration as the reverse process of differentiation, Integrate Algebraic polynomials including 1/X, logarithmic function.
2. Definite integrals and application to kinematics. Apply to V-t and S-t graphs
3. Areas under the curve. Trapezoidal rule. Volume of solids of revolution
WEEK 7

Theme: Pure Mathematics

Topic: Surds

Sub-Topic:
Content:
1 Definition of surds
2. Rules for manipulating surds.
3. Rationalization of the denominator
WEEK 7

Theme: Pure Mathematics

Topic: Trigonometry function

Sub-Topic:
Content:
1. Knowledge of six trigonometric functions of angles of any magnitude (sine, cosine, tangent, secant, cosecant, cotangent)
2. Range and domain of specified trigonometry
3. Graphs of trigonometric ratios with emphasis on their amplitude and periodicity
4. Relationship between graphs of trig ratio e.g sin x and sin 2x graphs of y=asin(bx) + c
Y=acos(bx) + c
Y=atan(bx) + c
5. Graphs of inverse by ratios
6. Solution of simple equation involving the six trigonometric function
7. Proofs of simple trigonometric identities e.g
sin 2x +cos 2x = 1 ;
sec 2x = 1 + tan 2x etc
WEEK 7

Theme: Pure Mathematics

Topic: Integration (Cont.)

Sub-Topic:
Content:
1. Understand integration as the reverse process of differentiation, Integrate Algebraic polynomials including 1/X, logarithmic function.
2. Definite integrals and application to kinematics. Apply to V-t and S-t graphs
3. Areas under the curve. Trapezoidal rule. Volume of solids of revolution
WEEK 8

Theme: Pure Mathematics

Topic: Functions

Sub-Topic:
Content:
1. Definition of function
2. Types of functions
- One to one function
- Onto function
- Inverse function
- Identity function
- Constant function
- Circular function
- Logarithmic function
- Exponential function
- Composite function
3. Application of functions
-solutions of problems of functions
WEEK 8

Theme: Pure Mathematics

Topic: Trigonometry function (Cont.)

Sub-Topic:
Content:
1. Knowledge of six trigonometric functions of angles of any magnitude (sine, cosine, tangent, secant, cosecant, cotangent)
2. Range and domain of specified trigonometry
3. Graphs of trigonometric ratios with emphasis on their amplitude and periodicity
4. Relationship between graphs of trig ratio e.g sin x and sin 2x graphs of y=asin(bx) + c
Y=acos(bx) + c
Y=atan(bx) + c
5. Graphs of inverse by ratios
6. Solution of simple equation involving the six trigonometric function
7. Proofs of simple trigonometric identities e.g
sin 2x +cos 2x = 1 ;
sec 2x = 1 + tan 2x etc
WEEK 8

Theme: Coordinate Geometry

Topic: Conic sections

Sub-Topic:
Content:
1. Equations of parabola, Ellipse, Hyperbola in rectangular Cartesian coordinates.
2. Parametric equations
WEEK 9

Theme: Pure Mathematics

Topic: Functions (Cont.)

Sub-Topic:
Content:
1. Definition of function
2. Types of functions
- One to one function
- Onto function
- Inverse function
- Identity function
- Constant function
- Circular function
- Logarithmic function
- Exponential function
- Composite function
3. Application of functions
-solutions of problems of functions
WEEK 9

Theme: Pure Mathematics

Topic: Binomial expansion

Sub-Topic:
Content:
1. Pascal triangle
2. Binomial expansion of (a+b)n, where n is positive integer, negative integer, fractional value
3. Finding nth term
4. Application of binomial expansion
WEEK 9

Theme: Coordinate Geometry

Topic: Conic sections (Cont.)

Sub-Topic:
Content:
1. Equations of parabola, Ellipse, Hyperbola in rectangular Cartesian coordinates.
2. Parametric equations

WEEK 10: REVISION AND EXAMININATION
WEEK 10: REVISION AND EXAMININATION
WEEK 10: REVISION AND EXAMININATION
SECOND TERM
SSS 1 SSS 2 SSS 3
WEEK 1: Revision
WEEK 1: Revision
WEEK 1: Revision
WEEK 2

Theme: Pure Mathematics

Topic: Sequence

Sub-Topic:
Content:
1. Definition of sequence
2. The nth term of a sequence
WEEK 2

Theme: Pure Mathematics

Topic: Differentiation

Sub-Topic:
Content:
1. Limits of a function
2. Differentiation from first principle
3. Differentiation of polynomials
4. Differentiation of transcendental functions like sin x, eax, log 3x
5. Rules of differentiation
- Product rule
- Quotient rule
- Function of function
6. Application of differentiation to
- Rate of change
- Gradient
- Maximum and minimum values
- Equation of motion
7. Higher derivatives
8. Differentiation of implicit function
WEEK 2

Theme: Statistics And Probability

Topic: Correlation

Sub-Topic:
Content:
1. Concept of correlation as measure of relationships.
2. Scatter diagrams
3. Rank correlation
4. Tied ranks
WEEK 3

Theme: Pure Mathematics

Topic: Series

Sub-Topic:
Content:
1. Definition of series
2. The nth sum of a series
3. Arithmetic and geometric progressive
WEEK 3

Theme: Pure Mathematics

Topic: Differentiation (Cont.)

Sub-Topic:
Content:
1. Limits of a function
2. Differentiation from first principle
3. Differentiation of polynomials
4. Differentiation of transcendental functions like sin x, eax, log 3x
5. Rules of differentiation
- Product rule
- Quotient rule
- Function of function
6. Application of differentiation to
- Rate of change
- Gradient
- Maximum and minimum values
- Equation of motion
7. Higher derivatives
8. Differentiation of implicit function
WEEK 3

Theme: Statistics And Probability

Topic: Probability distributions and approximations

Sub-Topic:
Content:
1. Binomial
2. Poisson
3. Normal distributions
4. Binomial approximations by Poisson distributions
5. Normal approximations by binomial distribution
WEEK 4

Theme: Pure Mathematics

Topic: Linear inequalities

Sub-Topic:
Content:
1. Linear inequalities in one variable
2. Linear inequalities in two variables
3. Graphs of linear inequalities in two variables
WEEK 4

Theme: Coodinate Geometry

Topic: Conic section: the circle

Sub-Topic:
Content:
1. Definition of circle
2. Equation of circle given center and radius
3. General equation of a circle
4. Finding center and radius of a given circle
5. Finding equation of a circle given the end point of the diameter
6. Equation of circle passing throught 3 points equation of tangent to a circle
7. Length of tangent to a circle
WEEK 4

Theme: Statistics And Probability

Topic: Probability distributions and approximations (Cont.)

Sub-Topic:
Content:
1. Binomial
2. Poisson
3. Normal distributions
4. Binomial approximations by Poisson distributions
5. Normal approximations by binomial distribution
WEEK 5

Theme: Pure Mathematics

Topic: Trigonometry ratios of special angles

Sub-Topic:
Content:
1. Trigonometric ratios of 30o,45o, 60o
2. Application of trigonometric ratios of 30o,45o, 60o
WEEK 5

Theme: Coodinate Geometry

Topic: Conic section: the circl (Cont.)

Sub-Topic:
Content:
1. Definition of circle
2. Equation of circle given center and radius
3. General equation of a circle
4. Finding center and radius of a given circle
5. Finding equation of a circle given the end point of the diameter
6. Equation of circle passing throught 3 points equation of tangent to a circle
7. Length of tangent to a circle
WEEK 5

Theme: Statistics And Probability

Topic: Variance

Sub-Topic:
Content:
1. Mean
2. Variance
3. Coefficient of variance of Binomial, Poisson and Normal distributions.
WEEK 6

Theme: Pure Mathematics

Topic: Logical reasoning

Sub-Topic:
Content:
1. Meaning of statements
2. Negation and contrapositive of statements
3. Antecedents and consequences of statements
4. Conditional statements
WEEK 6

Theme: Statistics

Topic: Probability

Sub-Topic:
Content:
1. Classical, frequential and axiomative approaches to probability
2. Sample space and event space
3. Mutually exclusive, independent and conditional events
4. Conditional probability
5. Probability trees.
WEEK 6

Theme: Mechanics

Topic: Statics

Sub-Topic:
Content:
1. Forces in equilibrium
2. Resultant of parallel forces (in the same direction and in opposite directions) acting on a rigid body.
3. Moment of a force (2 and 3 forces) acting at a point
4. Polygon of forces
5. Resolution of forces of friction
WEEK 7

Theme: Pure Mathematics

Topic: Calculating and processing device

Sub-Topic:
Content:
1. Calculating devices
– abacus
– calculating device
2. Decimal and binary systems
3. Flow charts
4. Application of flow charts
WEEK 7

Theme: Statistics

Topic: Probability (Cont.)

Sub-Topic:
Content:
1. Classical, frequently and axiomative approaches to probability
2. Sample space and event space
3. Mutually exclusive, independent and conditional events
4. Conditional probability
5. Probability trees.
WEEK 7

Theme: Mechanics

Topic: Statics (cont.)

Sub-Topic:
Content:
1. Forces in equilibrium
2. Resultant of parallel forces (in the same direction and in opposite directions) acting on a rigid body.
3. Moment of a force (2 and 3 forces) acting at a point
4. Polygon of forces
5. Resolution of forces of friction
WEEK 8

Theme: Coordinate Geometry

Topic: The straight line

Sub-Topic:
Content:
1. Mid-point of a line segment
2. Gradient of a straight line
3. Distance between two points
4. Conditions for parallelism and perpendicularity
WEEK 8

Theme: Statistics

Topic: Permutation & combinations

Sub-Topic:
Content:
1. Permutation on arrangement
2. Cyclic permutation
3. Arrangement of identical objects
4. Arrangement in which repetitions are allowed
5. Introduction to combination on selection
6. Conditional arrangements and selection
7. Probability arrangement problems involving arrangement and selection
WEEK 8

Theme: Operation Research

Topic: Modelling

Sub-Topic:
Content:
1. Introduction to modelling
2. Dependent and independent variables in mathematical modelling
3. Examples of some models
4. Construction of model
5. Methodology of modelling
6. Application to physical, biological, social and behavioral services
WEEK 9

Theme: Coordinate Geometry

Topic: The straight line

Sub-Topic:
Content:
1. Equation of a line
2. Transform relationship into linear form
3. Areas of triangles and quadrilaterals
WEEK 9

Theme: Statistics

Topic: Permutation & combinations (Cont.)

Sub-Topic:
Content:
1. Permutation on arrangement
2. Cyclic permutation
3. Arrangement of identical objects
4. Arrangement in which repetitions are allowed
5. Introduction to combination on selection
6. Conditional arrangements and selection
7. Probability arrangement problems involving arrangement and selection
WEEK 9

Theme: Operation Research

Topic: Games theory

Sub-Topic:
Content:
1. Introduction to games theory
2. Description of types of games
3. Solution of two person zero sum games using pure and mixed strategies
4. Matrix games

WEEK 10: REVISION AND EXAMININATION
WEEK 10: REVISION AND EXAMININATION
WEEK 10: REVISION AND EXAMININATION
THIRD TERM
SSS 1 SSS 2 SSS 3
WEEK 1: Revision
WEEK 1: Revision
WEEK 1: Revision
WEEK 2

Theme: Statistics

Topic: Measures of location

Sub-Topic:
Content:
Mean, mode, median, decile, percentile, quartiles.
WEEK 2

Theme: Mechanics

Topic: Vectors in three dimension

Sub-Topic:
Content:
1. Scalar product of vectors in three dimensions
2. Application of scalar product
3. Vector or cross product in three dimensions
4. Application of cross product.
WEEK 2

Theme:

Topic:

Sub-Topic:
Content:
WEEK 3

Theme: Statistics

Topic: Measures of location (Cont.)

Sub-Topic:
Content:
Mean, mode, median, decile, percentile, quartiles.
WEEK 3

Theme: Mechanics

Topic: Vectors in three dimension (Cont.)

Sub-Topic:
Content:
1. Scalar product of vectors in three dimensions
2. Application of scalar product
3. Vector or cross product in three dimensions
4. Application of cross product.
WEEK 3

Theme:

Topic:

Sub-Topic:
Content:
WEEK 4

Theme: Statistics

Topic: Measures of dispersion

Sub-Topic:
Content:
Range, inter-quartiles, mean deviation, standard deviation
WEEK 4

Theme: Mechanics

Topic: Dynamics

Sub-Topic:
Content:
1. Newton’s Laws of motion
2. Motion along inclined plane
3. Motion of connected particles
4. Work, Power and Energy Impulse and Momentum
5. Projectiles
- Trajectory of projectiles
- Greatest height reached
- Time of flight
- Range
- Projection along inclined plane
WEEK 4

Theme:

Topic:

Sub-Topic:
Content:
WEEK 5

Theme: Statistics

Topic: Measures of dispersion (Cont.)

Sub-Topic:
Content:
Range, inter-quartiles, mean deviation, standard deviation
WEEK 5

Theme: Mechanics

Topic: Dynamics (Cont.)

Sub-Topic:
Content:
1. Newton’s Laws of motion
2. Motion along inclined plane
3. Motion of connected particles
4. Work, Power and Energy Impulse and Momentum
5. Projectiles
- Trajectory of projectiles
- Greatest height reached
- Time of flight
- Range
- Projection along inclined plane
WEEK 5

Theme:

Topic:

Sub-Topic:
Content:
WEEK 6

Theme: Vectors

Topic: Vectors in two dimension

Sub-Topic:
Content:
1. Scalars and vectors
- Zero vector
- Negative vectors
2. Vector addition and subtraction
- Scalar multiplication of vectors
- Magnitude and direction of a vector
- Unit vector
3. The triangle law
- The parallelogram law
4. Resolution of vectors
5. Scalar (dot) product
- Application of scalar (dot) product
WEEK 6

Theme: Introduction To Operating Research

Topic: Inventory model

Sub-Topic:
Content:
1. Concept of inventory
2. Definitions of important terms in inventory
- Holding list
- Demand
- Ordering list e.t.c
3. Computation of optimal quantity [EOQ model]
WEEK 6

Theme:

Topic:

Sub-Topic:
Content:
WEEK 7

Theme: Vectors

Topic: Vectors in two dimension (Cont.)

Sub-Topic:
Content:
1. Scalars and vectors
- Zero vector
- Negative vectors
2. Vector addition and subtraction
- Scalar multiplication of vectors
- Magnitude and direction of a vector
- Unit vector
3. The triangle law
- The parallelogram law
4. Resolution of vectors
5. Scalar (dot) product
- Application of scalar (dot) product
WEEK 7

Theme: Introduction To Operating Research

Topic: Inventory model (Cont.)

Sub-Topic:
Content:
1. Concept of inventory
2. Definitions of important terms in inventory
- Holding list
- Demand
- Ordering list e.t.c
3. Computation of optimal quantity [EOQ model]
WEEK 7

Theme:

Topic:

Sub-Topic:
Content:
WEEK 8

Theme: Operations Research

Topic: History and nature of operation research

Sub-Topic:
Content:
Definition of operations research History and nature of operations research
WEEK 8

Theme: Introduction To Operating Research

Topic: Replacement model

Sub-Topic:
Content:
1. Concept of replacement
2. Individual Replacement of sudden failure item
3. Replacement of items that wear out gradually
WEEK 8

Theme:

Topic:

Sub-Topic:
Content:
WEEK 9

Theme: Operations Research

Topic: Models

Sub-Topic:
Content:
1. Linear programming models
2. Transportation models (least cost and not west corner)
3. Assignment model Practical application of the models
WEEK 9

Theme: Introduction To Operating Research

Topic: Replacement model (Cont.)

Sub-Topic:
Content:
1. Concept of replacement
2. Individual Replacement of sudden failure item
3. Replacement of items that wear out gradually
WEEK 9

Theme:

Topic:

Sub-Topic:
Content:

WEEK 10: REVISION AND EXAMININATION
WEEK 10: REVISION AND EXAMININATION
WEEK 10: REVISION AND EXAMININATION





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