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

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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

We provide educational resources/materials, curriculum guide, syllabus, scheme of work, lesson note & plan, waec, jamb, O-level & advance level GCE lessons/tutorial classes, on various topics, subjects, career, disciplines & department etc. for all the Class of Learners

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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We provide educational resources/materials, curriculum guide, syllabus, scheme of work, lesson note & plan, waec, jamb, O-level & advance level GCE lessons/tutorial classes, on various topics, subjects, career, disciplines & department etc. for all the Class of Learners