Further Mathematics Scheme of work (SS1 – SS3) Lagos NAPPS

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Further Maths Scheme of work for Senior Secondary School 1 – 3 – Edudelight.com

Further Mathematics NAPPS Scheme of work

First Term SS1 Further Mathematics Lagos State Scheme of work

WEEK(S) TOPICS

General revision and basic concept of set
Operation of set and venn diagram: Union, intersection, compliment, and cardinality of

Set.

BINARY OPERATIONAND BASIC LAWS: (a) definition of binary operation (b) solve simple operation of binary operations e.g a x b = – 2ab (b)Identity law of binary operation
BINARY OPERATION CONTINUES: (a) solve problems and application of laws of binary operation to given problems (b) identity and inverse element (d) draw addition and multiplication table for binary operation of modulo
INDICES: (a) basic laws of indices (b) use of indices laws in solving given problems
INDICIAL EQUATION AND GRAPH OF EXPONENTIAL FUNCTIONS: e.g Y = , where x 1.
Review of first half term and periodic test
LOGARITHMS; (a) state the laws of logarithms (b) application of law of logarithms to given problems (c) solve problems involving change of base
SURD: (a) definition of surd (b) state the rules of surds (c) solve basic operations involving addition, subtraction, multiplication, division and rationalization of surd with the use of conjugate surd.
MEASURE OF LOCATION: (a) mean, median and mode (b) estimating mode from histogram of grouped data.(c)estimating the median from histogram of groped data
REVISION
EXAMINATION
EXAMINATION

First Term SS2 Further Mathematics Lagos State Scheme of work

WEEKS TOPICS

Revision of SS 1 work

Nature of roots of quadratic equations and co-efficient
Intersection of a line and a given curve
Polynomials
Factorization of Polynomials
Sum of roots of Polynomials
Revision of first half and test
Legal reasoning
Trigonometric function
Relationship between graphs of trig ratios
Graph of inverse by ration
Revision and first term examination

First Term SS3 Further Mathematics Lagos State Scheme of work

Week 1

Review of SS2 examination questions. Quadratic inequalities and inequalities in two dimensions.

Week 2

Matrices and Determinants (2×2, 3×3):

basic definitions
Matrices as linear transformations.
determinants
Solution of 2×3 simultaneous equations.

Week 3

Partial fractions:

Basic definitions
Proper and rational functions with denominators as linear functions (distinct and repeated) and others.

Week 4

Integration:

Understand integration as the reverse of process of differentiation.
Integration of algebraic polynomials including ¹/x, logarithmic functions
Definite integrals and application to kinematics, velocity- time and speed-time graph
Area under the curve, trapezoidal rule, volume of solids of revolution

Week 5

Conic sections

Equations of parabola, hyperbola, ellipse in rectangular Cartesian coordinates
Parametric equations

Week 6

Correlation:

Concept of correlation as measure of relationships
Scatter diagrams
Rank correlation
Tied ranks

Week 7

Mid-term test

Week 8

Probability distributions and approximations

Binomial distribution
Poisson distribution
Normal distribution
Binomial approximations by Poisson distribution

Week 9

Probability distribution and variance

Normal approximations by binomial distribution
Mean
Variance
Coefficient of variance of binomial, Poisson and normal.

Week 10

Static forces

Forces in equilibrium
Resultant of parallel forces (in the same direction and in opposite direction) acting on a rigid body

Week 11

Revision

Week 12

Examination

Week 13

Vacation

Second Term SS1 Further Mathematics NAPPS Scheme of work Lagos

Week 1; Reviews of first term’s work and introduction to the concept of function:

Definition examples linear. Non linear.
Rational functions.

Week 2; – Definition:

– Examples linear

– Non – Linear

– Rational functions.

Week 2; Functions:

– One to one

– Onto

– Inverse

– Identity

– Constant

– Circular

– Logarithmic

– Exponential and composite

Application of functions solution of problems to function.

Week 3; Sequence and series arithmetic progression AP) nth term

Un = U₁ + (n – 1) d or a + (n – 1) d.

Arithmetic mean series

Sn= n/2 (2U₁ + (n – 1) d)

Sn = n/2 (U₁ + Un), d =

Common difference.

Week 4; Sequence and series (geometric progression GP) (i) nth term (Un)

U_n = ar^n-1,

(ii) Geometric Mean G.M. = U_n ae^n-1

(iii) Series

Sn = a(rⁿ -1)

r-1

/r/? 1 (divergent)

Sn = a(1-rⁿ)

1-r

/r/ <1 (convergent)

Sn = a n>00

1-r

Week 5; Linear inequalities in one variable (i) Number solution of x<a

X<a, x>a, x>a

(ii) Combine equalities

(a) a< x <b,

(b) a<x<b

Week 6; inequalities in two variables (a) drawing of graphs

ax + by <c, where a, b, and care constant.

(b) Definition of region satisfied by simultaneous line inequalities.

Week 7; Review of the 1^st term lessons and periodic test.

Week 8; trigonometrical ratios

(i) Revision of sine, cosine and tangent of acute angle.

(ii) Derive trigonometrical ratio of special angles 30⁰, 45⁰, and 60⁰.

(iii) Application of trigonometrical ratios of 30⁰, 45⁰, and 60⁰to solve problems without the use of table.

Week 8; logical reasoning simple true and false statement. Negation, converse.

Week 9; contra-positive of statement. Antecedents and consequence of statement. Compound statement connectives and their symbols. Conditional statement and symbols.

Week 10; Revision of second half term lesson and periodic test.

Week 11; Revision

Week 12 & 13; Examination

Second Term SS2 Further Maths Scheme of work

Week 1; Review of first term’s work and conic section: Definition of circles and part of circle.

Week 2; (i) Equation of circle given centre and radius.

(ii) General equation of a circle.

(iii) Finding centre and radius of given circle.

(iv) Finding equation of a circle given the end point of the diameter.

Week 3; (i) Equation of circle passing through 3 points.

(ii) Equation of tangent to a circle.

(iii) Length of tangent to a circle.

Week 4; Statistics

(i) Probability (a) Classical frequential and axiomatic approaches to probability.

(b) Sample space and event space.

(d) Conditional probability.

(e) Probability trees.

Week 5; Permutation

(i) Permutation on arrangement.

(ii) Cyclic permutation

(iii) Arrangement of identical object.

(iv) Arrangement in which repetitions are allowed

Week 6; Combination:

(i) Introduction to combination on selection.

(ii) Conditional arrangements and selection

(iii) Probability arrangement involving arrangement and selection.

(iv) Problems

Week 7; Review of the first half term’s and periodic test.

Week 8; Dynamics:

(i) Newton’s law of motion

(ii) Motion along inclined plane

(iii) Motion of connected particles.

Week 9; (i) Work, power and energy

(ii) Impulse and momentum.

Week 10; Projectiles:

(i) Trajectory of projectiles.

(ii) Greatest height reached. Projectiles conts

(iii) Time of flight.

(iv) Range

(v) Projection along inclined plane.

Week 11; Introduction to operation research: inventory model.

(i) Concept of inventory.

(ii) Definition of important terms in inventory holding list. Demand ordering list etc. computation of optimal quantity.

Week 12 & 13; Revision of second term’s work and preparation term examination.

Second Term SS3 Further Maths Scheme of work

Week 1; (i) Review of first term’s examination question.

(ii) STATIC Moment of a force (2 and 3 forces) acting at a point

Week 2; STATIC

(i) Polygon of forces.

Resolution of forces of friction.

Week 3; MODELLING:

(i) Introduction to modelling.

(ii) Dependent and independent variables in mathematical modelling.

(iii) Examples of some models

Week 4, MODELLING:

(i) Construction of model.

(ii) Methodology of modelling

(iii) Application to physical, biological, social and behaviuoral services.

Week 5; GAMES THEORY:

(i) Introduction to games theory. Description of types of games.

Week 6; GAMES THEORY:

(i) Solution of two-person zero sum games using pure and mixed strategies.

(ii) Matrix games

Week 7 – 12; Revision and mock examination.

Third Term SS1 Further Mathematics NAPPS Scheme of work

008	FURTHER MATHEMATICS
1.	-Revision of second term examination questions and introduction to calculation and processing devices -Identification and use of some calculating devices
2.	Calculating devices II -Number system used in computers (binary nos) -Flow charts – Preparation and application of flow charts
3.	-Coordinates Geometry straight line -Location of point on cartesuian plane (i) Mid points of a line segment (ii) Mid point of a line segment (iii) Gradient of a straight line (iv) Distance between two point
4.	Straight line continued: -Parallelism and perpendicularity -Equation of lines of different form -Intercept form, Gradient from, General form
5.	Coordinate Geometry: straight line (i) Transformation of non linear into linear form (ii) Areas of triangle and quadrilaterals
6.	Vectors in two Dimensions -Definition of vectors and scalar and their difference -Operations on vectors equality addition subtraction, scalar Multiplication magnitude and direction of a unit vector
7	Review of the first half term lessons and periodic test
8.	Vectors in two dimension II – The triangle law – Parallelogram Law – Resolution of vectors – Scalar (dot) -Product vectors
9.	Measure of dispersion: Range, Interquartile range, mean deviation, standard deviation and co-efficient of variation.
10.	History of nature of operation research modeling
11.	Revision
12.	Revision and Examination

Third Term SS2 Further Mathematics NAPPS Scheme of work

008	FURTHER MATHEMATICS
1.	-Revision of second term examination questions and introduction -Introduction of binomial expansion using Pascal’s triangle
2.	Binomial expansion of (a+b)’’, where n is positive negative integers and fractional power. Find with term and application of Binomial expansion
3.	Differentiation: i) Limits of a function. ii) Differentiation from first principle. iii) Differention of polynormals
4.	Differentiation of: i) Transcendental such as: y= sin ax y= cos ax y=log ax y= e^ax
5.	Rules of differentiation: i) Product rule: ii) Quotients rule iii) Functions of composite function y= (ax +b)ⁿ Application of differentiation to change
6.	(b) maximum and minimum problem c) Equation of motion. d) Gradients Review of first half term’s work and period test
7	Higher derivative differentiation of implicts
8.	Functions
9.	Mechanics: (i) Vector in three dimension (ii) Scalar product of vectors in three dimension
10.	Vector or cross product on three dimensions Application of cross product vector continue
11.	Operation Research (i) Concepts of replacement (ii) Individuals replacement of sudden failure item (iii) Replacement of items that wear out gradually
12.	Revision and examination