Further Maths Scheme of Work for SS2 Federal

Senior Secondary School Sciences Education Resource Centre. Further Maths Scheme of Work for SS2 Federal – Schemeofwork.com

Table of Contents

FURTHER MATHS SS2 FIRST TERM SCHEME FURTHER MATHS SS2 SECOND TERM SCHEME FURTHER MATHS SS2 THIRD TERM SCHEME

FURTHER MATHS SS2 FIRST TERM SCHEME

WEEK	TOPIC / CONTENT	ACTIVITIES
1	ROOTS OF QUADRATIC EQUATION i. Sum and product of roots ii. forming quadratic equation given sum and product of root iii. condition for quadratic equation to have: – Equal roots (b²=4ac) – Real roots (b²>4ac) – No roots (b²<4ac) (complex)	Teacher: leads students to find sum and products of roots of quadratic equation Students: use formular to find sum and product of roots of quadratic equation Instructional Resource: charts showing a quadratic equation
2	ROOTS OF QUADRATIC EQUATION II i. Conditions for given line to intersect a curve, be tangent to curve, not intersect a curve. ii. Solution of problems on roots of quadratic equation	Teacher: states condition for quadratic equation to have equal roots, real roots and no roots(complex roots). Students: solve various problems on root of quadratic equation Instructional Resource: charts showing condition for lines to intersect curve and not to intersect.
3	POLYNOMIALS i. Definition of polynomial a. addition b. subtraction c. multiplication ii. Division of polynomials by a polynomial of lesser degree	Teacher: gives definition and examples of polynomials Students: state definition and examples of polynomial Instructional Resource: charts giving examples of polynomials of various degrees.
4	POLYNOMIALS i. Reminder theorem ii. Factor theorem iii. Factorization of polynomials	Teacher: demonstrates how to find remainder when a polynomial is divided by another polynomial of lesser degree. Students: solve problems on remainder theorem and factor theorem Instructional Resource: charts showing sum of root and product.
5	POLYNOMIALS i. Roots of cubic equation a. Sum of roots α+ᵝ+ᵟ = -b/a b. sum products of two roots α ᵝ + αᵟ + ᵝᵟ = c/a c. product of roots αᵝᵟ = -d/a where ax³+bx²+cx+d=0	Teacher: leads students to solve problem on roots of cubic equation Students: solve problems on roots of cubic equation. Instructional Resource: charts showing sum of roots, sum of product of two roots and products of three roots of a cubic equation.
6	PROBABILITY i. Classical, frequential and axiomative approaches to probability ii. Sample space and event space iii. Mutually exclusive, independent and conditional events.	Teacher: leads students to evolve concepts of classical and frequential approaches using ludo dice. Students: identify the classical, frequential and axiomatic definition of probability Instructional Resource: ludo dice, coin, pack of cards.
7	PROBABILITY i. Conditional probability ii. Probability trees	Teacher: solves conditional probability Students: solve problems on conditional probability Instructional Resource: ludo dice, coin, pack of cards.
8	VECTORS IN THREE DIMENSIONS i. Scalar product of vector in three dimensions ii. Application of scalar product	Teacher: gives examples of vectors in three dimensions Students: write out more examples of three dimensional vectors Instructional Resource: charts depicting example of three dimensional vectors.
9	VECTORS IN THREE DIMENSIONS i. Vector or cross product in three dimensions ii. Application of cross product	Teacher: guides students to find cross product of two vectors and leads them to solve problems on application Students: solve problem on cross product of two vector and practical application of dot product. Instructional Resource: charts showing short cut method of finding dot product.
10	LOGICAL REASONING i. Fundamental issues in intelligent system ii. Fundamental definition iii. Modelling the world.	Teacher: guides students to identify fundamental issues in intelligent system Students: Identify fundamental issue in intelligent system Instructional Resource: charts showing critical issues in intelligent system.
11	LOGICAL REASONING i. Introduction to propositional and predicate logical resolution ii. Introduction to theorem proving	Teacher: introduces propositional and predicate logical resolution Students: explain propositional and predicate resolution Instructional Resource: charts showing points to note in proving of theorem.
12	Revisions	Revisions
13	Examinations	Examinations
14	Examinations	Examinations

Senior Secondary School Sciences Education Resource Centre. Further Maths Scheme of Work for SS2 Federal – Schemeofwork.com

FURTHER MATHS SS2 SECOND TERM SCHEME

WEEK	TOPIC / CONTENT	ACTIVITIES
1	DIFFERENTIATION i. Limits of a function ii. Differentiation from first principle iii. Differentiation of polynomials	Teacher: guides students on how to find limits of a function and differentiate from first principle. Students: Evaluate limits of a function at a given value and differentiate from first principle. Instructional Resource: charts showing rules of differentiation.
2	DIFFERENTIATION Differentiation of transcendental function such as sin x, e^ax, log 3x	Teacher: leads students to differentiate transcendental functions Students: Differentiate transcendental functions. Instructional Resource: chart showing areas of application
3	DIFFERENTIATION i. Rules of differentiation ii. Product rule iii. Quotient rule iv. Function of function	Teacher: guides students to use rules of differentiation Students: use rules of differentiation Instructional Resource: charts showing rules of differentiation
4.	DIFFERENTIATION i. Application of differentiation to a. rate of change b. gradient c. maximum and minimum values d. equation of motion	Teacher: leads students to use differentiation in finding: rate of change, gradient of a function and optimization involving maximum and minimum values. Students: use differentiation in finding: rate of change, gradient of a function and optimization involving maximum and minimum values. Instructional Resources: chart showing areas of application.
5	DIFFERENTIATION i. Higher derivatives ii. Differentiation of implicit functions.	Teacher: guides students to higher derivative and differentiation of implicit functions Instructional Resource: chart showing areas of application.
6	BINOMIAL EXPANSION i. Pascal triangle ii. Binomial expression of (a+b)ⁿ where n is +ve integer, -ve integer or fractional value	Teacher: guides students to demonstrate the Pascal triangle and write out the binomial expansion. Students: construct the Pascal triangle and write our binomial expansion. Instructional Resource: charts showing Pascal triangle
7	BINOMIAL EXPANSION i. Finding nth term ii. Application of binomial expansion	Teacher: leads students to extend the power of negative integer and fractional values. Students: use the knowledge of expansion of positive expansion to negative and fractional powers. Instructional Resources: charts showing n^th term of a given binomial expansion.
8	CONIC SECTION: THE CIRCLE i. Definition of circle ii. Equation of circle given centre and radius	Teacher: leads students to define circle and explain concept of a circle as conic section . Students: solve various types of problems on circles. Instructional Resources: chart depicting circle as section of a cone.
9	CONIC SECTION: THE CIRLCE i. General equation of a circle a. finding centre and radius of a given circle b. finding equation of a circle given the end point of the diameter c. equation of a circle passing through three points.	Teacher: guides students to solve various types of problems on circles. Students: solve various types of problems on circle. Instructional Resources: chart showing equation of circle passing through 3 points.
10	CONIC SECTION: THE CIRCLE i. Equation of tangent to a circle ii. Length of tangent to a circle	Teacher: leads students to find the equation of a tangent to circle Students: learn technique of finding equation of tangent to circle Instructional Resources: chart showing tangent of circle and length of tangent.
11	Revisions	Revisions
12	Examinations	Examinations
13	Examinations	Examinations

Senior Secondary School Sciences Education Resource Centre. Further Maths Scheme of Work for SS2 Federal – Schemeofwork.com

FURTHER MATHS SS2 THIRD TERM SCHEME

WEEK	TOPIC / CONTENT	ACTIVITIES
1	TRIGONOMETRIC FUNCTION i. Knowledge of six trigonometric functions of angles of any magnitude (since, cosine, tangent, secant, cosecant, cotangent). ii. Range and domain of specified trigonometric functions iii. Graphs of trigonometric ratios with emphasis on their amplitude and periodicity.	Teacher: leads students to identify and find trigonometric function of angles Students: identify angles of the six trigonometric ratios. Instructional Resources: charts showing relationship between the six trigonometric ratios.
2	TRIGONOMETRIC FUNCTION i. Relationship between graphs of trig ratios e.g. sin x and sin 2x graphs of y = a sin (bx) + c y = a cos (bx) + c y = a tan (bx) + c ii. Graphs of inverse by ratio	Teacher: leads students to identify relationship between graphs of trigonometric ratios. Students: identify relationship between the graphs of trigonometric ratios e.g. sinx and sin2x. Instructional Resource: charts showing sketches of inverse of sinx, cosx and tanx.
3	TRIGONOMETRIC FUNCTION i. solution of simple equation involving the six trigonometric functions ii. proofs of simple trigonometric identities e.g. sin ²x + cos²x = 1 sec²x = 1+tan ²x	Teacher: guides them to solve simple equations involving trigonometric ratios. Students: solve simple trigonometric equation. Instructional Resources: charts showing sketches of inverse of sin x, cosx and tanx.
4	PERMUTATIONS AND COMBINATIONS i. Permutation on arrangement ii. Cyclic permutation iii. Arrangement of identical object.	Teacher: guides students to solve problem on cyclic permutation and other types of permutation. Students: solve various problems on permutation Instructional Resources: charts showing : Functional notationⁿprⁿcr
5	PERMUTATIONS AND COMBINATIONS i. Arrangements in which repetitions are allowed ii. Introduction to combination on selection. a). Conditional arrangements and selection b). Probability arrangement problem involving arrangement and selection.	Teacher: demonstrates application of combination in probability. Students: use concept of combination to solve problem on probability. Instructional Resources: charts showing functional notation.
6	DYNAMICS i. Newton laws of motion ii. Motion along inclined plane	Teacher: explains Newton’s law of motion and states the three laws of motion. Students: write down the laws of motion and solve problems on Newton’s laws of motion. Instructional Resources: Ball and heavy block placed on table to demonstrate 3^rd law.
7	DYNAMICS i. Motion of connected particles ii. Work, Energy and Power iii. Impulse and Momentum	Teacher: guides students to solve problem involving application of Newton’s law of motion. Students: solve problem on motion along inclined plane. Instructional Resources: An inclined plane with object on it.
8	DYNAMICS i. Projectiles ii. Trajectory of projectiles iii. Projection along inclined plane.	Teacher: guide students to solve various problem on projectiles. Students: solves various problems on projectile Instructional Resources: Light smooth pulley with two blocks connected by string.
9.	INVENTORY MODEL i. Concept of inventory ii. Definitions of important terms in inventory. iii. Holding list iv. Ordering list etc. computation of optimal quantity [EOQ model].	Teacher: guide students to give practical examples on inventory. Students: define various terms on inventory Instructional Resources: charts depicting items on inventory.
10	REPLACEMENT MODEL i. Concept of replacement ii. Individual replacement of sudden failure item iii. Replacement of items that wear out gradually.	Teacher: explains the concept of replacement Students: gives practical examples of item that wear out suddenly and gradually. Instructional Resources: charts showing diagrams of items such as plugs, bulbs, generators, grinding machines etc.
11	Revisions	Revisions
12	Examinations	Examinations
13	Examinations	Examinations