i. Limits of a function
ii. Differentiation from first principle
iii. Differentiation of polynomials
Differentiation of transcendental function such as sin x, eax, log 3x
i. Rules of differentiation
ii. Product rule
iii. Quotient rule
iv. Function of function
i. Application of differentiation to
a. rate of change
c. maximum and minimum values
d. equation of motion
i. Higher derivatives
ii. Differentiation of implicit functions.
i. Pascal triangle
ii. Binomial expression of (a+b)n where n is +ve integer, -ve integer or fractional value
i. Finding nth term
ii. Application of binomial expansion
i. Definition of circle
ii. Equation of circle given centre and radius
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.
i. Equation of tangent to a circle
ii. Length of tangent to a circle
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.
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
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
i. Permutation on arrangement
ii. Cyclic permutation
iii. Arrangement of identical object.
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.
i. Newton laws of motion
ii. Motion along inclined plane
i. Motion of connected particles
ii. Work, Energy and Power
iii. Impulse and Momentum
ii. Trajectory of projectiles
iii. Projection along inclined plane.
i. Concept of inventory
ii. Definitions of important terms in inventory.
iii. Holding list
iv. Ordering list etc. computation of optimal quantity [EOQ model].
i. Concept of replacement
ii. Individual replacement of sudden failure item
iii. Replacement of items that wear out gradually.
Land ownership and tenure systems in Nigeria
Land use Act of 1978:
Role of government in Agricultural production e.g.
Forest management techniques:
Diseases of major crops: e.g.
ii. field observation and identification of different types of crop diseases and mouldy grains in storage.
Preventive and control measures:
Important insect pests of major crops:
Other important pests e.g.
i. Economic importance of pests e.g.
- reduction in quality of crops
- reduction in quantity of crops
- makes vegetables unattractive and unmarketable etc.
ii. Preventive and control measures:
- cultural methods
- biological methods
- chemical methods
iii. Side effects of the various preventive and control methods:
- chemical pollution, poisoning etc.
Morphology of the common grass and legume species of Nigerian pastures
i. Types of pastures: permanent pasture, rotational pasture, temporary pasture, irrigated pasture.
ii. Factors affecting pasture:
Methods of rangeland improvement:
Climatic factors: rainfall, temperature, light, and wind.
Biotic factors: predator, parasites, soil micro organisms, pests and disease organisms etc.
Edaphic facrors: soil types, soil PH, soil texture etc.
Factors: soil PH, excess of other nutrients, leaching, crop removal, oxidation etc.
Methods of replenishing plant nutrients:
Farming practices and the soil effects: bush burning, over-grazing, clean clearing, stumping, fertilizer application, inorganic manuring etc.