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How to Check Your Jamb Result

how to check jamb result

Introduction

Do you want to check your Jamb result?

There are two ways to achieve this. You can either check via SMS which is faster or you can check online.

In this post, I will share with you a step by step guide on how to check your Jamb result online

How to Check Your Jamb Result via SMS

To check your Jamb result via SMS, you need to follow the steps below:

  • All candidates can now send RESULT, via SMS, to 55019 using the same number that was used for registration (you must have a credit balance of at least N50 on your line).
  • The result, would be replied as an SMS shortly after.

How to Check Your Jamb Result Online

To check your Jamb result online, you need to:

  1. Go to JAMB result checking portal
  2. Enter your JAMB Registration Number/Email Address in the required column.
  3. Click on ‘Check My Results’.
  4. The portal will load your result if it’s ready.

If you are preparing for Jamb, you may want to check this article on how to pass Jamb in one sitting.

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The Complete WAEC Syllabus for Mathematics 20

WAEC Syllabus For Mathematics (General) |  AIMS OF THE SYLLABUS

The aims of the syllabus are to test candidates’:
(1) mathematical competency and computational skills;

(2) understanding of mathematical concepts and their relationship to the acquisition of entrepreneurial skills for everyday living in the global world;

(3) ability to translate problems into mathematical language and solve them using appropriate methods;

(4) ability to be accurate to a degree relevant to the problem at hand;

(5) logical, abstract and precise thinking.

This syllabus is not intended to be used as a teaching syllabus. Teachers are advised to use their own National teaching syllabuses or curricular for that purpose.

WAEC Syllabus For Mathematics (General) | EXAMINATION SCHEME

There will be two papers, Papers 1 and 2, both of which must be taken.

PAPER 1: will consist of fifty multiple-choice objective questions, drawn from the common areas of the syllabus, to be answered in 1½ hours for 50 marks.

PAPER 2: will consist of thirteen essay questions in two sections – Sections A and B, to be answered in 2½ hours for 100 marks. Candidates will be required to answer ten questions in all.

Section A – Will consist of five compulsory questions, elementary in nature carrying a total of 40 marks. The questions will be drawn from the common areas of the syllabus.

Section B – will consist of eight questions of greater length and difficulty. The questions shall include a maximum of two which shall be drawn from parts of the syllabuses which may not be peculiar to candidates’ home countries. Candidates will be expected to answer five questions for 60marks.

WAEC Syllabus For Mathematics (General) | DETAILED SYLLABUS

The topics, contents and notes are intended to indicate the scope of the questions which will be set. The notes are not to be considered as an exhaustive list of illustrations/limitations.

WAEC Syllabus For Mathematics (General) | A. NUMBER AND NUMERATION

( a ) Number bases

( i ) conversion of numbers from one base to another

( ii ) Basic operations on number bases

Conversion from one base to base 10 and vice versa. Conversion from one base to another base .

Addition, subtraction and multiplication of number bases.

(b) Modular Arithmetic

(i) Concept of Modulo Arithmetic.

(ii) Addition, subtraction and multiplication operations in modulo arithmetic.

(iii) Application to daily life

Interpretation of modulo arithmetic e.g. 6 + 4 = k(mod7), 3 x 5 = b(mod6), m = 2(mod 3), etc.

Relate to market days, clock,shift duty, etc.

( c ) Fractions, Decimals and Approximations

(i) Basic operations on fractions and decimals. (ii) Approximations and significant figures.

Approximations should be realistic e.g. a road is not measured correct to the nearest cm

WAEC Syllabus For Mathematics (General) | ( d ) Indices

( i ) Laws of indices

( ii ) Numbers in standard form ( scientific notation)

e.g. a x x a y = a x + y , a x ÷ a y = a x – y , ( a x ) y = a xy , etc where x , y are real numbers and a ≠0. Include simple examples of

negative and fractional indices.

Expression of large and small numbers in standard form e.g. 375300000 = 3.753 x 108 0.00000035 = 3.5 x 10-7 Use of tables of squares, square roots and reciprocals is accepted

( e) Logarithms

( i ) Relationship between indices and logarithms e.g. y = 10 k implies log10 y = k . ( ii ) Basic rules of logarithms e.g. log10( pq ) = log10 p + log10 q
log10( p / q ) = log10 p – log10 q
log10 p n = n log10 p . (iii) Use of tables of logarithms and antilogarithms.

Calculations involving multiplication, division, powers and roots

WAEC Syllabus For Mathematics (General) | ( f ) Sequence and Series

(i) Patterns of sequences.

(ii) Arithmetic progression (A.P.) Geometric Progression (G.P.)

Determine any term of a given sequence. The notation Un = the nth termof a sequence may be used.

Simple cases only, including word problems. (Include sum for A.P. and exclude sum for G.P

WAEC Syllabus For Mathematics (General) | ( g ) Sets

(i) Idea of sets, universal sets, finite and infinite sets, subsets, empty sets and disjoint sets. Idea of and notation for union, intersection and complement of sets.

(ii) Solution of practical problems involving classification using Venn diagrams

Notations: ℰ, ⊂, ∪, ∩, { }, ∅, P’( the compliment of P).

♦• properties e.g. commutative, associative and distributive

Use of Venn diagrams restricted to at most 3 sets

WAEC Syllabus For Mathematics (General) | ( h ) Logical Reasoning

Simple statements. True and false statements. Negation of statements, implications.

Use of symbols: ⟹,⇐, use of Venn diagrams

(i) Positive and negative integers, rational numbers

The four basic operations on rational numbers

Match Natural numbers with points on the number line

( j ) Surds (Radicals

Simplification and rationalization of simple surds

Surds of the form √, a√ and a ±√where a is a rational number and b is a positive integer. Basic operations on surds (exclude surd of the form √).

( k ) Matrices and Determinants

( i ) Identification of order, notation and types of matrices.

( ii ) Addition, subtraction, scalar multiplication and multiplication of matrices.

( iii ) Determinant of a matrix

Not more than 3 x 3 matrices. Idea of columns and rows.

Restrict to 2 x 2 matrices.

Application to solving simultaneous linear equations in two variables. Restrict to 2 x 2 matrices.

( l ) Ratio, Proportions and Rates

Ratio between two similar quantities. Proportion between two or more similar quantities.

Financial partnerships, rates of work, costs, taxes, foreign exchange, density (e.g. population), mass, distance, time and speed

Relate to real life situations.

Include average rates, taxes e.g. VAT, Withholding tax, etc

WAEC Syllabus For Mathematics (General) | ( m ) Percentages

Simple interest, commission, discount, depreciation, profit and loss, compound interest, hire purchase and percentage error

Limit compound interest to a maximum of 3 years

∗( n) Financial Arithmetic

( i ) Depreciation/ Amortization.

( ii ) Annuities

(iii ) Capital Market Instruments

Definition/meaning, calculation of depreciation on fixed assets, computation of amortization on capitalized assets

Definition/meaning, solve simple problems on annuities.

Shares/stocks, debentures, bonds, simple problems on interest on bonds and debentures.

WAEC Syllabus For Mathematics (General) | ( o ) Variation

Direct, inverse, partial and joint variations.

Expression of various types of variation in mathematical symbols e.g. direct (z ∝n ), inverse (z ∝ ), etc. Application to simple practical problems

B. ALGEBRAIC PROCESSES

( a ) Algebraic expressions

(i) Formulating algebraic expressions from given situations

( ii ) Evaluation of algebraic expressions

e.g. find an expression for the cost C Naira of 4 pens at x
Naira each and 3 oranges at y
naira each. Solution: C = 4 x + 3 y

e.g. If x =60 and y = 20, find C . C = 4(60) + 3(20) = 300 naira.

WAEC Syllabus For Mathematics (General) | ( b ) Simple operations on algebraic expressions

( i ) Expansion

(ii ) Factorization

 (iii) Binary Operations

e.g. ( a + b )( c + d ), ( a + 3)( c – 4), etc.

factorization of expressions of the form ax + ay, a ( b + c ) + d ( b + c ), a 2 – b 2, ax 2 + bx + c where a , b , c
are integers. Application of difference of two squares e.g. 492 – 472 = (49 + 47)(49 – 47) = 96 x 2 = 192.

Carry out binary operations on real numbers such as: a*b = 2a +b-ab etc.

WAEC Syllabus For Mathematics (General) | ( c ) Solution of Linear Equations

( i ) Linear equations in one variable

( ii ) Simultaneous linear equations in two variables.

Solving/finding the truth set (solution set) for linear equations in one variable.

Solving/finding the truth set of simultaneous equations in two variables by elimination, substitution and graphical methods. Word problems involving one or two variables

( d ) Change of Subject of a Formula/Relation

( i ) Change of subject of a formula/relation (ii) Substitution

e.g. if =
+ , find v. Finding the value of a variable e.g. evaluating v
given the values of u and f

WAEC Syllabus For Mathematics (General) | ( e ) Quadratic Equations

( i ) Solution of quadratic equations

(ii) Forming quadratic equation with given roots.

(iii) Application of solution of quadratic equation in practical problems

Using factorization i.e. ab = 0 ⇒ either a = 0 or b = 0. •∗♣♠By completing the square and use of formula

Simple rational roots only e.g. forming a quadratic equation whose roots are -3 and ⇒ ( x
+ 3)( x – ) = 0.

(f) Graphs of Linear and Quadratic functions

(i) Interpretation of graphs, coordinate of points, table of values, drawing quadratic graphs and obtaining roots from graphs.

( ii ) Graphical solution of a pair of equations of the form: y = ax2 + bx + c and y = mx + k

∗♣♠(iii) Drawing tangents to curves to determine the gradient at a given point

Finding: (i) the coordinates of maximum and minimum points on the graph. (ii) intercepts on the axes, identifying axis of symmetry, recognizing sketched graphs.

Use of quadratic graphs to solve related equations e.g. graph of y = x 2 + 5 x + 6 to solve x 2 + 5 x + 4 = 0. Determining the gradient by drawing relevant triangle

WAEC Syllabus For Mathematics (General) | ( g ) Linear Inequalities

(i) Solution of linear inequalities in one variable and representation on the number line.

∗(ii) Graphical solution of linear inequalities in two variables.

∗(iii) Graphical solution of simultaneous linear inequalities in two variables

Maximum and minimum values. Application to real life situations e.g. minimum cost, maximum profit, linear programming, etc

( h ) Algebraic Fractions

Operations on algebraic fractions with: ( i ) Monomial denominators

( ii ) Binomial denominators

( ii ) Binomial denominators

Simple cases only e.g. +

= ( x≠0, y≠ 0).
Simple cases only e.g. + = ! ! where a and b
are constants and x ≠ a or b . Values for which a fraction is undefined e.g. “is not defined for x=-3

(i) Functions and Relations

Types of Functions

One-to-one, one-to-many, many-to-one, many-to-many. Functions as a mapping, determination of the rule of a given mapping/function

C. MENSURATION

( a ) Lengths and Perimeters

(i) Use of Pythagoras theorem, ∗sine and cosine rules to determine lengths and distances. (ii) Lengths of arcs of circles, perimeters of sectors and segments. (iii) Longitudes and Latitudes.

No formal proofs of the theorem and rules are required.

Distances along latitudes and Longitudes and their corresponding angles

( b ) Areas

( i ) Triangles and special quadrilaterals – rectangles, parallelograms and trapeziums

(ii) Circles, sectors and segments of circles.

(iii) Surface areas of cubes, cuboids, cylinder, pyramids, right triangular prisms, cones andspheres.

Areas of similar figures. Include area of triangle = ½ base x height and ½absinC. Areas of compound shapes

Relationship between the sector of a circle and the surface area of a cone.

( c ) Volumes

(i) Volumes of cubes, cuboids, cylinders, cones, right pyramids and spheres.

( ii ) Volumes of similar solids

Include volumes of compound shapes.

D. PLANE GEOMETRY

(a) Angles

(i) Angles at a point add up to 360o. (ii) Adjacent angles on a straight line are supplementary. (iii) Vertically opposite angles are equal.

The degree as a unit of measure. Consider acute, obtuse, reflex angles, etc

(b) Angles and intercepts on parallel lines.

(i) Alternate angles are equal. ( ii )Corresponding angles are equal. ( iii )Interior opposite angles are supplementary ∗♣♠(iv) Intercept theorem

Application to proportional division of a line segment

(c) Triangles and Polygons

(i) The sum of the angles of a triangle is 2 right angles.

(ii) The exterior angle of a triangle equals the sum of the two interior opposite angles.

(iii) Congruent triangles.

( iv ) Properties of special triangles – Isosceles, equilateral, right-angled, etc

(v) Properties of special

quadrilaterals – parallelogram, rhombus, square, rectangle, trapezium.

( vi )Properties of similar triangles.

( vii ) The sum of the angles of a polygon

(viii) Property of exterior angles of a polygon.

(ix) Parallelograms on the same base and between the same parallels are equal in area

∗The formal proofs of those underlined may be required.

Conditions to be known but proofs not required e.g. SSS, SAS, etc.

Use symmetry where applicable.

Equiangular properties and ratio of sides and areas.

Sum of interior angles = (n – 2)180o or (2n – 4)right angles, where n is the number of sides

( d ) Circles

(i) Chords.

(ii) The angle which an arc of a circle subtends at the centre of the circle is twice that which it subtends at any point on the remaining part of the circumference.

(iii) Any angle subtended at the circumference by a diameter is a right angle.

(iv) Angles in the same segment are equal. (v) Angles in opposite segments are supplementary.

( vi )Perpendicularity of tangent and radius.

(vii )If a tangent is drawn to a circle and from the point of contact a chord is drawn, each angle which this chord makes with the tangent is

(ii) The angle which an arc of a circle subtends at the centre of the circle is twice that which it subtends at any point on the remaining part of the circumference.

(iii) Any angle subtended at the circumference by a diameter is a right angle.

(iv) Angles in the same segment are equal. (v) Angles in opposite segments are supplementary.

( vi )Perpendicularity of tangent and radius.

(vii )If a tangent is drawn to a circle and from the point of contact a chord is drawn, each angle which this chord makes with the tangent is equal to the angle in the alternate segment.
Angles subtended by chords in a circle and at the centre. Perpendicular bisectors of chords.

∗the formal proofs of those underlined may be required

( e ) Construction

( i ) Bisectors of angles and line segments (ii) Line parallel or perpendicular to a given line. ( iii )Angles e.g. 90o, 60o, 45o, 30o, and an angle equal to a given angle. (iv) Triangles and quadrilaterals from sufficient data

Include combination of these angles e.g. 75o, 105o,135o, etc

♠( f ) Loci

Knowledge of the loci listed below and their intersections in 2 dimensions. (i) Points at a given distance from a given point. (ii) Points equidistant from two given points. ( iii)Points equidistant from two given straight lines. (iv)Points at a given distance from a given straight line

Consider parallel and intersecting lines. Application to real life situations

E. COORDINATE GEOMETRY OF STRAIGHT LINES

(i) Concept of the x-y plane.

(ii) Coordinates of points on the x-y plane

Midpoint of two points, distance between two points i.e. |PQ| = # $− $!+ ’− ’!, where P(x1,y1) and Q(x2, y2), gradient (slope) of a line m= ( ) ( ), equation of a line in the form y = mx + c and y – y1 = m(x – x1), where m is the gradient (slope) and c is a constant

F. TRIGONOMETRY

(a) Sine, Cosine and Tangent of an angle

( b ) Angles of elevation and depression

(i) Sine, Cosine and Tangent of acute angles.

(ii) Use of tables of trigonometric ratios.

(iii) Trigonometric ratios of 30o 45o and 60o.

(iv) Sine, cosine and tangent of angles from 0o to 360o.

( v )Graphs of sine and cosine.

(vi)Graphs of trigonometric ratios.

Use of right angled triangles

Without the use of tables

Relate to the unit circle. 0o≤ x ≤ 360o.

e.g. y = a sin x , y = b cos x

Graphs of simultaneous linear and trigonometric equations. e.g. y = asin x + bcos x, etc

( c ) Bearings

(i) Bearing of one point from another.

(ii) Calculation of distances and angles

Notation e.g. 035o, N35oE

Simple problems only. Use of diagram is required.∗♣♠Sine and cosine rules may be used.

G. INTRODUCTORY CALCULUS

(i) Differentiation of algebraic functions

(ii) Integration of simple Algebraic functions.

CALCULUS

(i) Differentiation of algebraic functions.

(ii) Integration of simple Algebraic functions.
Concept/meaning of differentiation/derived function, +, +- , relationship between gradient of a curve at a point and the differential coefficient of the equation of the curve at that point. Standard derivatives of some basic function e.g. if y = x2, +, +- = 2x. If s = 2t3 + 4, +. +/ = v = 6t2, where s = distance, t = time and v = velocity. Application to real life situation such as maximum and minimum values, rates of change etc.

Meaning/ concept of integration, evaluation of simple definite algebraic equations

H. STATISTICS AND PROBABILITY

(i) Frequency distribution

( ii ) Pie charts, bar charts, histograms and frequency polygons

(iii) Mean, median and mode for both discrete and grouped data.

(iv) Cumulative frequency curve (Ogive).

(v) Measures of Dispersion: range, semi inter-quartile/interquartile range, variance, mean deviation and standard deviation

Construction of frequency distribution tables, concept of class intervals, class mark and class boundary.

Reading and drawing simple inferences from graphs, interpretation of data in histograms. Exclude unequal class interval. Use of an assumed mean is acceptable but not required.

For grouped data, the mode should be estimated from the histogram while the median, quartiles and percentiles are estimated from the cumulative frequency curve.

Application of the cumulative frequency curve to every day life.

Definition of range, variance, standard deviation, interquartile range. Note that mean deviation is the mean of the absolute deviations from the mean and variance is the square of the standard deviation. Problems on range, variance, standard deviation etc. ∗♣♠Standard deviation of grouped data

( b ) Probability

(i) Experimental and theoretical probability.

(ii) Addition of probabilities for mutually exclusive and independent events

(iii) Multiplication of probabilities for independent events

Include equally likely events e.g. probability of throwing a six with a fair die or a head when tossing a fair coin. With replacement. ∗without replacement

Simple practical problems only. Interpretation of “and” and “or” in probability

I. VECTORS AND TRANSFORMATION

(a) Vectors in a Plane

(b) Transformation in the Cartesian Plane

Vectors as a directed line segment.

Cartesian components of a vector

Magnitude of a vector, equal vectors, addition and subtraction of vectors, zero vector, parallel vectors, multiplication of a vector by scalar.

Reflection of points and shapes in the Cartesian Plane.

Rotation of points and shapes in the Cartesian Plane.

Translation of points and shapes in the Cartesian Plane.

Enlargement

(5, 060o)
e.g. 0.12345 673458.

Knowledge of graphical representation is necessary.

Restrict Plane to the x and y
axes and in the lines x = k, y
= x and y = k x , where k is an integer. Determination of mirror lines (symmetry).

Rotation about the origin and a point other than the origin. Determination of the angle of rotation (restrict angles of rotation to -180o to 180o).

Translation using a translation vector.

Draw the images of plane figures under enlargement with a given centre for a given scale factor.Use given scales to enlarge or reduce plane figures.

3. UNITS

Candidates should be familiar with the following units and their symbols.

( 1 ) Length 1000 millimetres (mm) = 100 centimetres (cm) = 1 metre(m). 1000 metres = 1 kilometre (km)

( 2 ) Area 10,000 square metres (m2) = 1 hectare (ha)

( 3 ) Capacity 1000 cubic centimeters (cm3) = 1 litre (l)

( 4 ) Mass 1000 milligrammes (mg) = 1 gramme (g)
1000 grammes (g) = 1 kilogramme( kg )
1000 ogrammes (kg) = 1 tonne.
( 5) Currencies
The Gambia – 100 bututs (b) = 1 Dalasi (D)
Ghana – 100 Ghana pesewas (Gp) = 1 Ghana Cedi ( GH¢)
Liberia – 100 cents (c) = 1 Liberian Dollar (LD) Nigeria – 100 kobo (k) = 1 Naira (N) Sierra Leone – 100 cents (c) = 1 Leone (Le) UK – 100 pence (p) = 1 pound (£) USA – 100 cents (c) = 1 dollar ($) French Speaking territories: 100 centimes (c) = 1 Franc (fr) Any other units used will be defined.

4. OTHER IMPORTANT INFORMATION

( 1) Use of Mathematical and Statistical Tables Mathematics and Statistical tables, published or approved by WAEC may be used in the examination room. Where the degree of accuracy is not specified in a question, the degree of accuracy expected will be that obtainable from the mathematical tables.

(2) Use of calculators The use of non-programmable, silent and cordless calculators is allowed. The calculators must, however not have the capability to print out nor to receive or send any information. Phones with or without calculators are not allowed.

(3) Other Materials Required for the examination Candidates should bring rulers, pairs of compasses, protractors, set squares etc required for papers of the subject. They will not be allowed to borrow such instruments and any other material from other candidates in the examination hall. Graph papers ruled in 2mm squares will be provided for any paper in which it is required.

( 4) Disclaimer In spite of the provisions made in paragraphs 4 (1) and (2) above, it should be noted that some questions may prohibit the use of tables and/or calculators.

Above is the WAEC syllabus for general mathematics 2020/2021.

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WAEC Syllabus for Economics 2020

waec syllabus for economics

This syllabus is designed to assess candidates’ knowledge of basic economic principles needed for rational decision making relating to individuals, businesses, government, and society. Such knowledge is necessary for enhancing their appreciation of government economic policies, problems of implementation and how they impact the economy.  This will help candidates to understand that economics is not only an academic field of study but also a practical subject.

OBJECTIVES

The syllabus will test candidates

  1. knowledge of the basic economic principles, concepts, and the tools for economic analysis;
  2. understanding of the structure and functioning of economic institutions – commercial, agricultural, industrial and financial institutions;
  3. understanding of the basis for rational economic decisions;
  4. ability to explain the basis and structure of the West African economy, including the roles of agriculture, industry and mining and their contributions to the national income;
  5. ability to follow the role and status of the West African countries in international economic relationships;
  6. ability to appreciate the problems West African countries encounter in their economic development.

EXAMINATION SCHEME

There will be two papers – Paper 1 and Paper 2; both of which will be in a composite paper to be taken at one sitting.

Paper 1: Will consist of fifty multiple-choice questions to be taken in 1 hour for 50 marks.

Paper 2: Will consist of eight essay- type questions in two sections: Sections A and B.  Section A will consist of two data response questions. Candidates will be required to answer four questions in all, choosing one question from Section A and any three questions from Section B. The paper shall last 2 hours for 80 marks. 

DETAILED SYLLABUS

1. DEFINITION AND SCOPE OF ECONOMICS

Scarcity and Choice, Scale of Preference, Opportunity Cost, Production Possibility Curve. Economic activities –  Production, Distribution and Consumption. Classification of economic activities – Primary, Secondary and Tertiary and their relative contributions in terms of output/income, employment, savings, investment and foreign exchange.

2. FACTORS OF PRODUCTION :

Land, labour, capital and entrepreneurship- meaning, characteristics and importance.

3. TYPES AND BASIC FEATURES OF ECONOMIC SYSTEMS

  • Types – capitalism, socialism and mixed economy.
  • Basic features of each
  • Advantages and disadvantages of each
  • Economic problems of society and the approaches for solving them under each of the systems.

4. BASIC TOOLS OF ECONOMIC ANALYSIS

Tables, graphs and charts.  Some basic statistical measures and representations –  arithmetic mean, median, mode and their simple applications.

5. DEMAND: 

Concept of demand and law of demand, the demand schedules and curve, reasons for exceptional demand curves,  types of demand (derived, composite, joint and   competitive); factors determining demand for goods and services – price of the commodity,prices of other commodities, income, tastes, price expectation, etc. Distinction between a shift of and movement along a demand curve; concept of elasticity of demand.  Types of elasticity of demand and their measurement – price, income and cross elasticities of demand: importance of the concept of elasticity of demand to consumers, producers and government.

6. SUPPLY

Concept of supply and law of supply, supply schedules and curve, types of Supply – composite, complementary and competitive. Factors determining supply – input prices, technology, prices of other commodities, climatic factors, etc.  Distinction between the shift of and movement along the supply curve. Concept and measurement of elasticity of supply and its importance to producers and government

7. THEORY OF CONSUMER BEHAVIOUR

The utility concepts- total utility, average utility, marginal utility and the calculation of utility schedules. The law of diminishing marginal utility, relationship between total utility, average utility and marginal utility. The concept of equilibrium of a consumer. Determination of consumer equilibrium. The effects of   changes in price on consumer   equilibrium. The relationship between marginal utility and the demand curve.

8. THEORY OF PRICE DETERMINATION

The Concept of the market; interaction between demand and supply. Price determination under free and regulated markets. Equilibrium price and quantity in product and factor markets. The effects of changes in supply and demand on equilibrium prices and quantities. Introduction to algebraic determination of equilibrium price and quantity. Price controls: maximum and minimum price regulations- meaning and their effects; rationing, black market (parallel market)

9. THEORY OF PRODUCTION

Production: division of labour and specialization: Scale of production (Internal and External economies), concept of total, average and marginal productivity and law of variable proportions.

10. THEORY OF COST AND REVENUE

(i)        Cost concepts: total cost, average cost, marginal cost, variable cost, fixed cost; short run and long run costs.

(ii)       Distinction between economist’s and accountant’s view of cost (opportunity cost and money cost).

(iii)     Revenue concepts: total, average and marginal revenue; Marginal revenue Product

11. MARKET STRUCTURE:

Concept of a market, characteristics of various market structures, determination o price and output under different structures – perfect competition and imperfect competition (monopoly and monopolistic competition). Review of cost and revenue concepts.  Price discrimination.

12. BUSINESS ORGANIZATIONS

Types and basic features of business enterprises – Sole Proprietorship; Partnership, Joint- Stock companies (Private and Public), Co-operatives; Statutory Corporation, Joint ventures. Sources of funds.  General and basic problems of business enterprises.  Privatization and Commercialization as solutions to problems of public enterprises. Indigenization and nationalization policies.

13. DISTRIBUTIVE TRADE

Process of distribution, role of producers, role of wholesalers, retailers and co-operatives: the role of government agencies in product distribution and the problems of distribution and their solutions.

14. POPULATION AND LABOUR MARKET

(a)   Population – determination and implication of size and growth of population, Rural – urban migration, Malthusian theory of population  Geographical, age, sex and occupational distribution.  Importance and problems of census.  Population and economic development (under – population, optimum population and over- population).

(b)  Labour Market

  • Concept of labour force and human capital, efficiency and mobility of labour, factors affecting the size of the labour force, particularly the population characteristics (age, sex, occupation, education, etc.)

(c) Supply of and demand for labour: wage determination. Concept of  unemployment and underemployment, Trade Unions, Employers’ association and Government policies on labour and wages.

15. AGRICULTURE

 Structure (e.g. food crops, export crops, livestock, fisheries): systems of agriculture easant, commercial, co-operative and state farming); importance of agriculture to the national economy: marketing of agricultural products (commodity boards).

Agricultural policies (minimum agricultural prices) problems of agriculture and remedies.

 16. INDUSTRIALIZATION

Meaning and types of industry. Definition of industrial concepts: plant, firm, industry and industrial estates. Location of industry, localization, role of industrialization in economic development.  Strategies of industrialization.

Problems of industrialization.The link between agricultural and industrial development.

17. NATIONAL INCOME

Meaning of major national income concepts e.g. Gross Domestic Product, Gross National Product.  Net National Product, etc.  Different ways of measuring national income and their problems.  Uses and limitations of national income

data; trends and structure of national income.

18. MONEY AND INFLATION

(a) Money – definition and historical development-barter and its problems, types, characteristics functions.  Supply of and demand for money, value of money and the price level.

(b)  Inflation: meaning types, causes, effects and control.

19 FINANCIAL INSTITUTIONS

Types (traditional, Central Bank, Commercial Bank, Development Bank, Merchant Bank, and Insurance Companies, Building Societies) : development and functions of financial institutions.  Money and capital markets; meaning, types and functions

20. PUBLIC FINANCE

Fiscal policy and objectives of public finance:  Sources of government revenue. Taxation -types(direct and indirect),objectives, merits, demerits and incidence; Principles/canons of taxation; Rates of taxation(proportional, progressive and  regressive) direct and indirect taxation:  incidence and effects of taxes, composition/ structure of public  expenditure (recurrent and capital expenditure): effects of public expenditure. Government budget and the national debt.

21.  ECONOMIC DEVELOPMENT AND PLANNING

Meaning of economic development, distinction between economic growth and development, characteristics and problems of developing countries, elements of development planning (objectives of planning, and  problems of planning). Types of plans (short term, medium term, perspective or long term, rolling plan etc.).

22. INTERNATIONAL TRADE AND BALANCE OF PAYMENTS

 (a)     International Trade: differences between domestic and international trade, the basis of international trade, absolute and comparative cost advantage,  terms of trade (definition and measurement) commercial policy (objectives) and  instruments –  tariffs (types) and direct control. Trend and structure of West African countries’ external trade.

  • Balance of Payments: role of money in international transactions, meaning and components of balance of payments, balance of payments disequilibrium, balance of payments adjustments (exchange rate policy exchange control, monetary and fiscal policies) and financing (the use of reserves and international borrowing).

23. ECONOMIC INTEGRATION

 Economic Integration (objectives, levels of  and features). Development and problems of economic integration in West Africa- ECOWAS

24. INTERNATIONAL ECONOMIC ORGANIZATIONS

Development and role of:

–  Organization of Petroleum Exporting Countries (OPEC)

– Economic Commission for Africa (ECA)

–  International Monetary Fund (IMF)

–  International Bank for Reconstruction and Development (IBRD)

–  African Development Bank (AfDB)

–  United Nations Conference on Trade and Development (UNCTAD)

etc. relevance of such organizations to West African Countries.

25. MAJOR NATURAL RESOURCES

Development of major natural resources (petroleum, gold, diamond,  timber, groundnut etc) effects on West African economies (positive and negative).

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The Complete WAEC Syllabus for English Language 2020

waec syllabus for english

This examination sets out to test the different basic skills of communicating in English using the mediums of speech and writing. The examination will test the receptive and productive abilities of candidates.

These abilities will be demonstrated in the following forms: reading, comprehension, summary, vocabulary, lexis and structure, listening comprehension and recognition of different aspects of spoken English.

PS: You can get your WAEC Scratch card here

WAEC Syllabus for English AIMS AND OBJECTIVES

The objective of the syllabus is to measure the extent to which the aims of the teaching syllabuses of member countries have been realized in candidates’ secondary school career. The examination sets out to examine candidates’ ability to

(i) use correct English;

(ii) write about incidents in English that are appropriate to specified audiences and situations;

(iii) organize material in paragraphs that are chronologically, spatially and logically coherent;

(iv) control sentence structures accurately;

(v) exhibit variety in the use of sentence patterns;

(vi) comply with the rules of grammar;

(vii) spell and punctuate correctly;

(viii) comprehend written and spoken English;

(ix) recognize implied meaning, tones, and attitudes;

(x) use an acceptable pronunciation that can be comprehended by others;

(xi) recognize the physical characteristics of English sounds and the letters that represent them.

(xii) pick out and summarize relevant information from set passages

SCHEME OF EXAMINATION

There will be three papers – Papers 1, 2 and 3, all of which must be taken. Papers 1 and 2 will be a composite paper to be taken at one sitting.
PAPER 1: Will consist of eighty multiple-choice questions, all of which should be answered within 1 hour for 40 marks.

PAPER 2: Will consist of five essay topics and a passage each to test candidates’ comprehension and summary skills. Candidates will be expected to write an essay on one of the topics and answer all the questions on the comprehension and summary passages.

The paper will last 2 hours and carry 100 marks.

PAPER 3: Will consist of sixty multiple choice items on Test of Orals for candidates in Nigeria and Liberia, and Listening Comprehension Test for candidates in the Gambia and Sierra Leone. All the questions should be answered in 45 minutes for 30 marks.

DETAILED SYLLABUS

PAPER 1: (For candidates in The Gambia, Nigeria, Sierra Leone and Liberia only)

This is an objective/multiple choice paper comprising eighty questions: forty lexical and forty structural questions. Each question will have four options lettered A to D.

A. LEXIS

In addition to items testing knowledge of the vocabulary of everyday usage (i.e home, social relationships, and common core school subjects) questions will be set to test candidates’ ability in the use of the general vocabulary associated with the following fields of human activity:

I. (a) Building and Building Construction; (b) Agriculture; (c) Fishing; (d) Stock exchange; (e) Health; (f) Environment; (g) Culture, Institutions and Ceremonies; (h) Law and Order; (i) Motor Vehicles and Travelling; (j) Government and Administration; (k) Sports; (l) Religion; (m) Science and Technology; (n) Animal husbandry; (o) Advertising; (p) Human Internal Body system and function.

II. Idioms, i.e. idiomatic expressions and collocations (e.g. ‘hook, line and sinker’, ‘every Tom, Dick and Harry” etc.) the total meaning of which cannot be arrived at simply by consideration of the dictionary meanings of the words in the structures in which they appear. III. Structural elements of English e.g. sequence of tenses, matching of pronouns with their antecedents, correct use of prepositions, etc.

IV. Figurative Usage

The term ‘general’ vocabulary refers to those words and usage of words normally associated with the fields of human activity in A1 above which are generally known, used and understood by most educated people who, while not engaged in that field of activity may have occasion to read, speak or write about it. Thus, for example, in the vocabulary of transportation by road, one would expect knowledge of terms such as ‘pedestrian bridge’ and ‘traffic signs’ which most educated people understand, but not ‘berm’ or ‘camber’ which are specialized.

All items will be phrased in such a way as to test the use and understanding of the required lexis, rather than dictionary definitions and explanations. In practice, the test of lexis will be so designed as to explore, not merely the extent of the candidates’ vocabulary but more importantly their ability to respond to sense relations in the use of lexical items e.g. synonyms, antonyms, and homonyms.

In the test of figurative language, candidates will be expected to recognize when an expression is used figuratively and not only when it is used literally.

B. STRUCTURE

Structure here includes: (i) The patterns of changes in word-forms which indicate number, tense, degree, etc; (ii) The patterns in which different categories of words regularly combine to form groups and these groups, in turn, combine to form sentences; (iii) The use of structural words e.g. conjunctions, determiners, prepositions, etc.

PAPER 1: (For candidates in Ghana only)
This is a multiple-choice objective paper comprising eighty questions which will be made up of two parts: Parts A and B. Part A will consist of thirty lexical and twenty structured questions, while Part B will have thirty objective questions on literature. Each question will have four options lettered A to D.

A. LEXIS

In addition to items testing knowledge of the vocabulary of everyday usage (i.e. home, social relationships, common core school subjects) questions will be set to test the candidates’ ability in the use of the general vocabulary associated with the following fields of human activity:

I. (a) Building;

(b) Plumbing;

(c) Fishing;

(d) Finance – commerce, banking, stock exchange, insurance;

(e) Photography;

(f) Mineral exploration;

(g) Common manufacturing industries;

(h) Printing, publishing, the press and libraries;

(i) Sea, road, rail and air transport;

(j) Government and politics;

(k) Sports and entertainment;

(l) Religion;

(m) Science and Technology;

(n) Power production – hydro, thermal, solar;

(o) Education;

(p) Communication;

(q) Military;

(r) Journalism and Advertising.

The term ‘general vocabulary’ refers to those words and usage of words normally associated with the relevant field of human activity in (i) above which are generally known, used and understood by most educated people, who, while not engaged in that field of activity, may have occasion to read, speak or write about it.

Thus, for example, in the vocabulary of transportation by sea, one would expect knowledge of terms such as “bridge” and “deck”, which most educated people understand but not “halyard”, “dodge”, “davit” or “thrust block”, which are specialized.

II. Idioms, i.e., idiomatic expressions and collocations (e.g. “hook, line and sinker”, “every Tom, Dick and Harry” etc) the total meaning of which cannot be arrived at simply by the consideration of the dictionary meanings of words in the structures in which they appear.

III. Structural elements of English e.g. sequence of tenses, concord and the use of correct prepositions, matching of pronouns with their antecedents, etc.

IV. Figurative Usage

All items will be phrased in such a way as to test the use and understanding of the required lexis, rather than dictionary definitions and explanations.

In practice, the test of lexis will be designed to explore, not merely the extent of the candidates’ vocabulary but more importantly their ability to respond to sense relations in the use of lexical items e.g. synonyms, antonyms and homonyms.

In the test of figurative language, candidates will be expected to recognize when an expression is used figuratively and not only when it is used.

B. STRUCTURE

The structure here includes:

(i) The patterns of changes in word-forms which indicate number, tense, degree, etc. (ii) The patterns in which different categories of words regularly combine to form groups and these groups, in turn, combine to form sentences; (iii) The use of structural words e.g. conjunctions, determiners, prepositions, etc.

C. LITERATURE

The objective questions on Literature will be as follows: 10 questions on Drama 10 questions on Prose 10 questions on Poetry

NOTE: For Prose and Drama the candidate is to study one prescribed text each.

PAPER 2: (For all candidates)

The paper will be divided into three sections: Sections A, B and C. Candidates will be required to spend 2 hours on this paper.

SECTION A:

ESSAY WRITING (50 marks)

Candidates will be required to spend 50 minutes on this section. There will be five questions in all and candidates will be required to answer only one question.

The questions will test candidates’ ability to communicate in writing. The topics will demand the following kinds of writing:

(i) letter;

(ii) speech;

(iii) narration;

(iv) description;

(v) argument/debate;

(vi) report;

(vii) article;

(viii) exposition;

(ix) creative writing.

Marks will be awarded for: (i) Content: relevance of ideas to the topic; (ii) Organization: formal features (where applicable), good paragraphing, appropriate emphasis and arrangement of ideas; (iii) Expression: effective control of vocabulary and sentence structure; (iv) Mechanical Accuracy: correct grammar, punctuation, spelling etc.

The minimum length will be 450 words.

SECTION B: COMPREHENSION (20 marks)

Candidates will be required to spend 30 minutes on this section. The section will consist of one passage of at least three hundred and fifty (350) words. Candidates will be required to answer all the questions on the passage.

The questions will test candidates’ ability to;

(i) find appropriate equivalents for selected words or phrases;

(ii) understand the factual content;

(iii) make inferences from the content of the passage;

(iv) understand the use of English expressions that reveal/reflect sentiments/emotions/attitudes;

(v) identify and label basic grammatical structures, words, phrases or clauses and explain their functions as they appear in the context;

(vi) identify and explain basic literary terms and expressions;

(vii) recast phrases or sentences into grammatical alternatives.

The passage will be chosen from a wide variety of sources all of which should be suitable for this level of examination in terms of theme and interest. The passage will be written in modern English that should be within the experience of candidates.

The comprehension test will include at least four questions based on (ii) above.

SECTION C: SUMMARY (30 marks)

Candidates will be required to spend 40 minutes on this section. The section will consist of one prose passage of about five hundred (500) words and will test candidates’ ability to

(i) extract relevant information;

(ii) summarize the points demanded in clear concise English, avoiding repetition and redundancy;

(iii) present a summary of specific aspects or portions of the passage.

The passage will be selected from a wide variety of suitable sources, including excerpts from narratives, dialogues and expositions of social, cultural, economic and political issues in any part of the world.

PAPER 3: ORAL ENGLISH (30 marks)

This paper will test candidates’ knowledge of Oral English. There will be two alternatives for this paper: Candidates in Ghana, The Gambia and Sierra Leone will be tested in listening comprehension and those in Nigeria and Liberia will take a paper on test of oral.

Listening Comprehension Test (For candidates in Ghana, The Gambia and Sierra Leone)

This will be made up of sixty multiple choice objective questions on:

Consonants, consonant clusters, vowels, diphthongs, stress and intonation patterns, dialogues and narratives.

Section 1: Test of word final voiced-voiceless consonants in isolated words mainly, but other features such as consonant clusters may also be tested.

Section 2: Test of vowel quality in isolated words.

Section 3: Test of vowel quality and consonant contrasts in isolated words.

Section 4: One of three options below will be used in different years:

(i) test of vowel and/or consonant contrasts in sentence contexts; (ii) test of vowel and consonant contrasts in isolated words- to be selected from a list of at least four-word contrasts; (iii) test of vowel and consonant contrasts through rhymes.

Section 5: Test of rhymes

Section 6: Test of comprehension of emphatic stress

Section 7: Test of understanding of the content of longer dialogues and narratives

NOTE: CD players will be used for the administration of this Listening Comprehension Test.

Features to be tested

1. CONSONANTS

(a) Single Consonants – Candidates should be able to recognize and produce all significant sound contrasts in the consonantal system of English. For the guidance of candidates, a few examples of such contrasts are given below.

Initial Medial Final they – day buzzes – buses boat – both ship – chip parcel – partial breathe – breed fan – van sopping – sobbing wash – watch pit – fit written – ridden leaf – leave pit – bit anger – anchor cup – cub tuck – duck faces – phrases cart – card card – guard prices – prizes gear – jeer

(b) Consonant Clusters – Candidates should be able to produce and recognize consonant clusters which may occur both initially and finally in a syllable. They should also be able to recognize and produce the consonant sounds in a consonant cluster in the right order. For the guidance of candidates, a few examples are given below.

Initial Final play – pray rains – range sting – string felt – felled scheme – scream sent – send crime – climb nest – next flee – free ask – axe three – tree lift – lived true – drew missed – mixed blight – bright seats – seeds tread – thread hens – hence drift – thrift lisp – lips glade – grade coast – coats marks – masks

II. VOWELS

(a) Pure Vowels

(b) Diphthongs

(c) Triphthongs

Candidates should be able to recognize and produce all the significant sound contrasts in the vowel system of English. For the guidance of candidates, a few examples of such contrasts are given below.

seat – sit sit – set peck – pack pack – park cart – cat load – lord pair – purr park – port hard – heard word – ward let – late cheer – chair pet – pat – part – pate hat – heart – height – hate – hut caught – cot – cut  curt pool – pull – pole bird – bed – bared but – bat

III. STRESS

(a) Word Stress – Candidates should be able to contrast stressed and unstressed syllables in words which are not otherwise distinguished. In addition, they should be aware of the possibility of shifting stress from one syllable to another in different derivations of the same word with consequent change in vowel quality. For the guidance of candidates, a few examples of changing word stress are given below.

‘increase (noun) in’crease (verb) ‘import “ im’port “ ‘rebel “ re’bel “ ‘convict “ con’vict “ ‘extract “ ex’tract “ ‘record “ re’ cord “ ‘subject “ sub’ject “

(b) Sentence Stress – Candidates should be aware that stress in sentences in English tends to occur at regular intervals in time. English is therefore called a stress-timed language. They should also be aware that in most sentences unless some sort of emphasis is introduced, only nouns, main verbs (not auxiliaries), adjectives and adverbs are stressed. Final pronouns should not be stressed unless some kind of contrast is intended: relative pronouns should not be stressed, nor should possessive pronouns. Thus, for example, the following sentences should be stressed as indicated:

He ‘went to the town and ‘bought some ‘oranges.

I ‘told him to ‘go to the ‘station to ‘ask when the train would ‘leave.

Did you ‘ask him?

I ‘read it but I did not understand it.

They ar’rived yesterday.

I ‘fetched his ‘book.

NOTE: There are a few words in English that are pronounced differently depending on whether or not they are stressed in the sentence. These are usually called strong and weak forms.

(c) Emphatic stress – Candidates should be aware of the use of emphatic stress, most commonly to indicate a contrast, which is realized partly as a change in pitch within the intonational pattern. This falling pitch illustrated below is one of the common ways of indicating this:

He borrowed ‘my newspaper. (i.e. not hers) He’ borrowed my newspaper. (i.e. he did not steal it) He borrowed my ‘newspaper.(i.e. not my book) ‘He borrowed my newspaper.(i.e. not someone else’s)

IV. INTONATION

Candidates should be made aware of the different forms that English intonation takes in relation to the grammar of the language and the attitudes conveyed by the speaker. There are two basic intonation patterns or tunes: the falling and rising patterns. They should also realize that whereas the normal place for the changing pitch in intonation is the last stressed syllable of the utterance(as indicated below), placing the changing pitch elsewhere implies a contrast to the item on which this changing pitch falls. For example:

(a) Falling Pattern

They ar’rived to’day. – Statement ‘Where did he ‘go? – WH question ‘Come ‘here! – Command

(b) Rising Pattern

Did he ‘see the ‘principal? – Yes/No question When the ‘train arrived. – Incomplete They arrived to’day? – Question

Note that (i) the two patterns indicated above may be combined in longer sentences, e.g. When the ‘train ar’rived, the passengers were on the platform. ()

(ii) candidates should note, in addition, that any unstressed syllable following the last stressed syllable of the sentence is said on a low level pitch when the pattern is falling but continues the rise if the pattern is rising. The same rule applies to tags following quoted speech.

Test Of Orals (For candidates in Nigeria and Liberia)

The test will also be of the multiple-choice objective type consisting of sixty questions on a wide range of areas or aspects of Orals as contained in the syllabus.

The test will cover the following areas:

1. Vowels – pure vowels and diphthongs;

2. Consonants and clusters;

3. Rhymes;

4. Word stress/Syllable Structure;

5. Emphatic Stress/Intonation Patterns;

6. Phonetic Symbols.

Above is the WAEC Syllabus For English Language for 20192/2020.

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WAEC Syllabus for Physics 2020

waec syllabus for physics

If you are preparing for your WAEC examination, then you know you need to read wide and far.

Rather than reading what is not needed, we have decided to help you lay hands on the WAEC syllabus for physics. You can download the free guide here as a pdf or simply just read this guide.

PS: If you need to check your WAEC result, you can purchase a WAEC Result Checker here

The Complete WAEC Syllabus For Physics

AIMS

The aims of the syllabus are to enable candidates

(1) acquire proper understanding of the basic principles and applications of Physics;

(2) develop scientific skills and attitudes as pre-requisites for further scientific activities;

(3) recognize the usefulness, and limitations of scientific method to appreciate its applicability ion other disciplines and in every life;

(4) develop abilities, attitudes and skills that encourage efficient and safe practice;

(5) develop scientific attitudes such as accuracy, precision, objectivity, integrity, initiative and inventiveness.

WAEC Syllabus For Physics ASSESSMENT OBJECTIVES

The following activities appropriate to Physics will be tested:
(1) Acquisition of knowledge and understanding:

Candidates should be able to demonstrate knowledge and understanding of
(a) Scientific phenomena, facts laws, definitions, concepts and theories;
(b) Scientific vocabulary, terminology and conventions (including symbols, quantities and units);
(c) The use of scientific apparatus, including techniques of operation and aspects of safety; (d) Scientific quantities and their determinations;
(e) Scientific and technological applications with their social economic and environmental implications.

(2) Information Handling and Problem-solving

Candidates should be able, using visual, oral, aural and written (including symbolic, diagrammatic, graphical and numerical) information to

(a) locate select, organize and present information from a variety of sources including
everyday experience;

(b) analyse and evaluate information and other data;

(c) use information to identify patterns, report trends and draw inferences;

(d) present reasonable explanations for natural occurrences, patterns and relationships;

(e) make predictions from data.

(3) Experimental and Problem-Solving Techniques Candidates should be able to

(a) follow instructions;

(b) carry out experimental procedures using apparatus;

(c) make and record observations, measurements and estimates with due regard to precision, accuracy and units;

(d) interpret, evaluate and report on observations and experimental data;

(e) identify problems, plan and carry out investigations, including the selection of techniques, apparatus, measuring devices and materials;

(f) evaluate methods and suggest possible improvements;

(g) state and explain the necessary precautions taken in experiments to obtain accurate results.

WAEC Syllabus For Physics SCHEME OF EXAMINATION

There will be three papers, Papers 1, 2 and 3, all of which must be taken. Papers 1 and 2 will be a composite paper to be taken at one sitting.

PAPER 1: Will consist of fifty multiple choice questions lasting 1¼ hours and carrying 50 marks.

PAPER 2: Will consist of two sections, Sections A and B lasting1½ hours and carrying 60 marks. Section A – Will comprise seven short-structured questions. Candidates will be required to answer any five questions for a total of 15 marks. Section B – Will comprise five essay questions out of which candidates will be required to answer any three for 45 marks.

PAPER 3: Will be a practical test for school candidates or an alternative to practical work paper for private candidates. Each version of the paper will comprise three questions out of which candidates will be required to answer any two in 2¾ hours for 50 marks.

DETAILED WAEC SYLLABUS for Physics

It is important that candidates are involved in practical activities in covering this syllabus.

Candidates will be expected to answer questions on the topics set in the column headed ‘ TOPIC’. The ‘NOTES’ are intended to indicate the scope of the questions which will be set but they are not to be considered as an exhaustive list of limitations and illustrations.

NOTE: Questions will be set in S.I. units. However, multiples or sub-multiples of the units may be used. PART 1 INTERACTION OF MATTER, SPACE & TIME

WAEC Syllabus For Physics

1. Concepts of matter

Simple Structure of Matter should be discussed. Three physics states of matter, namely solid, liquid and gas should be treated. Evidence of the particle nature of matter e.g. Brownian motion experiment, Kinetic theory of matter. Use of the theory to explain; states of matter (solid, liquid and gas), pressure in a gas, evaporation and boiling; cohesion, adhesion, capillarity. Crystalline and amorphous substances to be compared (Arrangement of atoms in crystalline structure to be described e.g. face centred, body centred

2. Fundamental and derived quantities and units (a) Fundamental quantities and units

(b) Derived quantities and units

Length, mass, time, electric current luminous intensity, thermodynamic temperature, amount of substance as examples of fundamental quantities and m, kg, s, A, cd, K and mol as their respective units.

Volume, density and speed as derived quantities and m3, kgm-3 and ms-1 as their respective units

3. Position, distance and displacement.

(a) Concept of position as a location of point-rectangular coordinates. (b) Measurement of distance

(c) Concept of direction as a way of locating a point –bearing (d) Distinction between distance and displacement

Position of objects in space using the X,Y,Z axes should be mentioned.

Use of string, metre rule, vernier calipers and micrometer screw gauge. Degree of accuracy should be noted. Metre (m) as unit of distance.

Use of compass and a protractor.

Graphical location and directions by axes to be stressed

WAEC Syllabus For Physics

4. Mass and weight

Distinction between mass and weight

Use of lever balance and chemical/beam balance to measure mass and spring balance to measure weight. Mention should be made of electronic/digital balance.

Kilogram (kg) as unit of mass and newton (N) as unit of weight

WAEC Syllabus For Physics

5. Time

(a) Concept of time as interval between physical events

(b) Measurement of time

The use of heart-beat, sand-clock, ticker-timer, pendulum and stopwatch/clock.

Second(s) as unit of time

WAEC Syllabus For Physics |

6. Fluid at rest

(a) Volume, density and relative density

(b) Pressure in fluids

(c) Equilibrium of bodies

(i) Archimedes’ principle

(ii) Law of flotation

Experimental determination for solids and liquids.

Concept and definition of pressure. Pascal’s principle, application of principle to hydraulic press and car brakes. Dependence of pressure on the depth of a point below a liquid surface. Atmospheric pressure. Simple barometer, manometer, siphon, syringe and pump. Determination of the relative density of liquids with U-tube and Hare’s apparatus.

Identification of the forces acting on a body partially or completely immersed in a fluid.

Use of the principle to determine the relative densities of solids and liquids.

Establishing the conditions for a body to float in

a fluid. Applications in hydrometer, balloons, boats, ships, submarines etc

7. Motion

(a) Types of motion: Random, rectilinear, translational, Rotational, circular, orbital, spin, Oscillatory.
(b) Relative motion
(c) Cause of motion

(d) Types of force: (i) Contact force (ii) Non-contact force(field force)

(e) Solid friction

Mass, distance, speed and time as examples of scalars.

Weight, displacement, velocity and acceleration as examples of vectors.

Use of force board to determine the resultant of two forces.

Obtain the resultant of two velocities analytically and graphically

(f) Viscosity (friction in fluids)

(g) Simple ideas of circular motion

Only qualitative treatment is required. Illustration should be given for the various types of motion.

Numerical problems on co-linear motion may be set.

Force as cause of motion.

Push and pull These are field forces namely; electric and magnetic attractions and repulsions; gravitational pull.

Frictional force between two stationary bodies (static) and between two bodies in relative motion (dynamic). Coefficients of limiting friction and their determinations. Advantages of friction e.g. in locomotion, friction belt, grindstone. Disadvantages of friction e.g reduction of efficiency, wear and tear of machines. Methods of reducing friction; e.g. use of ball bearings, rollers, streamlining and lubrication.

Definition and effects. Simple explanation as extension of friction in fluids. Fluid friction and its application in lubrication should be treated qualitatively. Terminal velocity and its determination.

Experiments with a string tied to a stone at one end and whirled around should be carried out to

(i) demonstrate motion in a Vertical/horizontal circle.

8. Speed and velocity

(a) Concept of speed as change of distance with time

(b) Concept of velocity as change of displacement with time

(c) Uniform/non-uniform speed/velocity

(d) Distance/displacement-time graph

Metre per second (ms-1) as unit of speed/velocity.

Ticker-timer or similar devices should be used to determine speed/velocity. Definition of velocity as ∆ s ∆t.

Determination of instantaneous speed/velocity from distance/displacement-time graph and by calculation.

9. Rectilinear acceleration

(a) Concept of Acceleration/deceleration as increase/decrease in velocity with time.

(b) Uniform/non-uniform acceleration

(c) Velocity-time graph

(d) Equations of motion with constant acceleration;

Motion under gravity as a special case.

Unit of acceleration as ms-2

Ticker timer or similar devices should be used to determine acceleration. Definition of acceleration as ∆ v ∆t .

Determination of acceleration and displacement from velocity-time graph

Use of equations to solve numerical problems

10. Scalars and vectors

(a) Concept of scalars as physical quantities with magnitude and no direction

(b) Concept of vectors as physical quantities with both magnitude and direction.

(c) Vector representation

(d) Addition of vectors

(e) Resolution of vectors

(f) Resultant velocity using vector representation.

Mass, distance, speed and time as examples of scalars.

Weight, displacement, velocity and acceleration as examples of vectors.

Use of force board to determine the resultant of two forces.

Obtain the resultant of two velocities analytically and graphically

11. Equilibrium of forces

(a) Principle of moments

(b) Conditions for equilibrium of rigid bodies under the action of parallel and non-parallel forces.

(c) Centre of gravity and stability

Torque/Moment of force. Simple treatment of a couple, e.g. turning of water tap, corkscrew and steering wheel.)

Use of force board to determine resultant and equilibrant forces. Treatment should include resolution of forces into two perpendicular directions and composition of forces Parallelogram of forces. Triangle of forces.

Should be treated experimentally. Treatment should include stable, unstable and neutral equilibra.

12. Simple harmonic motion

(a) Illustration, explanation and definition of simple harmonic motion (S.H.M

(b) Speed and acceleration of S.H.M.

(c) Period, frequency and amplitude of a body executing S.H.M.

(d) Energy of S.H.M

(e) Forced vibration and resonance

Use of a loaded test-tube oscillating vertically in a liquid, simple pendulum, spiral spring and bifilar suspension to demonstrate simple harmonic motion.

Relate linear and angular speeds, linear and angular accelerations. Experimental determination of ‘g’ with the simple pendulum and helical spring. The theory of the principles should be treated but derivation of the formula for ‘g’ is not required

Simple problems may be set on simple harmonic motion. Mathematical proof of simple harmonic motion in respect of spiral spring, bifilar suspension and loaded test-tube is not required.

13. Newton’s laws of motion:

(a) First Law: Inertia of rest and inertia of motion

(b) Second Law: Force, acceleration, momentum and impulse

(c) Third Law: Action and reaction

Distinction between inertia mass and weight

Use of timing devices e.g. ticker-timer to determine the acceleration of a falling body and the relationship when the accelerating force is constant.

Linear momentum and its conservation. Collision of elastic bodies in a straight line.

Applications: recoil of a gun, jet and rocket propulsions.

14. Energy: (a) Forms of energy

(b) World energy resources

(c) Conservation of energy.

Examples of various forms of energy should be mentioned e.g. mechanical (potential and kinetic), heat chemical, electrical, light, sound, nuclear.

Renewable (e.g. solar, wind, tides, hydro, ocean waves) and non-renewable (e.g. petroleum, coal, nuclear, biomass) sources of energy should be discussed briefly.

Statement of the principle of conservation of energy and its use in explaining energy transformations

15. Work, Energy and Power

(a) Concept of work as a measure of energy transfer

(b) Concept of energy as capability to do work

(c) Work done in a gravitational field.

(d) Types of mechanical energy

(i) Potential energy (P.E.)

(ii) Kinetic energy (K.E)

(e) Conservation of mechanical energy.

(f) Concept of power as time rate of doing work.

(g) Application of mechanical energymachines. Levers, pulleys, inclined plane, wedge, screw, wheel and axle, gears

Unit of energy as the joule (J)

Unit of energy as the joule (J) while unit of electrical consumption is KWh.

Work done in lifting a body and by falling bodies

Derivation of P.E and K.E are expected to be known. Identification of types of energy possessed by a body under given conditions.

Verification of the principle

Unit of power as the watt (W)

The force ratio (F.R), mechanical advantage (M.A), velocity ratio (V.R) and efficiency of each machine should be treated. Identification of simple machines that make up a given complicated machine e.g. bicycle. Effects of friction on Machines. Reduction of friction in machines

16. Heat Energy

(a) Temperature and its measurement

(b) Effects of heat on matter e.g

(i) Rise in temperature (ii) Change of phase state (iii) Expansion (iv) Change of resistance

(c) Thermal expansion – Linear, area and volume expansivities
Unit

(d) Heat transfer – Condition, convention and radiation.

(e) The gas laws-Boyle’s law Charles’ law, pressure law and general gas law

(f) Measurement of heat energy: (i) Concept of heat capacity (ii) Specific heat capacity.

(g) Latent heat (i) Concept of latent heat

(ii) Melting point and boiling Point

(iii) Specific latent heat of fusion and of vaporization

(h) Evaporation and boiling

(i) Vapour and vapour pressure

(j) Humidity, relative humidity and dew point

(k) Humidity and the weather

Concept of temperature as degree of hotness or coldness of a body. Construction and graduation of a simple thermometer. Properties of thermometric liquids. The following thermometer, should be treated: Constant – volume gas thermometer, resistance thermometer, thermocouple, liquid-in-glass thermometer including maximum and minimum thermometer and clinical thermometer, pyrometer should be mentioned. Celsius and Absolute scales of temperature. Kelvin and degree Celsius as units of temperature.

Use of the Kinetic theory to explain effects of heat.

Mention should be made of the following effects: Change of colour Thermionic emission Change in chemical properties

Qualitative and quantitative treatment Consequences and application of expansions. Expansion in buildings and bridges, bimetallic strips, thermostat, over-head cables causing sagging nd in railway lines causing buckling. Real and apparent expansion of liquids. Anomalous expansion of water.

Per Kelvin (K-1) as the unit of expansivity.

Use of the kinetic theory to explain the modes of heat transfer. Simple experimental illustrations. Treatment should include the explanation of land and sea breezes, ventilation and application s in cooling devices. The vacuum flask.

The laws should be verified using simple apparatus. Use of the kinetic theory to explain the laws. Simple problems may be set. Mention should be made of the operation of safety air bags in vehicles.

Use of the method of mixtures and the electrical method to determine the specific heat capacities of solids and liquids. Land and sea breezes related to the specific heat capacity of water and land, Jkg-1 K-1 as unit of specific heat capacity.

Explanation and types of latent heat.

Determination of the melting point of solid and the boiling point of a liquid. Effects of impurities and pressure on melting and boiling points. Application in pressure cooker.

Use of the method of mixtures and the electrical method to determine the specific latent heats of fusion of ice and of vaporization of steam. Applications in refrigerators and air conditioners.

Jkg-1 as unit of specific latent heat

Effect of temperature, humidity, surface area and draught on evaporation to be discussed.

Explanation of vapour and vapour pressure. Demonstration of vapour pressure using simple experiments. Saturated vapour pressure and its relation to boiling.

Measurement of dew point and relative humidity. Estimation of humidity of the atmosphere using wet and dry-bulb hygrometer.

Formation of dew, fog and rain

17. Production and propagation of waves

(a) Production and propagation of mechanical waves

(b) Pulsating system: Energy transmitted with definite speed, frequency and wavelength.

(c) Waveform

(d) Mathematical relationship connecting frequency (f), wavelength(), period (T) and velocity (v)

Use of ropes and springs (slinky) to generate mechanical waves

Use of ripple tank to show water waves and to demonstrate energy propagation by waves. Hertz(Hz) as unit of frequency.

Description and graphical representation. Amplitude, wave length, frequency and period. Sound and light as wave phenomena. V= f and T = simple problems may be set

18. Types of waves

(a) Transverse and longitudinal

(b) Mathematical representation of wave motion

Examples to be given

Equation y = A sin (wt±

) to be explained Questions on phase difference will not be set

19. Properties of waves: Reflection, refraction, diffraction, Interference, superposition of progressive waves producing standing stationary waves

Ripple tank should be extensively used to demonstrate these properties with plane and circular waves. Explanation of the properties

20. Light waves

(a) Sources of light

(b) Rectilinear propagation of light

(c) Reflection of light at plane surface: plane mirror

(d) Reflection of light at curved surfaces: concave and convex mirrors

(e) Refraction of light at plane surfaces: rectangular gla

(g) Application of lenses in optical instruments.

(h) Dispersion of white light by a triangular glass prism.

Natural and artificial. Luminous and non-luminous bodies

ss prism (block) and triangular prism.

(f) Refraction of light at curved

surfaces: Converging and diverging lenses

Formation of Shadows and eclipse. Pinhole camera. Simple numerical problems may be set.

Regular and irregular reflections. Verification of laws of reflection. Formation of images. Inclined plane mirrors. Rotation of mirrors. Applications in periscope, sextant and kaleidoscope.

Laws of reflection. Formation of images. Characteristics of images. Use of mirror formulae:
+ = and magnification m = to solve numerical problems. (Derivation of formulae is not required)

Experimental determination of the focal length of concave mirror. Applications in searchlight, parabolic and driving mirrors, car headlamps etc.

Laws of refraction. Formation of images, real and Apparent depths. Critical angle and total internal reflection. Lateral displacement and angle of deviation. Use of minimum deviation equation:

Sin (A + Dm) = 2

Sin A/2 (Derivation of the formula is not required) Applications: periscope, prism binoculars, optical fibres. The mirage.

Formation of images. Use of lens formulae + = and magnification tp solve numerical problems

(derivation of the formulae not required). Experimental determination of the focal length of converging lens. Power of lens in dioptres (D)

Simple camera, the human eye, film projector, simple and compound microscopes, terrestrial and astronomical telescopes. Angular magnification. Prism binoculars. The structure and function of the camera and the human eye should be compared. Defects of the human eye and their corrections.

Production of pure spectrum of a white light. Recombination of the components of the spectrum. Colours of objects. Mixing coloured lights

21. Electromagnetic waves: Types of radiation in electromagnetic Spectrum

Elementary description and uses of various types of radiation: Radio, infrared, visible light, ultra-violet, X-rays, gamma rays.

22. Sound Waves

(a) Sources of sound (b) Transmission of sound waves

(c) Speed of sound in solid, liquid and

air

(d) Echoes and reverberation

(e) Noise and music (f) Characteristics of sound

(g) Vibration in strings

(h) Forced vibration

(i) Resonance (ii) Harmonies and overtones

(i) Vibration of air in pipe – open and closed pipes

Experiment to show that a material medium is required.

To be compared. Dependence of velocity of sound

on temperature and pressure to be considered.

Use of echoes in mineral exploration, and determination of ocean depth. Thunder and multiple reflections in a large room as examples of reverberation.

Pitch, loudness and quality

The use of sonometer to demonstrate the dependence of frequency (f) on length (1), tension (T) and mass per unit length (liner density) (m) of string should be treated. Use of the formula:

o =

In solving simple numerical problems. Applications in stringed instruments: e.g. guitar, piano, harp and violin.

Use of resonance boxes and sonometer to illustrate forced vibration.

Use of overtones to explain the quality of a musical note. Applications in percussion instruments: e.g drum, bell, cymbals, xylophone.

Measurement of velocity of sound in air or frequency of tuning fork using the resonance tube. Use of the relationship v = in solving numerical problems. End correction is expected to be mentioned. Applications in wind instruments e.g. organ, flute, trumpet, horn, clarinet and saxophone

WAEC Syllabus For Physics – PART IV FIELDS

23. Description property of fields.

(a) Concept of fields: Gravitational, electric and Magnetic

(b) Properties of a force field

Use of compass needle and iron filings to show magnetic field lines

24. Gravitational field

(a) Acceleration due to gravity, (g)

(b) Gravitational force between two masses:

Newton’s law of gravitation

(c) Gravitational potential and escape velocity

G as gravitational field intensity should be mentioned, g = F/m.

Masses include protons, electrons and planets

Universal gravitational constant (G) Relationship between ‘G’ and ‘g’

Calculation of the escape velocity of a rocket from the earth’s gravitational field

25. Electric Field

(1) Electrostatics (a) Production of electric charges

(b) Types of distribution of charges

(c) Storage of charges

(d) Electric lines of force

(e) Electric force between point charges: Coulomb’s law

(f) Concepts of electric field, electric field intensity (potential gradient) and electric potential.

(g) Capacitance- Definition, arrangement and application

Production by friction, induction and contact.

A simple electroscope should be used to detect and compare charges on differently-shaped bodies.

Application in light conductors.

Determination, properties and field patterns of charges

Permittivity of a medium.

Calculation of electric field intensity and electric potential of simple systems.

Factors affecting the capacitance of a parallel-plate capacitor. The farad (F) as unit of capacitance. Capacitors in series and in parallel. Energy stored in a charged capacitor. Uses of capacitors: e.g. in radio and Television. (Derivation of formulae for capacitance is not required)

(2) Current electricity (a) Production of electric current from primary and secondary cells

(b) Potential difference and electric current

(c) Electric circuit

(d) Electric conduction through materials

(e) Electric energy and power

(f) Shunt and multiplier

(g) Resistivity and Conductivity

(h) Measurement of electric current, potential difference, resistance, e.m.f. and internal resistance of a cell

Simple cell and its defects. Daniel cell, Lechanché cell (wet and dry). Lead-acid accumulator. Alkalne-cadium cell. E.m.f. of a cell, the volt (V) as unit of e.m.f.

Ohm’s law and resistance. Verification of Ohm’s law. The volt (V), ampere (A) and ohm (Ω) as units of p.d., current and reisistance respectively.

Series and parallel arrangement of cells and resistors. Lost volt and internal resistance of batteries.

Ohmic and non ohmic conductors. Examples of ohmic conductors are metals, non-ohmic conductors are semiconductors.

Quantitative definition of electrical energy and power. Heating effect of an electric current and its application. Conversion of electrical energy to mechanical energy e.g. electric motors. Conversion of solar energy to electrical and heat energies: e.g. solar cells, solar heaters

Use in conversion of a galvanometer into an ammeter and a voltmeter.

Factors affecting the electrical resistance of a material should be treated. Simple problems may be set.

Principle of operation and use of ammeter, voltmeter, potentiometer. The wheatstone bridge and metre bridge

26. Magnetic field

(a) Properties of magnets and magnetic materials.

(b) Magnetization and demagnetization.

(c) Concept of magnetic field

(d) Magnetic force on: (i) a current-carrying conductor placed in a magnetic field; (ii) between two parallel current-carrying conductors (e) Use of electromagnets

(f) The earth’s magnetic field

(g) Magnetic force on a moving charged particle

Practical examples such as soft iron, steel and alloys.

Temporary and permanent magnets. Comparison of iron and steel as magnetic materials.

Magnetic flux and magnetic flux density. Magnetic field around a permanent magnet, a current-carrying conductor and a solenoid. Plotting of line of force to locate neutral points Units of magnetic flux and magnetic flux density as weber (Wb) and tesla (T) respectively.

Qualitative treatment only. Applications: electric motor and moving-coil galvanometer.

Examples in electric bell, telephone earpiece etc.

Mariner’s compass. Angles of dip and declination.

Solving simple problems involving the motion of a charged particle in a magnetic field, using F=qvB sin

27. Electromagnetic field

(a) Concept of electromagnetic field

(i) Shunt and multiplier

(j) Resistivity and Conductivity

(k) Measurement of electric current, potential difference, resistance, e.m.f. and internal resistance of a cell.

Identifying the directions of current, magnetic field and force in an electromagnetic field (Fleming’s lefthand rule

Use in conversion of a galvanometer into an ammeter and a voltmeter.

Factors affecting the electrical resistance of a material should be treated. Simple problems may be set.

Principle of operation and use of ammeter, voltmeter, potentiometer. The wheatstone bridge and metre bridge

28. Magnetic field

(h) Properties of magnets and magnetic materials.

(i) Magnetization and demagnetization.

(j) Concept of magnetic field

(k) Magnetic force on: (i) a current-carrying conductor placed in a magnetic field; (ii) between two parallel current-carrying conductors (l) Use of electromagnets

(m) The earth’s magnetic field

(n) Magnetic force on a moving charged particle

Practical examples such as soft iron, steel and alloys.

Temporary and permanent magnets. Comparison of iron and steel as magnetic materials.

Magnetic flux and magnetic flux density. Magnetic field around a permanent magnet, a current-carrying conductor and a solenoid. Plotting of line of force to locate neutral points Units of magnetic flux and magnetic flux density as weber (Wb) and tesla (T) respectively.

Qualitative treatment only. Applications: electric motor and moving-coil galvanometer.

Examples in electric bell, telephone earpiece etc.

Mariner’s compass. Angles of dip and declination.

Solving simple problems involving the motion of a charged particle in a magnetic field, using F=qvB sin

27. Electromagnetic field

(a) Concept of electromagnetic field

(b) Electromagnetic induction

Faraday’s law ,Lenz’s law and motor-generator effect

(c) Inductance

(d) Eddy currents

(e) Power transmission and distribution

Identifying the directions of current, magnetic field and force in an electromagnetic field (Fleming’s lefthand rule

Applications: Generator (d.c.and a.c.) induction coil and transformer. The principles underlying the production of direct and alternating currents should be treated. Equation E = Eo sinwt should be explained.

Qualitative explanation of self and mutual inductance. The unit of inductance is henry (H).

(E =
LI2)

Application in radio,T.V., transformer. (Derivation of formula is not required).

A method of reducing eddy current losses should be treated. Applications in induction furnace, speedometer, etc.

Reduction of power losses in high-tension transmission lines. Household wiring system should be discussed.

28. Simple a.c. circuits

(a) Graphical representation of e.m.f and current in an a.c. circult.

(b) Peak and r..m.s. values

(c) Series circuit containing resistor, inductor and capacitor

(d) Reactance and impedance

(e) Vector diagrams

(f) Resonance in an a.c, circuit

(g) Power in an a.c. circuit

Graphs of equation I – Io sin wt and\E = Eo sinwt should be treated.

Phase relationship between voltage and current in the circuit elements; resistor, inductor and capacitor

Simple calculations involving a.c. circuit. (Derivation of formulae is not required.)

XL and Xc should be treated. Simple numerical problems may be set.

Applications in tuning of radio and T.V. should be discussed

WAEC Syllabus For Physics | PART V

ATOMIC AND NUCELAR PHYSICS

29. Structure of the atom

(a) Models of the atom

(b) Energy quantization

(c) Photoelectric effect

(d) Thermionic emission

(e) X-rays

Thomson, Rutherford, Bohr and electroncloud (wave-mechanical) models should be discussed qualitatively. Limitations of each model. Quantization of angular momentum (Bohr)

Energy levels in the atom. Colour and light frequency. Treatment should include the following: Frank-Hertz experiment, Line spectra from hot bodies, absorption spectra and spectra of discharge lamps.

Explanation of photoelectric effect. Dual nature of light. Work function and threshold frequency. Einstein’s photoelectric equation and its explanation. Application in T.V., camera, etc. Simple problems may be set.

Explanation and applications

Production of X-rays and structure of X-ray tube. Types, characteristics, properties, uses and hazards of X-rays. Safety precautions

30. Structure of the nucleus

(a) Composition of the nucleus

(a) Radioactivity – Natural and artificial

(b) Nuclear reactions — Fusion and Fission

Radioactive elements, radioactive emissions (,β,)and their properties and uses. Detection of radiations by G – M counter, photographic plates, etc. should be mentioned. Radioactive decay, half-life and decay constant. Transformation of elements. Applications of radioactivity in agriculture, medicine, industry, archaeology, etc.

Distinction between fusion and fission. Binding energy, mass defect and energy equation:

E= ∆ mc2

Nuclear reactors. Atomic bomb. Radiation hazards and safety precautions. Peaceful uses of nuclear reactions

31. Wave-particle paradox

(a) Electron diffraction (b) Duality of matter

Simple illustration of the dual nature of light

HARMONISED TOPICS FOR SHORT STRUCTURED QUESTIONS FOR ALL MEMBER COUNTRIES

WAEC Syllabus For Physics | 1. Derived quantities and dimensional Analysis

Fundamental quantities and units e.g. Length, mass, time, electric current, luminous intensity e.t.c., m, kg,s, A, cd, e.t.c. as their respective units Derived quantities and units. e.g. volume, density, speed e.t.c. m3, kgm-3, ms-1 e.t.c. as their respective unit Explanation of dimensions in terms of fundamental and derived quantities. Uses of dimensions – to verity dimensional correctness of a given equation – to derive the relationship between quantities – to obtain derived units.

2. Projectile motion concept of projectiles as an object thrown/release into space

Applications of projectiles in warfare, sports etc. Simple problems involving range, maximum height and time of flight may be set.

3. Satellites and rockets

Meaning of a satellite comparison of natural and artificial satellites parking orbits, Geostationary satellites and period of revolution and speed of a satellite. Uses of satellites and rockets

4. Elastic Properties of solid: Hooke’s law, Young’s modules and work done in springs and string

Thermal conductivity: Solar energy collector and Black body Radiation.

Behaviour of elastic materials under stress – features of load – extension graph Simple calculations on Hook’s law and Young’s modulus.

Solar energy; solar panel for heat energy supply. Explanation of a blackbody. Variation of intensity of black body radiation with wavelength at different temperatures

5. Fibre Optics

Explanation of concept of fibre optics. Principle of transmission of light through an optical fibre Applications of fibre optics e.g. local area Networks (LAN) medicine, rensing devices, carrying laser beams e.t.c

6. Introduction to LASER

Meaning of LASER Types of LASERS (Solid state, gas, liquid and semi-conductor LASERS Application of LASERS (in Scientific research, communication, medicine military technology, Holograms e.t.c. Dangers involved in using LASERS

7. Magnetic materials

Uses of magnets and ferromagnetic materials

8. Electrical Conduction through materials [Electronic]

Distinction between conductors, semiconductors and insulators in term of band theory. Semi conductor materials (silicon and germanium) Meaning of intrinsic semiconductors. (Example of materials silicon and germanium). Charge carriers Doping production of p-type and n-type extrinsic semi conductors. Junction diode – forward and reverse biasing, voltage characteristics. Uses of diodes Half and full wave rectification

9. Structure of matter

Use of kinetic theory to explain diffusion.

10. Wave – particle paradox

Electron diffraction Duality of matter Simple illustrations of dual nature of light.

Above is the WAEC Syllabus For WAEC 2020/2021

You can download the WAEC Syllabus for PHYSICS as a PDF

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12 Cheapest Universities in Nigeria 2020

cheapest universities in Nigeria

looking for the cheapest universities in Nigeria?

Education is usually said to be expensive and we cannot deny that it is. However, the importance of education cannot be over-emphasized, so the cost is also not an excuse.

Thankfully, there are schools where the cost is relatively cheap compared to other schools in Nigeria.

Federal schools, especially, fall into this category because the federal government subsidizes the price.

These federal universities provide education at an affordable rate, so both candidates from humble and well-to-do backgrounds can be confident to apply.

In no particular order, find the cheapest federal universities in Nigeria:

#1: Ahmadu Bello University, Zaria: One of the largest universities in Nigeria and regarded as the best university in Northern Nigeria by many, ABU is one of the first generation universities in Nigeria. The university established in 1962 operates two campuses in Samaru and Kongo, both in Zaria. It is home to both undergraduate and postgraduate courses as well as several other programs. Based on the department, the school fees of ABU is between N20,000 to N33,000.

#2: Federal University of Agriculture: Established in 1988 in the capital city of Ogun state, UNAAB is the first University of Agriculture in Nigeria. The university, which was formerly situated in Isale-Igbein in the heart of Abeokuta, has now moved to the permanent site at a 10,000-hectare campus located on the 15km Abeokuta-Ibadan Road. The school fees of UNAAB ranges from N18,250 to N33,000 depending on the department.

#3: University of Ibadan: The premier university was established in 1948. Located in the city of Ibadan, it is regarded as one of the best universities in Nigeria. The school boasts as one of the institutions with the highest number of professors in West Africa. With 12 faculties including Law and the College of Medicine, the school fees of UI are between N20,000 to N35,000, depending on the department.

#4: University of Benin: Established in 1970, the University of Benin started as an Institute of Technology and was accorded the status of a full-fledged University by National Universities Commission (NUC) in 1971. The school which boasts of 12 faculties excluding the school of medicine, has been able to retain its enviable reputation as one of the best universities in Nigeria. The school fees of UNIBEN is between N13,000 and N49,000, depending on the department.

#5: University of Lagos: One of the most popular universities in Nigeria, it has the facade of being expensive but it is actually one of the cheapest schools in Nigeria. Established in 1962, the school operates two campuses at Akoka, Yaba and the College of Medicine at Idi-Araba, Surulere with both campuses housing about 14 faculties. University of Lagos’ school fees ranges from N14,500 to about N65,000, based on the department.

#6: Obafemi Awolowo University: Formerly University of Ife, Obafemi Awolowo University was established in 1961 in the ancient city of Ile-Ife by the regional government of Western Nigeria, led by late Chief Samuel Ladoke Akintola. The school maintains its outstanding standard and is consistently in the list of the best schools in Nigeria. OAU offers both undergraduate and postgraduate programs in different fields. Depending on the department, the school fees range from about N19,500 to N65,000.

#7: Bayero University: Located in the heart of one of the most populous cities in Nigeria, Kano, Bayero University was founded in 1977. The school, which started as a University College, was named after the former Emir of Kano, Abdullahi Bayero. One of the most popular and one of the best universities in Northern Nigeria, BUK offers programs in 12 faculties. The school fees range from N26,000 to N40,000 based on the department.

#8: University of Ilorin: Established by a decree of the Federal Military Government in 1975, Unilorin has successfully held its own among the best universities in Nigeria alongside the first generation universities. Offering courses in more than 16 faculties, the school is one of the cheapest in Nigeria. The school fees of Unilorin is between about N10,700 to N18,300, depending on the faculty.

#9: University of Abuja: Located in the nation’s Federal Capital Territory, Abuja, Uniabuja was founded in 1988. The youngest school on this list, the school is highly recognized for its Law Faculty. The institution has a mini-campus at Gwagwalada while the main campus is on a site covering about 11,824 hectares which can be seen along the Kaduna – Lokoja – Abuja Road. The school fees range from N39,300 to N42,300 based on the department.

#10: Usman Danfodiyo University: The school was established in 1975 in the ancient city of Sokoto and named after the founder of the Sokoto Caliphate, Usman Dan Fodio. The school has four campuses around the city of Sokoto. The school fees of UDUS is between N24,000 and N54,000, depending on the department.

#11: Federal University of Technology: It was established under a drive by the Federal Government to create different universities that specialized in producing graduates with practical as well as theoretical knowledge of technologies. Currently offering programs from seven schools, the school fees of FUTA is between N13,000 and N52,000 based on the department.

#12: University of Calabar: Located in the city of Calabar, the school was a campus of the University of Nigeria until 1975. The school is arguably one of the best universities in the South-South region. The school fees range from N30,000 to N24,000 depending on the department.

In conclusion, it is important to note that these were the school fees as at the time this article was written and the school fees do experience changes sometimes. Remember for you to gain admission into any of these universities, you need to pass your WAEC and Jamb Examinations.

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The Complete WAEC Syllabus For Biology 2020

waec syllabus for biology

This is an examination syllabus drawn up from the curricula of the member countries of the West African Examinations Council. It should be used alongside the appropriate teaching syllabus(es) of the country where the candidates are domiciled.

This examination syllabus is divided into three sections: Sections A, B and C. Section A is for all candidates, Section B is for candidates in Ghana only and Section C is for candidates in Nigeria, Sierra Leone The Gambia and Liberia.

WAEC Syllabus For Biology: AIMS AND OBJECTIVES

This syllabus is designed to assess candidates’
1 . understanding of the structure and functions of living organisms as well as appreciation of nature;
2. acquisition of adequate laboratory and field skills in order to carry out and evaluate experiments and projects in Biology;
3. acquisition of necessary scientific skills for example observing, classifying and interpreting biological data;
4. acquisition of the basic relevant knowledge in Biology needed for future advanced studies in biological sciences;
5. acquisition of scientific attitudes for problem solving;
6. ability to apply biological principles in everyday life in matters that affect personal, social, environmental, community health and economic problems;

7. awareness of the existence of interrelationships between biology and other scientific disciplines.

WAEC Syllabus For Biology: SCHEME OF EXAMINATION

There will be three papers: Papers 1, 2 and 3, all of which must be taken. Papers 1 and 2 will be a composite paper to be taken at one sitting.

PAPER 1: Will consist of fifty multiple-choice objective questions drawn from Section A of the syllabus (the section of the syllabus which is common to all countries). It will carry 50 marks and last for 50 minutes.

PAPER 2: Will consist of six essay questions drawn from the entire syllabus. The paper will be put into three sections, Sections A, B and C.

Section A:

Will consist of four questions drawn from Section A of the syllabus.

Section B:

Will be for candidates in Ghana only and will be drawn from Section B of the syllabus (ie the section of the syllabus perculiar to Ghana). It will consist of short-structured questions.

Section C:

Will be for candidates in Nigeria, Sierra Leone, The Gambia and Liberia and will be drawn from Section C of the syllabus (ie the section of the syllabus containing material for those countries only). It will also consist of short-structured questions.
Candidates will be expected to answer two questions from Section A and all the short-structured questions from either Section B or Section C.

Each question in Section A will carry 20 marks while the compulsory short-structured questions in Sections B and C will carry 30 marks. The total score will be 70 marks. The paper shall take 1 hour 40 minutes.

PAPER 3: Will be a practical test (for school candidates) or a test of practical work (for private candidates) lasting 2 hours and consisting of three sections: Sections A, B and C.

Section A:

This will consist of two compulsory questions drawn from Section A of the syllabus, each carrying 25 marks.

Section B:

This will be for candidates in Ghana only. It will consist of one question drawn from Section B of the syllabus and will carry 30 marks.

Section C:

This will be for candidates in Nigeria, Sierra Leone, The Gambia and Liberia. It will consist of one question drawn from Section C of the syllabus and will carry 30 marks.

Candidates will be expected to answer all the questions in Section A and one question in either Section B or C. The paper will carry a total score of 80 marks.

A. Concept of Living

1. Classification

(a) Living and non-living things

(b) Classification of living things into Kingdoms: Monera, Protoctista (Protista), Fungi, Plantae, Animalia

(c) Differences between plants and animals

Classification of objects into living and nonliving, giving examples of each group. Viruses should be mentioned as a link between living and non living things.

Kingdom Monera (Prokaryotes), singlecelled, motile or non-motile organisms without definite nucleus e.g. bacteria and blue-green algae.

Major characteristics of the major phyla of Kingdoms Protoctista and Fungi.

Kingdom Protista (Eukaryotes), single-celled, motile or non-motile organisms. Cell structure complex with definite nucleus e.g. Chlamydomonas, Amoeba. Major phyla of Kingdom Protoctista include: Rhizopoda, Zoomastigina, Apicomplexa, Ciliophora, Euglenophyta, Oomycota, Chlorophyta, Rhodophyta and Phaeophyta.

Kingdom Fungi (Eukaryotes), mainly nonmotile organisms composed of hyphae containing nuclei e.g. moulds, mushrooms and Rhizopus. Major phyla of Kingdom Fungi include: Zygomycota, Ascomycota and Basidiomycota.

Kingdom Plantae (Eukaryotes), mainly multicellular non-motile organisms which contain chlorophyll that enable them to photosynthesize e.g. mosses, ferns, pines, oil palms and yam plants. Characteristics of the major divisions and classes: Bryophyta (Hepaticae, Musci), Lycopodophyta, Filicinophyta, Coniferophyta, Cycadophyta and Angiospermophyta (Monocotyledoneae and Dicotyledoneae).

Kingdom Animalia (Eukaryotes), multicellular motile organisms that feed on other organisms e.g. corals, worms, insects, snails, fishes, frogs, snakes, monkeys cows. Characteristics of the major phyla and classes of Kingdom Animalia. The external features of the following organisms should be mentioned: cockroach, butterfly, Tilapia, toad/frog, lizard, domestic fowl/pigeon

2. Organization of life

(a) Levels of organization (i) cell (single-celled organisms): Amoeba, Euglena, Paramecium

(ii) Tissue: Hydra

(iii) Organ (storage organ) bulb, rhizome and heart.

(iv) System/Organ System: In mammals, flowering plants – reproductive system, excretory system etc.

(b) Complexity of organization in higher organisms: advantages and disadvantages.

3. Forms in which living cells exist:

(a) Single and free-living: Amoeba, Paramecium, Euglena, and Chlamydomonas

(b) Colony: Volvox
(c) Filament: Spirogyra
(d) Part of a living organism: Cheek cells, onion root tip cells and epidermis of fleshy leaves

The examples should be used to illustrate differentiation and specialization in organisms.

The significance of different levels of organization including volume/surface area ratio should be mentioned.

The structure of these organisms in relation to the forms of existence should be studied to illustrate dependence and interdependence.

Distinguish groups of cells that form tissues from those that form colonies or filaments

4. (a) Cell structure and functions of cell components.

(b) Similarities and differences between plant and animal cells.

5. The Cell and its environment:

Physical and Biophysical processes. (a) diffusion (b) osmosis (c) active transport

6. Properties and functions of the living cell

(a) Nutrition

(i) Autotrophic (photosynthesis)

(ii) Heterotrophic (holozoic)

(b) Cellular respiration

Definition and processes of:

(i) aerobic respiration
(ii) anaerobic respiration
(iii) energy release

WAEC Syllabus For Biology | (c) Excretion

(i) Excretion in single-celled aquatic organisms. Diffusion by body surface and by contractile vacuole.

(ii) Waste products of metabolism.

(d) Growth

(i) Basis of growth – cell division (mitosis), enlargement and differentiation.

(ii) Aspects of growth: Increase in dry weight, irreversible increase in size and length and increase in number of cells.

(iii) Regions of fastest growth in plants.

(iv) Influence of growth hormones and auxins.

(v) Growth curvatures (Tropisms)

(e) Development:

Enlargement and differentiation.

(f) Movement

(i) Organelles for movement: cilia and flagella, (ii) Cyclosis.

(g) Reproduction: Types of reproduction.

(i) Asexual: fission, budding and vegetative propagation.

(ii) Sexual: Conjugation, formation of male and female gametes (gametogenesis), fusion of gametes fertilization

Cell structure should include: Cell wall, cell membrane, nucleus, cytoplasm, cytoplasmic organelles: mitochondria, lysosomes, chloroplasts, endoplasmic reticulum, ribosomes, centrosomes, Golgi bodies, chromosomes. The function performed by organelles should be known.

The significance of these processes should be mentioned as factors that affect cell activities in its environment.

Haemolysis, plasmolysis, turgidity and crenation should be mentioned.

These should be mentioned as processes occurring within living cells.

Nutrition in Euglena, Chlamydomonas and Spirogyra should be mentioned.

Nutrition in Amoeba and Paramecium should be mentioned

A simplified outline of the chemical processes involved in glycolysis and Kreb’s cycle; Reference should be made to the role of ATP.

The importance of anaerobic respiration in food processing should be mentioned.

Reference should be made to carbon dioxide, water and ammonia as examples of waste products.

Observation of root tip and shoot tip are required.

Regulation of growth by hormones should be mentioned.

Types of tropisms should be demonstrated.

Microscopic examination of the different regions of growth and development: region of cell division, elongation, differentiation and maturation.

Processes that result in primary and secondary growth.

Prepared slides of: (a) fission in Paramecium (b) budding in yeast and Chlamydomonas; should be observed and drawn.

Prepared slides of conjugation in Paramecium and Spirogyra should be studied. The process of meiosis should be mentioned

7. (a) Tissues and supporting systems:

Skeleton and supporting systems in animals:
(i) Biological significance.

(ii) Skeletal materials, e.g. bone, cartilage and chitin.
(iii) Types of skeleton: exoskeleton, endoskeleton and hydrostatic skeleton.
(iv) Bones of the vertebral column, girdles and long bones of the appendicular skeleton.
(v) Mechanism of support in animals.
(vi) Functions of skeleton in animals: Protection, support, locomotion and respiratory movement.

(b) Different types of supporting tissues in plants.

(i) Main features of supporting tissues in plants.
(ii) Functions of supporting tissues in plants: strength, rigidity (resistance against the forces of the wind and water), flexibility and resilience.

The location and arrangement of skeletal and supporting tissues in animals should be mentioned. Candidates should be familiar with the general plan of mammalian skeleton and the different types of joints. They should be able to identify, draw, label and state the functions of the individual bones listed in the content column. Detailed structure of the skull will not be required. Histological structure of bones and cartilages will also not be required.

Candidates should be able to explain how these functions are performed. The relationship of skeleton and muscles during movement should be used to illustrate the different functions of the skeleton.
The different types of supporting tissues: turgid parenchyma, collenchyma, xylem (wood) sclerenchyma should be studied.

Candidates should be able to cut and draw the low power of the T.S. of stem and root of a herbaceous plant and label the different tissues; epidermis, cortex and stele

WAEC Syllabus For Biology | 8. Transport System:

(a) Need for transport:
(i) surface area/volume ratio. (ii) substances have to move greater distances.

(b) Transport in animals.
(i) Structure of the heart, arteries, veins and capillaries.

(ii) Composition and function of blood and lymph.
(iii) Materials for transport: excretory products, gases, digested food, and other nutrients.

(c) Transport in plants (i) Uptake and movement of water and mineral salts in plants.

(ii) Translocation

(iii) Transpiration

(iv) Movement of water to the apex of trees and herbs.

Source of materials and forms in which they are transported and where they are transported to should be studied. Media of transport: cytoplasm in cells, cell sap or latex in most plants and body fluid in invertebrates.

Candidates should be familiar with the general circulatory system. Open circulatory systems in invertebrates. The names of the blood vessels responsible for transporting excretory products, gases, digested food and other nutrients should be mentioned.

Description of uptake of water and mineral salts from the soil into a plant. Movement of water and mineral salts through the plant. Experiments using eosin solution to show water and mineral salts uptake.

Movement of organic materials from leaves to roots. Basic theories (Pressure flow hypothesis and cytoplasmic streaming) underlying translocation. Ringing experiment to demonstrate that transport of synthesized organic nutrients occurs through the phloem.

Advantages and disadvantages of transpiration. Types of transpiration. Environmental factors affecting transpiration. Determination of the rate of transpiration.

Physiological factors affecting the rise of water in the xylem: Root pressure, transpiration, cohesion- tension mechanism, adhesion, water potential gradient. Experiments to measure the rate of transpiration.

9. Respiratory System:

(a) Body surface: cutaneous, gills and lungs.

(b) Mechanisms of gaseous exchange in fish, toad, mammals and plants.

10. Excretory Systems and Mechanisms Types of excretory systems: Kidney, stomata and lenticels

WAEC Syllabus For Biology | 11. Regulation of Internal Environment (Homeostasis)

(a) Kidney: Structure and functions

(b) Liver

Functions of the liver.

(c) The skin:

Structure and function.

Characteristics of respiratory surfaces in these systems should be studied. Respiratory organs of insects should be mentioned.

Candidates should be able to observe, draw and label the respiratory organs of a bony fish (e.g. Tilapia) and a small mammal (e.g. rat)
Respiratory movements in these animals should be mentioned. The mechanisms of opening and closing of stomata should be mentioned.
Characteristics of excretory organs in these systems should be studied. Candidates should observe, draw and label the excretory organs of a small mammal (e.g. rat).

Explanation of the concept of excretion in plants. Excretory products of plants (water, carbon dioxide, oxygen, alkaloids, tannins, gums, resins and acids) should be mentioned.

Osmoregulation, excretion and maintenance of acid-base balance should be mentioned. The conditions that affect functions of the kidney such as the water and salt content of the blood, environmental temperature should also be mentioned.
Excretory products such as urea, water, salts, uric acid should be mentioned

Candidates should be able to identify the liver; and its position relative to the gall bladder, bile duct, pancreas, duodenum and stomach.
Candidates should observe, draw and label the mammalian skin. The regulation of internal environment by the skin should be emphasized

12. Hormonal Coordination

(a) Animal hormones: Site of secretion, functions and effects of over and undersecretion.

(b) Plant hormones

Endocrine glands: pituitary, thyroid, adrenal, pancreas, gonads and their secretions should be mentioned. The stages in the metamorphosis of toad and the role of thyroxine should be mentioned.

The effects of auxins on lateral bud development, leaf fall and initiation of adventitious roots should be mentioned. Reference to crop harvesting, growth and weed control should be mad

13. Nervous Coordination
(a) The central nervous system (i) Components of the central nervous system
(ii) Parts of the brain and their functions; cerebrum, cerebellum, medulla oblongata, hypothalamus and their functions
(iii) Structure and function of the Spinal Cord.
(b) Peripheral Nervous System.
(i) Somatic Nervous System
(ii) Autonomic nervous system.

(iii) Structure and functions of the neurone.
(iv) Classification of neurones.

(c) Types of nervous actions

(i) The reflex arc
(ii) Reflex and voluntary actions
(iii) Differences between reflex and voluntary actions.
(iv) Conditioned reflex and its role on behaviour.

Candidates should be able to locate the position of the brain and spinal cord in a dissected vertebrate and identify the various regions of the brain.

Functions of the sympathetic and parasympathetic systems only.

Candidates should observe, draw and label a neurone from a slide

Afferent (sensory), efferent (motor) and intermediate neurones should be mentioned

Candidates should perform experiments to illustrate reflex actions such as blinking of the eyes, knee jerk and withdrawal of hand from hot objects.

WAEC Syllabus For Biology | 14. Sense Organs: Structure and function of the

(a) Eye.

(b) Ear.

Candidates should be able to enumerate conditioned reflexes such as salivation, driving a car, walking and swimming.

Candidates should examine the mammalian eye noting the shape, colour and positions of the optic muscle and optic nerve.
Mention should be made of eye defects and their corrections

15 (a) Reproductive system of mammals

(i) Structure and function of male and female reproductive systems.

(ii) Differences between male and female reproductive organs.

(iii) Structure of the gametes (sperm and ovum)
(iv) Fertilization, development of the embryo and birth.
(v) Birth control

(b) Metamorphosis in insects, life histories of butterfly and cockroach.

Candidates should examine and draw dissected male and female small mammals showing the reproductive organs. They should also draw sperm and ovum from prepared slides.

Explanation of the different methods of birth control.

(c) Comparison of reproduction in fish, amphibian, reptile, bird and mammal.

(d) Reproduction in flowering plants

(i) Arrangements of floral parts of a named insect-pollinated flower and a named wind-pollinated flower.
(ii) Structure and function of the male and female parts of a flower. (e) Pollination in Plants
(i) Types of pollination
(ii) Features of cross-pollinated and selfpollinated flowers
(iii) Agents of Pollination

(iv) Kinds of placentation: axile, marginal and parietal.

(f) Process of development of zygote in flowering plants: Fertilization.

(g) (i) Types of fruits (classification).
(ii) Structure of fruits

(h) Dispersal of fruits and seeds: Agents of dispersal

Candidates should examine and draw dissected male and female small mammals showing the reproductive organs. They should also draw sperm and ovum from prepared slides.

Explanation of the different methods of birth control.

These examples should be used to illustrate complete and incomplete metamorphosis. The period it takes to develop from egg to adult should be studied. The different stages in the life history of butterfly and cockroach should be drawn and labelled.

Reference should be made to the method of fertilization, number of eggs and parental care.

Named examples should be used to illustrate the types of pollination.

The features of the flower should be related to the agents of pollination.

Pollen grains germinated in sucrose solution should be observed, prepared slides or charts showing various stages of embryo development in flowering plants should be observed and drawn.
Fruits should be classified into dry and fleshy fruits.
The internal structure of a leguminous fruit, orange, maize and tomato should be examined and drawn.

The following fruits should be studied as examples to show the features that aid their respective methods of dispersal. Sunflower (achene) Combretum, cotton, Crotalaria/bean, Desmodium, Bidens sp. Tridax sp. and Coconut.

WAEC Syllabus For Biology | B. Plant and Animal Nutrition

1. Plant Nutrition

(a) Photosynthesis:
(i) Process of photosynthesis and its chemical equation
(ii) Light and dark reactions
(iii) Materials and conditions necessary for photosynthesis
(iv) Evidence of photosynthesis

(b) Mineral requirement of plants
(i) Mineral nutrition: Macro and micro-nutrients

(ii) Soil and atmosphere as sources of mineral elements

Distinguishing differences between a fruit and a seed should be mentioned.

Biochemical nature of photosynthesis, photoactivation of chlorophyll resulting in the conversion of light energy to ATP and the reduction of NADP (Biochemical detail is not required)

The translocating and storage of excess food as a result of photosynthesis should be mentioned. Test for starch in green leaves should be carried out. Fate of the products of photosynthesis should be mentioned.

Macro elements should include: carbon, hydrogen, oxygen, nitrogen, potassium, phosphorus, magnesium, sulphur, calcium and iron. The micro elements should include: copper, manganese, zinc and boron.

Candidates should distinguish between food produced and mineral elements

2. Animal Nutrition

(a) Food substances; classes and sources

(b) Balanced diet and its importance

(c ) Food tests

(d) Digestive enzymes: Classes, characteristics and functions

(e) Modes of Nutrition (i) Autotrophic: Photosynthesis,

(ii) Heterotrophic: holozoic, parasitic, symbiotic and saprophytic.

(f) Alimentary System:

Alimentary tract of different animals.

(g) Dental Formula

h) Feeding in protozoa and mammals

Local examples as sources of food substance should be given. Reference should be made to food relationship between plants and animals.
Importance of each class of food in a balanced diet should be stressed. Candidates should relate the idea of balanced diet to their own diet. Malnutrition and its effects on humans should be mentioned.

Tests for starch, reducing sugar, protein, fats and oil should be carried out.
Candidates should perform experiments to show that ptyalin in saliva changes cooked starch to reducing sugar. Candidates should know source, site of action, substrate and effect of each digestive enzyme.

Experiments to show the characteristics of enzymes, including effects of pH, temperature and concentration should be carried out.

Named examples should be used to illustrate different modes of nutrition.
Comparison should be made using dissected named bird and mammal.
Description and functions of parts of the alimentary canal and modification of parts to reflect their digestive functions should be mentioned.

Meaning of dental formula. Determination of the dental formulae of mammals. Arrangements of teeth in the jaw bones of

herbivores, carnivores and of humans. Importance of dental care in humans

WAEC Syllabus For Biology | C. Basic Ecological Concepts

1. Ecosystem:

Components of the ecosystem and sizes
(a) Ecological components: environment, biosphere, habitat, population, biotic community and ecosystem.

(b) Components of the ecosystem: Biotic and abiotic

2. Ecological factors:

Ecological factors in aquatic and terrestrial ecosystems

3. Simple Measurement of Ecological Factors.

(a) Physical factors: Climatic, topographic and gaseous.
(b) Edaphic factors: Chemical and physical composition, moisture content and soil texture.

4. Food webs and trophic levels

(a) Autotrophs and Heterotrophs
(i) Producers: autotrophs
(ii) Consumers: heterotrophs
(iii) Decomposers
(b) Trophic levels energy

relationships
(i) Food chain
(ii) Food web
(c) Energy flow
(i) Food/Energy relationship in aquatic and terrestrial environment.
(ii) Pyramid of energy and Pyramid of numbers.

(d) Decomposition in nature
(i) Decomposers: (micro and macro-decomposers)
(ii) Gaseous products
(iii) Role of decomposers

Reference should be made to feeding habits in protozoa and mammals.

Examples and explanation are required.

Importance of ecological factors common to all habitat should be mentioned. The importance of ecological factors to population of animals and plants should be stressed.

Candidates should measure some of the ecological factors including humidity, temperature, wind speed, rainfall and light intensity.

Candidates should be able to classify organisms as producers, consumers and decomposers.

Aquatic and terrestrial producers, consumers and decomposers should be known

Candidates should illustrate food relationships in a food chain and food web using specific examples.

Non-cyclic nature of energy transfer should be mentioned.

Candidates should be able to construct and explain pyramid of energy, pyramid of numbers and point out the major differences between them.

Candidates should observe demonstrations to show that carbon dioxide, hydrogen sulphide, heat energy are released during decomposition.

WAEC Syllabus For Biology | 6. Ecological Management:

(a) Biological Associations
Type of associations: Parasitism, symbiosis, commensalism and saprophytism.
(b) Adaptation of organisms to habitats.

(c) Pollution of the atmosphere

(i) Nature, names, sources and effects of air pollutants.

(ii) Effect of noise

(d) Water and Soil Pollution Type and effects of pollutants.

Features of biological importance associated with each type should be mentioned. Named examples should be used to illustrate these associations.

Adaptations of plants and animals to environmental conditions with particular

reference to differences in habitats should be mentioned.

Examples of air pollutants should include carbon monoxide, sulphur dioxide, oxides of nitrogen, smoke, smog, dust and particles released into the air from factories. Health hazards and damage to the environment should be emphasized.

Harmful effect of noise from generators, aeroplane and electronic sound gadgets, e.t.c. should be mentioned.

Water and soil pollutants to be studied include: synthetic substances (detergent), insecticides, artificial fertilizers, herbicides, sewage, domestic and industrial wastes, crude oil and decaying organic matter. The health hazards and harmful effects of water and soil pollutants on organisms should also be mentioned. Mention should be made of oil spillage and its effects

7. Ecology of population

(a) Ecological succession

(i) Structural changes in species composition, variety or diversity and increase in numbers.
(ii) General characteristics and outcomes of succession
(b) Primary succession. Succession in terrestrial and aquatic habitats.

(c) Secondary succession, climax of the succession: characteristic of a stable ecosystem.

(d) Factors that affect population size: natality, mortality, emigration, immigration, food shortage, predation,competition and diseases.

(e) Preservation and storage of foods

(f) The life of selected insects; (i) Weevils and cotton strainers.

(ii) Control of pests

Candidates should study succession in an abandoned farmland, lawn, and in a pond over a period of time to discover a definite sequence of colonization by plants

Reference should be made to population.

Description of various methods of preserving and storing food. The use of ionizing radiations (x-ray, etc) should be mentioned. Explanation of the biological basis of preserving and storing food. Local methods of preserving food such as drying, salting and smoking should be mentioned.

External features of weevils and cotton stainers, their mode of life, adaptation to their habitats and their economic importance

8. Microorganisms:

Man and health (a) Carriers of microorganisms

(b) Microorganisms in action (i) Beneficial effects in nature, medicine and industries.

(ii) Harmful effects of microorganisms, diseases caused by microorganisms: cholera, measles, malaria and ring worm.

(c) Towards better Health (i) Methods of .controlling harmful microorganisms: high temperature, antibiotics, antiseptics, high salinity and

dehydration.
(ii) Ways of controlling the vectors.

(d) Public Health: The importance of the following towards the maintenance of good health practices:

(i) Refuse and sewage disposal.

(ii) Immunization, vaccination and inoculation (control of diseases)

Various methods of pest control: physical, chemical biological, etc; and their advantages and disadvantages should be mentioned.

Effects of micro-organisms on our bodies should be mentioned. Examples of carriers: housefly; mosquitoes; tsetsefly should be mentioned.
Candidates should perform experiments on fermentation, curdling of milk etc. to illustrate the beneficial uses of microorganisms.

The diseases should be studied with respect to the causative organisms, mode of transmissio

and symptoms.

Effects of these methods on the microorganisms should be mentioned.

Methods of controlling housefly and mosquito should be studied.
Candidates should be familiar with the proper methods of carrying out these public health practices in their community.

WAEC Syllabus For Biology | D. Conservation of Natural Resources:

1. Resources to be conserved: soil, water, wildlife, forest and minerals.
2. Ways of ensuring conservation

The meaning and need for conservation of natural resources should be mentioned.

Problems of conservation should be mentioned in relation to economic and social development, overgrazing and poaching.

The following should be studied: (a) agencies responsible for conservation (b) conservation education (c) conservation laws (d) benefits of conservation.

E. Variation in Population

1. Morphological variations in the physical appearance of individuals

(a) size, height and weight

b) colour (skin, eye, hair coat of animals)

(c) finger prints

2. Physiological Variations

(a) Ability to roll tongue

(b) Ability to taste phenylthiocarbamide (PTC)
(c) Blood groups (ABO) classification)

Variation can be classified into morphological and physiological or continuous and discontinuous

Candidates are required to measure heights and weights of pupils of the same age group and plot graphs of frequency distribution of the height and weight.
Observe and record various skin colour, colour pattern of some animals (cow, goat, rabbits), colour pattern of plants (maize cob and leaves).
Make finger prints and classify them into arches, loops, whorls and compounds.

WAEC Syllabus For Biology | F. Biology of Heredity (Genetics)

1. Genetic terminologies

2. Transmission and expression of characteristics in organisms.

(a) Hereditary variation
(b) Mendel’s work in genetics

(i) Mendel’s experiments

(ii) Mendelian traits

(iii) Mendelian laws

3. Chromosomes: The basis of heredity

(a) Structure

(b) Process of transmission of hereditary characters from parents to offspring.

4. Probability in genetics (Hybrid formation).

5. Linkage, sex determination and sex linked characters.

6. Application of the principles of heredity in:

(a) Agriculture

(b) Medicine

Definition of the following basic genetic terms such as gene, genotype, phenotype, dominant, recessive, allele, locus, test cross, and back cross.

Reference should be made to characters that can be transmitted from generation to generation such as colour of skin, eye, hair, blood group, sickle cell, shape of face and nose.
Mendel’s experiment with red and white flowered peas should be mentioned.

Mendel’s experiment on monohybrid and dihybrid inheritance should be mentioned.

Reference should be made to dominant and recessive characters in plants and animals.

Candidates should observe chromosomes in permanently prepared slides of cells and root tips of onion or lily. Candidates should study the structure of DNA and gene replication using models and charts.

Segregation of genes at meiosis and recombination at fertilization should be used to explain the process of transmission of hereditary characters from parents to offspring.

Computation of probability is not required.

Explanation of the terms linkage, sex determination and sex linked characters such as haemophilia, colour blindness, baldness and hairy ear lobes.

Data on cross-breeding experiments should be studied.
Examples of new varieties of crops and livestock obtained through cross-breeding should be mentioned. The advantages and disadvantages of cross-fertilization, out and inbreeding should be explained.

The application of knowledge of heredity in marriage counseling with particular reference to sickle cell anaemia and rhesus factor should be mentioned.

WAEC Syllabus For Biology | G. Adaptation for survival and Evolution.

1. Behavioural Adaptations in Social Animals.

(a) Termites (b) Bee

2. Evolution.

(a) Evidence of evolution.

(b) Theories of evolution

Candidates should be able to identify the various castes of social insects.

The division of labour in social insects and the roles of different castes should be stressed. Examples of communication among animals such as contact notes and warning cries should be mentioned.

Reference should be made to basking by lizard, territorial behaviour in birds and lizards and behaviour of other animals under unfavourable conditions-hibernation and aestivation.

The behaviour of an organism as a member of a group and the effect of grouping on the behaviour of an organism should be mentioned.
Candidates are expected to know the evolutionary trends in plants and animals such as from simple to complex structural adaptations and from aquatic to terrestrial organisms.
The role of mutation in evolution should be mentioned.

The following evidence of evolution should be mentioned: Paleontology (fossil records), comparative biochemistry, geographical distribution, comparative anatomy and physiology, adaptive radiation, comparative embryology and systematics.
The contributions of Lamarck and Darwin to the development of the theory of evolution should be mentioned.

SECTION B (For candidates in Ghana only)

WAEC Syllabus For Biology | A. Introducing Biology

1. Biology as a science of life

2. Procedure for biological work

3. Importance of Biology

4. Body symmetry, sectioning and orientation

5. The microscope

6. Biological drawings

The meaning of biology. Candidates must be able to differentiate between a living thing and an organism. The two major branches of biology: Botany and zoology; specialized areas: bacteriology, molecular biology, histology, cell biology, ecology etc.

Description of skills required by biologists in their work. The scientific method: Identifying the problem, defining the problem, hypothesizing, experimenting, recording, analyzing and concluding. Description of following steps for writing report on biological experiment or investigation: Aim, hypothesis/ scientific framework, materials/ drawing of set-up, method, results/ observation, discussion and conclusion.

Application of biology to everyday life. Careers associated with the study of biology.

Description of the following terms : (i) Body symmetry (bilateral and radial) (ii) Sectioning: longitudinal and transverse and vertical (iii) Body orientation of specimen: anterior, posterior, lateral, dorsal and ventral views). Distinction between (i) posterior and anterior views

(ii) dorsal and ventral views (iii) transverse and longitudinal section

Examination of simple light, compound light and stereoscopic light microscopes and identification of the various parts.

Handling and caring for microscopes. Use of the light microscope to observe prepared slides. Techniques involved in the preparation of temporary slides of animal and plant cells. Mounting varieties of specialized eukaryotic cells. Drawing of cells as seen under the microscope.

Resolution and magnification of microscope. Determination of magnification of drawings. Measuring lengths using compound light microscope. Electron microscope should be mentioned

Appropriate headings for biological drawings. Magnification/ size of biological drawings. Quality of biological drawings e.g. clarity of lines, neatness of labels, labels of biological drawings

WAEC Syllabus For Biology | B. Cell Biology

1. Movement of substances into and out of cells: Endocytosis and Exocytosis

2. Nucleic acids

3. DNA structure and replication, RNA transcription.

4. Protein synthesis

5. Cell cycle

Description of the process of protein synthesis. The roles of m-RNA, t-RNA, and r-RNA and ribosomes in protein synthesis must be emphasized. Importance of protein synthesis. Examples of proteins synthesized by humans.

Explanation of the of the term cell cycle. Phases of the cell cycle [Interphase: G + S + G2 phases, Mitosis: M phase ( karyokinesis and cytokinesis)]. The processes of mitosis and meiosis and their importance. Preparation of a squash of onion root tip and observing stages of meiosis under the microscope. Observing stages of meiosis in plant and animal cells (Permanent slides may be used)

WAEC Syllabus For Biology | C. Life Processes in Living Things

1. Amoeba, Paramecium, and Euglena

2. Spirogyra and Rhizopus

3. Mosses and ferns

External structure and life processes of Amoeba, Paramecium, and Euglena. Mounting of Paramecium and Euglena under the compound light microscope.

Structure of Spirogyra and Rhizopus. Nutrition and reproduction of Spirogyra and Rhizopus. Identification of stages of conjugation of Spirogyra.

Structure of mosses (Brachymenium and Funaria) and ferns (Nephrolepis, ( Platycerium, Phymatodes). Description of external features of mosses and ferns. Nutrition and reproduction in mosses. Reproduction in ferns

WAEC Syllabus For Biology | D. Diversity of Living Things

1. Characteristics of some of the orders of Class Insecta

2. Identification of organisms using biological keys

Orders of Class Insecta (Odonata Orthoptera, Coleoptera, Hymenoptera, Hemiptera, Diptera, Isoptera, Lepidoptera, Dictyoptera, and Neuroptera)

WAEC Syllabus For Biology | E. Interactions in Nature Soil

Identification of organisms using numbered and dichotomous keys. Construction of identification keys

F. Mammalian Anatomy and Physiology

1. Dissection of a small mammal

2. Transport: Structure of the mammalian heart.

3. Cellular respiration

4. Movement:

(a) Muscles

(b) Skeletal tissues 5. Reproduction (a) Secondary sexual characteristics

(b) Prenatal/Antenatal care

Identification of organisms using numbered and dichotomous keys. Construction of identification keys.

Identification of mineral salts (Ca2+, Fe2+, Fe3+, Mg2+, K+, SO4 -, NO3 -, PO4 -) in a soil sample. Soil reclamation.

The arrangement of internal organs of mammals. Functions of the internal organs. Candidates should be able to cut open a chloroformed mammal (guinea pig, rat, mouse and rabbit) and draw the internal organs.

Mechanism of the heartbeat: excitation and contractions (SAN, AVN, Purkinge tissue)

Determination of respiratory quotient (RQ) of different substrates. Explanation of the significance of RQ.

Types of muscle (Smooth, striated and cardiac muscles). Description of how muscles bring about movement. Explanation of sliding filament model of muscle contraction.

Description of the structure of skeletal tissues( Bones and cartilage).

Physical changes that occur in males and females during puberty. The role of hormones in the development of secondary sexual

characteristics in humans.

Meaning of antenatal care. Antenatal visits requirements. Nutrition and diet. Exercise during pregnancy. Benefits of the use of natural products by mother and child.

WAEC Syllabus For Biology | G. Plant Structure and Physiology

1. Morphology of monocotyledonous and dicotyledonous plants.

2. Transport: Guttation

3. Reproduction: Floral formula

External features of monocotyledonous and dicotyledonous plants. Functions of roots, stems and leaves of monocotyledonous and dicotyledonous plants. Differences between monocotyledonous and dicotyledonous plants. Modifications of roots, stems and leaves.

Biological principles underlying guttation.

H. Humans and their Environment

1. Integrated water resources management.

2. Health and hygiene

(a) Drug abuse

(b) Community health (c) First Aid

Determination and writing of the floral formulae of the following flowers: Flamboyant (Delonix), Pride of Barbados (Caesalpinia) and Rattle box (Crotalaria). Floral diagrams are not required.

Description of the integrated water resources management (IWRM). Explanation of how IWRM can reduce undesirable change in the environment.

Definition of terms: health, hygiene, and sanitation. Means of achieving personal cleanliness/ hygiene.

Explanation of the term drug abuse. Consequences of drug abuse.

Importance of town planning and its effects on health of the community.

Explanation of the term First Aid. Different methods of administering First Aid.

WAEC Syllabus For Biology | I. Evolution

Recombinant DNA Technology

Explanation of the term Recombinant DNA Technology and state its application

J. Biology and Industry

1. Biology and water industry

(a) Contamination of water

(b) Identification of polluted water
(c) Waste water treatment

2. Biology and fishing industry

(a) Fish stock management

(b) Fish farming

3. Biology and food industry: Food additives

4. Biology and agriculture

5. Biotechnology

6. Biological fuel generation manufacture of food such as cheese, yoghurt, kenkey, bread and butter. The role of microorganisms in the production of alcoholic drinks and organic acids. The role of microorganisms in pharmaceutical, tanning and mining industries.

Explanation of the need for new sources of energy. The use of biogas, use of green crops to produce ethanol, the generation of hydrogen gas from chloroplasts should be mentioned

Candidates should carry out experiments to test water samples for bacterial contamination.

The use of Biological Oxygen Demand (BOD) in the measurement of the level of organic pollution in water.

Description of biological processes of purifying sewage. Cesspit activated sludge process should be mentioned.

Explanation of why fish is an efficient converter of plankton into flesh. Description of ways of conserving fish stocks in water bodies.

Importance of fish farming. Advantages and disadvantages of fish farming.

Explanation of the term food additives. Identification of the categories of food additives (Naturally occurring and artificial food additives). Health implications in the use of food additives.

Explanation of the biological principles by which fertilizer, pesticides, selective breeding, resistance to disease and irrigation can respectively lead to successful agriculture.

Explanation of the concept of biotechnology. The use of micro-organisms in the

SECTION C (For candidates in Nigeria, Sierra Leone, The Gambia and Liberia

WAEC Syllabus For Biology | A. Concept of Living

1. Cell theory

2. Irritability as a basic characteristic of protoplasm

(a) Types of responses: taxis and nastism

(b) Environmental factors that evoke responses; temperature, pH etc
3. Excretory Systems
(a) Diseases of the kidney: Nephritis, kidney stone and diuresis, Their

effects and remedies.

(b) Diseases of the liver: infective hepatitis, cancer of the liver and gall stones. Their effects and remedies.
4. Sense organs.
(a) Nose.

(b) Tongue.

(c) The skin.

5. Reproduction (a) Courtship behaviour in animals: (i) Pairing (ii) Display e.g. peacocks (iii) Territoriality (iv) Seasonal migration associated with breeding in herrings, eels and birds.
(b) Metamorphosis and life history of housefly.
(c) Adaptive features in a developing animal:
(i) Yolk in egg of fish, toad and birds for nourishment
(ii) Placenta in animals

(d) Germination of seeds

(i) Essential factors which affect developing embryo.

(ii) Types of germination

The cell theory including the work of Hooke, Dujardin, Schleiden and Schwann should be outlined

Excretory organs of earthworm and insects should be mentioned.

The process of perception of smell including the roles of sensory cells in nose and olfactory lobes should be studied.

Experiments should be carried out to determine the different areas of the tongue associated with different tastes. The association between the organs of taste and smell should be mentioned. Mention should be made of taste buds.
The function of the skin as a sensory organ should be emphasized.

Courtship pattern in male and female animals and territorialism in lizards should be observed.

The content (yolk and albumen) of birds’ egg should be examined
Candidates should observe the connection of the foetus to the mother and the adaptive features of

the placenta, umbilical cord and amnion in a dissected pregnant rat. The meaning of oviparity and viviparity should be mentioned

WAEC Syllabus For Biology | B. Plant and Animal Nutrition

1. Nitrogen cycle

2. Modes of nutrition: autotrophic, chemosynthetic, carnivorous plants

3. Alimentary System (a) Alimentary tracts of different animals
(b) Description and function of various parts.

4. Feeding habits (a) Categories: Carnivorous, herbivorous and omnivorous
(b) Modifications and mechanisms associated with the following habits; filter feeding, fluid feeding, feeding adaptation in insects, saprophytic feeding, parasitic feeding etc.

Experiments to show the importance of oxygen, adequate moisture and suitable temperature, should be carried out.

The stages in hypogeal and epigeal germination should be observed and drawn

The names and roles of bacteria involved in nitrogen cycle should be mentioned. Candidates to observe root nodules in leguminous plants.

Examples of carnivorous plants should be studied.

Comparison should be made using dissected earthworm, grasshopper/cockroach to show the important features of the alimentary canal.
Use a bird and cockroach/grasshopper to show modifications for functions

WAEC Syllabus For Biology | C. Basic Ecological Concepts

1. Ecological Components: Lithosphere, hydrosphere, atmosphere, niche

2.Population Studies by Sampling (a) Population size (b) Dominance (c) Density

3. Energy transformation in nature:
(a) Energy loss in the ecosystem

(b) Solar radiation: its intake and loss at

the earth’s surface.

(c ) Energy loss in the biosphere.

WAEC Syllabus For Biology | 4. Nutrient Cycling in Nature

(a) Carbon Cycle:
(i) Process of carbon cycle
(ii) Importance of carbon in nature.

(b) Water Cycle: (i) Importance of water cycle, (ii) Importance of water to living organisms.

5. Ecological Management: Tolerance, Minimum and maximum range

6. Habitats (a) Aquatic habitat: marine, estuarine fresh water under the following headings: (i) characteristics of habitat (ii) distribution of plants and animals in the habitat, (iii) adaptive features of plants and animals in the habitat.

(b) Terrestrial habitat: marsh, forest, grass land, arid land should be studied under the following headings

(i) characteristics of habitat

(ii) distribution of plants and animals in habitat.

(c) Balance in Nature Dynamic equilibrium population and population density.

WAEC Syllabus For Biology | 7. Relevance of Biology to Agriculture:

(a) Classification of plants based on life cycle

(b) Effects of agricultural practices on ecology
(i) Bush burning
(ii) Tillage
(iii) Fertilizer
(iv) Herbicide/pesticide
(v) Different farming methods

WAEC Syllabus For Biology | 8. Microorganisms: Man and His Health.

(a) Microorganisms around us
(i) Microorganisms in air and water (ii) Groups of microorganisms: bacteria, viruses, some algae, protozoa and some fungi.
(b) Microorganisms in our bodies and food

c) Public Health Food hygiene and health organization.

Mosquito larva, housefly, butterfly, cockroach, adult mosquito, maize weevil, rhizopods, tapeworm should be used to illustrate the different types of feeding mechanisms and various modifications.

Candidates are expected to explain and give examples of the terms.

Candidates are required to carry out a project to determine population density by counting the individual types of plants and animals and record such count in a given plot.

Laws of thermodynamics and its application to ecological phenomena should be mentioned. The laws of thermodynamics should be used to explain energy flow across tropic levels.

Candidates should discuss energy as a limiting factor in primary production i.e production of autotrophs.
Reference should be made to harvest as a means of measuring primary production.

Candidates should be able to draw the carbon cycle, list the sources of carbon (burning, respiration, decay) and discuss the relative importance of the cycle.

Reference should be made to carbon dioxideoxygen balance in nature. Candidates should carry out experiments to show absorption of carbon dioxide and release of oxygen during photosynthesis.

Candidates should carry out experiments to show the presence of water in expired air and that water is given off during respiration.
Candidates should perform experiments to show the limit of tolerance of Tilapia to various concentrations of salt solution or sensitivity of wood lice to temperature.

Measurement of physical factors: temperature, salinity, light intensity, turbidity, current, pH, should be carried out.

The pattern of distribution including dominant types and seasonal changes of population, size of organisms in the habitat should be noted

The measurement of the physical factors, temperature, relative humidity, light, wind, and pH should be carried out.
Reference should be made to edaphic factors.
The effect of physical factors on distribution of plants and animals should be mentioned.

The process by which carnivores maintain a constant population should be mentioned.

Effects of human activities on ecological systems should be mentioned.

Microorganisms in air, water and expired air should be observed and identified by their colour, pattern of growth and appearance of their colony

Microorganisms under the finger nails, mouth cavity, expired air, and decomposing food substance should be observed and identified by their colour, pattern of growth, and appearance of colony

WAEC Syllabus For Biology | D. Application of Variations

1. Crime detection

2. Blood transfusion

3. Determination of paternity

Reference should be made to the roles of national and international health organizations in maintenance of good public health.

The uniqueness of each individual’s finger print should be mentioned in relation to crime detection.
Reference should be made to importance of knowledge of blood groups in blood transfusion and determination of paternity.

WAEC Syllabus For Biology | E. Evolution 1. Adaptation for survival

(a) Factors that bring about competition
(b) Intra and Inter-species competition

(c) Relationship between competition and succession

2. Structural Adaptation for; (a) obtaining food (b) protection and defense (c) securing mates for reproduction (d) regulating body temperature (e) conserving water

3. Adaptive Colouration (a) Plants and animals (b) Colouration and their functions

Reference should be made to the factors such as food, space, water, light and mates which organisms share and form the basis of competition.
The effects of intra-species competition should be observed by growing many seedlings of maize in a small area, while the effects of interspecies competition can be observed by planting many seedlings of maize and pepper in a small area.
Candidates should observe competition and succession on a moistened exposed slice of bread over a period of time.

Candidates should observe examples of

organisms that show structural adaptation for obtaining food, escaping from enemies, securing mates, regulating body temperature and conserving water.

Candidates are required to observe examples of adaptive colouration in plants and animals.

Above is the WAEC Syllabus For Biology 2020/2021

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The Jamb Syllabus for Mathematics 2020

jamb syllabus for mathematics

The aim of the Unified Tertiary Matriculation Examination (UTME) syllabus in Mathematics is to prepare the candidates for the Board’s examination. It is designed to test the achievement of the course objectives, which are to:


(1) acquire computational and manipulative skills;
(2) develop precise, logical and formal reasoning skills;
(3) develop deductive skills in interpretation of graphs, diagrams and data;
(4) apply mathematical concepts to resolve issues in daily living.


This syllabus is divided into five sections:
I. Number and Numeration.
II. Algebra
III. Geometry/Trigonometry.
IV. Calculus
V. Statistics

SECTION I: NUMBER AND NUMERATION

1. Number bases:

Topics:

(a) operations in different number bases from 2 to 10;
(b) conversion from one base to another including fractional parts.

Objectives:

Candidates should be able to:

i. perform four basic operations (x,+,-,÷)
ii. convert one base to another.

2. Fractions, Decimals, Approximations and Percentages:

Topics: 

(a) fractions and decimals;
(b) significant figures;
(c) decimal places;
(d) percentage errors;
(e) simple interest;
(f) profit and loss percent;
(g) ratio, proportion and rate;
(h) shares and valued added tax (VAT).

Objectives: 

Candidates should be able to:

i. perform basic operations (x,+,-,÷) on fractions and decimals;
ii. express to specified number of significant figures and decimal places;
iii. calculate simple interest, profit and loss percent; ratio proportion and rate;
iv. Solve problems involving share and VAT.

3. Indices, Logarithms and Surds:

Topics:

(a) laws of indices;
(b) standard form;
(c) laws of logarithm;
(d) logarithm of any positive number to a given base;
(e) change of bases in logarithm and application;
(f) relationship between indices and logarithm;
(g) surds.

Objectives:

Candidates should be able to:

i. apply the laws of indices in calculation;
ii. establish the relationship between indices and logarithms in solving problems;
iii. solve problems in different bases in logarithms;
iv. simplify and rationalize surds;
v. perform basic operations on surds.

4. Sets:

Topics:

(a) types of sets
(b) algebra of sets
(c) venn diagrams and their applications.

Objectives:

Candidates should be able to:

i. identify types of sets, i.e empty, universal, complements, subsets, finite, infinite and disjoint sets;
ii. solve problems involving cardinality of sets;
iii. solve set problems using symbol;
iv. use venn diagrams to solve problems involving not more than 3 sets.

SECTION II: ALGEBRA.

1. Polynomials:

Topics:

(a) change of subject of formula
(b) factor and remainder theorems
(c) factorization of polynomials of degree not exceeding 3.
(d) multiplication and division of polynomials
(e) roots of polynomials not exceeding degree 3
(f) simultaneous equations including one linear one quadratic;
(g) graphs of polynomials of degree not greater than 3.

Objectives:

Candidates should be able to:

i. find the subject of the formula of a given equation;
ii. apply factor and remainder theorem to factorize a given expression;
iii. multiply and divide polynomials of degree not more than 3;
iv. factorize by regrouping difference of two squares, perfect squares and cubic expressions; etc.
v. solve simultaneous equations – one linear, one quadratic;
vi. interpret graphs of polynomials including applications to maximum and minimum values.

2. Variation:

Topics:

(a) direct
(b) inverse
(c) joint
(d) partial
(e) percentage increase and decrease.

Objectives:

Candidates should be able to:

i. solve problems involving direct, inverse, joint and partial variations;
ii. solve problems on percentage increase and decrease in variation.

3. Inequalities:

Topics:

(a) analytical and graphical solutions of linear inequalities;
(b) quadratic inequalities with integral roots only.

Objective:

Candidates should be able to:

i. solve problems on linear and quadratic inequalities;
ii. interpret graphs of inequalities.

4. Progression:

Topics:

(a) nth term of a progression
(b) sum of A. P. and G. P.

Objectives:

Candidates should be able to:

i. determine the nth term of a progression;
ii. compute the sum of A. P. and G.P;
iii. sum to infinity of a given G.P.

5. Binary Operations:

Topics:

(a) properties of closure, commutativity, associativity and distributivity;
(b) identity and inverse elements (simple cases only).

Objectives: 

Candidates should be able to:

i. solve problems involving closure, commutativity, associativity and distributivity;
ii. solve problems involving identity and inverse elements.

6. Matrices and Determinants:

Topics:

(a) algebra of matrices not exceeding 3 x 3;
(b) determinants of matrices not exceeding 3 x 3;
(c) inverses of 2 x 2 matrices [excluding quadratic and higher degree equations].

Objectives: 

Candidates should be able to:

i. perform basic operations (x,+,-,÷) on matrices;
ii. calculate determinants;
iii. compute inverses of 2 x 2 matrices.

SECTION III: GEOMETRY AND TRIGONOMETRY

1. Euclidean Geometry:

Topics:

(a) Properties of angles and lines
(b) Polygons: triangles, quadrilaterals and general polygons;
(c) Circles: angle properties, cyclic quadrilaterals and intersecting chords;
(d) construction.

Objectives:

Candidates should be able to:

i. identify various types of lines and angles;
ii. solve problems involving polygons;
iii. calculate angles using circle theorems;
iv. identify construction procedures of special angles, e.g. 30°, 45°, 60°, 75°, 90° etc.

2. Mensuration:

Topics:

(a) lengths and areas of plane geometrical figures;
(b) lengths of arcs and chords of a circle;
(c) Perimeters and areas of sectors and segments of circles;
(d) surface areas and volumes of simple solids and composite figures;
(e) the earth as a sphere:- longitudes and latitudes.

Objectives:

Candidates should be able to:

i. calculate the perimeters and areas of triangles, quadrilaterals, circles and composite figures;
ii. find the length of an arc, a chord, perimeters and areas of sectors and segments of circles;
iii. calculate total surface areas and volumes of cuboids, cylinders. cones, pyramids, prisms, spheres and composite figures;
iv. determine the distance between two points on the earth’s surface.

3. Loci:

Topic:

locus in 2 dimensions based on geometric principles relating to lines and curves.

Objectives:

Candidates should be able to:

identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles.

4. Coordinate Geometry:

Topics:

(a) midpoint and gradient of a line segment;
(b) distance between two points;
(c) parallel and perpendicular lines;
(d) equations of straight lines.

Objectives: 

Candidates should be able to:

i. determine the midpoint and gradient of a line segment;
ii. find the distance between two points;
iii. identify conditions for parallelism and perpendicularity;
iv. find the equation of a line in the two-point form, point-slope form, slope intercept form and the general form.

5.Trigonometry:

Topics:

(a) trigonometrical ratios of angels;
(b) angles of elevation and depression;
(c) bearings;
(d) areas and solutions of triangle;
(e) graphs of sine and cosine;
(f) sine and cosine formulae.

Objectives:

Candidates should be able to:
i. calculate the sine, cosine and tangent of angles between – 360° ≤ θ ≤ 360°;
ii. apply these special angles, e.g. 30°, 45°, 60°, 75°, 90°, 105°, 135° to solve simple problems in trigonometry;
iii. solve problems involving angles of elevation and depression;
iv. solve problems involving bearings;
v. apply trigonometric formulae to find areas of triangles;
vi. solve problems involving sine and cosine graphs.

SECTION IV: CALCULUS

I. Differentiation:

Topics: 

(a) limit of a function
(b) differentiation of explicit algebraic and simple trigonometrical functions-sine, cosine and tangent.

Objectives: 

Candidates should be able to:

i. find the limit of a function
ii. differentiate explicit algebraic and simple trigonometrical functions.

2. Application of differentiation:

Topics:

(a) rate of change;
(b) maxima and minima.

Objective: 

Candidates should be able to:

solve problems involving applications of rate of change, maxima and minima.

3. Integration:

Topics:

(a) integration of explicit algebraic and simple trigonometrical functions;
(b) area under the curve.

Objectives:

Candidates should be able to:

i. solve problems of integration involving algebraic and simple trigonometric functions;
ii. calculate area under the curve (simple cases only).

SECTION V: STATISTICS

1. Representation of data:

Topics:

(a) frequency distribution;
(b) histogram, bar chart and pie chart.

Objectives:

Candidates should be able to:

i. identify and interpret frequency distribution tables;
ii. interpret information on histogram, bar chat and pie chart

2. Measures of Location:

Topics:

(a) mean, mode and median of ungrouped and grouped data – (simple cases only);
(b) cumulative frequency.

Objectives:

Candidates should be able to:

i. calculate the mean, mode and median of ungrouped and grouped data (simple cases only);
ii. use ogive to find the median, quartiles and percentiles.

3. Measures of Dispersion:

Topic:

range, mean deviation, variance and standard deviation.

Objective:

Candidates should be able to:

calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data.

4. Permutation and Combination:

Topics:

(a) Linear and circular arrangements;
(b) Arrangements involving repeated objects.

Objective:

Candidates should be able to:

solve simple problems involving permutation and combination.

5. Probability:

Topics

(a) experimental probability (tossing of coin, throwing of a dice etc);
(b) Addition and multiplication of probabilities (mutual and independent cases).

Objective:

Candidates should be able to:

solve simple problems in probability (including addition and multiplication).

RECOMMENDED TEXTS

Adelodun A. A (2000) Distinction in Mathematics: Comprehensive Revision Text, (3rd Edition) Ado -Ekiti: FNPL.

Anyebe, J. A. B (1998) Basic Mathematics for Senior Secondary Schools and Remedial Students in Higher/ institutions, Lagos: Kenny Moore.

Channon, J. B. Smith, A. M (2001) New General Mathematics for West Africa SSS 1 to 3, Lagos: Longman.

David -Osuagwu, M. et al (2000) New School Mathematics for Senior Secondary Schools, Onitsha: Africana – FIRST Publishers.

Egbe. E et al (2000) Further Mathematics, Onitsha: Africana – FIRST Publishers

Ibude, S. O. et al (2003) Agebra and Calculus for Schools and Colleges: LINCEL Publishers.

Tuttuh – Adegun M. R. et al (1997), Further Mathematics Project Books 1 to 3, Ibadan: NPS Educational

Wisdomline Pass at Once JAMB.

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10 Best Universities in Nigeria and their School Fees

best universities in nigeria and their school fees

Are you wondering which Nigeria universities are the best and how much are their current school fees?

According to Malcolm X, “Education is the passport to the future, for tomorrow belongs to those who prepare for it today.”

Also, according to Victor Hugo, “he, who opens a school door, closes a prison.”

The importance of education cannot be overemphasized in the society. It is no wonder that some of the most educated nations are not only one of the most developed but the nations with the most advanced citizens.

The schools established to impart knowledge on students can, therefore, be celebrated as a reservoir of knowledge.

In Nigeria, there are many such schools. However, like in every case, some stand out above the others due to their standards.

PS: Learn how to pass Jamb Successful or if you are yet to check your WAEC result, you can do so by buying waec scratch card online

In no particular order, here are the top 10 best universities in Nigeria:

1: University of Ibadan

Established in 1948, the University of Ibadan is the premier university in Nigeria. It was started as a College under the University of London before it became a full-fledged university in 1962. The university is one of the top universities in Nigeria, having trained some notable Nigerians, including Wole Soyinka, Chinua Achebe, Emeka Anyaoku amongst others. Today, the institution offers academic programmes in 16 faculties including Arts, Science, Medicine and Engineering. The school fees are largely based on faculty.

For fresh students, the school fees range from N19,000 to N45,000 and for returning students, it ranges from N13,000 to N35,000.

2: University of Nigeria, Nsukka

Established in 1960 in the suburban city of Nsukka in Enugu state, UNN is a co-educational school that is regarded as one of the top universities in Nigeria. The school, which also has campuses in Enugu, Ituku-Ozalla and Aba, is the first autonomous university in Nigeria. The institutions trained some notable Nigerians, including Charles Soludo, Dora Akunyili, Pat Utomi, and Peter Obi amongst others. The university that started with 220 students now offers 82 undergraduate programmes and 211 postgraduate programmes.

The school fee for fresh students is N76,000 at most and N70,000 at least while that of returning students is N40,000 at least and N50,000 at most, all depending on the department.

3: University of Lagos

The University of Lagos was founded in 1962 in the urban metropolis of Lagos. UNILAG, as it is fondly called, is located in Akoka, Yaba with another campus in Idi-Araba, Yaba. It is called the “school of first choice and the nation’s pride” and also known for its strong social life as well its academic prowess by Nigerian students. The school offers programmes from 12 faculties. Some of the notable alumni include Yemi Osibanjo, Akinwunmi Ambode, Oluwaseyi Makinde, Dr D.K. Olukoya, Pst. E.A. Adeboye, Oby Ezekwesili amongst others.

The school fees for non-science programmes is about N67,000 for new students and about N20,000 for returning students while that of art-based programmes is about N56,000 for new students and about N15,000 for returning students.

4: Obafemi Awolowo University

Obafemi Awolowo University was established in 1962 in Ile-Ife, Osun state. The school was initially the University of Ife before it was renamed after one of the prominent nationalists and one of the first leaders of independent Nigeria, Chief Obafemi Awolowo. OAU, as it is fondly called, is one of the top universities in Nigeria, having trained many notable Nigerians such as Akinwumi Adesina, Toyin Falola, Biyi Bandele, Dele Momodu and Ibukun Awosika amongst others. It is one of the largest schools in Nigeria, in terms of landmass and is known for its selective admission policy.

The school fees range from N44,000 to N58,000 for new students and from N20,000 to N32,000 for returning students, depending on the faculty.

5: Covenant University

Established in 2002 in Ota, Ogun State, Covenant University or CU, as it is fondly called, was founded by the Living Faith Church as a part of the Liberation Commission, with the vision to become the leading world-class Christian mission university. Some notable Nigerians who were trained in the institution include Simi, Bez, Ishaya Bako, and Chef Fregz amongst others.

The school fees range from about N820,000 to N885,000 for returning students and about N930,000 to N1,003,000 for fresh students.

6: Ahmadu Bello University

Located in Zaria, Kaduna state, Ahmadu Bello University was established in 1962. The university is a product of the recommendation of the Ashby Commission on Post School Certificate and Higher Education in Nigeria to establish a university in Northern Nigeria. Named after the Sardauna of Sokoto, Sir Ahmadu Bello, the school has 12 faculties and 2 beautiful campuses. Some of the notable alumni include Late President Umaru Musa Yar’adua, Namadi Sambo, Atiku Abubakar, Nuhu Ribadu and Ahmed Makarfi amongst others.

The school fees for new students is between N44,000 to N45,000 depending on the department and between N23,000 to N40,000 depending on the level for returning students.

7: Federal University of Technology, Minna

FUT Minna, as it is fondly called, was established in 1983 as a result of the country’s drive to improve in science and technology. The main faculties in the school are technologically or science-based. Since its establishment, the institution has recorded a number of innovations. Notable alumni include Kemi Adesoye, Arc. Mrs Suswam and Paul Obiefule amongst others.

The school fee is about N62,000 for fresh students and N28,000 for returning students.

8: University of Ilorin

Established in 1975, the university was initially started at the temporary campus of the Kwara State Polytechnic. The university has since then become a force to reckon with, being the first university in Nigeria to be ranked among the top 20 top universities in Africa. The school currently has 15 faculties. Some of the notable alumni include Nkem Owoh, Femi Adebayo, Josephine Odumakin, Tope Oshin, Dunsin Oyekan and the late Pius Adesanmi.

The school fee is between N15,000 to N60,000 depending on the department and the level.

9: University of Benin

Established in 1970, the University of Benin is one of the top universities in Nigeria. Located in Benin City, Edo State, the university is known to collaborate with both academic and non-academic institutions as well as international bodies across the globe. Some notable Nigerians trained in the school include Babatunde Raji Fashola, Richard Mofe-Damijo, Omoni Oboli and Victor Uwaifo amongst others.

The school fee is between N70,000 and N74,000 depending on the department while the acceptance fee is N60,000 for all students.

10: University of Abuja

Established in 1988, the university is located in the federal capital of Nigeria. The school started at a temporary site of a primary school in Gwagwalada, Abuja before the permanent site was allocated to them along Abuja Airport road. The school has ten faculties, one postgraduate school and one school of remedial studies. Notable alumni include Abdulmumin Jibrin, Uzee Usman, Natasha Akpoti, Ebuka Obi-Uchendu and Lilian Esoro amongst others.

The school fee is between N38,000 to N43,000 for fresh students and between N20,000 to N23,000 for returning students, depending on the department.

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How to Pass Jamb 2020: The Best & Guarantee Way to Pass Jamb Successful

how to pass jamb successfully

Sshh!!

Do you want to know the secret to pass your Jamb 2020 successfully and getting a high score that ensured you gain admission into any Nigerian university of your choice?

If you are ready, then drop everything you are doing and pay attention to this point. In this article, I will share with you how you can pass your Jamb excellently.

Ready?

Let’s dive in.

What is JAMB?

JAMB also known as Joint Admissions and Matriculation Board. It is the body responsible for conducting the Unified Tertiary Matriculation Examination for prospective students seeking admission into Nigerian tertiary institutions. Since 1978 when the organization was founded, the body has organized and determined the admission of students into Nigerian tertiary institutions.


When Is JAMB 2020 Going To Take Place?

There is no date fixed yet for Jamb UTME 2020.

Contrary to the false information spreading, the registration for JAMB 2020 has not commenced and there is no announced date for the exams yet. The news spreading can be based on the fact that in previous years, registration started around December of the preceding year. But this year, things seem to be different.

JAMB also announced that applicants are very likely to be required to identify themselves with the NIN (National Identification Number) and so, the board urges all prospective applicants to make sure to take part in the ongoing NIN registration before it is too late.


How to Pass Jamb UTME 2020 Successfully by Step by Step

  • Register for NIN
  • Determine on the score you want to get
  • Study wide
  • Start studying past questions
  • Study with exam-focused textbook
  • Practice timed test with past questions
  • Rest and Eat well.

Every examination is nerve-racking. As humans, we just generally get anxious about examinations even when we know that we have a high chance of acing it. So, how can you get past the nerves – or at least, reduce it? By preparing adequately. How do you prepare adequately for the 2020 JAMB UTME?

Now let’s discuss them in full one after the other.

  • Register for NIN: This might not seem like part of the examination but it is as important as the main examination itself. While JAMB has not categorically said the NIN will definitely be a requirement, the board has made it clear that it will likely be a requirement. Therefore, it is important to be safe than sorry. Even if they end up changing their mind about requiring NIN, you have nothing to lose for having it. So, while there is still time, it is important to go register now.
  • Determine the score you want now: According to the Holy Book, “as a man thinks in his heart, so is he.” It is very important that you settle in your mind the score you are aiming for. This will give you a goal and help your study be focused. However, this is not really determined by what you want or feel you can achieve, but what the course and institution you want to apply to require. Luckily, you have the JAMB brochure or institution brochure to check the cut-off mark, so you have an idea of what you should be aiming for. It is, however, advisable, to aim higher than what you need.  So, in case there is any issue, you can – at least – drop to the score you need. According to a wise saying, “aim for the moon’ if you miss, you may hit a star.”
  • Study wide: No matter how much you pray or how much faith you have, if you do not study, you will be wasting your time. Studying is the only solution to doing excellently well in any exam. It is advisable to start studying now. It is more profitable to study for even an hour consistently until the exams than to try to study the whole syllabus in a few days. The JAMB UTME is even more difficult than the school examination because you can get questions from any year of Secondary School. This is why it is important to start studying early. It is also great to study widely to acquire knowledge and not just for the mentality to pass the exams. This is not only good for you in the long run but also because some of the questions might come from general knowledge.
  • Study past questions: Due to the bulky nature of the syllabus you are expected to concentrate on, it is pertinent to get some sort of direction. This is what past questions will offer to you. Get at least past questions of the last 5 years (or 10 years), so you can study the pattern of questioning and also have an idea the direction to take when studying. Most exams usually follow the same pattern and many times, they repeat the same questions. The patterns will help you streamline your study and the repeated questions will keep you from wasting time on them in the examination hall because you already know the answer to them.
  • Study exam focus textbooks: Based on the title, exam focus textbooks points you to the focus of the examination. As pointed out above, one of the major issues candidates have is the bulky nature of the syllabus and it can be so overwhelming that study becomes a chore. Exam focus has made that job easier because they have put together the focus of the exam in one textbook. The beauty of these textbooks is that they come in different subjects, so you can get for the subjects you are registering for. They also have practice questions to help you practice for the UTME. However, you need to remember that this does not mean you shouldn’t go an extra mile to study outside the scope of the textbooks because you never can tell with an exam and no knowledge is a waste.
  • Practice timed tests with the past questions: JAMB UTME is about speed and accuracy. You might be good but you also have to be fast. So, you should definitely practice within the set time or less that JAMB will give you. It is advisable to do this as regularly as you can, especially in the weeks close to the examination, so you can master it.
  • Rest and eat well: Yes, you need to rest as well while you study. This is why it is great to start studying early. Most of the people who don’t have time to rest properly are those who start studying late and want to cover the syllabus in a few days. Rest and good food is important when preparing for an examination. Your brain is working even more during that period and it needs to be fuelled and recharged.

Passing Jamb does not require any special skill sets. All you need to do is prepare well by following the tips in this article.

Check out the full Jamb Syllabus 2020

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