Mathematics Waec Syllabus
Below is this years Waec Syllabus for Mathematics. Note that this syllabus is for both internal and external candidates.
Aims and Objectives
 Mathematical competency and computational skills
 Understanding of mathematical concepts and their relationship to the Â Â acquisition of entrepreneurial skills for everyday living in the global world
 The ability to translate problems into mathematical language and solve them using appropriate methods
 The ability to be accurate to a degree relevant to the problem at hand
 Logical, abstract, and precise thinking
Scheme of Examination
There will be two papers, Papers 1 and 2, both of which must be taken.
PAPER 1:
The first paper will consist of fifty multiplechoice objective questions, drawn from the common areas of the syllabus, to be answered in 1Â½ hours for 50 marks.
PAPER 2:
The second paper will consist of thirteen essay questions in two sections, Sections A and B, to be answered in 2Â½ hours for 100 marks. Candidates will be required to answer ten questions in all.
Section A
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
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 that may not be peculiar to candidatesâ€™ home countries. Candidates will be expected to answer five questions for 60 marks.
Detailed Mathematics Syllabus
NUMBER AND NUMERATION

 Number bases
 conversion of numbers from one base to another
 Basic operations on number bases

 Modular Arithmetic
 Concept of Modulo Arithmetic
 Addition, subtraction, and multiplication operations in modulo arithmetic
 Application to daily life

 Fractions, Decimals and Approximations
 Basic operations on fractions and decimals.
 Approximations and significant figures.

 Indices
 Laws of indices
 Numbers in standard form ( scientific notation)

 Logarithms
 Relationship between indices and logarithms: e.g., y = 10k implies log_{10}y = k.
 Basic rules of logarithms
 Use of tables of logarithms and antilogarithms
 Calculations involving multiplication, division, powers, and roots.

 Sequence and Series
 Patterns of sequences.
 Arithmetic progression (A.P.) and Geometric Progression (G.P.)

 Sets
 Idea of sets, universal sets, finite and infinite sets, subsets, empty sets, and disjoint sets.
 Solution of practical problems involving classification using Venn diagrams.

 Logical Reasoning
 Simple statements.
 True and false statements.
 Negation of statements and implications.
 Use of symbols: use of Venn diagrams

 Positive and negative integers, rational numbers
 The four basic operations on rational numbers.
 Match rational numbers with points on the number line.
 Notation: natural numbers (N), integers ( Z ), and rational numbers ( Q ).

 Surds (Radicals)
 Simplification and rationalization of simple surds.
 Surds of the form, a and b, where a is a rational number and b is a positive integer.
 Basic operations on surds (exclude surd of the form ).

 Matrices and Determinants
 Identification of order, notation, and types of matrices.
 Addition, subtraction, scalar multiplication, and multiplication of matrices.
 Determinant of a matrix

 Ratio, Proportions and Â Rates
 The ratio between two similar quantities.
 The 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.

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

 Financial Arithmetic
 Depreciation/Amortization.
 Annuities
 Capital Market Instruments

 Variation
 Direct, inverse, partial, and joint variations.
 Application to simple, practical problems.
ALGEBRAIC PROCESSES

 Algebraic expressions
 Formulating algebraic expressions from given situations
 Evaluation of algebraic expressions

 Simple operations on algebraic expressions
 Expansion
 Factorization

 Solution of Linear Equations
 Linear equations in one variable
 Simultaneous linear equations in two variables.

 Change of Subject of a Formula/Relation
 Change of subject of a formula or relationship
 Substitution.

 Quadratic Equations
 Solution of quadratic equations
 Forming a quadratic equation with the given roots.
 Application of a solution to a quadratic equation in practical problems.

 Graphs of Linear and Quadratic functions
 Interpretation of graphs, the coordinate of points, tables of values, drawing quadratic graphs, and obtaining roots from graphs.
 Graphical solution of a pair Â of equations of the form: y = ax2 + bx + c and y = mx + k
 drawing tangents to curves to determine the gradient at a given point.

 Linear Inequalities
 Solution of linear inequalities in one variable and representation on the number line.
 Graphical solution of linear inequalities in two variables.
 Graphical solution of simultaneous linear inequalities in two variables.

 Algebraic Fractions
Operations on algebraic fractions with:
 Monomial denominators
 Binomial denominators

 Functions and Relations
 Types of Functions
 Onetoone, onetomany, manytoone, manytomany.
 Functions as a mapping, determination of the rule of a given mapping or function.
MENSURATION

 Lengths andÂ Perimeters
 Use of Pythagoras theorem, sine, and cosine rules to determine lengths and distances.
 lengths of arcs of circles, perimeters of sectors, and segments.
 Longitudes and latitudes.

 Areas
 Triangles and special Â quadrilaterals: rectangles, parallelograms and trapeziums
 Circles, sectors, and segments of circles.
 Surface areas of cubes, cuboids, cylinders, pyramids, right triangular prisms, cones, and spheres.
 Areas of similar figures. Include the area of the triangle = Â½ base x height and Â½absinC.
 Areas of compound shapes.
 Relationship between the sector of a circle and the surface area of a cone.

 Volumes
 Volumes of cubes, cuboids, cylinders, cones, right pyramids and spheres.
 Volumes of similar solids
PLANE GEOMETRY

 Angles
 Angles at a point add up to Â 360 degrees.
 Adjacent angles on a straight line are supplementary.
 Vertically opposite angles are equal.

 Angles and intercepts on parallel lines
 Alternate angles are equal.
 Corresponding angles are equal.
 Interior opposite angles are supplementary
 Intercept theorem.

 Triangles and polygons
 The sum of the angles of aÂ triangle is 2 right angles.
 The exterior angle of a triangle equals the sum of the two interior opposite angles.
 congruent triangles.
 Properties of special triangles: isosceles, equilateral, rightangled, etc
 Properties of special quadrilaterals: parallelogram, rhombus, Â square, rectangle, trapezium.
 Properties of similar triangles.
 The sum of the angles of a Â polygon
 Property of exterior angles of a polygon.
 Parallelograms on the same base and between the same parallels are equal in area.

 Circles
 Chords.
 The angle at which an arc of a Â circle subtends at the centre of the circle is twice that which it subtends at any point on the remaining part of the circumference.
 Any angle subtended at the circumference by a diameter is a right angle.
 Angles in the same segment are equal.
 Angles in opposite segments are supplementary.
 Perpendicularity of tangent and radius.
 If a tangent is drawn to a circle and from the point of contact a chord is drawn, each angle that this chord makes with the tangent is equal to the angle in the alternate segment.

 Construction
 Bisectors of angles and line segments
 Line parallel or perpendicular to a given line.
 Angles, e.g., 90^{0}, 60^{0}, 45^{0}, 30^{0}, and an angle equal to a given angle.
 Triangles and quadrilaterals from sufficient data.

 Loci
Knowledge of the loci listed below and their intersections in 2 dimensions.
 Points at a given distance from a given point.
 Points equidistant from two given points.
 Points equidistant from two given straight lines.
 Points at a given distance from a given straight line.
COORDINATE GEOMETRY OF Â STRAIGHT LINES

 Concept of the xy plane

 Coordinates of points on the xy plane
TRIGONOMETRY

 Sine, Cosine and Tangent of an angle.
 Sine, Cosine and Tangent of acute angles.
 Use of tables of trigonometric ratios.
 Trigonometric ratios of 30^{0}, 45^{0}, and 60^{0}
 Sine, cosine, and tangent of angles from 0^{0} to 360^{0}
 Graphs of sine and cosine.
 Graphs of trigonometricÂ ratios.

 Angles of elevation and depression
 Calculating angles of elevation and depression.
 Application to heights and distances.

 Bearings
 Bearing of one point from another.
 Calculation of distances and angles
INTRODUCTORY CALCULUS

 Differentiation of algebraic functions.

 Integration of simple Algebraic functions.
 Concept/meaning of differentiation/derived function: the relationship between the 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 reallife situations such as maximum and minimum values, rates of change, etc.
 Meaning or concept of integration, evaluation of simple definite algebraic equations.
STATISTICS AND PROBABILITY

 Statistics
 Frequency distribution
 Pie charts, bar charts, histograms and frequency polygons
 Mean, median, and mode for both discrete and grouped data.
 Cumulative frequency curve (Ogive).
 Measures of Dispersion: range, semi interquartile/interquartile range, variance, mean deviation and standard deviation

 Probability
 Experimental and theoretical probability.
 Addition of probabilities for mutually exclusive and independent events.
 Multiplication of probabilities for independent events.
VECTORS AND TRANSFORMATION

 Vectors in a Plane
 Vectors as a directed line segment.
 Cartesian components of a vector
 The magnitude of a vector, equal vectors, addition and subtraction of vectors, zero vector, parallel vectors, and multiplication of a vector by a scalar.

 Transformation in the Cartesian Plane
 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
UNITS

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

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

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

 Mass
 milligrammes (mg) = 1 gramme (g)
 1000 grammes (g) = 1 kilogramme( kg )
 1000 kilogrammes (kg) = 1 tonne.

 Currencies
 The Gambia â€“ 100 bututs (b) = 1 Dalasi (D)
 Ghana – 100 Ghana pesewas (Gp) = 1 Ghana Cedi ( GHÂ¢)
 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 (Â£)
 USA – 100 cents (c) = 1 dollar ($)
 French Speaking territories: 100 centimes (c) = 1 Franc (fr)
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