Mathematics Waec Syllabus

NUMBER AND NUMERATION

1. Number bases
   • conversion of numbers from one base to another
   • Basic operations on number bases
2. Modular Arithmetic
   • Concept of Modulo Arithmetic
   • Addition, subtraction, and multiplication operations in modulo arithmetic
   • Application to daily life
3. Fractions, Decimals and Approximations
   • Basic operations on fractions and decimals.
   • Approximations and significant figures.
4. Indices
   • Laws of indices
   • Numbers in standard form ( scientific notation)
5. Logarithms
   • Relationship between indices and logarithms: e.g., y = 10k implies log₁₀y = k.
   • Basic rules of logarithms
   • Use of tables of logarithms and anti-logarithms
     • Calculations involving multiplication, division, powers, and roots.
6. Sequence and Series
   • Patterns of sequences.
   • Arithmetic progression (A.P.) and Geometric Progression (G.P.)
7. 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.
8. Logical Reasoning
   • Simple statements.
   • True and false statements.
   • Negation of statements and implications.
   • Use of symbols: use of Venn diagrams
9. 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 ).
10. 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 ).
11. Matrices and Determinants
    • Identification of order, notation, and types of matrices.
    • Addition, subtraction, scalar multiplication, and multiplication of matrices.
    • Determinant of a matrix
12. Ratio, Proportions and  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.
13. Percentages
    • Simple interest, commission, discount, depreciation, profit and loss, compound interest, hire purchase, and percentage error.
14. Financial Arithmetic
    • Depreciation/Amortization.
    • Annuities
    • Capital Market Instruments
15. Variation
    • Direct, inverse, partial, and joint variations.
    • Application to simple, practical problems.

ALGEBRAIC PROCESSES

1. Algebraic expressions
   • Formulating algebraic expressions from given situations
   • Evaluation of algebraic expressions
2. Simple operations on algebraic expressions
   • Expansion
   • Factorization
3. Solution of Linear Equations
   • Linear equations in one variable
   • Simultaneous linear equations in two variables.
4. Change of Subject of a Formula/Relation
   • Change of subject of a formula or relationship
   • Substitution.
5. 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.
6. 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  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.
7. 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.
8. Algebraic Fractions

   Operations on algebraic fractions with:

   • Monomial denominators
   • Binomial denominators
9. 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 or function.

MENSURATION

1. Lengths and 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.
2. Areas
   • Triangles and special  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 = ½ base x height and ½absinC.
     • Areas of compound shapes.
     • Relationship between the sector of a circle and the surface area of a cone.
3. Volumes
   • Volumes of cubes, cuboids, cylinders, cones, right pyramids and spheres.
   • Volumes of similar solids

PLANE GEOMETRY

1. Angles
   • Angles at a point add up to  360 degrees.
   • Adjacent angles on a straight line are supplementary.
   • Vertically opposite angles are equal.
2. Angles and intercepts on parallel lines
   • Alternate angles are equal.
   • Corresponding angles are equal.
   • Interior opposite angles are supplementary
   • Intercept theorem.
3. Triangles and polygons
   • The sum of the angles of a  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, right-angled, etc
   • Properties of special quadrilaterals: parallelogram, rhombus,  square, rectangle, trapezium.
   • Properties of similar triangles.
   • The sum of the angles of a  polygon
   • Property of exterior angles of a polygon.
   • Parallelograms on the same base and between the same parallels are equal in area.
4. Circles
   • Chords.
   • The angle at 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.
   • 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.
5. Construction
   • Bisectors of angles and line segments
   • Line parallel or perpendicular to a given line.
   • Angles, e.g., 90⁰, 60⁰, 45⁰, 30⁰, and an angle equal to a given angle.
   • Triangles and quadrilaterals from sufficient data.
6. 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  STRAIGHT LINES

1. Concept of the x-y plane
2. Coordinates of points on the x-y plane

TRIGONOMETRY

1. Sine, Cosine and Tangent of an angle.
   • Sine, Cosine and Tangent of acute angles.
   • Use of tables of trigonometric ratios.
   • Trigonometric ratios of 30⁰, 45⁰, and 60⁰
   • Sine, cosine, and tangent of angles from 0⁰ to 360⁰
   • Graphs of sine and cosine.
   • Graphs of trigonometric ratios.
2. Angles of elevation and depression
   • Calculating angles of elevation and depression.
   • Application to heights and distances.
3. Bearings
   • Bearing of one point from another.
   • Calculation of distances and angles

INTRODUCTORY CALCULUS

1. Differentiation of algebraic functions.
2. 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 real-life 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

1. 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 inter-quartile/inter-quartile range, variance, mean deviation and standard deviation
2. Probability
   • Experimental and theoretical probability.
   • Addition of probabilities for mutually exclusive and independent events.
   • Multiplication of probabilities for independent events.

VECTORS AND TRANSFORMATION

1. 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.
2. 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

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
   • milligrammes (mg) = 1 gramme (g)
   • 1000 grammes (g) = 1 kilogramme( kg )
   • 1000 kilogrammes (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)