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   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.


The first paper 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.


The second paper 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

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 candidates’ home countries. Candidates will be expected to answer five questions for 60 marks.

Detailed Mathematics Syllabus


  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.


  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.


  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


  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.


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


  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


  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.


  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.


  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


  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)

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