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

Detailed Mathematics 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)

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