# Mathematics Waec Syllabus

Below is this 2024 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 multiple-choice 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

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 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.
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 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.
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 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.
2. 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.
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 Â 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 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, right-angled, 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.
4. 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.
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 Â 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 trigonometricÂ 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 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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