JAMB 2025 MATHEMATICS SYLLABUS

Introduction:

JAMB 2025 MATHEMATICS SYLLABUS aims to prepare the candidates for the Board’s examination. It is designed to test the achievement of the course objectives, which are to:

1. Acquire computational and manipulative skills.
2. Develop precise, logical, and formal reasoning skills.
3. Develop deductive skills in the interpretation of graphs, diagrams, and data.
4. Apply mathematical concepts to resolve issues in daily living.

This syllabus is divided into five sections:

• Section I: Number and Numeration
• Section II: Algebra
• Section III: Geometry/Trigonometry
• Section IV: Calculus
• Section V: Statistics

Table of Contents

• Introduction:
• Section I: Number and Numeration
  • 1. Number Bases
  • 2. Fractions, Decimals, Approximations, and Percentages
  • 3. Indices, Logarithms, and Surds
  • 4. Sets
• Section II: Algebra
  • 1. Polynomials
  • 2. Variation
  • 3. Inequalities
  • 4. Progression
  • 5. Binary Operations
  • 6. Matrices and Determinants
• Section III: Geometry and Trigonometry
  • 1. Euclidean Geometry
  • 2. Mensuration
• 3. Loci
  • 4. Coordinate Geometry
  • 5. Trigonometry
• Section IV: Calculus
  • 1. Differentiation
  • 2. Application of Differentiation
  • 3. Integration
• Section V: Statistics
  • 1. Representation of Data
  • 2. Measures of Location
  • 3. Measures of Dispersion
  • 4. Permutation and Combination
  • 5. Probability
  • Recommended Texts:

Section I: Number and Numeration

1. Number Bases

• Topics:
  • Operations in different number bases (from 2 to 10).
  • Conversion from one base to another, including fractional parts.
• Objectives:
  • Perform basic operations (x, +, -, ÷) in various bases.
  • Convert numbers between different bases.

2. Fractions, Decimals, Approximations, and Percentages

• Topics:
  • Fractions and decimals.
  • Significant figures.
  • Decimal places.
  • Percentage errors.
  • Simple interest.
  • Profit and loss percent.
  • Ratio, proportion, and rate.
  • Shares and VAT.
• Objectives:
  • Perform basic operations (x, +, -, ÷) on fractions and decimals.
  • Express numbers to specified significant figures and decimal places.
  • Calculate simple interest, profit and loss percent, and solve problems involving ratio, proportion, rate, shares, and VAT.

3. Indices, Logarithms, and Surds

• Topics:
  • Laws of indices.
  • Standard form.
  • Laws of logarithms.
  • Logarithm of any positive number to a given base.
  • Change of bases in logarithms and their applications.
  • Relationship between indices and logarithms.
  • Surds.
• Objectives:
  • Apply the laws of indices in calculation.
  • Establish the relationship between indices and logarithms in solving problems.
  • Solve problems in different bases in logarithms.
  • Simplify and rationalize surds.
  • Perform basic operations on surds.

4. Sets

• Topics:
  • Types of sets.
  • Algebra of sets.
  • Venn diagrams and their applications.
• Objectives:
  • Identify types of sets (empty, universal, complements, subsets, finite, infinite, and disjoint sets).
  • Solve problems involving the cardinality of sets.
  • Solve set problems using symbols.
  • Use Venn diagrams to solve problems involving up to 3 sets.

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Section II: Algebra

1. Polynomials

• Topics:
  • Change of subject of formula.
  • Factor and remainder theorems.
  • Factorization of polynomials of degree not exceeding 3.
  • Multiplication and division of polynomials.
  • Roots of polynomials of degree ≤ 3.
  • Simultaneous equations, including one linear and one quadratic.
  • Graphs of polynomials of degree ≤ 3.
• Objectives:
  • Find the subject of the formula for a given equation.
  • Apply the factor and remainder theorem to factorize an expression.
  • Multiply and divide polynomials of degree ≤ 3.
  • Factorize by regrouping differences of two squares, perfect squares, and cubic expressions.
  • Solve simultaneous equations involving one linear and one quadratic equation.
  • Interpret graphs of polynomials, including applications to maximum and minimum values.

2. Variation

• Topics:
  • Direct, inverse, joint, partial variations.
  • Percentage increase and decrease.
• Objectives:
  • Solve problems involving direct, inverse, joint, and partial variations.
  • Solve problems on percentage increase and decrease in variation.

3. Inequalities

• Topics:
  • Analytical and graphical solutions of linear inequalities.
  • Quadratic inequalities with integral roots only.
• Objectives:
  • Solve problems involving linear and quadratic inequalities.
  • Interpret graphs of inequalities.

4. Progression

• Topics:
  • nth term of a progression.
  • Sum of arithmetic progression (A.P.) and geometric progression (G.P.).
• Objectives:
  • Determine the nth term of a progression.
  • Compute the sum of A.P. and G.P.
  • Sum to infinity of a given G.P.

5. Binary Operations

• Topics:
  • Properties of closure, commutativity, associativity, and distributivity.
  • Identity and inverse elements (simple cases only).
• Objectives:
  • Solve problems involving closure, commutativity, associativity, and distributivity.
  • Solve problems involving identity and inverse elements.

6. Matrices and Determinants

• Topics:
  • Algebra of matrices (up to 3×3).
  • Determinants of matrices (up to 3×3).
  • Inverses of 2×2 matrices (excluding quadratic and higher degree equations).
• Objectives:
  • Perform basic operations (x, +, -, ÷) on matrices.
  • Calculate determinants.
  • Compute inverses of 2×2 matrices.

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Section III: Geometry and Trigonometry

1. Euclidean Geometry

• Topics:
  • Properties of angles and lines.
  • Polygons: triangles, quadrilaterals, and general polygons.
  • Circles: angle properties, cyclic quadrilaterals, and intersecting chords.
  • Construction.
• Objectives:
  • Identify various types of lines and angles.
  • Solve problems involving polygons.
  • Calculate angles using circle theorems.
  • Identify construction procedures for special angles (e.g., 30°, 45°, 60°, 75°, 90° etc.).

2. Mensuration

• Topics:
  • Lengths and areas of plane geometrical figures.
  • Lengths of arcs and chords of a circle.
  • Perimeters and areas of sectors and segments of circles.
  • Surface areas and volumes of simple solids and composite figures.
  • The earth as a sphere: longitudes and latitudes.
• Objectives:
  • Calculate the perimeters and areas of triangles, quadrilaterals, circles, and composite figures.
  • Find the length of an arc, a chord, perimeters, and areas of sectors and segments of circles.
  • Calculate total surface areas and volumes of cuboids, cylinders, cones, pyramids, prisms, spheres, and composite figures.
  • Determine the distance between two points on the earth’s surface.

3. Loci

• Topics:
  • Locus in 2 dimensions based on geometric principles relating to lines and curves.
• Objectives:
  • Identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors, and circles.

4. Coordinate Geometry

• Topics:
  • Midpoint and gradient of a line segment.
  • Distance between two points.
  • Parallel and perpendicular lines.
  • Equations of straight lines.
• Objectives:
  • Determine the midpoint and gradient of a line segment.
  • Find the distance between two points.
  • Identify conditions for parallelism and perpendicularity.
  • Find the equation of a line in the two-point form, point-slope form, slope-intercept form, and the general form.

5. Trigonometry

• Topics:
  • Trigonometric ratios of angles.
  • Angles of elevation and depression.
  • Bearings.
  • Areas and solutions of triangles.
  • Graphs of sine and cosine.
  • Sine and cosine formulae.
• Objectives:
  • Calculate the sine, cosine, and tangent of angles between -360° ≤ θ ≤ 360°.
  • Apply these special angles (e.g., 30°, 45°, 60°, 75°, 90°, 105°, 135°) to solve simple problems in trigonometry.
  • Solve problems involving angles of elevation and depression.
  • Solve problems involving bearings.
  • Apply trigonometric formulae to find areas of triangles.
  • Solve problems involving sine and cosine graphs.

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Section IV: Calculus

1. Differentiation

• Topics:
  • Limit of a function.
  • Differentiation of explicit algebraic and simple trigonometric functions (sine, cosine, and tangent).
• Objectives:
  • Find the limit of a function.
  • Differentiate explicit algebraic and simple trigonometric functions.

2. Application of Differentiation

• Topics:
  • Rate of change.
  • Maxima and minima.
• Objectives:
  • Solve problems involving applications of rate of change, maxima, and minima.

3. Integration

• Topics:
  • Integration of explicit algebraic and simple trigonometric functions.
  • Area under the curve.
• Objectives:
  • Solve problems of integration involving algebraic and simple trigonometric functions.
  • Calculate area under the curve (simple cases only).

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Section V: Statistics

1. Representation of Data

• Topics:
  • Frequency distribution.
  • Histogram, bar chart, and pie chart.
• Objectives:
  • Identify and interpret frequency distribution tables.
  • Interpret information on histograms, bar charts, and pie charts.

2. Measures of Location

• Topics:
  • Mean, mode, and median of ungrouped and grouped data (simple cases only).
  • Cumulative frequency.
• Objectives:
  • Calculate the mean, mode, and median of ungrouped and grouped data (simple cases only).
  • Use ogive to find the median, quartiles, and percentiles.

3. Measures of Dispersion

• Topics:
  • Range, mean deviation, variance, and standard deviation.
• Objectives:
  • Calculate the range, mean deviation, variance, and standard deviation of ungrouped and grouped data.

4. Permutation and Combination

• Topics:
  • Linear and circular arrangements.
  • Arrangements involving repeated objects.
• Objectives:
  • Solve simple problems involving permutation and combination.

5. Probability

• Topics:
  • Experimental probability (tossing of coin, throwing of a dice, etc.).
  • Addition and multiplication of probabilities (mutual and independent cases).
• Objectives:
  • Solve simple problems in probability (including addition and multiplication).

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Recommended Texts:

• Adelodun A. A (2000) Distinction in Mathematics: Comprehensive Revision Text (3rd Edition)
• Anyebe, J. A. B (1998) Basic Mathematics for Senior Secondary Schools and Remedial Students
• Channon, J. B. & Smith, A. M (2001) New General Mathematics for West Africa SSS 1 to 3
• David-Osuagwu, M. et al (2000) New School Mathematics for Senior Secondary Schools
• Ibude, S. O. et al (2003) Algebra and Calculus for Schools and Colleges
• Tuttuh-Adegun M. R. et al (1997) Further Mathematics Project Books 1 to 3