The Unified Tertiary Matriculation Examination (UTME) Mathematics Syllabus 2025 is designed to help candidates prepare effectively for the exam. It outlines the key topics, objectives, and recommended resources for success.
JAMB wants candidates to:
- Acquire computational and manipulative skills.
- Develop precise, logical, and formal reasoning.
- Build deductive skills for interpreting graphs, diagrams, and data.
- Apply mathematical concepts to real-life problem solving.
The syllabus is divided into five main sections:
- I. Number and Numeration
- II. Algebra
- III. Geometry and Trigonometry
- IV. Calculus
- V. Statistics
Section I: Number and Numeration
1. Number Bases
- Operations in bases 2–10.
- Conversion between bases (including fractions).
Objectives: Candidates must perform basic operations (+, −, ×, ÷) and convert numbers between bases.
2. Fractions, Decimals, Approximations & Percentages
- Fractions, decimals, significant figures, decimal places.
- Percentage errors.
- Simple interest, profit and loss.
- Ratio, proportion, rates.
- Shares and Value Added Tax (VAT).
Objectives: Solve problems involving these concepts and apply them in daily contexts.
3. Indices, Logarithms & Surds
- Laws of indices.
- Standard form.
- Laws of logarithms, including change of base.
- Relationship between indices and logarithms.
- Surds (simplification, rationalisation).
Objectives: Use indices and logarithms in calculations, simplify surds, and perform operations on surds.
4. Sets
- Types of sets.
- Algebra of sets.
- Venn diagrams and applications.
Objectives: Identify types of sets, solve problems using set notation, and apply Venn diagrams (up to 3 sets).
Section II: Algebra
1. Polynomials
- Change of subject.
- Factor and remainder theorems.
- Factorisation (up to degree 3).
- Multiplication and division of polynomials.
- Roots of polynomials (≤ degree 3).
- Simultaneous equations (one linear, one quadratic).
- Graphs of polynomials.
Objectives: Factorize, solve, and graph polynomial functions.
2. Variation
- Direct, inverse, joint, partial variation.
- Percentage increase/decrease.
Objectives: Solve problems involving all forms of variation.
3. Inequalities
- Analytical and graphical solutions of linear inequalities.
- Quadratic inequalities (integral roots only).
Objectives: Solve and interpret inequalities, including graphing.
4. Progression
- nth term of sequences.
- Arithmetic and geometric progressions (A.P. & G.P.).
- Sum to infinity of G.P.
Objectives: Compute terms and sums of sequences.
5. Binary Operations
- Closure, commutativity, associativity, distributivity.
- Identity and inverse elements.
Objectives: Apply binary operations in solving problems.
6. Matrices & Determinants
- Algebra of matrices (up to 3×3).
- Determinants (up to 3×3).
- Inverses of 2×2 matrices.
Objectives: Perform operations with matrices, find determinants and inverses.
Section III: Geometry & Trigonometry
1. Euclidean Geometry
- Angles and lines.
- Polygons: triangles, quadrilaterals, general polygons.
- Circles: cyclic quadrilaterals, intersecting chords, angle properties.
- Constructions.
Objectives: Use geometric theorems, solve polygon problems, apply circle theorems, and construct special angles.
2. Mensuration
- Lengths, areas of plane figures.
- Arcs, chords, sectors, and segments of circles.
- Surface areas and volumes of solids.
- Earth as a sphere (longitudes, latitudes).
Objectives: Calculate perimeters, areas, volumes, and solve Earth distance problems.
3. Loci
- Geometric loci in 2D (lines, bisectors, circles).
Objectives: Interpret and apply loci principles.
4. Coordinate Geometry
- Midpoint and gradient of lines.
- Distance between two points.
- Parallelism and perpendicularity.
- Equations of straight lines.
Objectives: Derive equations and solve coordinate problems.
5. Trigonometry
- Ratios of angles.
- Elevation, depression, bearings.
- Areas and solutions of triangles.
- Sine and cosine rules.
- Graphs of sine and cosine.
Objectives: Apply trigonometric ratios, solve navigation problems, and use trigonometric graphs.
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Section IV: Calculus
1. Differentiation
- Limits of functions.
- Differentiation of algebraic and simple trig functions (sine, cosine, tangent).
2. Applications
- Rates of change.
- Maxima and minima.
3. Integration
- Integration of algebraic and simple trig functions.
- Area under curves (simple cases).
Objectives: Apply calculus to solve problems in change, optimisation, and area.
Section V: Statistics
1. Data Representation
- Frequency distributions.
- Histogram, bar chart, pie chart.
2. Measures of Location
- Mean, median, mode (grouped and ungrouped).
- Cumulative frequency, quartiles, percentiles.
3. Measures of Dispersion
- Range, mean deviation, variance, standard deviation.
4. Permutations & Combinations
- Linear and circular arrangements.
- Repeated objects.
5. Probability
- Experimental probability (coin, dice, etc).
- Addition and multiplication rules.
Objectives: Interpret data, compute averages, measure spread, and solve probability problems.
Recommended Textbooks for JAMB Mathematics 2025
- Adelodun A. A. (2000) – Distinction in Mathematics (3rd Edition).
- Anyebe J. A. B. (1998) – Basic Mathematics for Senior Secondary Schools.
- Channon J. B., Smith A. M. (2001) – New General Mathematics for West Africa.
- David-Osuagwu M. et al. (2000) – New School Mathematics.
- Egbe E. et al. (2000) – Further Mathematics.
- Ibude S. O. et al. (2003) – Algebra and Calculus for Schools and Colleges.
- Tuttuh-Adegun M. R. et al. (1997) – Further Mathematics Project Books 1–3.
- Wisdomline – Pass at Once JAMB.
Final Tips for Candidates
- Practice past questions to understand the pattern.
- Use CBT practice apps to simulate real exam conditions.
- Focus on weak areas by revisiting topics you struggle with.
- Balance all five sections – don’t ignore statistics or calculus.
- Be time-conscious while solving problems.
Credit: Jambportal, Allcbts
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