Home » JAMB Syllabus » Do you want to study a science, engineering or calculation-related course at the university? Then you should be prepared to write Mathematics in your Unified Tertiary Matriculation Examination.
The exam covers topics like algebra, trigonometry, geometry, and statistics and is designed to test your problem-solving skills.
JAMB mathematics is often easier for students who did further mathematics in their senior secondary schools. The trick to excellent performance in JAMB math is efficiency and speed. You only need answers and not step-by-step workings.
This syllabus is divided into five sections:
The aim of the Unified Tertiary Matriculation Examination (UTME) syllabus in Mathematics is to prepare the candidates for the 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 interpretation of graphs, diagrams and data;
(4) Apply mathematical concepts to resolve issues in daily living.
| JAMB MATHEMATICS SYLLABUS | ||
|---|---|---|
| SN | TOPICS | OBJECTIVES |
| 1 | NUMBER AND NUMERATION | |
| 1. Number bases: operations in different number bases from 2 to 10; conversion from one base to another including fractional parts 2. Fractions, Decimals, Approximations and Percentages: fractions and decimals; significant figures; decimal places; percentage errors; simple interest; profit and loss percent; ratio, proportion and rate; shares and valued added tax (VAT). 3. Indices, Logarithms and Surds: laws of indices; standard form; laws of logarithm; logarithm of any positive number to a given base; change of bases in logarithm and application; relationship between indices and logarithm; surds. 4. Sets: types of sets algebra of sets venn diagrams and their applications. | Candidates should be able to: i. perform four basic operations (x,+,-,÷) ii. convert one base to another. Candidates should be able to: i. perform basic operations (x,+,-,÷) on fractions and decimals; ii. express to specified number of significant figures and decimal places; iii. calculate simple interest, profit and loss percent; ratio proportion and rate; iv. Solve problems involving share and VAT. Candidates should be able to: i. apply the laws of indices in calculation; ii. establish the relationship between indices and logarithms in solving problems; iii. solve problems in different bases in logarithms; iv. simplify and rationalize surds; v. perform basic operations on surds. Candidates should be able to: i. identify types of sets, i.e empty, universal, complements, subsets, finite, infinite and disjoint sets; ii. solve problems involving cardinality of sets; iii. solve set problems using symbol; iv. use venn diagrams to solve problems involving not more than 3 sets. | |
| 2 | ALGEBRA. | |
| 1. Polynomials: 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 not exceeding degree 3 simultaneous equations including one linear one quadratic; graphs of polynomials of degree not greater than 3. 2. Variation: direct inverse joint partial percentage increase and decrease. 3. Inequalities: analytical and graphical solutions of linear inequalities; quadratic inequalities with integral roots only. 4. Progression: nth term of a progression sum of A. P. and G. P. 5. Binary Operations: properties of closure, commutativity, associativity and distributivity; identity and inverse elements (simple cases only). 6. Matrices and Determinants: algebra of matrices not exceeding 3 x 3; determinants of matrices not exceeding 3 x 3; inverses of 2 x 2 matrices [excluding quadratic and higher degree equations]. | Candidates should be able to: i. find the subject of the formula of a given equation; ii. apply factor and remainder theorem to factorize a given expression; iii. multiply and divide polynomials of degree not more than 3; iv. factorize by regrouping difference of two squares, perfect squares and cubic expressions; etc. v. solve simultaneous equations – one linear, one quadratic; vi. interpret graphs of polynomials including applications to maximum and minimum values. Candidates should be able to: i. solve problems involving direct, inverse, joint and partial variations; ii. solve problems on percentage increase and decrease in variation. Candidates should be able to: i. solve problems on linear and quadratic inequalities; ii. interpret graphs of inequalities. Candidates should be able to: i. determine the nth term of a progression; ii. compute the sum of A. P. and G.P; iii. sum to infinity of a given G.P. Candidates should be able to: i. solve problems involving closure, commutativity, associativity and distributivity; ii. solve problems involving identity and inverse elements. Candidates should be able to: i. perform basic operations (x,+,-,÷) on matrices; ii. calculate determinants; iii. compute inverses of 2 x 2 matrices | |
| 3 | GEOMETRY AND TRIGONOMETRY | |
| 1. Euclidean Geometry: Properties of angles and lines Polygons: triangles, quadrilaterals and general polygons; Circles: angle properties, cyclic quadrilaterals and intersecting chords; construction. 2. Mensuration: 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. 3. Loci: locus in 2 dimensions based on geometric principles relating to lines and curves. 4. Coordinate Geometry: midpoint and gradient of a line segment; distance between two points; parallel and perpendicular lines; equations of straight lines. 5. Trigonometry: trigonometric ratios of angels; angles of elevation and depression; bearings; areas and solutions of triangle; graphs of sine and cosine; sine and cosine formulae. | Candidates should be able to: i. identify various types of lines and angles; ii. solve problems involving polygons; iii. calculate angles using circle theorems; iv. identify construction procedures of special angles, e.g. 30°, 45°, 60°, 75°, 90° etc. Candidates should be able to: i. calculate the perimeters and areas of triangles, quadrilaterals, circles and composite figures; ii. find the length of an arc, a chord, perimeters and areas of sectors and segments of circles; iii. calculate total surface areas and volumes of cuboids, cylinders. cones, pyramids, prisms, spheres and composite figures; iv. determine the distance between two points on the earth’s surface. Candidates should be able to: identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles. Candidates should be able to: i. determine the midpoint and gradient of a line segment; ii. find the distance between two points; iii. identify conditions for parallelism and perpendicularity; iv. find the equation of a line in the two-point form, point-slope form, slope intercept form and the general form. Candidates should be able to: i. calculate the sine, cosine and tangent of angles between – 360° ≤ θ ≤ 360°; ii. apply these special angles, e.g. 30°, 45°, 60°, 75°, 90°, 105°, 135° to solve simple problems in trigonometry; iii. solve problems involving angles of elevation and depression; iv. solve problems involving bearings; v. apply trigonometric formulae to find areas of triangles; vi. solve problems involving sine and cosine graphs. | |
| 4 | CALCULUS | |
| 1. Differentiation: limit of a function differentiation of explicit algebraic and simple trigonometric functions-sine, cosine and tangent. 2. Application of differentiation: rate of change; maxima and minima. 3. Integration: integration of explicit algebraic and simple trigonometric functions; area under the curve | Candidates should be able to: i. find the limit of a function ii. differentiate explicit algebraic and simple trigonometric functions. Candidates should be able to: solve problems involving applications of rate of change, maxima and minima. Candidates should be able to: i. solve problems of integration involving algebraic and simple trigonometric functions; ii. calculate area under the curve (simple cases only). | |
| 5 | STATISTICS | |
| 1. Representation of data: frequency distribution; histogram, bar chart and pie chart. 2. Measures of Location: mean, mode and median of ungrouped and grouped data – (simple cases only); cumulative frequency. 3. Measures of Dispersion: range, mean deviation, variance and standard deviation. 4. Permutation and Combination: Linear and circular arrangements; Arrangements involving repeated objects. 5. Probability: experimental probability (tossing of coin, throwing of a dice etc); Addition and multiplication of probabilities (mutual and independent cases). | Candidates should be able to: i. identify and interpret frequency distribution tables; ii. interpret information on histogram, bar chart and pie chart Candidates should be able to: i. calculate the mean, mode and median of ungrouped and grouped data (simple cases only); ii. use ogive to find the median, quartiles and percentiles Candidates should be able to: calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data Candidates should be able to: solve simple problems involving permutation and combination. Candidates should be able to: solve simple problems in probability (including addition and multiplication). |
There is no official pass mark, but scores above 50 are considered good. However, you should try to score as high as you can because the higher you score, the better your chances of admission for your chosen course and institution.
The entire exam takes 2 hours. While there is no estimated time for each subject, I would advise you to spend about 30-45 seconds on each question so you can have enough time to go over your work again. Do not spend too much time on questions you do not know.
The UTME Mathematics exam covers algebra, geometry, statistics, and trigonometry. A full list of topics to study is listed above.
You are not allowed to use calculators. However, there will be a calculator on your computer screen for all calculations. If you’re found with a calculator, your exam will be canceled immediately and you will be sanctioned.
If you intend to study courses like Computer Science, Mathematics, Statistics, Accounting, and Engineering, you will have to write Mathematics. Please consult your brochure to see the recommended subject combinations for each course and specific requirements for schools.
You will be required to answer 40 multiple-choice questions based on the syllabus listed above
Not at all. You can read and ace your exams yourself. All you need to do is to have a consistent reading habit.
However, tutorials can also help you prepare better, connect with your peers, and gauge your confidence levels.
Here are a few tips for you:
Start studying early enough. Avoid last minute reading at all costs. Also try practicing time management so you can utilize your time well. Endeavor to study past questions as often as possible and most importantly,get a goodnight rest a day for your exam.
Goodluck!
