Mathematics (JAMB)

MATHEMATICS

GENERAL OBJECTIVES

JAMB Syllabus for Mathematics
The aim of this 2019 JAMB Mathematics Syllabus for Unified Tertiary Matriculation Examination (UTME), is 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 interpretation of graphs, diagrams and data;
(4) apply mathematical concepts to resolve issues in daily living.

This syllabus is divided into five sections:

I. Number and Numeration.
II. Algebra
III. Geometry/Trigonometry.
IV. Calculus
V. Statistics

SECTION I: NUMBER AND NUMERATION

1. Number bases

Topics:

(a) operations in different number bases from 2 to 10;
(b) conversion from one base to another including fractional parts.

2. Fractions, Decimals, Approximations and Percentages

Topics

(a) fractions and decimals;
(b) significant figures;
(c) decimal places;
(d) percentage errors;
(e) simple interest;
(f) profit and loss percent;
(g) ratio, proportion and rate;
(h) shares and valued added tax (VAT).

3. Indices, Logarithms and Surds

Topics

(a) laws of indices;
(b) standard form;
(c) laws of logarithm;
(d) logarithm of any positive number to a given base;
(e) change of bases in logarithm and application;
(f) relationship between indices and logarithm;
(g) surds

4. Sets

Topics

(a) types of sets
(b) algebra of sets
(c) venn diagrams and their applications.

 SECTION II: ALGEBRA.

1. Polynomials

Topics

(a) change of subject of formula
(b) factor and remainder theorems
(c) factorization of polynomials of degree not exceeding 3.
(d) multiplication and division of polynomials
(e) roots of polynomials not exceeding degree 3
(f) simultaneous equations including one linear one quadratic;
(g) graphs of polynomials of degree not greater than 3.

2. Variation

Topics:

(a) direct
(b) inverse
(c) joint
(d) partial
(e) percentage increase and decrease.

3. Inequalities

Topics:

(a) analytical and graphical solutions of linear inequalities;
(b) quadratic inequalities with integral roots only.

4. Progression

(a) nth term of a progression
(b) sum of A. P. and G. P.

5. Binary Operations

Topics:

(a) properties of closure, commutativity, associativity and distributivity;
(b) identity and inverse elements (simple cases only).

6. Matrices and Determinants

Topics:

(a) algebra of matrices not exceeding 3 x 3;
(b) determinants of matrices not exceeding 3 x 3;
(c) inverses of 2 x 2 matrices [excluding quadratic and higher degree equations].

SECTION III: GEOMETRY AND TRIGONOMETRY

1. Euclidean Geometry

Topics:

(a) Properties of angles and lines
(b) Polygons: triangles, quadrilaterals and general polygons;
(c) Circles: angle properties, cyclic quadrilaterals and intersecting chords;
(d) construction.

2. Mensuration

Topics:

(a) lengths and areas of plane geometrical figures;
(b) lengths of arcs and chords of a circle;
(c) Perimeters and areas of sectors and segments of circles;
(d) surface areas and volumes of simple solids and composite figures;
(e) the earth as a sphere:- longitudes and latitudes.

3. Loci

Topic:

locus in 2 dimensions based on geometric principles relating to lines and curves.

4. Coordinate Geometry

Topics:

(a) midpoint and gradient of a line segment;
(b) distance between two points;
(c) parallel and perpendicular lines;
(d) equations of straight lines.

5.Trigonometry

Topics:

(a) trigonometrical ratios of angels;
(b) angles of elevation and depression;
(c) bearings;
(d) areas and solutions of triangle;
(e) graphs of sine and cosine;
(f) sine and cosine formulae.

SECTION IV: CALCULUS

Topics: 

(a) limit of a function
(b) differentiation of explicit algebraic and simple trigonometrical functions-sine, cosine and tangent.

2. Application of differentiation

Topics:

(a) rate of change;
(b) maxima and minima.

3. Integration

Topics:

(a) integration of explicit algebraic and simple trigonometrical functions;
(b) area under the curve.

SECTION V: STATISTICS

1. Representation of data

Topics:

(a) frequency distribution;
(b) histogram, bar chart and pie chart.

2. Measures of Location

Topics:

(a) mean, mode and median of ungrouped and grouped data – (simple cases only);
(b) cumulative frequency.

3. Measures of Dispersion

Topic:

range, mean deviation, variance and standard deviation.

4. Permutation and Combination

Topics:

(a) Linear and circular arrangements;
(b) Arrangements involving repeated objects.

5. Probability

Topics

(a) experimental probability (tossing of coin, throwing of a dice etc);
(b) Addition and multiplication of probabilities (mutual and independent cases).

Wishing you SPEED and ACCURACY!