# Mathematics Jamb Syllabus 2023

The aim of the Unified Tertiary Matriculation Examination (UTME) syllabus in Mathematics 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) 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:

(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:

(a) fractions and decimals

(b) significant figures

(c) decimal places

(d) percentage errors

(e) simple interest

(f) profit and loss per cent

(g) ratio, proportion and rate

3. Indices, Logarithms and Surds:

(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.

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 per cent,

ratio proportion and rate.

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

(f) relationship between indices and

logarithm

(g) surds

4. Sets:

(a) types of sets

(b) algebra of sets

(c) venn diagrams and their applications.

SECTION II: ALGEBRA

1. Polynomials:

(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:

(a) direct

(b) inverse

(c) joint

(d) partial

(e) percentage increase and decrease.

3. Inequalities:

(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:

(a) properties of closure, commutativity,

associativity and distributivity.

(b) identity and inverse elements.

Candidates should be able to:

i. identify types of sets, i.e empty, universal,

compliments, subsets, finite, infinite and disjoint

sets;

ii. solve set problems using symbol;

iii. use venn diagrams to solve problems involving

not more than 3 sets.

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, etc.;

v. solve simultaneous equations – one linear, one

quadratic;

vi. interpret graphs of polynomials including

application 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:

solve problems on linear and quadratic inequalities

both analytically and graphically

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 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.

6. Matrices and Determinants:

(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: GEOMETRIC AND

TRIGONOMETRY

1. Euclidean Geometry:

(a) angles and lines

(b) polygon; triangles,

quadrilaterals and general

polygon.

(c) circles, angle properties, cyclic,

quadrilaterals and intersecting

chords.

(d) construction.

2. Mensuration:

(a) lengths and areas of plane geometrical

figures.

(b) length s of arcs and chords of a circle.

(c) 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:

locus in 2 dimensions based on geometric

principles relating to lines and curves.

4. Coordinate Geometry:

(a) midpoint and gradient of a line

segment.

(b) distance between two points.

(c) parallel and perpendicular lines

(d) equations of straight lines.

Candidates should be able to:

i. perform basic operations (x,+,-,÷) on matrices;

ii. calculate determinants;

iii. compute inverses of 2 x 2 matrices

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. 30º, 45º, 60º, 75º, 90º 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 and areas of

sectors and segments of circles;

iii. calculate total surface areas and volumes of

cuboids, cylinders. cones, pyramids, prisms,

sphere 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 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.

5.Trigonometry:

(a) trigonometric ratios of angels.

(b) angles of elevation and depression

and bearing.

(c) areas and solutions of triangle

(d) graphs of sine and cosine

(e) sine and cosine formulae.

SECTION IV: CALCULUS

I. Differentiation:

(a) limit of a function;

(b) differentiation of explicit

algebraic and simple

trigonometric functions –

sine, cosine and tangent.

2. Application of differentiation:

(a) rate of change

(b) maxima and minima

3. Integration:

(a) integration of explicit

algebraic and simple

trigonometric functions.

(a) area under the curve.

SECTION V: STATISTICS

1. Representation of data:

(a) frequency distribution

(b) histogram, bar chart and pie chart.

2. Measures of Location:

(a) mean, mode and median of ungrouped

and grouped data – (simple cases only)

(b) cumulative frequency

Candidates should be able to:

i. calculate the sine, cosine and tarigent of

angles between – 360º ≤ 0 ≤ 360º;

ii. apply these special angles, e.g. 30º, 45º, 60º,

75º, 90º, 135º to solve simple problems in

trigonometry;

iii. solve problems involving angles of elevation

and depression and bearing;

iv. apply trigonometric formulae to find areas of

triangles;

v. solve problems involving sine and cosine

graphs.

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).

Candidates should be to:

i. identify and interpret frequency distribution

tables;

ii. interpret information on histogram, bar chat

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

3. Measures of Dispersion:

range, mean deviation, variance and standard

deviation.

4. Permutation and Combination

5.Probability

percentiles.

Candidates should be able to:

calculate the range, mean deviation, variance and

standard deviation of ungrouped and group 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).