# 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,
(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
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
equations].

SECTION III: GEOMETRIC AND
TRIGONOMETRY
1. Euclidean Geometry:
(a) angles and lines
(b) polygon; triangles,
polygon.
(c) circles, angle properties, cyclic,
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
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