Mathematics JAMB UTME Syllabus

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The Mathematics JAMB UTME Syllabus is designed to assess your mathematical proficiency across various topics. It covers many areas, including number and numeration, algebra, geometry, trigonometry, calculus, and statistics. Each of these components is equally important and requires dedicated preparation. By familiarizing yourself with the syllabus, you can tailor your study plan to address each area effectively.

1. GENERAL OBJECTIVES

The aim of the Unified Tertiary Matriculation Examination (UTME) syllabus in Mathematics is to guide candidates in their preparation for the Board’s examination. It is designed to evaluate the candidates’ ability to:

acquire computational and manipulative skills;
develop precise, logical and formal reasoning skills;
develop deductive skills in the interpretation of graphs, diagrams and data;
apply mathematical concepts to resolve issues in daily living.

2. The syllabus consists of FIVE sections as stated below:

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

3. DETAILED SYLLABUS/CONTENTS

SECTION 1: NUMBER AND NUMERATION

TOPIC 1. Number bases-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

Candidates should be able to:

i. perform four basic operations (x,+,-,÷)

ii. convert one base to another.

TOPIC 2. Fractions, Decimals, Approximations and Percentages

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

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.

TOPIC 3. Indices, Logarithms and Surds:

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

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.

TOPIC 4. Sets

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

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 symbols;
iv. Be able to use Venn diagrams to solve problems involving not more than 3 sets.

SECTION 2: ALGEBRA

TOPIC 1. Polynomials-

Subtopics:-

(a) change of subject of the 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 and one quadratic;
(g) graphs of polynomials of degree not greater than 3.

OBJECTIVES OF THIS TOPIC

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 the 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.

TOPIC 2. Variation-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

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.

TOPIC 3. Inequalities-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

Candidates should be able to:

i. Solve problems on linear and quadratic inequalities;
ii. interpret graphs of inequalities.

TOPIC 4. Progression-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

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.

TOPIC 5. Binary Operations-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

Candidates should be able to:

i. Solve problems involving closure, commutativity, associativity and distributivity;
ii. solve problems involving identity and inverse elements.

TOPIC 6. Matrices and Determinants-

Subtopics:-

(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].

OBJECTIVES OF THIS TOPIC

Candidates should be able to:

i. perform basic operations (x,+,-,÷) on matrices;
ii. calculate determinants;
iii. compute inverses of 2 x 2 matrices.

SECTION 3: GEOMETRY AND TRIGONOMETRY

TOPIC 1. Euclidean Geometry-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

Candidates should be able to:

i. Identify various types of lines and angles;
ii. calculate angles using circle theorems;
iii. solve problems involving polygons;
iv. identify construction procedures of special angles, e.g. 30°, 45°, 60°, 75°, 90° etc.

TOPIC 2. Mensuration-

Subtopics:-

(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.

OBJECTIVES OF THIS TOPIC

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.

TOPIC 3. Loci-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

Candidates should be able to:

i. identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles.

TOPIC 4. Coordinate Geometry-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

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.

TOPIC 5. Trigonometry-

Subtopics:-

(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.

OBJECTIVES OF THIS TOPIC

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.

SECTION 4: CALCULUS

TOPIC 1. Differentiation-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

Candidates should be able to:

i. find the limit of a function
ii. differentiate explicit algebraic and simple trigonometrical functions.

TOPIC 2. Application of differentiation-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

Candidates should be able to:

i. solve problems involving applications of rate of change, maxima and minima.

TOPIC 3. Integration-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

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).

SECTION 4: STATISTICS

TOPIC 1. Representation of data-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

Candidates should be able to:

i. identify and interpret frequency distribution tables;
ii. interpret information on histogram, bar chat and pie chart

TOPIC 2. Measures of Location-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

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.

TOPIC 3. Measures of Dispersion-

Subtopics:-

(a) – range, mean deviation, variance and standard deviation.

OBJECTIVES OF THIS TOPIC

Candidates should be able to:

i. Calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data.

TOPIC 4. Permutation and Combination-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

Candidates should be able to:

i. solve simple problems involving permutation and combination.

TOPIC 5. Probability-

Subtopics:-

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

OBJECTIVES OF THIS TOPIC

Candidates should be able to:

solve simple problems in probability (including addition and multiplication).