UTME Syllabus – Mathematics

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

(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).

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;

iv. Solve problems involving share and VAT.

(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.

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

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. use Venn diagrams to solve problems involving not more than 3 sets.

(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.

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

i. solve problems involving direct, inverse, joint and partial variations;
ii. solve problems on percentage increase and decrease in variation.

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

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

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

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

(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].

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

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.

(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.

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.

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

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

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

(a) trigonometrical ratios of angles;
(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.

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

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

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

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

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

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

range, mean deviation, variance and standard deviation.

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

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

i. solve simple problems involving permutation and combination.

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

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