MATHEMATICS

JAMB SYLLABUS ON MATHEMATICS

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GENERAL OBJECTIVES:

The aim of the Unified Tertiary Matriculation Examination (UTME) syllabus in Mathematics is toprepare the candidates for the Board’s examination. It is designed to test the achievement of thecourse 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



DETAILED SYLLABUS

SECTION I: NUMBER ANDNUMERATION.
TOPICS/CONTENTS/NOTES
OBJECTIVES, Candidates should be able to:

1. Number bases:

(a) operations in different number basesfrom 2 to 10;

(b) conversion from one base to anotherincluding fractional parts.		i. perform four basic operations (x,+,-,÷);

ii. convert one base to another.

2. Fractions, Decimals, Approximationsand Percentages:

(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 significantfigures and decimal places;

iii. calculate simple interest, profit and loss per cent;ratio proportion and rate;

iv. Solve problems involving share and VAT.

3. Indices, Logarithms and Surds:

(a) laws of indices;

(b) standard form;

(c) laws of logarithm;

(d) logarithm of any positive number to agiven base;

(e) change of bases in logarithm andapplication;

(f) relationship between indices andlogarithm;

(g) Surds. 		i. apply the laws of indices in calculation;

ii. establish the relationship between indices andlogarithms in solving problems;

iii. solve problems in different bases in logarithms;

iv. simplify and rationalize surds;

v. perform basic operations on surds.

4. Sets:

(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 disjointsets;

ii. solve problems involving cardinality of sets;

iii. iii. solve set problems using symbols;

iv. iv. use Venn diagrams to solve problems involvingnot more than 3 sets.
SECTION II: ALGEBRA.
TOPICS/CONTENTS/NOTES
OBJECTIVES, Candidates should be able to:

1. Polynomials:

(a) change of subject of formula

(b) factor and remainder theorems

(c) factorization of polynomials of degree notexceeding 3.

(d) multiplication and division of polynomials

(e) roots of polynomials not exceeding degree 3

(f) simultaneous equations including one linearone quadratic;

(g) graphs of polynomials of degree not greaterthan 3.		 i. find the subject of the formula of a givenequation;

ii. apply factor and remainder theorem to factorizea given expression;

iii. multiply and divide polynomials of degree notmore than 3;

iv. factorize by regrouping difference of twosquares, perfect squares and cubic expressions;etc.

v. solve simultaneous equations – one linear, onequadratic;

vi. interpret graphs of polynomials includingapplications to maximum and minimum values.

2. Variation:

(a) direct

(b) inverse

(c) joint

(d) partial

(e) percentage increase and decrease. 		i. solve problems involving direct, inverse, jointand partial variations;

ii. solve problems on percentage increase anddecrease in variation.

3. Inequalities:

(a) analytical and graphical solutions of linearinequalities;

(b) quadratic inequalities with integral rootsonly.		i. solve problems on linear and quadraticinequalities;

ii. interpret graphs of inequalities.

4. Progression:

(a) nth term of a progression

(b) sum of A. P. and G. P.		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.

5. Binary Operations:

(a) properties of closure, commutativity,associativity and distributivity;

(b) identity and inverse elements (simplecases only).		 i. solve problems involving closure,commutativity, associativity and distributivity;

ii. solve problems involving identity and inverseelements.

6. Matrices and Determinants:

(a) algebra of matrices not exceeding 3 x 3;

(b) determinants of matrices not exceeding3 x 3;

(c) inverses of 2 x 2 matrices[excluding quadratic and higher degreeequations].		i. perform basic operations (x,+,-,÷) on matrices;

ii. calculate determinants;

iii. compute inverses of 2 x 2 matrices.
SECTION III: GEOMETRY ANDTRIGONOMETRY.
TOPICS/CONTENTS/NOTES
OBJECTIVES, Candidates should be able to:

1. Euclidean Geometry:

(a) Properties of angles and lines

(b) Polygons: triangles, quadrilaterals andgeneral polygons;

(c) Circles: angle properties, cyclicquadrilaterals 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 specialangles, e.g. 300, 450, 600, 750, 900 etc.

2. Mensuration:

(a) lengths and areas of plane geometricalfigures;

(b) lengths of arcs and chords of a circle;

(c) Perimeters and areas of sectors andsegments of circles;

(d) surface areas and volumes of simplesolids and composite figures;

(e) the earth as a sphere: longitudes andlatitudes. 		i. calculate the perimeters and areas oftriangles, quadrilaterals, circles andcomposite figures;

ii. find the length of an arc, a chord, perimetersand areas of sectors and segments of circles;

iii. calculate total surface areas and volumes ofcuboids, cylinders. cones, pyramids, prisms,spheres and composite figures;

iv. determine the distance between two points onthe earth’s surface.

3. Loci:

locus in 2 dimensions based on geometricprinciples relating to lines and curves.		 identify and interpret loci relating to parallellines, perpendicular bisectors, angle bisectorsand circles.

4. Coordinate Geometry:

(a) midpoint and gradient of a linesegment;

(b) distance between two points;

(c) parallel and perpendicular lines;

(d) equations of straight lines. 		i. determine the midpoint and gradient of a linesegment;

ii. find the distance between two points;

iii. identify conditions for parallelism andperpendicularity;

iv. find the equation of a line in the two-pointform, point-slope form, slope intercept formand the general form.

5. Trigonometry:

(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.		 i. calculate the sine, cosine and tangent of anglesbetween - 3600 ≤ Ɵ ≤ 3600;

ii. apply these special angles, e.g. 30º, 45º, 60º,750, 900, 1050, 1350 to solve simple problemsin trigonometry;

iii. solve problems involving angles of elevationand depression;

iv. solve problems involving bearings;

v. apply trigonometric formulae to find areas oftriangles;

vi. solve problems involving sine and cosinegraphs.

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SECTION IV: CALCULUS
TOPICS/CONTENTS/NOTES
OBJECTIVES, Candidates should be able to:

I. Differentiation:

(a) limit of a function

(b) differentiation of explicitalgebraic and simpletrigonometrical functions –sine, cosine and tangent. 		i. find the limit of a function

ii. differentiate explicit algebraic and simpletrigonometrical functions.

2. Application of differentiation:

(a) rate of change;

(b) maxima and minima.		solve problems involving applications of rate ofchange, maxima and minima.

3. Integration:

(a) integration of explicitalgebraic and simpletrigonometrical functions;

(b) area under the curve. 		i. solve problems of integration involvingalgebraic and simple trigonometricfunctions;

ii. calculate area under the curve (simple casesonly).
SECTION V: STATISTICS
TOPICS/CONTENTS/NOTES
OBJECTIVES, Candidates should be able to:

1. Representation of data:

(a) frequency distribution;

(b) histogram, bar chart and pie chart. 		i. identify and interpret frequency distributiontables;

ii. interpret information on histogram, bar chatand pie chart.

2. Measures of Location:

(a) mean, mode and median of ungroupedand grouped data – (simple cases only);

(b) cumulative frequency.		i. calculate the mean, mode and median ofungrouped and grouped data (simple casesonly);

ii. use ogive to find the median, quartiles andpercentiles.

3. Measures of Dispersion:

range, mean deviation, variance and standarddeviation.		calculate the range, mean deviation, variance andstandard deviation of ungrouped and groupeddata.

4. Permutation and Combination:

(a) Linear and circular arrangements;

(b) Arrangements involving repeated objects.		 solve simple problems involving permutation andcombination.

5. Probability:

(a) experimental probability (tossing of coin,throwing of a dice etc);

(b) Addition and multiplication of probabilities(mutual and independent cases). 		solve simple problems in probability (includingaddition and multiplication).

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A. RECOMMENDED TEXTS

Adelodun A. A. (2000) Distinction in Mathematics: Comprehensive Revision Text, (3rd Edition)Ado –Ekiti: FNPL.

Anyebe, J. A. B. (1998) Basic Mathematics for Senior Secondary Schools and Remedial Studentsin Higher Institutions, Lagos: Kenny Moore.

Channon, J. B. Smith, A. M. (2001) New General Mathematics for West Africa SSS 1 to 3, Lagos:Longman.

David –Osuagwu, M. et al. (2000) New School Mathematics for Senior Secondary Schools,Onitsha: Africana - FIRST Publishers.

Egbe. E et al (2000) Further Mathematics, Onitsha: Africana – FIRST Publishers

Ibude, S. O. et al.. (2003) Algebra and Calculus for Schools and Colleges: LINCEL Publishers.

Tuttuh – Adegun M. R. et al. (1997) Further Mathematics Project Books 1 to 3, Ibadan: NPSEducational

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