UTME SYLLABUS – MATHEMATICS
GENERAL OBJECTIVES
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) 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:
SECTION A: Number and Numeration
SECTION B: Algebra
SECTION C: Geometry and Trigonometry
SECTION D: Calculus
SECTION E: Statistics
DETAILED SYLLABUS
SECTION A: Number and Numeration
TOPICS/CONTENTS/NOTES | OBJECTIVES |
1. Number bases:
(a) operations in different number bases from 2 to 10; |
Candidates should be able to: i. perform four basic operations (x,+,-,÷); ii. convert one base to another. |
2. Fractions, Decimals, Approximations and Percentages:
(a) fractions and decimals; |
Candidates should be able to:
i. perform basic operations 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. |
3. Indices, Logarithms and Surds:
(a) laws of indices; |
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. |
4. Sets:
(a) types of sets |
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. use Venn diagrams to solve problems involving not more than 3 sets. |
SECTION B: Algebra
TOPICS/CONTENTS/NOTES | OBJECTIVES |
1. Polynomials:
(a) change of subject of formula |
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 and cubic expressions; etc. v. solve simultaneous equations – one linear, one quadratic; vi. interpret graphs of polynomials including applications to maximum and minimum values. |
2. Variation:
(a) direct |
Candidates should be able to:
i. solve problems involving direct, inverse, joint and partial variations; |
3. Inequalities:
(a) analytical and graphical solutions of linear inequalities; |
Candidates should be able to: i. solve problems on linear and quadratic inequalities; ii. interpret graphs of inequalities. |
4. Progression:
(a) nth term of a progression |
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. |
5. Binary Operations:
(a) properties of closure, commutativity, associativity and distributivity; |
Candidates should be able to:
i. solve problems involving closure, commutativity, associativity and distributivity; |
6. Matrices and Determinants:
(a) algebra of matrices not exceeding 3 x 3; |
Candidates should be able to: i. perform basic operations (x,+,-,÷) on matrices; ii. calculate determinants; iii. compute inverses of 2 x 2 matrices. |
SECTION C: Geometry and Trigonometry
TOPICS/CONTENTS/NOTES | OBJECTIVES |
1. Euclidean Geometry:
(a) Properties of angles and lines |
Candidates should be able to:
i. identify various types of lines and angles; |
2. Mensuration:
(a) lengths and areas of plane geometrical figures; |
Candidates should be able to:
i. calculate the perimeters and areas of triangles, quadrilaterals, circles and composite figures; |
3. Loci:
locus in 2 dimensions based on geometric principles relating to lines and curves. |
Candidates should be able to:
i. identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles. |
4. Coordinate Geometry:
(a) midpoint and gradient of a line segment; |
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. |
5. Trigonometry:
(a) trigonometrical ratios of angles; |
Candidates should be able to: i. calculate the sine, cosine and tangent of angles between – 360º ≤ Ɵ ≤ 360º; ii. apply these special angles, e.g. 30º, 45º, 60º, 75º, 90º, 105o, 135º 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 D: Calculus
TOPICS/CONTENTS/NOTES | OBJECTIVES |
1. Differentiation:
(a) limit of a function |
Candidates should be able to: i. find the limit of a function ii. differentiate explicit algebraic and simple trigonometrical functions. |
2. Application of differentiation:
(a) rate of change; |
Candidates should be able to:
i. solve problems involving applications of rate of change, maxima and minima. |
3. Integration:
(a) integration of explicit algebraic and simple trigonometrical functions; |
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 E: Statistics
TOPICS/CONTENTS/NOTES | OBJECTIVES |
1. Representation of data:
(a) frequency distribution; |
Candidates should be able to: i. identify and interpret frequency distribution tables; ii. interpret information on histogram, bar chat and pie chart. |
2. Measures of Location:
(a) mean, mode and median of ungrouped and grouped data – (simple cases only); |
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. |
3. Measures of Dispersion:
range, mean deviation, variance and standard deviation. |
Candidates should be able to:
i. calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data. |
4. Permutation and Combination:
(a) Linear and circular arrangements; |
Candidates should be able to:
i. solve simple problems involving permutation and combination. |
5. Probability:
(a) experimental probability (tossing of coin, throwing of a dice etc); |
Candidates should be able to:
i. solve simple problems in probability (including addition and multiplication). |
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 Students in 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: NPS
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