**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, 105 ^{o}, 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

Educational

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