**Hello and Welcome!**

**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) 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**

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**UTME CBT Practice Tests – Mathematics (Registered Users) – Click Here**

**SECTION I: NUMBER AND NUMERATION.**

**1. Number bases:**

**(a) operations in different number bases from 2 to 10;**

**(b) conversion from one base to another including fractional parts.**

**2. Fractions, Decimals, Approximations and Percentages:**

**(a) fractions and decimals**

**(b) significant figures**

**(c) decimal places (d) percentage errors (e) simple interest**

**(f) profit and loss per cent**

**(g) ratio, proportion and rate**

**3. Indices, Logarithms and Surds:**

**(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**

**4. Sets:**

**(a) types of sets**

**(b) algebra of sets**

**(c) venn diagrams and their applications.**

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*UTME CBT Practice Tests – Mathematics (Registered Users) – Click Here*

**SECTION II: ALGEBRA**

**1. Polynomials:**

**(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**

**2. Variation:**

**(a) direct **

**(b) inverse **

**(c) joint**

**(d) partial**

**(e) percentage increase and decrease.**

**3. Inequalities:**

**(a) analytical and graphical solutions of linear inequalities.**

**(b) quadratic inequalities with integral roots only.**

**4. Progression:**

**(a) nth term of a progression**

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

**5. Binary Operations:**

**(a) properties of closure, commutativity, associativity and distributivity.**

**(b) identity and inverse elements.**

**6. Matrices and Determinants:**

**(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].**

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*UTME CBT Practice Tests – Mathematics (Registered Users) – Click Here*

**SECTION III: GEOMETRIC AND TRIGONOMETRY**

**1. Euclidean Geometry:**

**(a) angles and lines**

**(b) polygon; triangles, quadrilaterals and general polygon.**

**(c) circles, angle properties, cyclic, quadrilaterals and intersecting chords.**

**(d) construction.**

**2. Mensuration:**

**(a) lengths and areas of plane geometrical figures.**

**(b) length s of arcs and chords of a circle. **

**(c) 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**

**3. Loci:**

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

**4. Coordinate Geometry:**

**(a) midpoint and gradient of a line segment.**

**(b) distance between two points.**

**(c) parallel and perpendicular lines**

**(d) equations of straight lines.**

**5.Trigonometry:**

**(a) trigonometric ratios of angels.**

**(b) angles of elevation and depression and bearing.**

**(c) areas and solutions of triangle**

**(d) graphs of sine and cosine**

**(e) sine and cosine formulae.**

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*UTME CBT Practice Tests – Mathematics (Registered Users) – Click Here*

**SECTION IV: CALCULUS**

**1. Differentiation:**

**(a) limit of a function;**

**(b) differentiation of explicit algebraic and simple trigonometric functions – sine, cosine and tangent.**

**2. Application of differentiation:**

**(a) rate of change**

**(b) maxima and minima**

**3. Integration:**

**(a) integration of explicit algebraic and simple trigonometric functions.**

**(a) area under the curve.**

*UTME CBT Practice Tests – Mathematics (FREE Access) – Click Here*

*UTME CBT Practice Tests – Mathematics (Registered Users) – Click Here*

**SECTION V: STATISTICS**

**1. Representation of data:**

**(a) frequency distribution**

**(b) histogram, bar chart and pie chart.**

**2. Measures of Location:**

**(a) mean, mode and median of ungrouped and grouped data – (simple cases only)**

**(b) cumulative frequency**

**3. Measures of Dispersion:**

** – range, mean deviation, variance and standard deviation.**

**4. Permutation and Combination**

**5.Probability**

*UTME CBT Practice Tests – Mathematics (FREE Access) – Click Here*

*UTME CBT Practice Tests – Mathematics (Registered Users) – Click Here*

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