The Unified Tertiary Matriculation Examination (UTME) syllabus was used to design this course. The course content is also relevant for other exams, such as the National Examination Council (NECO) exams, the West African Examination Council (WEAC) exams, and the General Certificate of Education (GCE) exams.

**Sample Mathematics CBT**

**Sample Mathematics CBT**

The Unified Tertiary Matriculation Examination (UTME) syllabus was used to design this course. The course content is also relevant for other exams, such as the National Examination Council (NECO) exams, the West African Examination Council (WEAC) exams, and the General Certificate of Education (GCE) exams.

Course Instructor

Logical thinking is a transferable skill, and it is needed in every career. Employers don’t expect every employee to come into a job with subject-matter expertise, but they do expect that people can think critically and learn quickly. Math education builds these logical thinking skills. This course will help you acquire those skills you need to pass your exam, thrive in your tertiary education, and succeed in the workplace.

Assistant Course Instructor

At the end of this course, candidates should be able to:

(i) Acquire computational and manipulative skills;

(ii) Develop precise, logical, and formal reasoning skills;

(iii) Develop deductive skills in interpretation of graphs, diagrams, and data;

(iv) Apply mathematical concepts to resolve issues in daily living.

The aim of this course is to prepare the candidates for the examination. It is designed to make candidates achieve the course the objectives, which are to:

(i) acquire computational and manipulative skills;

(ii) develop precise, logical, and formal reasoning skills;

(iii) develop deductive skills in interpretation of graphs, diagrams, and data;

(iv) apply mathematical concepts to resolve issues in daily living.

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 percent;

(g) ratio, proportion, and rate;

(h) shares and valued-added tax (VAT)

3. Indices, Logarithms, and Surds:

(a) laws of indices;

(b) standard form;

(c) laws of logarithm;

(d) the 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.

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 (simple cases only).

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].

1. Euclidean Geometry:

(a) Properties of angles and lines

(b) Polygons: triangles, quadrilaterals and

general polygons;

(c) Circles: angle properties, cyclic

quadrilaterals and intersecting chords;

(d) construction.

2. Mensuration:

(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.

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) trigonometrical ratios of angels;

(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. Differentiation:

(a) limit of a function

(b) differentiation of explicit

algebraic and simple

trigonometrical 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

trigonometrical functions;

(b) area under the curve

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:

(a) Linear and circular arrangements;

(b) Arrangements involving repeated objects.

5.Probability:

(a) experimental probability (tossing of coin,

throwing of a dice etc);

(b) Addition and multiplication of probabilities

(mutual and independent cases).

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