TWITTER

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 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 © 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 © laws of logarithm (d) logarithm of any positive
number to a given base. (e) change of bases in
logarithm and application. Candidates should be
able to: i. perform four basic
operations (x,
+,-,÷); ii. convert one base to
another. Candidates should be
able to: i. perform basic
operations; (x,+,-,÷) on
fractions and decimals; ii. express to specified
number of significant
figures and decimal
places; iii. calculate simple
interest, profit and loss
per cent, ratio
proportion and rate. 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 (f) relationship between
indices and logarithm (g) surds 4. Sets: (a) types of sets (b) algebra of sets © venn diagrams and
their applications. SECTION II: ALGEBRA 1. Polynomials: (a) change of subject of
formula (b) factor and remainder
theorems © 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 © 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. Candidates should be
able to: i. identify types of sets, i.e
empty, universal,
compliments, subsets,
finite, infinite and disjoint
sets; ii. solve set problems
using symbol; iii. use venn diagrams to
solve problems involving
not more than 3 sets. 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, etc.; v. solve simultaneous
equations - one linear,
one quadratic; vi. interpret graphs of
polynomials including
application to maximum
and minimum values. Candidates should be
able to: i. solve problems
involving direct, inverse,
joint and partial
variations; ii. solve problems on
percentage increase and
decrease in variation. Candidates should be
able to: solve problems on linear
and quadratic inequalities
both analytically and
graphically 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 a given
G.P Candidates should be
able to: i. solve problems
involving closure,
commutativity,
associativity and
distributivity; ii. solve problems
involving 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. © inverses of 2 x 2
matrices [excluding quadratic and
higher degree equations]. SECTION III: GEOMETRIC AND TRIGONOMETRY 1. Euclidean
Geometry: (a) angles and lines (b) polygon; triangles,
quadrilaterals and
general polygon. © 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. © 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. © parallel and
perpendicular lines (d) equations of straight
lines. Candidates should be
able to: i. perform basic
operations (x,
+,-,÷) on matrices; ii. calculate determinants; iii. compute inverses of 2
x 2 matrices Candidates should be
able to: i. identify various types of
lines and angles; ii. solve problems
involving polygons; iii. calculate angles using
circle theorems; iv. identify construction
procedures of special
angles, e.g. 30°,
45°, 60°,
75°, 90° etc. Candidates should be
able to: i. calculate the perimeters
and areas of triangles,
quadrilaterals, circles and
composite figures; ii. find the length of an
arc, a chord and areas of
sectors and segments of
circles; iii. calculate total surface
areas and volumes of
cuboids, cylinders. cones,
pyramids, prisms, sphere
and composite figures; iv. determine the distance
between two points on
the earth's surface. Candidates should be
able to: identify and interpret loci
relating to parallel lines,
perpendicular bisectors,
angle bisectors and
circles. Candidates should be
able to: i. determine the midpoint
and gradient of a line
segment; ii. find 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) trigonometric ratios of
angels. (b) angles of elevation and
depression and bearing. © areas and solutions of
triangle (d) graphs of sine and
cosine (e) sine and cosine
formulae. SECTION IV: CALCULUS I. 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. 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 Candidates should be
able to: i. calculate the sine,
cosine and tarigent of
angles between -
360° less than or
equal to 0 (Zero) less
than or equal to 360°; ii. apply these special
angles, e.g. 30°,
45°, 60°,
75°, 90°,
135° to solve
simple problems in trigonometry; iii. solve problems
involving angles of
elevation and
depression and
bearing; iv. apply trigonometric
formulae to find areas
of triangles; v. solve problems
involving sine and
cosine graphs. Candidates should be
able to: i. find the limit of a
function; ii. differentiate explicit
algebraic and simple
trigonometric
functions. Candidates should be
able to: solve problems
involving applications
of rate of change,
maxima and minima. 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). Candidates should be
to: i. identify and interpret
frequency distribution
tables; ii. interpret information
on histogram, bar chat
and pie chart. 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. 4. Permutation and
Combination 5. Probability Candidates should be
able to: calculate the range, mean
deviation, variance and
standard deviation of
ungrouped and group
data. Candidates should be
able to: solve simple problems
involving permutation
and combination. Candidates should be
able to: solve simple problems in
probability (including
addition and
multiplication). 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. name(s)? (2000). New School
Mathematics for Senior Secondary Schools, Onitsha: Africana - FIRST Publishers. Egbe. E name(s)? (2000). Further Mathematics,
Onitsha: Africana - FIRST Publishers Ibude, S. O. name(s)? (2003). Agebra and Calculus
for Schools and Colleges: LINCEL Publishers. Tuttuh - Adegun M. R. name(s)? (1997). Further
Mathematics Project Books 1 to 3, Ibadan: NPS
Educational

Star