MATHEMATICS UNIT
COURSE OUTLINE FOR THE MATHEMATICSREMEDIAL PROGRAMME
FIRST SEMESTER
MATH 011 NUMBER AND NUMERATION
Number system
Fraction
Types of fraction
Ratio, Proportion, percentages
Percentage Error
Calculations involving percentage error
Variation
Direction variation
Inverse variation
Joint variation
Partial variation
Decimal Approximation and Significant Figures
Decimal notation
Decimal division and multiplication
Approximations
Rounding off numbers
Significant figures
Simplification:
Simplification of numbers
Number Bases:
Conversion from Base 10 to other Bases
Conversion from other Bases to Base 10
Determining an unknown Base
Addition and subtraction of number Base
Multiplication and division of number Base
Standard form
Writing numbers in standard form
Simplifying numbers in standard form
Indices and Logarithms
Indicial laws and their applications
Exponential equations
The operating rules for logarithms
Special exponential equation
Surds
Definition of rational and irrational numbers
Formulae involving operations with surds
Addition and subtraction of surds
Multiplication and division of surds
Rationalizing the denominator
Matrices and Determinants
Definition of matrix
Some basic definitions of matrices: [Equal matrices, zero (null) matrix,
Unit identity matrix, diagonal (triangular) matrix, symmetric matrix and skew  symmetric matrix]
Addition and subtraction of matrices
Multiplication of matrices
Square matrices, transpose of a matrix, inverse matrix
Definition of determinants
Sarrus’ rule
Minors, cofactors and adjoint
Matrix method for solving simultaneous equations (Crammer’s rule)
Use of determinants in finding the area of a triangle.
MATH 012 ALGEBRA
Algebraic expressions and equations
Simplifications of algebraic equations
Subject of the formula
Quadratic Equations
Solutions by:
Factorization
Completing the square method
Formula
Graphical method
Roots of quadratic equation
Simultaneous Linear Equation in two and three Variables
Solution by elimination
Solution by substitution
Solution of one linear and one quadratic simultaneous equation.
Graphical method
Polynomials:
Definition and basic operations
Remainder theorem
Factor theorem
Inequalities:
Properties of inequalities
Simple linear inequality (in one variable)
Simultaneous inequalities (in one variable)
Quadratic inequality (in one variable)
Simultaneous linear inequalities (in two variables)
Quadratic inequality (in two variables)
Sequences:
Arithmetic progression (AP), Arithmetic mean
Geometric progression (GP),
Geometric mean
Partial Fraction
Type 1: Denominator contains unrepeated linear factors
Type 2: 'Denominator contains repeated linear factors
Type 3; Denominator contains irreducible quadratic factors
Sets and Binary Operations
Definition of sets, subset, universal, empty, finite and infinite set.
Set operations: union, intersection, complement
Use of Venn diagrams to solve problem (not more than 3 sets).
Basic laws in set algebra
Definition and representation of binary operation
Properties:  closure, associative, commutative distributive, identity elements, inverse elements
MATH 013 Plane Geometry and Trigonometry
Definition: point, line and angle
Angles And Types Of Angle
Triangle /Types Of Triangle
Triangle Theorems
Quadrilaterals
Polygons
Circle Theorems
Mensuration
Use of Pythagoras Theorem
Perimeter And Area Of Plane Circle
Surface Area of Solids
Volume of Solids
Trigonometry
Sine, Cosine And Tangent Of Angles
Angles of Elevation And Depression
Solution of trigonometry equations
Sine And Cosine Rule
Bearings
Latitude And Longitude
Further Trigonometry
Basic identities
Addition formulae
Half angle
Multiple angle
Factor formula
tformula
SECOND SEMESTER
MATH 021 DIFFERENTIAL AND INTEGRAL CALCULUS
Function and Mapping
Definition of mapping, domain, codomain, range
Types:
Into mapping, onto mapping, oneone mappings, identity and constant mapping
Composition of functions.
Inverse functions.
Limits of algebraic and simple trigonometric functions
Differential Calculus
Differentiation from first principles
Differentiation by using formula
Differentiation of sum, difference product and quotient
Differentiation of function of a function
Differentiation of implicit functions
Differentiation of simple trigonometric, logarithmic and exponential functions.
Integral Calculus
Definition
Properties of integration
Integration of simple trigonometric function.
Definite and indefinite integrals
MATH 022 COORDINATE GEOMETRY
The Cartesian Coordinates (Abscissa and ordinate)
Distance between 2 points
Division or Section Formula
The Gradient of a straight line
Equation of a straight line
Slopeintercept form
Pointslope form
Twopoints form
Interceptform
Angle between two lines
Parallel and Perpendicular lines
The Circle
Definition
Equation of a circle
The standard form (x  a)2 + (y  b)2 = r2
The General form x2 + y2 + 2gx + 2fy + c = 0.
Equations of tangent and normal to a circle.
Length of tangents to a circle from a given point
Point of contacts of circles
MATH 023 STATISTICS AND PROBABILITY
Definition
Data
Types of data: district and continuous
Data Collection
The Frequency Table
Grouped and Ungrouped Data
Data Representation:
Pie chart
Bar chart
Histogram frequency polygon
Cumulative, frequency curve
The Measure of Central Tendency
Mean
Median
Mode
Measure of Dispersion
Range
Mean Deviation
Variance
Standard Deviation.
Probability
Simply Probability
Addition Law
Multiplication Law
Conditional probability
Correlation and regression
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