Mathematics 1
Contents
 1 11.1.0 MATHEMATICS I
 2 11.1.03 MODULE UNIT SUMMARY AND TIME ALLOCATION
 3 NUMBER SYSTEM
 4 INDICES AND LOGARITHMS
 5 ALGEBRA
 6 GEOMETRY AND SCALE DRAWING
 7 SEQUENCE AND SERIES
 8 GRAPHS
 9 TRIGONOMETRY
 10 LATITUDES AND LONGITUDES
 11 COORDINATE GEOMETRY AND LOCI
 12 MENSURATION=
 13 PERMUTATIONS, COMBINATIONS AND BINOMIAL EXPANSION
 14 VECTORS
 15 PROBABILITY I
 16 STATISTICS I
11.1.0 MATHEMATICS I
11.1.01 INTRODUCTION TO THE MODULE
This module unit is designed to equip the trainee with the relevant mathematical knowledge, skills, techniques and attitudes necessary to enhance better understanding of the respective trade area.
11.1.02 GENERAL OBJECTIVES
At the end of the module unit, the trainee should be able to:
 Use mathematical concepts and techniques in solving problems related to respective trade area
 Organise, draw simple deductions and conclusions from a given data
 Interpret graphical representation of functions relevant to the respective trade area
11.1.03 MODULE UNIT SUMMARY AND TIME ALLOCATION
CODE  SUBMODULE UNIT  CONTENT  TIME(HOURS) 
11.1.1  NUMBER SYSTEMS 

3 
11.1.2  INDICES AND LOGARITHMS 

3 
11.1.3  ALGEBRA 
 linear with 2 unknowns  linear with 3 unknowns  linear and quadratic

6 
11.1.4  GEOMETRY AND SCALE DRAWING 

4 
11.1.5  SEQUENCE AND SERIES 

6 
11.1.6  GRAPHS 
 linear  quadratic

4 
11.1.7  TRIGONOMETRY 
 radian measure  minutes and seconds
 formula  half angle formula  tangent rule  factor formula  further trigonometric equations  parametric equations  Heron’s formula 
6 
11.1.8  LATITUDES AND LONGITUDES 

4 
11.1.9  COORDINATE GEOMETRY AND LOCI 

5 
11.1.10  MENSURATION 

6 
11.1.11  PERMUTATIONS, COMBINATIONS AND BINOMIAL EXPANSION 
 pascal triangle  binomial theorem  power series using binomial theorem  roots of numbers by binomial theorem  apply binomial theorem to approximations 
5 
11.1.12  VECTORS 

6 
11.1.13  PROBABILITY I 

4 
11.1.4  STATISTICS I 

6 
TOTAL  66 
NUMBER SYSTEM
THEORY
Specific Objectives
By the end of the submodule unit, the trainee should be able to:
 identify types of numbers
 carry out arithmetic operations on numbers
 state the place value of digit in a number
 round off numbers
 state accuracy to given significant figures
 express numbers as product of prime factors
 find the GCD and LCM of a set of numbers
 perform operations on fractions and decimals
Content
 Types of numbers: natural, integers, rational, irrational, decimals, fractions on numbers.
 Arithmetic operations on numbers
 Arithmetic operations on numbers
 Place value of digits
 Rounding off
 Prime factors
 GCD and LCM Fractional and decimals
Competence
Ability to:
 performs arithmetic operations and numbers accurately
Suggested Learning/Teaching Resources
 Charts
 Number line
 Factor tree diagrams
 Bells
 Alarm
 Flickering lights
Suggested Learning Teaching Activities
 Demonstration
 Question and answer
 Group work
 Discussion
 Working out problems
Suggested Assessment Methods
 Oral tests
 Written
 Number games
 Quizzes
INDICES AND LOGARITHMS
THEORY
Specific Objectives
By the end of the submodule unit, the trainee should be able to:
 define an index of a number
 state the laws of indices
 perform indicial operations
 write numbers in standard form
 state laws of logarithms
 perform logarithmic operations
 Evaluate natural logarithms
 convert numbers from one
 solve logarithmic equations base to another
 use calculator/tables
Content
 Definition of an index of a number
 Laws of indices
 Indicial operations
 Numbers in standard form
 Laws of logarithms
 Logarithmic operations
 Natural logarithms
 Logarithmic equations
 Calculator/tables
Competence
Ability to:
 use logarithms to solve mathematical problems
Suggested Learning Resources
 Charts
 Number line
 Factor tree diagrams
 Bells
 Alarm
 Flickering lights
ALGEBRA
THEORY
Specific Objectives
By the end of the submodule unit, the trainee should be able to:
 write statements in algebraic form.
 simplify algebraic expressions
 factorise algebraic expressions
 change the subject of a formula
 divide polynomials
 solve equations
 obtain partial fractions from composite fractions
 solve simultaneous equation
 evaluate polynomials
 apply the remainder factor
Content
 Statement in algebraic form
 Simplification of algebraic expressions
 Factorisation of algebraic expression
 Transposition of formulae
 Division of polynomials
 Solution of equations
 linear  quadratic  cubic
 Partial fractions
 Simultaneous equations
 linear in 2 unknown  linear in 3 unknown  linear and quadratic
 Evaluation of polynomials
 Remainder and factor theorems
Competence
Ability to:
 perform algebraic operations accurately
Suggested Learning/Teaching Resources
 Charts
 Number line
 Factor tree diagrams
 Bells
 Alarm
 Flickering lights
Suggested Learning Teaching Activities
 Demonstration
 Question and answer
 Group work
 Discussion
 Working out problems
Suggested Assessment Methods
 Oral tests
 Written
 Number games
 Quizzes
GEOMETRY AND SCALE DRAWING
THEORY
Specific Objectives
By the end of the submodule unit, the trainee should be able to:
 conversion of scales
 draw plane figures to a given scale
 state the properties of different types of triangles
 solve problems involving angle properties of a circle
 draw regular solids
Content
 Scale
 Scale drawing
 Types of triangles
 Angle properties of a circle
 Simple solids: cube, cuboids, cylinder, cones, pyramids
Suggested Learning/Teaching Resources
 Charts
 Number line
 Factor tree diagrams
 Bells
 Alarm
 Flickering lights
Suggested Learning Teaching Activities
 Demonstration
 Question and answer
 Group work
 Discussion
 Working out problems
Suggested Assessment Methods
 Oral tests
 Written
 Number games
 Quizzes
SEQUENCE AND SERIES
THEORY
Specific Objectives
By the end of the submodule unit, the trainee should be able to:
 distinguish between a sequence and a series
 solve problems related to series
 use series to calculate simple and compound interest
 determine series convergence
Content
 A sequence and a series
 Series
 arithmetic progression  geometric progression
 Simple and compound interest
 Convergent series
GRAPHS
THEORY
Specific Objectives
By the end of the submodule, the trainee should be able to:
 identify linear functions
 plot graphs of linear
 identify quadratic functions
 plot graphs of quadratic functions
 identify exponential functions
 plot graphs of exponential functions
 solve quadratic equation by graph
 solve simultaneous equations – two linear with two unknowns
 solve simultaneous equations – one linear one quadratic
 determine linear laws
 linearize nonlinear laws
 determine nonlinear laws
Content
 Linear functions
 Straight line graph
 Quadratic functions
 Graphs of quadratic functions
 Exponential functions of the forms:
 y=abx  y=axb  y=aex
 Graphs of exponential functions
 Graphical solution of simultaneous quadratic equations
 Graphical solution of equations – two linear with two unknowns
 Solve simultaneous equations – one linear one quadratic
 Determine linear laws
 Linearization
 Determination of nonlinear laws
Competences
Ability to:
 Plot graphs of functions
 Solve equations by suing graphs
 Determine laws
Suggested Learning/Teaching Resources
 Charts
 Number line
 Factor tree diagrams
 Bells
 Alarm
 Flickering lights
Suggested Learning Teaching Activities
 Demonstration
 Question and answer
 Group work
 Discussion
 Working out problems
Suggested Assessment Methods
 Oral tests
 Written
 Number games
 Quizzes
TRIGONOMETRY
THEORY
Specific Objectives
By the end of the submodule, the trainee should be able to:
 convert angles from one measurement to another
 define the trigonometric ratios and their reciprocals
 draw graphs of trigonometric functions
 solve problems related to trigonometric ratios
 calculate angles of elevation and depression
 derive the sine and cosine rule
 solve problems using the cosine and sine rule
 drive compound angle formula
 use the compound angle formula in solving problems
 deduce the double angle formula
 solve problems using the double angle formula
 derive the trigonometric identities
Content
 Conversion of angles
 radian measure  minutes and seconds
 Trigonometric ratios and their reciprocals
 Graphs of trigonometric functions
 Equations involving trigonometric ratios
 Angles of elevation and depression
 Sine and Cosine rule
 Use of sine and cosine rules
 The compound angle formula
 Using the compound angle formula
 Double angle formula Using the double angle formula
 Trigonometric identities
 tformulae  factor formulae  halfangle formulae  tangent rule
Suggested Learning/Teaching Resources
 Charts
 Number line
 Factor tree diagrams
 Bells
 Alarm
 Flickering lights
Suggested Learning Teaching Activities
 Demonstration
 Question and answer
 Group work
 Discussion
 Working out problems
Suggested Assessment Methods
 Oral tests
 Written
 Number games
 Quizzes
LATITUDES AND LONGITUDES
THEORY
Specific Objectives
By the end of the submodule, the trainee should be able to:
 differentiate between latitudes and longitudes
 identify the Equator and the Greenwich Meridian
 determine the distance between two points along the small and great circles
 calculate time between longitudes
 calculate speed
Content
 Latitudes and longitudes
 The equator and the Greenwich Meridian
 Distance between two points along small and great circles
 Time between longitudes
 Speed
Suggested Leaning Activities
 Discussion
 Question and answer
 Demonstration
Suggested Learning Resources
 Sphere
COORDINATE GEOMETRY AND LOCI
THEORY
Specific Objectives
By the end of the submodule, the trainee should be able to:
 define polar equations
 convert polar equations to Cartesian equations and vice versa
 plot graphs of polar equations
 define the locus of a point
 determine the locus of points in relation to other points to other points, lines, planes, eclipses, parabola and hyper bola
Content
 Definition of polar equations
 Conversion of polar equations to Cartesian equations and vice versa
 Graphs of polar equation
 Definition of a locus of a point
 Locus of points
Suggested Learning/Teaching Resources
 Charts
 Number line
 Factor tree diagrams
 Bells
 Alarm
 Flickering lights
Suggested Learning Teaching Activities
 Demonstration
 Question and answer
 Group work
 Discussion
 Working out problems
Suggested Learning Resources
 Charts
 Graphs
 Plotting paper
 Geometrical instruments ns
MENSURATION=
THEORY
SPECIFIC OBJECTIVES
By the end of the submodule, the trainee should be able to:
 state different units of measurements
 calculate perimeters and areas of regular figures
 determine volumes of regular solids
 calculate surface areas of regular solids
 calculate areas of irregular figures
 determine area and volume of solids using Pappus theorem
Content
 Units of measurement
 Perimeter and area of regular figures
 Volume of regular solids
 Surface area of regular solids
 Area of irregular figures
 Trapezoidal rule  Simpson’s rule
 Pappus theorem
Competence
Ability to:
 Solve op problems in combinations and binomial exercises
Suggested Learning/Teaching Resources
 Charts
 Number line
 Factor tree diagrams
 Bells
 Alarm
 Flickering lights
Suggested Learning Teaching Activities
 Measuring
 Drawing and sketching figures
 Measuring lengths of models
Suggested Assessment Methods
 Written tests
 Assignments
Suggested Learning Resources
 Charts of solids
PERMUTATIONS, COMBINATIONS AND BINOMIAL EXPANSION
THEORY
SPECIFIC OBJECTIVES
By the end of the submodule, the trainee should be able to:
 define permutation and combinations
 simplify problem using factorial notation
 determine binomial coefficients
 deduce the binomial theorem
 obtain binomial series using binomial expansion
 approximate roots and errors using binomial theorem
Content
 Definitions of permutation and combination
 Factorial notation
 Binomial expansion
 coefficients using  Pascal’s triangle  binomial theorem
 Deduction of binomial theorem from Pascal’s triangle
 Power series using binomial theorem
 Approximations, roots and errors using binomial theorem
Suggested Learning Resources
 Charts
 Audio/visual materials
VECTORS
THEORY
Specific Objectives
By the end of the submodule, the trainee should be able to:
 define a vector
 represent a vector by a directed straight line
 add vectors
 subtract vectors
 write a vector in terms of components
 multiply a vector with a scalar
 write a vector in terms of component unit vectors
 set up the coordinate system for representing vectors
 obtain the direction cosines of a vector
 calculate the scalar product
Content
 Definition of scalar and vector quantity
 Vector representation
 Addition of vectors
 Subtraction of vectors
 Components of a vector
 Scalar multiplication
 Components of a vector in terms of unit vectors
 Vectors in space
 Direction cosines
 Scalar/dot product of two vectors
PROBABILITY I
THEORY
Specific Objectives
By the end of the submodule, the trainee should be able to:
 define the term probability
 state and apply the laws of probability
 distinguish between mutually exclusive, dependent and independent events
 compute conditional probabilities
 use tree diagram to solve probability problems
 draw probability space of a given case
 pick a sample point from probability space
 draw a Venn diagram for a given situation
Content
 Definition of probability
 Laws of probability
 Mutually exclusive, dependent and independent events
 Conditional probabilities
 Probability tree diagrams
 Probability space
 Sample point
 Venn diagram
Suggested Learning Resources
 Charts
 Audio/visual materials
 Balls
 Beads
 Cards
 Coins
STATISTICS I
THEORY
Specific Objectives
By the end of the submodule, the trainee should be able to:
 distinguish between discrete and continuous data
 construct frequency distribution tables
 construct cumulative frequency table
 determine class boundaries, class intervals, central values
 represent data graphically
 determine measures of central tendency
 determine measures of dispersion
Content
 Types of data
 Frequency table grouped/ungrouped data
 Cumulative frequency table
 Class boundaries, class intervals, central values
 Histogram, frequency polygons, bar groups, pie charts, pictograms
 Mean, mode, median
 Range, variance and standard deviation