Mathematics 1

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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:

  1. Use mathematical concepts and techniques in solving problems related to respective trade area
  2. Organise, draw simple deductions and conclusions from a given data
  3. Interpret graphical representation of functions relevant to the respective trade area


11.1.03 MODULE UNIT SUMMARY AND TIME ALLOCATION

CODE SUB-MODULE UNIT CONTENT TIME(HOURS)
11.1.1 NUMBER SYSTEMS
  • Types of numbers: natural integers, rational, irrational
  • Place value, rounding off, significant figures
  • Factors and prime numbers, GCF and LCM
  • Powers, fractions and decimals
3
11.1.2 INDICES AND LOGARITHMS
  • Powers
  • Laws of indices
  • Indices operations/logarithms
  • Laws of logarithms
  • Operations
  • Base e
  • Change of base
  • Logarithmic equations
  • Scientific calculator
3
11.1.3 ALGEBRA
  • Algebraic expressions
  • Operations of algebraic expressions
  • Factorization of algebraic expressions
  • Quadratic expressions
  • Solution of equations
  • linear
  • quadratic
  • cubic and polynomial
  • Partial fractions
  • Simultaneous equations

- linear with 2 unknowns - linear with 3 unknowns - linear and quadratic

  • Transposition of formulae
  • Evaluation of polynomials
  • Division of polynomials, remainder and factor theorem
6
11.1.4 GEOMETRY AND SCALE DRAWING
  • Scale
  • Drawing basic figures plane
  • Drawing of solids
4
11.1.5 SEQUENCE AND SERIES
  • Sequences, arithmetic and geometric progressions
  • Series
  • Solution of problems related to simple and compound interest
  • Convergent series
6
11.1.6 GRAPHS
  • Linear
  • Quadratic
  • Exponential
  • Solution of equations

- linear - quadratic

  • Linear and quadratic
  • Tangents
  • Determination of laws
4
11.1.7 TRIGONOMETRY
  • Angles

- radian measure - minutes and seconds

  • Trigonometric ratios and their reciprocals
  • Angles of elevation and depression
  • Sine rule
  • Cosine rule
  • Solution of triangles
  • Graphs of trigonometric functions
  • Compound angle formula
  • Derivation of double angle formula
  • Basic trigonometric equations

- formula - half angle formula - tangent rule - factor formula - further trigonometric equations - parametric equations - Heron’s formula

6
11.1.8 LATITUDES AND LONGITUDES
  • Latitudes and longitudes
  • The equator and the Greenwich meridian
  • Distance between two points along small and great circles
  • Time between longitude
  • Speed
4
11.1.9 COORDINATE GEOMETRY AND LOCI
  • Polar equations
  • Conversion of Cartesian to polar and vice versa
  • Graphs of polar equations
  • Definitions of locus in relation points, lines, planes, ellipses, parabola, hyperbola
5
11.1.10 MENSURATION
  • Units of measurements
  • Perimeter and areas of regular figures
  • Volume of regular solids
  • Surface areas of regular solids
  • Area of irregular figures
  • Area and volumes using Pappus theorem
6
11.1.11 PERMUTATIONS, COMBINATIONS AND BINOMIAL EXPANSION
  • Definition of terms – permutation and combination
  • factorial notation
  • Solving problems involving permutations and combinations
  • 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
  • Vectors and scalar in two and three dimensions
  • operations on vectors: Addition and subtraction
  • Position vectors
  • Resolution of vectors
  • Scalar product
6
11.1.13 PROBABILITY I
  • Definitions
  • Laws of probability
  • Mutually exclusive, independent events, conditional probability
  • Tree diagram, sample point, Venn diagram
4
11.1.4 STATISTICS I
  • Data arrangement
  • Representation of data
  • Measures of central tendency
  • Measures of dispersion
6
TOTAL 66


NUMBER SYSTEM

THEORY

Specific Objectives

By the end of the sub-module unit, the trainee should be able to:

  1. identify types of numbers
  2. carry out arithmetic operations on numbers
  3. state the place value of digit in a number
  4. round off numbers
  5. state accuracy to given significant figures
  6. express numbers as product of prime factors
  7. find the GCD and LCM of a set of numbers
  8. perform operations on fractions and decimals

Content

Competence

Ability to:

  1. performs arithmetic operations and numbers accurately

Suggested Learning/Teaching Resources


Suggested Learning Teaching Activities


Suggested Assessment Methods


INDICES AND LOGARITHMS

THEORY

Specific Objectives

By the end of the sub-module unit, the trainee should be able to:

  1. define an index of a number
  2. state the laws of indices
  3. perform indicial operations
  4. write numbers in standard form
  5. state laws of logarithms
  6. perform logarithmic operations
  7. Evaluate natural logarithms
  8. convert numbers from one
  9. solve logarithmic equations base to another
  10. use calculator/tables

Content

Competence

Ability to:

  1. use logarithms to solve mathematical problems

Suggested Learning Resources

ALGEBRA

THEORY

Specific Objectives

By the end of the sub-module unit, the trainee should be able to:

  1. write statements in algebraic form.
  2. simplify algebraic expressions
  3. factorise algebraic expressions
  4. change the subject of a formula
  5. divide polynomials
  6. solve equations
  7. obtain partial fractions from composite fractions
  8. solve simultaneous equation
  9. evaluate polynomials
  10. apply the remainder factor

Content

- linear - quadratic - cubic

- linear in 2 unknown - linear in 3 unknown - linear and quadratic

Competence

Ability to:

  1. perform algebraic operations accurately

Suggested Learning/Teaching Resources

Suggested Learning Teaching Activities

Suggested Assessment Methods


GEOMETRY AND SCALE DRAWING

THEORY

Specific Objectives

By the end of the sub-module unit, the trainee should be able to:

  1. conversion of scales
  2. draw plane figures to a given scale
  3. state the properties of different types of triangles
  4. solve problems involving angle properties of a circle
  5. draw regular solids

Content

Suggested Learning/Teaching Resources

Suggested Learning Teaching Activities

Suggested Assessment Methods


SEQUENCE AND SERIES

THEORY

Specific Objectives

By the end of the sub-module unit, the trainee should be able to:

  1. distinguish between a sequence and a series
  2. solve problems related to series
  3. use series to calculate simple and compound interest
  4. determine series convergence

Content

- arithmetic progression - geometric progression

GRAPHS

THEORY

Specific Objectives

By the end of the sub-module, the trainee should be able to:

  1. identify linear functions
  2. plot graphs of linear
  3. identify quadratic functions
  4. plot graphs of quadratic functions
  5. identify exponential functions
  6. plot graphs of exponential functions
  7. solve quadratic equation by graph
  8. solve simultaneous equations – two linear with two unknowns
  9. solve simultaneous equations – one linear one quadratic
  10. determine linear laws
  11. linearize non-linear laws
  12. determine non-linear laws

Content

- y=abx - y=axb - y=aex

Competences

Ability to:

  1. Plot graphs of functions
  2. Solve equations by suing graphs
  3. Determine laws

Suggested Learning/Teaching Resources

Suggested Learning Teaching Activities


Suggested Assessment Methods


TRIGONOMETRY

THEORY

Specific Objectives

By the end of the sub-module, the trainee should be able to:

  1. convert angles from one measurement to another
  2. define the trigonometric ratios and their reciprocals
  3. draw graphs of trigonometric functions
  4. solve problems related to trigonometric ratios
  5. calculate angles of elevation and depression
  6. derive the sine and cosine rule
  7. solve problems using the cosine and sine rule
  8. drive compound angle formula
  9. use the compound angle formula in solving problems
  10. deduce the double angle formula
  11. solve problems using the double angle formula
  12. derive the trigonometric identities

Content

- radian measure - minutes and seconds

- t-formulae - factor formulae - half-angle formulae - tangent rule

Suggested Learning/Teaching Resources

Suggested Learning Teaching Activities

Suggested Assessment Methods


LATITUDES AND LONGITUDES

THEORY

Specific Objectives

By the end of the sub-module, the trainee should be able to:

  1. differentiate between latitudes and longitudes
  2. identify the Equator and the Greenwich Meridian
  3. determine the distance between two points along the small and great circles
  4. calculate time between longitudes
  5. calculate speed

Content

Suggested Leaning Activities

Suggested Learning Resources

COORDINATE GEOMETRY AND LOCI

THEORY

Specific Objectives

By the end of the sub-module, the trainee should be able to:

  1. define polar equations
  2. convert polar equations to Cartesian equations and vice versa
  3. plot graphs of polar equations
  4. define the locus of a point
  5. determine the locus of points in relation to other points to other points, lines, planes, eclipses, parabola and hyper bola

Content


Suggested Learning/Teaching Resources

Suggested Learning Teaching Activities

Suggested Learning Resources

MENSURATION=

THEORY

SPECIFIC OBJECTIVES

By the end of the sub-module, the trainee should be able to:

  1. state different units of measurements
  2. calculate perimeters and areas of regular figures
  3. determine volumes of regular solids
  4. calculate surface areas of regular solids
  5. calculate areas of irregular figures
  6. determine area and volume of solids using Pappus theorem

Content

- Trapezoidal rule - Simpson’s rule

Competence

Ability to:

  1. Solve op problems in combinations and binomial exercises

Suggested Learning/Teaching Resources

Suggested Learning Teaching Activities

Suggested Assessment Methods

Suggested Learning Resources


PERMUTATIONS, COMBINATIONS AND BINOMIAL EXPANSION

THEORY

SPECIFIC OBJECTIVES

By the end of the sub-module, the trainee should be able to:

  1. define permutation and combinations
  2. simplify problem using factorial notation
  3. determine binomial coefficients
  4. deduce the binomial theorem
  5. obtain binomial series using binomial expansion
  6. approximate roots and errors using binomial theorem

Content

- coefficients using - Pascal’s triangle - binomial theorem

Suggested Learning Resources

VECTORS

THEORY

Specific Objectives

By the end of the sub-module, the trainee should be able to:

  1. define a vector
  2. represent a vector by a directed straight line
  3. add vectors
  4. subtract vectors
  5. write a vector in terms of components
  6. multiply a vector with a scalar
  7. write a vector in terms of component unit vectors
  8. set up the coordinate system for representing vectors
  9. obtain the direction cosines of a vector
  10. calculate the scalar product

Content

PROBABILITY I

THEORY

Specific Objectives

By the end of the sub-module, the trainee should be able to:

Content

Suggested Learning Resources

STATISTICS I

THEORY

Specific Objectives

By the end of the sub-module, the trainee should be able to:

  1. distinguish between discrete and continuous data
  2. construct frequency distribution tables
  3. construct cumulative frequency table
  4. determine class boundaries, class intervals, central values
  5. represent data graphically
  6. determine measures of central tendency
  7. determine measures of dispersion

Content

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