PRE-REQUISITE STUDIES
ALGEBRA
TUTORIAL 1 - BASIC ALGEBRA
Explain the use of Symbols.
Exolain the Conformity of Units in Equations.
Manipulate equations and Expressions
The Distributive Law
Products of Two Binomials
TUTORIAL 2 - STRAIGHT LINE LAWS
Gradients
Intercepts
Proportional Relationships
Inversely Proportional Relationships
TUTORIAL 3 - SOLUTION OF EQUATIONS
Definitions
Substitution Method
Elimination Method
Matrix Method
Cubic Equations
Graphical Solutions
TUTORIAL 4 - AREAS AND VOLUMES
Areas of Geometric Shapes.
Volumes of Geometric Shapes
Surface Areas of Geometric Shapes
TUTORIAL 5 - LOGARITHMS
Definitions
Base
Powers and Indexes
Power Laws
Applications
Logarithmic Graphs
TUTORIAL 6 - SIMPLIFICATION AND EXPANSION
Explain the Summation Symbol
Explain and Use Factorials
Explain and Use the Binomial Expansion
TUTORIAL 7 - EXPONENTIAL AND HYPERBOLIC FUNCTIONS
Logarithmic equations with logarithms.
Define the Exponential Function
Linearise functions with logarithms
Define the Hyperbolic Function
Compare Hyperbolic and Trigonometric functions
TUTORIAL 8 - MATHEMATICAL SERIES AND PROGRESSIONS
The sigma notation
The binomial coefficent and Pascal's Triangle.
Convergence and divergence.
Limiting values.
The binomial expansion and theorem.
Maclaurin's expansion
TRIGONOMETRY
TUTORIAL 1 - BASIC TRIGONOMETRY
Angular Measurement
The Right Angle Triangle
Trig Ratios
Sine, Cosine and Tangent
Sinusoidal Functions
Harmonic Motion
Frerquency and Periodic Time
Angular Velocity
TUTORIAL 2 - MORE TRIGONOMETRY
Revise Basics
Cartesian and Polar Coordinates
Sine Rule
Cosine Rule
The Areas of Triangles
TUTORIAL 3 - PERIODIC FUNCTIONS
Phase and Displacement
Square Waves
Phasor Diagrams
Complex Numbers
VECTORS
COORDINATE SYSTEMS
Cartesian and Polar Co-ordinates.
Cylindrical and Spherical Coordinates.
Conversion Between Coordinates
BASIC VECTOR THEORY
Cartesian and Polar Co-ordinates.
Vector addition and subtraction.
Vector resolution.
Unit Vector
Three Dimensional vectors
Spherical coordinates
MOMENTS OF AREA
CENTROIDS AND FIRST MOMENTS OF AREA
SECOND MOMENTS OF AREA
PARALLEL AXIS THEOREM
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LEVEL 1 MATHS
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PARTIAL FRACTIONS
Division of Polynomials
Remainder Theorem
First Degree Partial Fractions
Second Degree Partial fractions
ADVANCED VECTOR THEORY
Vector Products
Dot or Scalar Product
Cross or Vector Product
Triple Scalar Product
Triple Vector Product
MATRICES
BASIC MATRIX THEORY
Definitions
Column Vectors
Arrays
Diagonal, Unit, Zero and Transpose Matrices
Trace of a Matrix
Adding Arrays
Multiplying Arrays
MORE MATRIX THEORY
Representing Simultaneous Equations
Determinants
Minors and Cofactors
The Adjoint Matrix
The Inverse Matrix
Solving Simultaneous Equations
EIGEN VALUES AND VECTORS
Definitions
The Power method
Use of the Identity matrix
CALCULUS
INTEGRATION TUTORIAL 1
Basic Numerical Integration
Finding Areas Under Graphs
Standard Forms
Integration Between Limits
Moments of Area and Inertia
INTEGRATION TUTORIAL 2
Integrate Polynomials
Integrate Trigonometric Expressions
Integrate Logarithmic Expressions
Integrate Exponentials
Integration by Substitution
Inegration by Parts
INTEGRATION TUTORIAL 3
Numerical Methods of Integration
Areas under graphs
Mid-ordinate rule
Trapezoidal rule
Engineerng Applications.
Simpson's Rule
DIFFERENTIATION TUTORIAL 1
Gradients of functions
Differential Coefficients
Standard Forms
Higher Order Differentials
Engineerng Applications.
DIFFERENTIATION TUTORIAL 2
Differentiate a Sum
Differentiate a Product
Differentiate a Quotient
Turning Points
MAXIMUM AND MINIMUM THEORY
Turning points of functions
Graphical determination.
Determination by successive differentiation.
Engineering examples
STATISTICS AND PROBABILITY
STATISTICS TUTORIAL 1
Grouped and Ungrouped Data
Mean and Median
Ogives, Histograms and Bar Charts
Qaurtiles
Normal Distribution
Variance and Standard deviation
STATISTICS TUTORIAL 2
Curve Fitting
Method of Least Squares
Use of Excel to Find Functions
STATISTICS TUTORIAL 3
Probability
Permutations
Combinations
Events
Multiple Events
Sample Space
STATISTICS TUTORIAL 4
Sample Space
Accumulative Probability
Binomial Distribution
Normal Distribution
Poisson Distribution
COMPLEX NUMBERS
Argand Diagrams
Polar Co-ordinates
Multiplication and Division of Complex Numbers
Conjugate Numbers
Phasors and Phasor Diagrams
Complex Impedance
LAPLACE AND FOURIER TRANSFORMS
Transforms of common time functions
Transform Tables
Inverse Transforms
Fourier transforms of basic functions of s
Changing functions into complex numbers
ADVANCED MOMENTS OF AREA
ADVANCED SECOND MOMENTS
PRODUCT SECOND MOMENT
UNSYMMETRICAL SECTIONS
PRINCIPAL AXES
MAXIMUM AND MINIMUM SECOND MOMENTS
POLAR SECOND MOMENTS
QUESTIONS AND SOLUTIONS TO THE 2004 PAPER
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