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