ALGEBRA

TUTORIAL 1 - BASIC ALGEBRA Explain the use of Symbols. Indices, Modulus and Polynomials Manipulate Equations and Expressions The Distributive Law Products of Two Binomials

TUTORIAL 2 -INDICES, LOGARITHMS and FUNCTIONS Definitions Base 10 and Base e, Natural Logarithms Powers and Indexes Power Laws Applications Exponential Growth and Decay

TUTORIAL 3 - EQUATIONS and GRAPHS Types of Functions Proportional Relationships Inversely Proportional Relationships Logarithmic Graphs Simultaneous Equations Graphical Solutions

TUTORIAL 4 -FACRORISATION and QUADRATICS Common Factors Quadratic Equations and Roots Graphical Solutions Solving by Factorisation Perfect Square Roots Completing the Square Quadratic Formula

TUTORIAL 5 - PARTIAL FRACTIONS First Degree Linear Factors Remainder Theorem Factor Theorem Repeated Factors Second Degree Facgtors Series Expansion

TUTORIAL 6 - SIMPLIFICATION AND EXPANSION Explain the Summation Symbol Explain and Use Factorials Series - Arithmetical, Geometric Binomial Theorem

TUTORIAL 7 - EXPONENTIAL, TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS Logarithmic Equations Exponential Equations Natural Logarithms Linearising Equations Hyperbolic Functions

TUTORIAL 8 - SERIES AND PROGRESSIONS Arithmetic, Geometric and Advanced Limits, Convergence, Divergence D'Alembert's Ratio Absolute Convegence Factorials, Pascal's Triangle The Binomial Expansion Maclaurin's Expansion

TUTORIAL 9 - AREAS AND VOLUMES Areas of Geometric Shapes. Volumes of Geometric Shapes Surface Areas of Geometric Shapes

SELECT BY CLICKING BELOW Tutorial 1 Tutorial 2 Tutorial 3 Tutorial 4 Tutorial 5 Tutorial 6 Tutorial 7 Tutorial 8 Tutorial 9

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TRIGONOMETRY

TUTORIAL 1 - ANGLES and TRIANGLES Angular Measurement Cartesian and Polar Coordinates The Right Angle Triangle Pythagoras's Law Trig Ratios Sine, Cosine and Tangent Sinusoidal Functions Inverse Functions Areas of Triangles

TUTORIAL 2 - PERIODIC FUNCTIONS Angular Frequency and Periodic Time Phase and Displacement Co-Sinusoidal Waveforms Harmonic Waves Phasor Diagrams Complex Numbers

TUTORIAL 3 - IDENTITIES Compound Angles Double Angles Half Angles Products and Sums Changing Cos to Sin and Sin to Cos

TUTORIAL 4 - COORDINATE SYSTEMS 2 Dimensional Cartesian and Polar Co-ordinates. 3 Dimensional Coordinates Cartesian, Cylindrical and Spherical Coordinates. Conversion Between Coordinates Cartesian Planes

TUTORIAL 5 - VECTORS Vectors and Scalars Notation and Basic Rules The Unit Vector Vector Addition and Subtraction Vector Resolution Three Dimension Vectors Scalar and Vector products Use of the Matrix Determinant

SELECT BY CLICKING BELOW Tutorial 1 Tutorial 2 Tutorial 3 Tutorial 4 Tutorial 5

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OTHER TOPICS

BASIC MOMENTS OF AREA Centroids and First Moments of Area Second Moments of Area for Symmetrical Shapes Polar Second Moments of Area

ADVANCED MOMENTS OF AREA Types and Definitions Unsymmetrical Sections Principal Axis Maximum and Minimum Second Mom of Area

COMPLEX NUMBERS Argand Diagrams Polar Co-ordinates Multiplication and Division of Complex Numbers Conjugate Numbers Phasors and Phasor Diagrams Complex Impedance

SOLUTIONS TO SELF ASSESSMENT EXERCISES

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SAE SOLUTIONS BASIC MOMENTS ADVANCED MOMENTS COMPLEX NUMBERS