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Summary

Mathematics, Surveying and Transportation EngineeringALGEBRA Set Theory  Theory of Equations - Descartes Rule of Sign  Principle of Inclusion and Exclusion  Progression - Arithmetic Progression - Geometric Progression - Infinite Geometric Progression - Arithmetic Mean - Geometric Mean - Harmonic...

Description

Mathematics, Surveying and Transportation Engineering

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ALGEBRA

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Set Theory Theory of Equations - Descartes Rule of Sign Principle of Inclusion and Exclusion Progression - Arithmetic Progression - Geometric Progression - Infinite Geometric Progression - Arithmetic Mean - Geometric Mean - Harmonic Mean - Quadratic Mean Worded Problem - Motion Problem - Clock Problem - Work Problem Quadratic Equation - Sum of Roots - Product of Roots Binomial Theorem - rth term - Sum of Coefficients TRIGONOMETRY

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Angle Measurement - Sexagesimal System - Centesimal System - Circular System Oblique Triangles - Sine Law - Cosine Law Other Trigonometric Function Trigonometric Identities Wave Function Spherical Trigonometry - Sine Law - Cosine Laws - Sum of Spherical Triangle’s Angle - Area of Spherical Triangle

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Distance between two points Midpoint of Line Segment

Conic Sections a. Circle - Standard Form - General Form - Radical Center of Circles b. Parabola - Standard Form - General Form - Draw the Parabola c. Ellipse - Standard Form - General Form - Draw and formula of Ellipse - Terms for Ellipse - Flatness of Ellipse d. Hyperbola - Standard Form - General Form - Draw and Formula for Hyperbola Translation of Axes Polar Coordinates

PLANE AND SOLID GEOMETRY 

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ANALYTIC GEOMETRY  

Centroid of Polygon (vertices given) Distance between point and line Distance between two lines

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Common Plane Geometry Formulas - Sum of Interior Angles of Polygon - Number of Diagonals - Area of Regular Polygon - Area of Triangle Triangle Inequalities Triangle Centers - Centroid - Incenter - Circumcenter - Orthocenter - Excentre Apollonius Theorem General Quadrilateral - Area (given diagonals and included angle) - Area (given four sides and sum of two opposite angles) Area of Trapezoid Area of Parallelogram

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Division/Extension of Lines Segment Area of Polygon by Coordinates Angle between two lines (slope given)

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Area of Rhombus Area of Kite Area of Cyclic Quadrilateral Ptolemy’s Theorem Radius of Circumscribing Circle on Quad

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Radius of Inscribing Circle on Quad Circle Theorems Similar Solids Platonic Solids - Euler’s Characteristic Equation Common Platonic Solids - Tetrahedron - Hexahedron - Octahedron - Dodecahedron - Icosahedron Solid with constant cross-section Solid with similar cross-section Pyramids Cylinder Frustrum (any kind) Sphere - Volume - Spherical Segment (1 and 2 bases) - Spherical Sector - Spherical Lune and Wedge - Area and Volume of Spherical Polygons VECTORS AND 3D GEOMETRY

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Length of Vector Dot Product Cross Product Unit Vector Application of Vectors - 3D Forces - Work - Moment - Shortest distance b/n two vectors - Area of Parallelogram - Volume of Parallelepiped - Distance b/n point and a plane - Center of Sphere/Circle - Area of Triangle Form of Vectors - Symmetric Form - Parametric Form DIFFERENTIAL CALCULUS

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Asymptotes

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- For Polar - For Parametric Center of Curvature Curvilinear Motion - Velocity - Acceleration (change in velocity) - Acceleration (change in direction) Tangent Plane Equation Normal Plane Equation Angle between two curves @ (x,y) INTEGRAL CALCULUS

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Plane Areas Solid of Revolution Length of Curve - Rectangular - Parametric - Polar Surface Area Centroid - For Area - For Volume - For Surface Area - For Polar Curves Moment of Inertia - Polar Moment of Inertia - Product of Inertia STAT AND PROBABILITY

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Statistics of Ungrouped Data - Mean/Average - Mode - Median - Range - Sample Standard Deviation - Sample Variance Measures of Position - Quartile - Decile - Percentile - Interquartile Range Principle of Counting - Permutation - Combination Circular Permutation - If # of sample = # of slot - If # of sample not equal to the slot

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- Horizontal Asymptote - Vertical Asymptote - Inclined Asymptote Radius of Curvature - For Rectangular

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Basic Probability Conditional Probability - Baye’s Law - Total Probability Formula Probability Distribution

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Binomial Distribution Negative Binomial Distribution Geometric Distribution Multinomial Distribution Hypergeometric Distribution Poisson’s Distribution Normal Distribution

ENGINEERING ECONOMY       

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Simple Interest Compound Interest Annuities Gradients Effective Rate of Interest Interest Rate Factor Perpetuity - 1 interval - For more than 1 interval Depreciation - Straight Line Method - Sum of Year’s Method - Declining Method - Double Declining Method - Sinking Fund Method Inflation

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PHYSICS     

Rectilinear Motion Rotational Motion Curvilinear Motion Projectile Motion Erratic Motion

SURVEYING AND TRANSPORTATION ENGINEERING 

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Correction in Distance Measurement - Correction due to Temperature - Correction due to Pull - Correction due to Sag - Correction due to Slope - Sea Level Correction - Normal Tension Correction in Distance

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Standard Error of the Mean Probable Error of Single Observation - Probable Error of the Mean - Relative Error/Precision - Summation of Errors - Product of Errors Rules for Weighted Measurements Differential Leveling Two Peg Tests Bubble Sensitivity Effect of Earth’s Curvature and Refraction Compass Surveying Transverse Surveying: Error of Closure - Linear Error of Closure - Relative Error of Closure Transverse Surveying: Balancing a Survey - Compass Rule - Transit Rule Area Computation - Double Meridian Distance (DMD) - Double Parallel Distance (DPD) Tacheometry Simple Curve - Tangent Distance - Long Chord - External Distance - Middle Ordinate - Degree of Curvature (Arc & Chord) - Deflection Angle Compound Curve Reverse Curve Transition Curves - Length of Spiral Curve, Ls - Spiral Angle, (theta) - Offset Distance, x - Deflection Angle - Length of Yc - Length of Throw Symmetrical Parabolic Vertical Curve Unsymmetrical Parabolic Vertical Curve

Measurement - Most Probable Value - Error/Residual/Deviation - Standard Deviation of Any Single Observation...