College Algebra
Exponents and radicalsLogarithm and division by zeroQuadratic equation, quadratic formula, and roots of quadratic equationSpecial products and factoringBinomial expansion and Pascal's triangleVerbal problem categoriesNumber problemsDigit problemsClock problemsAge problemsMixture problemsWork problemsMotion problems
Plane and Spherical Trigonometry
The six trigonometric functionsTrigonometric identitiesSum and difference of two anglesThe spherical triangleRight spherical triangleOblique spherical triangle
Plane Geometry
TriangleCenters of a TriangleProperties of TriangleQuadrilateralCyclic quadrilateralPolygonRegular polygonCircle, sector of a circle, segment of a circle
Solid Mensuration / Solid Geometry
Solids for which volume is the product of base area and altitudePrismCube and rectangular parallelipipedCylinderRight Circular CylinderSolids for which volume is one-third of the product of base area and altitudeConeRight circular conePyramidRegular pyramidRegular tetrahedronFrustumFrustum of a Regular PyramidFrustum of a Right Circular ConeSimilar FiguresSphereSpherical sectorSpherical segmentSpherical wedge and spherical luneSpherical zone
Analytic Geometry
Conic sectionsEllipseHyperbolaParabola
Differential Calculus
Maxima and minimaApplication of maxima and minima / Optimization problemsTime ratesDifferentiation of trigonometric and inverse trigonometric functionsOptimization using trigonometric functionsProblems involving inverse trigonometric functions
Integral Calculus
Indefinite IntegralsProperties of integralsDefinite integrationThe General Power FormulaLogarithmic formulaExponential formulaIntegration of trigonometric functionsIntegration of inverse trigonometric functionsIntegration by partsIntegration by algebraic substitutionIntegration by trigonometric substitutionIntegration of rational fractionsPlane areas in rectangular coordinatesPlane areas in polar coordinatesSolids of revolution by integration
Engineering Mechanics
Components of planar and space forcesMomentCoupleResultant of concurrent forcesResultant of parallel forcesResultant of non-concurrent non-parallel forcesEquilibrium of concurrent forcesEquilibrium of parallel forcesEquilibrium of non-concurrent non parallel forcesTruss analysisMethod of jointsMethod of sectionsSimple frame analysisFriction forcesFriction on wedges
Strength of Materials / Mechanics of Materials
Axial DeformationShearing DeformationStatically Indeterminate MembersThermal StressTorsionFlanged bolt couplingsTorsion of thin-walled tubeHelical SpringsShear and Moment in BeamsShear and Moment DiagramsRelationship Between Load, Shear, and MomentLoad and moment diagrams for a given shear diagramMoving LoadsFlexure FormulaEconomic SectionsFloor FramingUnsymmetrical BeamsSuperimposed or Built-up BeamsHorizontal Shearing StressDesign for Flexure and ShearSpacing of Rivets or Bolts in Built-Up BeamsBeam DeflectionsBeam Deflection by Double Integration MethodMoment Diagrams by PartsBeam Deflection by Area-Moment MethodDeflection of Cantilever BeamsDeflections in Simply Supported BeamsBeam Deflection by Method of Superposition
Engineering Economy
Simple interestCompound interestAnnuityOrdinary annuity, annuity due, deffered annuity, and perpetuity
Derivation of Formulas
Quadratic formulaSum and product of roots of a quadratic equationArithmetic progressionSum of finite and infinite geometric progressionArithmetic mean, harmonic mean, and geometric mean •, Depreciation formula: SYD methodProof of Ptolemy's theoremArea of cyclic quadrilateralRadius of circumcircleRadius of incircleHero's formula for triangle of given three sidesFundamental identitiesPythagorean identitiesCosine lawPythagorean theoremSine lawSum and difference of two anglesDouble angle formulasHalf angle formulasVolume of the frustumVolume of sphereSurface of the sphereLateral area of right circular cone
List of Greek alphabets and its English equivalentMeter, kilogram, second, and other base units in SINewton, Pascal, Watt, Coluomb and other derived SI unitsSI unit prefixes from Yocto to YottaThe English system of units