Plane Geometry Triangle • Centers of a Triangle • Properties of Triangle • Quadrilateral • Cyclic quadrilateral • Polygon • Regular polygon • Circle, sector of a circle, segment of a circle

Solid Mensuration / Solid Geometry Solids for which volume is the product of base area and altitude • Prism • Cube and rectangular parallelipiped • Cylinder • Right Circular Cylinder • Solids for which volume is one-third of the product of base area and altitude • Cone • Right circular cone • Pyramid • Regular pyramid • Regular tetrahedron • Frustum • Frustum of a Regular Pyramid • Frustum of a Right Circular Cone • Similar Figures • Sphere • Spherical sector • Spherical segment • Spherical wedge and spherical lune • Spherical zone

Differential Calculus Maxima and minima • Application of maxima and minima / Optimization problems • Time rates • Differentiation of trigonometric and inverse trigonometric functions • Optimization using trigonometric functions • Problems involving inverse trigonometric functions

Integral Calculus Indefinite Integrals • Properties of integrals • Definite integration • The General Power Formula • Logarithmic formula • Exponential formula • Integration of trigonometric functions • Integration of inverse trigonometric functions • Integration by parts • Integration by algebraic substitution • Integration by trigonometric substitution • Integration of rational fractions • Plane areas in rectangular coordinates • Plane areas in polar coordinates • Solids of revolution by integration

Derivation of Formulas Quadratic formula • Sum and product of roots of a quadratic equation • Arithmetic progression • Sum of finite and infinite geometric progression • Arithmetic mean, harmonic mean, and geometric mean •, Depreciation formula: SYD method • Proof of Ptolemy's theorem • Area of cyclic quadrilateral • Radius of circumcircle • Radius of incircle • Hero's formula for triangle of given three sides • Fundamental identities • Pythagorean identities • Cosine law • Pythagorean theorem • Sine law • Sum and difference of two angles • Double angle formulas • Half angle formulas • Volume of the frustum • Volume of sphere • Surface of the sphere • Lateral area of right circular cone

Strength of Materials / Mechanics of Materials Axial Deformation • Shearing Deformation • Statically Indeterminate Members • Thermal Stress • Torsion • Flanged bolt couplings • Torsion of thin-walled tube • Helical Springs • Shear and Moment in Beams • Shear and Moment Diagrams • Relationship Between Load, Shear, and Moment • Load and moment diagrams for a given shear diagram • Moving Loads • Flexure Formula • Economic Sections • Floor Framing • Unsymmetrical Beams • Superimposed or Built-up Beams • Horizontal Shearing Stress • Design for Flexure and Shear • Spacing of Rivets or Bolts in Built-Up Beams • Beam Deflections • Beam Deflection by Double Integration Method • Moment Diagrams by Parts • Beam Deflection by Area-Moment Method • Deflection of Cantilever Beams • Deflections in Simply Supported Beams • Beam Deflection by Method of Superposition