Mathematics & Physics Overview

Cheatsheet Content

### Mathematics #### Number and Operations - Operations, ratio and proportion, averages, percentage, elementary number theory, fractions and decimals. - Squares and square roots, cubes and cube roots, exponents and powers, H.C.F. and L.C.M. - Arithmetic Progressions, $n^{th}$ term, sum of first $n$ terms of A.P. and their application in solving problems. #### Algebra and Functions - Expressions (up to cubic level), equations (up to quadratic level). - Properties of functions (linear, polynomial, rational). #### Linear Equations in Two Variables - Focus on linear equations of the type $ax + by + c = 0$. - Applications in solving problems. #### Geometry and Mensuration - Plane Geometry: Lines and angles, triangles, squares, rectangles, parallelogram, trapezium, rhombus, quadrilaterals and circles. - Co-ordinate Geometry: Lines and circles. - Three-dimensional Solids: Surface area and volume of cubes, cylinders, cones, spheres and combination of shapes. #### Trigonometry - Trigonometric ratios of an acute angle of a right-angle triangle. - Heights and Distances: Angle of elevation, angle of depression and problems based on these. #### Permutations and Combinations - Fundamental principle of counting. - Factorial $n$. ($n!$), Permutations ($^nP_r$) and Combinations ($^nC_r$), simple applications. #### Probability - Events; occurrence of events, Probability of an event and related problems. - Bayes' theorem. ### Physics #### Mechanics - **Kinematics:** Velocity, acceleration, and motion in one dimension. - **Dynamics:** Force, Newton's laws, statics and friction. - **Energy and Momentum:** Potential and kinetic energy, work, power, impulse and conservation laws. - **Circular Motion:** Uniform circular motion and centripetal force. - **Simple Harmonic Motion:** Pendulum. - **Gravitation:** Universal law of gravitation, Kepler's laws, force of gravitation of the earth (gravity), acceleration due to gravity, mass and weight. #### Electricity and Magnetism - **Electric Fields, Forces, and Potentials:** Coulomb's law, induced charge, field and potential of groups of point charges, and charged particles in electric fields. - **Capacitance:** Parallel-plate capacitors and time-varying behavior in charging/discharging. - **Circuit Elements and DC Circuits:** Resistors, light bulbs, series and parallel networks, Ohm's law, and Joule's law. - **Magnetism:** Permanent magnets, fields caused by currents, particles in magnetic fields, Faraday's law, and Lenz's law. #### Waves and Optics - **General Wave Properties:** Wave speed, frequency, wavelength, superposition, standing wave diffraction, Doppler effect and Young's double slit experiment. - **Reflection and Refraction:** Snell's law and changes in wavelength and speed. - **Ray Optics:** Image formation using pinholes, mirrors, and lenses. #### Heat and Thermodynamics - **Thermal Properties:** Temperature, heat transfer, specific and latent heat, and thermal expansion. - **Laws of Thermodynamics:** First and second laws, internal energy, enthalpy, entropy, and heat engine efficiency. #### Floatation - Thrust and pressure, Archimedes' Principle, Buoyancy. #### Mechanical Properties of Solids - Stress-strain relationship, Hooke's law, Young's modulus, Poisson's ratio. #### Mechanical Properties of Fluids - Pressure due to a fluid column; Pascal's law and its applications, effect of gravity on fluid pressure. - Viscosity, Stokes' law, streamline and turbulent flow, Bernoulli's theorem and its applications. #### Thermal Properties of Matter - Heat, temperature, thermal expansion. - Heat transfer: Conduction, convection and radiation, Stefan's law.