Quadratic Formula and Trigonometric Functions

Quadratic Formula

• The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a, where ax² + bx + c = 0.

Trigonometric Functions

• sin A = a / c, sin B = b / c, sin C = c / c
• c² = a² + b² - 2ab cos C
• cos α + cos β = 2 cos ((a + b) / 2) cos ((a - b) / 2)
• cos α - cos β = -2 sin ((a + b) / 2) sin ((a - b) / 2)

Mathematical Signs and Symbols

• = (equals)
• ≅ (equals approximately)
• ~ (is the order of magnitude of)
• > (greater than)
• >> (much greater than)
• 0 (upward and downward motion)

Binomial Theorem

• (1 - x)ⁿ = 1 - nx + nx(n-1)x² / 2! - nx(n-1)(n-2)x³ / 3! + ...
• (1 - x)⁻ⁿ = 1 + nx + nx(n+1)x² / 2! + nx(n+1)(n+2)x³ / 3! + ...

Physics Textbook

• The physics textbook is divided into two parts, with 15 chapters in total.
• The textbook development team aims to help students appreciate the beauty and logic of physics.

National Curriculum Framework

• The National Curriculum Framework-2005 (NCF-2005) was revised during a curriculum renewal process at the school level.
• The higher secondary stage syllabus was developed accordingly.

Physics in Other Branches

• Physics is basic to the understanding of almost all branches of science and technology.
• Physics concepts are increasingly being used in other branches such as economics and commerce, and behavioral sciences.

Quarks and Gluons

• The three quarks within a proton can sometimes appear to be free, although no free quarks have ever been observed.
• Quarks have a quantum mechanical property called 'color' and interact with each other through the exchange of particles called 'gluons'.

CARTOSAT-1

• CARTOSAT-1 is a state-of-the-art remote sensing satellite built by ISRO.
• It has a mass of 156 kg at lift-off and was launched into a 618 km high polar Sun Synchronous Orbit (SSO) by ISRO's Polar Satellite Launch Vehicle, PSLV-C6.
• It is mainly intended for cartographic applications.

Units and Measurement

• Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit.
• The result of a measurement of a physical quantity is expressed by a number (or numerical measure) accompanied by a unit.
• There are seven base units in the SI system, which are used for international usage in scientific, technical, industrial, and commercial work.

SI Units

• The SI units used the decimal system, making conversions within the system simple and convenient.
• The unit for plane angle is radian (rad) and the unit for solid angle is steradian (sr).