Chapter 1
Algebraic Identities
Standard Algebraic Identities
(a + b)² = a² + 2ab + b² | (a - b)² = a² - 2ab + b² | (a + b)(a - b) = a² - b²
Essential formulas for factorization and instant quadratic expansion.
Variables: a, b are real numbers or algebraic expressions
Exam Tip: Difference of squares (a² - b² = (a+b)(a-b)) is the single most tested identity in Olympiads.
Product Identity with Common Term
(x + a)(x + b) = x² + (a + b)x + ab
Foundation for middle-term splitting in quadratic factorizations.
Variables: x is variable, a and b are constants
Exam Tip: If signs are negative: (x - a)(x - b) = x² - (a + b)x + ab.
Chapter 2
Mensuration (2D & 3D)
Trapezium & Rhombus Area
SI: m² or cm²Area of Trapezium = 1/2 × (a + b) × h | Area of Rhombus = 1/2 × d1 × d2
Diagonals of a rhombus bisect each other at right angles (90°).
Variables: a, b = parallel sides, h = perpendicular distance; d1, d2 = diagonals
Exam Tip: Side of rhombus s = √((d1/2)² + (d2/2)²) via Pythagoras theorem.
Cuboid & Cylinder 3D Formulas
SI: Volume: m³, Surface Area: m²Cuboid Volume = l × b × h, Total Surface Area = 2(lb + bh + hl) | Cylinder Volume = πr²h, CSA = 2πrh, TSA = 2πr(r + h)
CSA is curved surface only; TSA includes both circular top and bottom flat bases.
Variables: l=length, b=breadth, h=height, r=radius
Exam Tip: Diagonal of cuboid = √(l² + b² + h²). Maximum length of rod that can fit in a room.