- Identity: a + 0 = a, a × 1 = a
- Inverse: a + (-a) = 0, a × (1/a) = 1
- Distributive Property: a × (b + c) = a × b + a × c
- Factorization: a² - b² = (a + b)(a - b), (a - b)³ = a³ - 3a²b + 3ab² - b³


- Pythagoras Theorem: a² + b² = c², where c is the hypotenuse and a, b are the other two sides of a right-angled triangle.
- Similarity: Two triangles are similar if their corresponding angles are equal.
- Circle: Circumference (C) = 2πr, Area (A) = πr²


- Area of Rectangle: A = length × width
- Area of Square: A = side × side
- Area of Triangle: A = (1/2) × base × height
- Area of Circle: A = πr², where r is the radius of the circle
- Surface Area of Cuboid: SA = 2(lw + lh + wh)
- Volume of Cuboid: V = l × w × h


- Mean: Average of a set of numbers = sum of all numbers / total count of numbers
- Median: Middle value of a set of numbers when arranged in ascending or descending order
- Mode: Most frequently occurring value in a set of numbers


- Probability: Number of favorable outcomes / Total number of outcomes
- Addition Rule: P(A or B) = P(A) + P(B) - P(A and B), where A and B are two events
- Multiplication Rule: P(A and B) = P(A) × P(B), for independent events A and B


- Distance Formula: Distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by √[(x₂ - x₁)² + (y₂ - y₁)²]
- Midpoint Formula: Midpoint between two points P(x₁, y₁) and Q(x₂, y₂) is given by [(x₁ + x₂)/2, (y₁ + y₂)/2