Kerala Board Class 10 Mathematics — Flashcards for Quick Revision

A: An arithmetic sequence is a sequence where we add the same number repeatedly to get from one term to the next. Definition: A sequence starting with a number and proceeding by adding one fixed number

A: The common difference (d) is the fixed number added to get from any term to the next term. How to find it: Common difference = Any term - Previous term d = a₂ - a₁ = a₃ - a₂ = a₄ - a₃, etc. Example:

A: Step 1: Check if the difference between consecutive terms is constant 7 - 3 = 4 11 - 7 = 4 15 - 11 = 4 19 - 15 = 4 Step 2: Since all differences are equal to 4, this IS an arithmetic sequence. Comm

A: A tangent to a circle is a line that touches the circle at exactly one point. When we have a chord through points A and X on a circle, and we move point X closer and closer to point A along the circle

A: Property: The tangent at a point to a circle is perpendicular to the radius through that point. Proof: Consider chord AX where X moves closer to A. In triangle OAX (O is center), OA = OX (radii), so

A: Step 1: Mark the given point on the circle Step 2: Draw the radius from the center to this point Step 3: At the given point, construct a perpendicular to this radius Step 4: This perpendicular line is

A: The inscribed angle is half the central angle subtending the same arc. Formula: Inscribed angle = (1/2) × Central angle Example: If central angle = 120°, then inscribed angle = 60° This relationshi

A: You should use a 60° angle. Step-by-step reasoning: 1. 1/3 of circle = central angle of 120° 2. Using the inscribed angle theorem: inscribed angle = (1/2) × central angle 3. Required inscribed angle

A: An angle inscribed in a semicircle is always 90° (a right angle). Proof: - Semicircle has central angle = 180° - Inscribed angle = (1/2) × 180° = 90° This is known as Thales' theorem and is very use