Mathematics Last Minute Revision
Quick-fire revision for BSE Telangana Class 10 Maths — must-know formulas, trigonometry value shortcuts, geometry facts, and exam day strategy for the final 24 hours.
Must-Know Formulas
- →AP nth term: aₙ = a + (n−1)d · Sum: Sₙ = n/2[2a + (n−1)d]
- →Quadratic Formula: x = [−b ± √(b²−4ac)] / 2a · D = b²−4ac
- →Distance = √[(x₂−x₁)² + (y₂−y₁)²] · Midpoint = [(x₁+x₂)/2, (y₁+y₂)/2]
- →sin²θ + cos²θ = 1 · 1 + tan²θ = sec²θ · 1 + cot²θ = cosec²θ
- →Cone CSA = πrl, l = √(r²+h²) · Sphere SA = 4πr², Volume = 4/3πr³
Trig Values — Quick Recall
- →sin: 0, 1/2, 1/√2, √3/2, 1 (for 0°, 30°, 45°, 60°, 90°)
- →cos: 1, √3/2, 1/√2, 1/2, 0 (for 0°, 30°, 45°, 60°, 90°)
- →tan: 0, 1/√3, 1, √3, undefined (for 0°, 30°, 45°, 60°, 90°)
- →Memory trick: sin values = √0/2, √1/2, √2/2, √3/2, √4/2
Geometry — Key Facts
- →Tangent from external point P to circle: two tangents PA = PB (always equal)
- →BPT: if DE || BC in triangle ABC, then AD/DB = AE/EC
- →Similar triangles: area ratio = (corresponding side ratio)²
- →Angle in semicircle = 90° (Thales' theorem)
Statistics Shortcuts
- →Mean by step-deviation: x̄ = a + (Σfᵢuᵢ / Σfᵢ) × h — find a as the middle value
- →Median: find n/2, locate cumulative frequency class, use l + [(n/2 − cf)/f] × h
- →Mode: identify highest frequency class, apply l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h
- →For probability: always write the sample space for dice, coins, cards problems first
Exam Day Strategy
- →Spend first 10 minutes reading all questions — note which ones you can solve fully vs partially
- →Attempt 1-mark and 2-mark questions first — guaranteed easy marks
- →Show all steps: in Maths, method marks exist even if final answer is wrong
- →In constructions, use a sharp pencil and ruler/compass — precision is graded
- →After answering, go back and verify 5-mark problems by substituting answer back