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.
Ch. 1 Real Numbers & Logarithms — Quick Recall
- →HCF × LCM = Product of two numbers · Decimal terminates ↔ denominator = 2ᵃ × 5ᵇ only
- →Irrational proof: assume p/q (lowest terms), square, show prime divides p then q — contradiction
- →Log definition: aˣ = N ⟺ logₐN = x · logₐa = 1 · logₐ1 = 0
- →Product: logₐ(xy) = logₐx + logₐy · Quotient: logₐ(x/y) = logₐx − logₐy · Power: logₐ(xⁿ) = n·logₐx
- →Ch. 2 Sets: n(A∪B) = n(A)+n(B)−n(A∩B) · 3-set: add n(A∩B∩C) at end
Algebra Formulas — Must Know
- →Quadratic Formula: x = [−b ± √(b²−4ac)] / 2a · D = b²−4ac (discriminant)
- →AP: aₙ = a+(n−1)d · Sₙ = n/2[2a+(n−1)d] · If last term l: Sₙ = n/2(a+l)
- →GP: aₙ = arⁿ⁻¹ · Sₙ = a(rⁿ−1)/(r−1) · Common ratio r = a₂/a₁
- →Polynomials: sum of zeros = −b/a, product = c/a (for quadratic ax²+bx+c)
Trigonometry Values — Quick Recall
- →sin: 0, 1/2, 1/√2, √3/2, 1 (at 0°, 30°, 45°, 60°, 90°)
- →cos: 1, √3/2, 1/√2, 1/2, 0 (reverse order of sin values)
- →tan: 0, 1/√3, 1, √3, undefined (at 0°, 30°, 45°, 60°, 90°)
- →Identities: sin²θ+cos²θ=1 · 1+tan²θ=sec²θ · 1+cot²θ=cosec²θ
Geometry — Key Facts
- →BPT (Thales): DE∥BC in ΔABC ⟹ AD/DB = AE/EC (and converse)
- →Tangent ⊥ radius; two tangents from external point P: PA = PB
- →Tangent length = √(d²−r²) where d = distance from point to centre
- →Area ratio of similar triangles = (corresponding sides)²
- →Pythagoras: hyp² = base² + height²
Mensuration & Statistics Shortcuts
- →Cone: l = √(r²+h²); Frustum volume = πh/3(r₁²+r₂²+r₁r₂)
- →Sphere: V = 4/3πr³; Hemisphere: V = 2/3πr³, TSA = 3πr²
- →Mean (step-deviation): x̄ = A + (Σfᵢuᵢ/Σfᵢ)×h
- →Median: l + [(n/2−cf)/f]×h · Mode: l + [(f₁−f₀)/(2f₁−f₀−f₂)]×h
- →Probability: P(E) = favourable/total · P(E)+P(Ē)=1
Exam Day Strategy
- →TS SSC Maths: Paper I and Paper II — 50 marks each (40 external + 10 internal)
- →Read all questions first (10 min) — attempt 1-mark, 2-mark, 4-mark, then 5-mark
- →Show every step — partial marks are awarded even if final answer is wrong
- →Constructions: use sharp pencil, draw with compass first then label clearly
- →Verify answers: substitute back into original equation to check