Mathematics Last Minute Revision
Quick-fire revision for BSE AP Class 10 Maths — must-know formulas, trigonometry value shortcuts, geometry facts, and exam day strategy for the final 24 hours.
Algebra Formulas — Must Know
- →HCF × LCM = Product of two numbers · Decimal terminates ↔ denominator = 2ᵃ × 5ᵇ only
- →Quadratic formula: x = [−b ± √(b²−4ac)] / 2a · D = b²−4ac
- →AP: aₙ = a+(n−1)d · Sₙ = n/2[2a+(n−1)d] = n/2(first + last)
- →Polynomials: sum of zeros = −b/a, product = c/a (for 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 of sin)
- →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 ⟹ AD/DB = AE/EC (and converse)
- →Similar triangles: area ratio = (corresponding sides)²
- →Tangent ⊥ radius; two tangents from external P: PA = PB
- →Tangent length = √(d²−r²); Sector area = (θ/360)×πr²
Mensuration & Statistics
- →Cone: l = √(r²+h²); Frustum V = πh/3(r₁²+r₂²+r₁r₂)
- →Sphere: V = 4/3πr³; Hemisphere 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
AP SSC Exam Pattern & Strategy
- →AP SSC Maths: 100 marks, 3h 15m (15 min reading), 4 sections, 33 questions
- →Section I: 12×1=12M (objective) → Section II: 2M → Section III: 4M → Section IV: 8M (choice)
- →Attempt Section I first (all 12 questions, 1 mark each) — guaranteed marks
- →Show every step — method marks are awarded even if final answer is wrong
- →Section IV has internal choice — read both options before deciding which to attempt
Probability — Quick Recall
- →P(E) = favourable outcomes / total outcomes · P(E)+P(Ē)=1
- →Cards: total 52 (13 each suit: ♠♣♥♦) · 4 aces, 4 kings, 4 queens, 4 jacks · 26 red, 26 black
- →Dice: 1-6 each die · two dice = 36 outcomes · P(sum=7) = 6/36 = 1/6
- →Coins: 1 coin → {H,T}; 2 coins → {HH,HT,TH,TT} = 4 outcomes