ICSE Class 10 Last Minute Revision

GST — SGST, CGST, list price, discount, inverse cases

Recurring Deposit — maturity value formula: MV = P×n + I, interest formula

Shares & Dividends — income = shares × rate × FV; return = (income/investment) × 100

Quadratic equations — nature of roots: b²−4ac > 0, = 0, < 0; factorisation; formula

Linear Inequations — solve and represent on number line

Ratio & Proportion — componendo, dividendo

Factor Theorem — f(x) = 0; Remainder Theorem — f(a) = remainder

Matrices — 2×2 addition, subtraction, multiplication

AP — Tn = a + (n−1)d; Sn = n/2[2a + (n−1)d]

GP — Tn = ar^(n−1); Sn = a(rⁿ−1)/(r−1)

Reflection — in x=0, y=0, x=a, y=a, origin; invariant points

Section formula — P = (m₁x₂+m₂x₁)/(m₁+m₂), (m₁y₂+m₂y₁)/(m₁+m₂); midpoint

Slope — m = (y₂−y₁)/(x₂−x₁); parallel lines: m₁=m₂; perpendicular: m₁m₂=−1

Equation of line — y = mx + c; y − y₁ = m(x − x₁)

Similarity — SSS, SAS, AA; ratio of areas = ratio of squares of sides

Loci — perpendicular bisector, angle bisector, concentric circles

Circles — angle at centre = 2× angle at remaining arc; angles in same segment equal; angle in semicircle = 90°; opposite angles of cyclic quadrilateral supplementary

Tangent — perpendicular to radius; from external point: two tangents equal; tangent-chord angle = alternate segment angle

Cylinder — CSA = 2πrh; TSA = 2πr(r+h); V = πr²h

Cone — CSA = πrl; TSA = πr(r+l); V = ⅓πr²h; l = √(r²+h²)

Sphere — SA = 4πr²; V = 4/3πr³; hemisphere: CSA = 2πr², TSA = 3πr², V = 2/3πr³

Identities — sin²A + cos²A = 1; 1 + tan²A = sec²A; 1 + cot²A = cosec²A

Heights & Distances — angle of elevation (from below), angle of depression (from above); tan = opposite/adjacent

Mean — direct: Σfx/Σf; step-deviation: A + (Σft/Σf)×i

Median — from ogive; upper quartile, lower quartile, inter-quartile range

Mode — from histogram (highest frequency class)

Probability — P(E) = favourable outcomes / total outcomes; 0 ≤ P(E) ≤ 1