List the five most important formulas a Class 9 AP student must know for Mathematics, with one example use of each.

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TOP 5 FORMULAS FOR AP CLASS 9 MATHEMATICS: (1) THREE EQUATIONS OF MOTION (cross-listed with Physics) — V=u+at, s=ut+½at², v²=u²+2as. [But in Mathematics context, the algebraic identities are more relevant.] ALGEBRAIC IDENTITY: a³−b³ = (a−b)(a²+ab+b²). Example: Factorise 8x³−27 = (2x)³−(3)³ = (2x−3)(4x²+6x+9). (2) REMAINDER THEOREM: p(a) = remainder when p(x) is divided by (x−a). Example: p(x) = x³−2x+1 divided by (x−1): p(1) = 1−2+1 = 0. Remainder = 0, so (x−1) is a FACTOR. (3) MENSURATION — CONE VOLUME: V = ⅓πr²h. Example: Cone with r=7, h=24. l=√(49+576)=25. V=⅓×π×49×24 = 1232π/3 cm³. (4) CYCLIC QUADRILATERAL: ∠A + ∠C = 180°. Example: ∠A = (2x+10)°, ∠C = (3x−20)° → 5x−10=180 → x=38. ∠A=86°, ∠C=94°. (5) MEDIAN OF GROUPED DATA: Median = L + [(N/2−CF)/f] × h. Example: N=40, N/2=20, median class 20-30, L=20, CF=14, f=12, h=10. Median = 20 + [(20−14)/12]×10 = 20+5 = 25.

Practice — Mathematics — Real Numbers, Polynomials, Geometry & Statistics (AP Class 9)

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