SOME IMPORTANT MATHEMATICAL FORMULAE

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• Anku S

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Basic Math Formula

• 1
SOME IMPORTANT MATHEMATICAL FORMULAE Circle : Area = It 12 Circumference = 2 Tr. Square : Area = .x2 ; Perimeter = 4x. Rectangle: Area = xy ; Perimeter = 2(x+y). 1 Triangle : Area = — (base)(height) ; Perimeter 2 Area of equilateral triangle 4 4 = a+b+c. Sphere Cube Cone Cuboid Cylinder : Surface Area = 4 ltr2 ; Volume = 1.3 3 : Surface Area = 6a2 ; Volume = ag : Curved Surface Area = TCrl; Volume = n r I -F It 12 Total surface area = 1 — Ttr2h 3 : Total surface area = 2 (ab + bh + lh); Volume = lbh. : Curved surface area = 2 Ttrh; Volume = Ttr2h Total surface area (open) = 2 Tt rh; Total surface area (closed) = 2 Tt rh+2 lt12 . SOME BASIC ALGEBRAIC FORMULAE; I + = a2 + 2ab+ b2 . 2. (a - -2ab+b2. 3.(a + = a 3 + b3 + 3ab(a + b). 4. (a - - b3 - 3ab(a - b). 5.(a + b + = a2 + b2 + c 2 +2ab+2bc +2ca. 6.(a + b + = a3 + b3 + c3+3a2b+3a2c + 3b2C +3b2a +3C2a +3c2a+6abc. 7.a2 8.a3 — b3 (a — b) (a2 + ab+ b2 ). 9.a3 + b3 = (a + b) (a2 - ab+ b2 + + (a - = 4ab. Ili(a + - (a - -2(a2 + b2 12.1fa + b -FC —O, then a3 + b3 + c 3 INDICES AND SURDS l. am an-am + n n a —3 abc. mn a 5. b a a bm a = b 10. a ± 206 = , where x + y — m = am bm (ab) 4. 1 8. ax y a — a and xy = b.
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LOGARITHMS = m log m=x(a>O and l) loga mn logm + logn. loga = logm— logn. a l. 2 3. 4. 5. 6. 7. 8. 9. loga mn = n logm. logba — log a log I logba — logal= 0 loga log b 1 loga b log (m +n) # logm +logn. 10. e logs 11. logaax x. PROGRESSIONS ARITHMETIC PROGRESSION a, a + d, a+2d, are in A.P. term, Tn = a + (n-l)d. Sum to n terms S 2 If a, b, c are in A.P, then 2b — a + c. GEOMETRIC PROGRESSION a, ar, ar2 , are in G.P. a(l —r n ) Sum to n terms, Sn — I—r Sum to infinite terms of G P If a, b, c are in ASP, then b2 HARMONIC PROGRESSION _ a(rn -1) if r < I and Sn — a — ace ifr> l. Reciprocals of the terms of A-P are in 1--1.1) 1 1 1 are in H.P 2ac If a, b, c are in H.P, then b — MATHEMATICAL INDUCTION 1 +2+3 + 12+22 +32 + 2 2 n(n + l) 2 n(n + + l) 6

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