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Notes On Mathematical Formulae

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Published in: Mathematics
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MATHEMATICAL FORMULAE for School Students

Vinod K / Dubai

12 years of teaching experience

Qualification: MBA (Master degree of Business Administration) , Master degree of Mathematics , Bachelor Degree of mathematics

Teaches: Business Studies, Physics, Management, Maths, Mathematics, Psychology

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  1. MATHEMATICAL FORMULAE Algebra 17. a 2. 3. 4. 5. 6. 7. 8. 10. 11. 12. 13. 14. 16. 18. 20. 21. 22. 23. 24. 25. 26. 27. 28. - 20b (a b = a2 + b2 + 2(ab + = + b3 + 3ab(a + b); 03 + = — b3 — 3ab(a —b); a3 cr3 — b3 03 + b3 —3b2 + . =a.a.a...n times a n if m > n = 1 if m = n 1 if m < n; a e (ab)n — an bn 15 a ao = 1 where a e R, a 0 ap/q _ 19. If am - an ap — an and a 4-1, a * O then m = n If an = bn where n O, then a = -kb If V•'7, are quadratic surds and if a -f- N/F, then a = O and = y If v/7, are quadratic surds and if a -+ = b+ y,'ü then a = b and = y If a, m, n are positive real numbers and a 1, then logo mn = loga m+loga n If a, m, n are positive real numbers, a 1, then logo = loga m — loga n If a and m are positive real numbers, a 1 then loga mn = n loga m ogk a If a, b and k are positive real numbers, b 1, k 1, then logb a — logk b logb a — where a, b are positive real numbers, a 1, b 1 logo b if a, m, n are positive real numbers, a 1 and if logo m = loga n, then Typeset by -4WTEX
  2. 2 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. if a + O where i = V/Ä, then a = b O if a + ib = + i", wherei = v"Ä, then a = and b = y The roots of the quadratic equation a:r2 +b:r+c = O; a O are 20 — 4ac The solution set of the equation is 20 where A = discriminant = b2 — 4ac The roots are real and distinct if A > O. The roots are real and coincident if A = O. The roots are non-real if A < O. 20 If and (3 are the roots of the equation a:r2 -+ + c = O, a 0 then -b coeff. of a: coeff. of constant term ii) a •/3— coeff. of The quadratic equation whose roots are and (3 is (x i.e. — ST -F P = O where S =Sum of the roots and P =Product of the roots. For an arithmetic progression (A.P.) whose first term is (a) and the common difference is (d). i) nth term= tn = a + (n — l)d ii) The sum of the first (n) terms = — where I =last term= a + (n — l)d. 2 2 For a geometric progression (G.P.) whose first term is (a) and common ratio is i) n h term= tn = a-y ii) The sum of the first (n) terms: 1 a(7j' 1) if7 < 1 if > 1 if where Sn =Sum of the first (n) For any sequence terms. = 12 22 + 32 Sn—l — 2 6
  3. 42 • 43. 44. 45 46. 13 23 -f- 33 + 43 + . (n — l).n. n! = — 1)! = — l)(n bn,n > 1. -+- = + 1)2. 4 an—2b2 + 2) an—3b3 + .

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