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Mathematics Basic Formulae

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Basic Mathematics Formulae for school students and teachers

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Mathematics Basic Formulae

  1. 1. List of Basic Formulae in Mathematics for Students M. D. Raghu
  2. 2. BASIC FORMULAE FOR STUDENTS MATHEMATICS ยฉ2014 MDR www.learningforknowledge.com/glg ๐’™ ๐’Ž. ๐’™ ๐’ = ๐’™ ๐’Ž+๐’ ๐’™ ๐’Ž ๐’™ ๐’ = ๐’™ ๐’Žโˆ’๐’ ๐’™ ๐’Ž ๐’ = ๐’™ ๐’Ž๐’ ๐’™ ๐’‘ ๐’’ = ๐’’ ๐’™ ๐’‘ Algebra Indices Logarithms ๐‘ฐ๐’‡ ๐’š = ๐’ƒ ๐’™ ๐’•๐’‰๐’†๐’ ๐’™ = log ๐’ƒ ๐’š log ๐’ƒ ๐’™๐’š = log ๐’ƒ ๐’™ + log ๐’ƒ ๐’š log ๐’ƒ ๐’™ ๐’š = log ๐‘ ๐’™ โˆ’ log ๐’ƒ ๐’š log ๐’ƒ ๐’™ ๐’ = ๐’ log ๐’ƒ ๐’™ log ๐’‚ ๐’™ = log ๐‘ ๐’™ log ๐’ƒ ๐’‚
  3. 3. BASIC FORMULAE FOR STUDENTS MATHEMATICS ยฉ2014 MDR www.learningforknowledge.com/glg Arithmetic ๐’ ๐’•๐’‰ ๐’•๐’†๐’“๐’Ž ๐’• ๐’ = ๐’‚ + ๐’ โˆ’ ๐Ÿ ๐’… ๐‘ด๐’†๐’‚๐’ ๐’…๐’Š๐’‡๐’‡๐’†๐’“๐’†๐’๐’„๐’† ๐’… = ๐’• ๐’+๐Ÿ โˆ’ ๐’• ๐’ ๐‘บ๐’–๐’Ž ๐’๐’‡ ๐’ ๐’•๐’†๐’“๐’Ž๐’” ๐’” ๐’ = ๐’ ๐Ÿ ๐Ÿ๐’‚ + ๐’ โˆ’ ๐Ÿ ๐’… ๐’” ๐’ = ๐’‚ ๐Ÿโˆ’๐’“ ๐’ ๐Ÿโˆ’๐’“ , ๐’“ โ‰  ๐Ÿ ๐’• ๐’ = ๐’‚ ๐’“ ๐’โˆ’๐Ÿ ๐’“ = ๐’• ๐’ ๐’• ๐’โˆ’๐Ÿ ๐’”โˆž = ๐’‚ ๐Ÿโˆ’๐’“ , ๐’“ < ๐Ÿ Arithmetic Series ๐‘Ž, ๐‘Ž + ๐‘‘, ๐‘Ž + 2๐‘‘, โ€ฆ Geometric Series ๐‘Ž, ๐‘Ž๐‘Ÿ, ๐‘Ž๐‘Ÿ2, โ€ฆ
  4. 4. BASIC FORMULAE FOR STUDENTS MATHEMATICS ยฉ2014 MDR www.learningforknowledge.com/glg ๐‘ด๐’Š๐’…๐’‘๐’๐’Š๐’๐’• ๐’™ ๐Ÿ + ๐’™ ๐Ÿ ๐Ÿ , ๐’š ๐Ÿ + ๐’š ๐Ÿ ๐Ÿ ๐‘ฎ๐’“๐’‚๐’…๐’Š๐’†๐’๐’• ๐’Ž = ๐’š ๐Ÿ โˆ’ ๐’š ๐Ÿ ๐’™ ๐Ÿ โˆ’ ๐’™ ๐Ÿ ๐‘ซ๐’Š๐’”๐’•๐’‚๐’๐’„๐’† ๐’™ ๐Ÿ โˆ’ ๐’™ ๐Ÿ ๐Ÿ + ๐’š ๐Ÿ โˆ’ ๐’š ๐Ÿ ๐Ÿ ๐‘ท๐’‚๐’“๐’‚๐’๐’๐’†๐’ ๐‘ณ๐’Š๐’๐’†๐’” ๐’Ž ๐Ÿ = ๐’Ž ๐Ÿ ๐‘ท๐’†๐’“๐’‘๐’†๐’๐’…๐’Š๐’„๐’–๐’๐’‚๐’“ ๐‘ณ๐’Š๐’๐’†๐’” ๐’Ž ๐Ÿ ๐’Ž ๐Ÿ = โˆ’๐Ÿ Analytical Geomtery Line Coordinates and Gradients
  5. 5. BASIC FORMULAE FOR STUDENTS MATHEMATICS ยฉ2014 MDR www.learningforknowledge.com/glg ๐‘จ๐’™๐’†๐’” ๐‘ฐ๐’๐’•๐’†๐’“๐’„๐’†๐’‘๐’• ๐’™ ๐’‚ + ๐’š ๐’ƒ = ๐Ÿ ๐‘ซ๐’Š๐’”๐’•๐’‚๐’๐’„๐’† ๐’๐’‡ ๐’‘๐’๐’Š๐’๐’• ๐’™ ๐Ÿ, ๐’š ๐Ÿ ๐’‡๐’“๐’๐’Ž ๐’๐’Š๐’๐’† ๐’‚๐’™ + ๐’ƒ๐’š + ๐’„ = ๐ŸŽ ๐’‚๐’™ ๐Ÿ + ๐’ƒ๐’š ๐Ÿ + ๐’„ ๐’‚ ๐Ÿ + ๐’ƒ ๐Ÿ ๐‘บ๐’Š๐’๐’ˆ๐’๐’† ๐‘ท๐’๐’Š๐’๐’• ๐’š โˆ’ ๐’š ๐Ÿ = ๐’Ž ๐’™ โˆ’ ๐’™ ๐Ÿ ๐‘บ๐’๐’๐’‘๐’† ๐‘ฐ๐’๐’•๐’†๐’“๐’„๐’†๐’‘๐’• ๐’š = ๐’Ž๐’™ + ๐’„ Analytical Geomtery Line Equations
  6. 6. BASIC FORMULAE FOR STUDENTS MATHEMATICS ยฉ2014 MDR www.learningforknowledge.com/glg ๐’”๐’Š๐’ ๐œฝ = ๐’š ๐’“ ๐’„๐’๐’” ๐œฝ = ๐’™ ๐’“ ๐’•๐’‚๐’ ๐œฝ = ๐’š ๐’™ ๐’„๐’๐’”๐’†๐’„ ๐œฝ = ๐’“ ๐’š ๐’”๐’†๐’„ ๐œฝ = ๐’“ ๐’™ ๐’„๐’๐’• ๐œฝ = ๐’™ ๐’š Trigonometry Ratios x y r ฮธ
  7. 7. BASIC FORMULAE FOR STUDENTS MATHEMATICS ยฉ2014 MDR www.learningforknowledge.com/glg cosโˆ’1 ๐’™ ๐’“ = ๐œฝ sinโˆ’1 ๐’š ๐’“ = ๐œฝ tanโˆ’1 ๐’š ๐’™ = ๐œฝ cotโˆ’1 ๐’™ ๐’š = ๐œฝ cosecโˆ’1 ๐’“ ๐’š = ๐œฝ secโˆ’1 ๐’“ ๐’™ = ๐œฝ Trigonometry Inverse of Ratios x y r ฮธ
  8. 8. BASIC FORMULAE FOR STUDENTS MATHEMATICS ยฉ2014 MDR www.learningforknowledge.com/glg tan ๐œฝ = sin ๐œฝ cos ๐œฝ tan2 ฮธ + 1= sec2 ฮธ sin2 ฮธ + cos2 ฮธ = 1 cosec ๐œฝ = ๐Ÿ sin ๐œฝ Trigonometry Identities sec ๐œฝ = ๐Ÿ cos ๐œฝ cot ๐œฝ = cos ๐œฝ sin ๐œฝ cot2 ฮธ + 1= cosec2 ฮธ tan ฮธ ร— cot ฮธ = 1
  9. 9. BASIC FORMULAE FOR STUDENTS MATHEMATICS ยฉ2014 MDR www.learningforknowledge.com/glg Trigonometry Products 2 cos ๐ด cos ๐ต = cos ๐ด โˆ’ ๐ต + cos ๐ด + ๐ต 2 cos ๐ด sin ๐ต = sin ๐ด + ๐ต โˆ’ sin ๐ด โˆ’ ๐ต 2 sin ๐ด cos ๐ต = sin ๐ด + ๐ต + sin ๐ด โˆ’ ๐ต 2 sin ๐ด sin ๐ต = cos ๐ด โˆ’ ๐ต โˆ’ cos ๐ด + ๐ต
  10. 10. BASIC FORMULAE FOR STUDENTS MATHEMATICS ยฉ2014 MDR www.learningforknowledge.com/glg Trigonometry Sums cos ๐ถ + cos ๐ท = 2 cos ๐ถ + ๐ท 2 ร— cos ๐ถ โˆ’ ๐ท 2 sin ๐ถ โˆ’ sin ๐ท = 2 cos ๐ถ + ๐ท 2 ร— sin ๐ถ โˆ’ ๐ท 2 cos ๐ถ โˆ’ cos ๐ท = โˆ’2 sin ๐ถ + ๐ท 2 ร— sin ๐ถ โˆ’ ๐ท 2 sin ๐ถ + sin ๐ท = 2 sin ๐ถ + ๐ท 2 ร— cos ๐ถ โˆ’ ๐ท 2
  11. 11. BASIC FORMULAE FOR STUDENTS MATHEMATICS ยฉ2014 MDR www.learningforknowledge.com/glg tan ๐ด โˆ’ ๐ต = tan ๐ด โˆ’ tan ๐ต 1 + tan ๐ด tan ๐ต sin ๐ด โˆ’ ๐ต = sin ๐ด cos ๐ต โˆ’ cos ๐ด sin ๐ต cos ๐ด + ๐ต = cos ๐ด cos ๐ต โˆ’ sin ๐ด sin ๐ต sin ๐ด + ๐ต = sin ๐ด cos ๐ต + cos ๐ด sin ๐ต cos ๐ด โˆ’ ๐ต = cos ๐ด cos ๐ต + sin ๐ด sin ๐ต tan ๐ด + ๐ต = tan ๐ด + tan ๐ต 1 โˆ’ tan ๐ด tan ๐ต Trigonometry Compound Angles
  12. 12. BASIC FORMULAE FOR STUDENTS MATHEMATICS ยฉ2014 MDR www.learningforknowledge.com/glg ๐‘ƒ = ๐‘Ž + ๐‘ + ๐‘ ๐ถ = 2๐œ‹๐‘Ÿ ๐‘ƒ = 2 ๐‘™ + 2 ๐‘ ๐ด = ๐‘™ ๐‘ ๐ด = ๐œ‹ ๐‘Ÿ2 ๐ด = 1 2 ๐‘ โ„Ž Geometry Perimeter AreaShape a b c h l b r
  13. 13. BASIC FORMULAE FOR STUDENTS MATHEMATICS ยฉ2014 MDR www.learningforknowledge.com/glg Author: M. D. Raghu glg@learningforknowledge.com Ganit Learning Guides Thank you Design and Layout: www.narayanasoftware.com For exemplars and proofs of formulae Visit: www.learningforknowledge.com/glg

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