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Mathematics Basic Formulae
- 1. List of Basic Formulae in Mathematics for Students M. D. Raghu
- 2. BASIC FORMULAE FOR STUDENTS MATHEMATICS ©2014 MDR www.learningforknowledge.com/glg 𝒙 𝒎. 𝒙 𝒏 = 𝒙 𝒎+𝒏 𝒙 𝒎 𝒙 𝒏 = 𝒙 𝒎−𝒏 𝒙 𝒎 𝒏 = 𝒙 𝒎𝒏 𝒙 𝒑 𝒒 = 𝒒 𝒙 𝒑 Algebra Indices Logarithms 𝑰𝒇 𝒚 = 𝒃 𝒙 𝒕𝒉𝒆𝒏 𝒙 = log 𝒃 𝒚 log 𝒃 𝒙𝒚 = log 𝒃 𝒙 + log 𝒃 𝒚 log 𝒃 𝒙 𝒚 = log 𝑏 𝒙 − log 𝒃 𝒚 log 𝒃 𝒙 𝒏 = 𝒏 log 𝒃 𝒙 log 𝒂 𝒙 = log 𝑏 𝒙 log 𝒃 𝒂
- 3. BASIC FORMULAE FOR STUDENTS MATHEMATICS ©2014 MDR www.learningforknowledge.com/glg Arithmetic 𝒏 𝒕𝒉 𝒕𝒆𝒓𝒎 𝒕 𝒏 = 𝒂 + 𝒏 − 𝟏 𝒅 𝑴𝒆𝒂𝒏 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒅 = 𝒕 𝒏+𝟏 − 𝒕 𝒏 𝑺𝒖𝒎 𝒐𝒇 𝒏 𝒕𝒆𝒓𝒎𝒔 𝒔 𝒏 = 𝒏 𝟐 𝟐𝒂 + 𝒏 − 𝟏 𝒅 𝒔 𝒏 = 𝒂 𝟏−𝒓 𝒏 𝟏−𝒓 , 𝒓 ≠ 𝟏 𝒕 𝒏 = 𝒂 𝒓 𝒏−𝟏 𝒓 = 𝒕 𝒏 𝒕 𝒏−𝟏 𝒔∞ = 𝒂 𝟏−𝒓 , 𝒓 < 𝟏 Arithmetic Series 𝑎, 𝑎 + 𝑑, 𝑎 + 2𝑑, … Geometric Series 𝑎, 𝑎𝑟, 𝑎𝑟2, …
- 4. BASIC FORMULAE FOR STUDENTS MATHEMATICS ©2014 MDR www.learningforknowledge.com/glg 𝑴𝒊𝒅𝒑𝒐𝒊𝒏𝒕 𝒙 𝟏 + 𝒙 𝟐 𝟐 , 𝒚 𝟏 + 𝒚 𝟐 𝟐 𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕 𝒎 = 𝒚 𝟐 − 𝒚 𝟐 𝒙 𝟐 − 𝒙 𝟏 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒙 𝟏 − 𝒙 𝟐 𝟐 + 𝒚 𝟏 − 𝒚 𝟐 𝟐 𝑷𝒂𝒓𝒂𝒍𝒍𝒆𝒍 𝑳𝒊𝒏𝒆𝒔 𝒎 𝟏 = 𝒎 𝟐 𝑷𝒆𝒓𝒑𝒆𝒏𝒅𝒊𝒄𝒖𝒍𝒂𝒓 𝑳𝒊𝒏𝒆𝒔 𝒎 𝟏 𝒎 𝟐 = −𝟏 Analytical Geomtery Line Coordinates and Gradients
- 5. BASIC FORMULAE FOR STUDENTS MATHEMATICS ©2014 MDR www.learningforknowledge.com/glg 𝑨𝒙𝒆𝒔 𝑰𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕 𝒙 𝒂 + 𝒚 𝒃 = 𝟏 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒐𝒇 𝒑𝒐𝒊𝒏𝒕 𝒙 𝟏, 𝒚 𝟏 𝒇𝒓𝒐𝒎 𝒍𝒊𝒏𝒆 𝒂𝒙 + 𝒃𝒚 + 𝒄 = 𝟎 𝒂𝒙 𝟏 + 𝒃𝒚 𝟏 + 𝒄 𝒂 𝟐 + 𝒃 𝟐 𝑺𝒊𝒏𝒈𝒍𝒆 𝑷𝒐𝒊𝒏𝒕 𝒚 − 𝒚 𝟏 = 𝒎 𝒙 − 𝒙 𝟏 𝑺𝒍𝒐𝒑𝒆 𝑰𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕 𝒚 = 𝒎𝒙 + 𝒄 Analytical Geomtery Line Equations
- 6. BASIC FORMULAE FOR STUDENTS MATHEMATICS ©2014 MDR www.learningforknowledge.com/glg 𝒔𝒊𝒏 𝜽 = 𝒚 𝒓 𝒄𝒐𝒔 𝜽 = 𝒙 𝒓 𝒕𝒂𝒏 𝜽 = 𝒚 𝒙 𝒄𝒐𝒔𝒆𝒄 𝜽 = 𝒓 𝒚 𝒔𝒆𝒄 𝜽 = 𝒓 𝒙 𝒄𝒐𝒕 𝜽 = 𝒙 𝒚 Trigonometry Ratios x y r θ
- 7. BASIC FORMULAE FOR STUDENTS MATHEMATICS ©2014 MDR www.learningforknowledge.com/glg cos−1 𝒙 𝒓 = 𝜽 sin−1 𝒚 𝒓 = 𝜽 tan−1 𝒚 𝒙 = 𝜽 cot−1 𝒙 𝒚 = 𝜽 cosec−1 𝒓 𝒚 = 𝜽 sec−1 𝒓 𝒙 = 𝜽 Trigonometry Inverse of Ratios x y r θ
- 8. BASIC FORMULAE FOR STUDENTS MATHEMATICS ©2014 MDR www.learningforknowledge.com/glg tan 𝜽 = sin 𝜽 cos 𝜽 tan2 θ + 1= sec2 θ sin2 θ + cos2 θ = 1 cosec 𝜽 = 𝟏 sin 𝜽 Trigonometry Identities sec 𝜽 = 𝟏 cos 𝜽 cot 𝜽 = cos 𝜽 sin 𝜽 cot2 θ + 1= cosec2 θ tan θ × cot θ = 1
- 9. BASIC FORMULAE FOR STUDENTS MATHEMATICS ©2014 MDR www.learningforknowledge.com/glg Trigonometry Products 2 cos 𝐴 cos 𝐵 = cos 𝐴 − 𝐵 + cos 𝐴 + 𝐵 2 cos 𝐴 sin 𝐵 = sin 𝐴 + 𝐵 − sin 𝐴 − 𝐵 2 sin 𝐴 cos 𝐵 = sin 𝐴 + 𝐵 + sin 𝐴 − 𝐵 2 sin 𝐴 sin 𝐵 = cos 𝐴 − 𝐵 − cos 𝐴 + 𝐵
- 10. BASIC FORMULAE FOR STUDENTS MATHEMATICS ©2014 MDR www.learningforknowledge.com/glg Trigonometry Sums cos 𝐶 + cos 𝐷 = 2 cos 𝐶 + 𝐷 2 × cos 𝐶 − 𝐷 2 sin 𝐶 − sin 𝐷 = 2 cos 𝐶 + 𝐷 2 × sin 𝐶 − 𝐷 2 cos 𝐶 − cos 𝐷 = −2 sin 𝐶 + 𝐷 2 × sin 𝐶 − 𝐷 2 sin 𝐶 + sin 𝐷 = 2 sin 𝐶 + 𝐷 2 × cos 𝐶 − 𝐷 2
- 11. BASIC FORMULAE FOR STUDENTS MATHEMATICS ©2014 MDR www.learningforknowledge.com/glg tan 𝐴 − 𝐵 = tan 𝐴 − tan 𝐵 1 + tan 𝐴 tan 𝐵 sin 𝐴 − 𝐵 = sin 𝐴 cos 𝐵 − cos 𝐴 sin 𝐵 cos 𝐴 + 𝐵 = cos 𝐴 cos 𝐵 − sin 𝐴 sin 𝐵 sin 𝐴 + 𝐵 = sin 𝐴 cos 𝐵 + cos 𝐴 sin 𝐵 cos 𝐴 − 𝐵 = cos 𝐴 cos 𝐵 + sin 𝐴 sin 𝐵 tan 𝐴 + 𝐵 = tan 𝐴 + tan 𝐵 1 − tan 𝐴 tan 𝐵 Trigonometry Compound Angles
- 12. BASIC FORMULAE FOR STUDENTS MATHEMATICS ©2014 MDR www.learningforknowledge.com/glg 𝑃 = 𝑎 + 𝑏 + 𝑐 𝐶 = 2𝜋𝑟 𝑃 = 2 𝑙 + 2 𝑏 𝐴 = 𝑙 𝑏 𝐴 = 𝜋 𝑟2 𝐴 = 1 2 𝑏 ℎ Geometry Perimeter AreaShape a b c h l b r
- 13. BASIC FORMULAE FOR STUDENTS MATHEMATICS ©2014 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