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Find the Formulae in Mathematics for School Students
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Mathematics Formulae
for School Students
M. D. Raghu
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
𝒙𝒎 .𝒙𝒏=𝒙𝒎+𝒏
𝒙𝒎
𝒙𝒏 =𝒙𝒎−𝒏
(𝒙𝒎)𝒏=𝒙𝒎𝒏
𝒙𝒑𝒒=
𝒒√𝒙𝒑
Algebra
Indices Logarithms
log𝒃𝒙𝒚=log𝒃𝒙+ log𝒃𝒚
log𝒃𝒙𝒚
=log𝑏 𝒙− log𝒃 𝒚
log𝒃𝒙𝒏=𝒏 log𝒃𝒙
log𝒂𝒙=log𝑏𝒙log𝒃𝒂
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Algebra
Quadratic Equations
(𝑎2−𝑏2 )=(𝑎−𝑏)(𝑎+𝑏)
(𝑎−𝑏)2=𝑎2−2𝑎𝑏+𝑏2(𝑎+𝑏 )2=𝑎2+2𝑎𝑏+𝑏2
Binomial Expansion
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Algebra
Binomial Theorem
h𝑤 𝑒𝑟𝑒𝑛𝐶𝑟=𝑛 !
(𝑛−𝑟 )!×𝑟 !
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Arithmetic
𝒕𝒏=𝒂𝒓𝒏−𝟏
𝒓=𝒕𝒏𝒕𝒏−𝟏
Arithmetic Series
𝑎 ,𝑎+𝑑 ,𝑎+2𝑑 ,…Geometric Series
𝑎 ,𝑎𝑟 ,𝑎𝑟2 ,…
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Arithmetic
Complex Numbers
(𝒛𝟏± 𝒛𝟐 )=𝒛𝟏 . 𝒛𝟐
𝒛 𝒛=|𝒛|𝟐
|𝒛𝟏 . 𝒛𝟐|=|𝒛𝟏||𝒛𝟐|
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Arithmetic
Parametric Complex Numbers
De Moivre’s Theorem
(𝐜𝐨𝐬𝜽+𝒊𝐬𝐢𝐧 𝜽 )𝒏=𝐜𝐨𝐬𝒏𝜽+𝒊𝐬𝐢𝐧𝒏𝜽
𝒛=𝒓 (𝐜𝐨𝐬𝜽+𝒊𝐬𝐢𝐧 𝜽 )
𝒓=|𝒛|=√𝒙𝟐+𝒚𝟐
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Analytical Geomtery
Line Coordinates and Gradients
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Analytical Geomtery
Line Equations
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
𝒔𝒊𝒏𝜽=𝒚𝒓
𝒄𝒐𝒔 𝜽=𝒙𝒓
𝒕𝒂𝒏𝜽=𝒚𝒙
𝒄𝒐𝒔𝒆𝒄 𝜽=𝒓𝒚
𝒔𝒆𝒄 𝜽=𝒓𝒙
𝒄𝒐𝒕 𝜽=𝒙𝒚
Trigonometry
Ratios
x
y
r
θ
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
cos−1𝒙𝒓
=𝜽
sin−1𝒚𝒓
=𝜽
tan−1𝒚𝒙
=𝜽 cot−1𝒙𝒚
=𝜽
c o se c−1𝒓𝒚
=𝜽
sec−1𝒓𝒙
=𝜽
Trigonometry
Inverse of Ratios
x
y
r
θ
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
tan𝜽=¿sin𝜽cos𝜽
¿
tan 2𝜽+1=sec 2𝜽
sin 2𝜽+cos2𝜽=1
cosec 𝜽=𝟏sin 𝜽
Trigonometry
Identities
sec𝜽=𝟏cos𝜽
cot 𝜽=cos𝜽sin 𝜽
cot 2𝜽+1=cosec 2𝜽
tan 𝜽×cot 𝜽=1
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Trigonometry
Products
2cos 𝐴 cos𝐵=cos (𝐴−𝐵 )+cos ( 𝐴+𝐵 )
2cos 𝐴 sin𝐵=sin ( 𝐴+𝐵 )− sin ( 𝐴−𝐵 )
2sin 𝐴 cos𝐵=sin ( 𝐴+𝐵 )+sin ( 𝐴−𝐵 )
2sin 𝐴sin 𝐵=cos ( 𝐴−𝐵 )− cos ( 𝐴+𝐵 )
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Trigonometry
Sums
cos𝐶+cos𝐷=2cos(𝐶+𝐷 )2
× cos(𝐶−𝐷 )2
sin𝐶−sin𝐷=2cos(𝐶+𝐷 )2
×sin(𝐶−𝐷 )2
cos𝐶− cos𝐷=−2sin(𝐶+𝐷 )2
×sin(𝐶−𝐷 )2
sin𝐶+sin𝐷=2sin(𝐶+𝐷 )2
×cos(𝐶−𝐷 )2
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
tan ( 𝐴−𝐵 )= tan 𝐴− tan𝐵1+ tan 𝐴 tan𝐵
sin ( 𝐴−𝐵 )=sin 𝐴cos 𝐵− cos 𝐴 sin𝐵
cos ( 𝐴+𝐵 )=cos 𝐴cos 𝐵− sin 𝐴sin𝐵
sin ( 𝐴+𝐵 )=sin 𝐴 cos𝐵+cos 𝐴sin𝐵
cos ( 𝐴−𝐵 )=cos 𝐴 cos𝐵+sin 𝐴sin𝐵
tan ( 𝐴+𝐵 )= tan 𝐴+ tan𝐵1− tan 𝐴 tan𝐵
Trigonometry
Compound Angles
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
𝑨=𝟏𝟐𝒓𝟐𝜽
𝝅 𝒓𝒂𝒅𝒊𝒂𝒏𝒔=𝟏𝟖𝟎°
𝒂𝟐=𝒃𝟐+𝒄𝟐−𝟐𝒃𝒄cos𝑨
𝒂sin 𝑨
=𝒃
sin𝑩=
𝒄sin𝑪
𝒔=𝒓 𝜽
𝑨=𝟏𝟐𝒂𝒃sin𝑪
Trigonometry
Rules
Sine Rule
Cosine Rule
Area of a triangle
Radians
Length of arc
Area of sector
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Trigonometry
General Solutions
sin (90−𝜃)=cos𝜃
cos (90−𝜃 )=sin𝜃
tan (90−𝜃 )=cot 𝜃
Complementary angles Multiple angles
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
𝑃=2𝑙+2𝑏 𝐴=𝑙𝑏
𝐶=2𝜋 𝑟 𝐴=𝜋 𝑟2
Geometry
Perimeter AreaShape
a
b
ch
l
b
r
𝑃=𝑎+𝑏+𝑐 𝐴=12𝑏 h
𝑠=12(𝑎+𝑏+𝑐) 𝐴=√𝑠 (𝑠−𝑎 ) (𝑠−𝑏) (𝑠−𝑐 )
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Geometry
Surface AreaShape Volume
𝑉=43𝜋 𝑟3
𝑉=𝜋 𝑟2h
Sphere
Cylinder
Cone
𝑉=13𝜋𝑟2h
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Geometry
Surface AreaShape Volume
𝑉=𝑙3
𝑉= h𝑙𝑏
𝑉= (𝐵𝐴 )h
Cube
Cuboid
Prism
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Geometry
Conic Sections
𝑥2
𝑎2+ 𝑦2
𝑏2=1
AlgebraicShape Parametric
Circle
Ellipse
Hyperbolae
𝑥2
𝑎2−𝑦 2
𝑏2=1 𝑥=𝑎 sec 𝜃 , 𝑦=𝑏 tan 𝜃
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Geometry
Conic Sections
𝑥2=4𝑎𝑦
Algebraic EquationShape
Parabola
General Equation to a Conic
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Calculus
Limits
lim𝑥→ 0
sin𝜃𝜃
=1 lim𝑛→∞
𝑎𝑥𝑛
=𝑎
Incremental Limits
𝑑𝑦𝑑𝑥
= 𝑓 ′ (𝑥 )=limh→0
𝑓 (𝑥+h )− 𝑓 (𝑥)h
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Calculus
Differentiation
𝐺𝑖𝑣𝑒𝑛 𝑦= 𝑓 (𝑥 )𝑎𝑛𝑑 𝑦 ′= 𝑓 ′ (𝑥 )=𝑑𝑦𝑑𝑥
c 0
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Calculus
Differentiation Rules
𝐺𝑖𝑣𝑒𝑛𝑢= 𝑓 (𝑥 )𝑎𝑛𝑑 𝑣=𝑔 (𝑥 )
Product Rule Quotient Rule
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Calculus
Differentiation Rules
𝐺𝑖𝑣𝑒𝑛𝑢=𝑔 (𝑥 )𝑎𝑛𝑑 𝑦= 𝑓 (𝑢)
𝑑𝑦𝑑𝑥
=𝑑𝑦𝑑𝑢.𝑑𝑢𝑑𝑥
Chain Rule or Composite Function Rule
Gradient
𝑑𝑦𝑑𝑥
𝑜𝑓 𝑓 (𝑥 )𝑎𝑡 𝑝𝑜𝑖𝑛𝑡 (𝑥1 , 𝑦1 )=𝑚
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Calculus
Integration
k
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Calculus
Integration Rules
∫𝑎
𝑏
𝑓 ′ (𝑥 )ⅆ 𝑥= 𝑓 (𝑏)− 𝑓 (𝑎)
∫ 𝑓 (𝑥 )𝑔 (𝑥 )ⅆ 𝑥= 𝑓 (𝑥 )∫𝑔 (𝑥 )ⅆ 𝑥−∬𝑔 (𝑥 )ⅆ 𝑥𝑑𝑓 (𝑥)ⅆ 𝑥
Volume Integral
𝑉=𝜋∫𝑎
𝑏
𝑦2ⅆ 𝑥
FORMULAEFOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Author: M. D. Raghu
Email: [email protected]
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