mathematics formulae
DESCRIPTION
Find the Formulae in Mathematics for School StudentsTRANSCRIPT
Mathematics Formulae
for School Students
M. D. Raghu
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
ππ .ππ=ππ+π
ππ
ππ =ππβπ
(ππ)π=πππ
πππ=
πβππ
Algebra
Indices Logarithms
logπππ=logππ+ logππ
logπππ
=logπ πβ logπ π
logπππ=π logππ
logππ=logππlogππ
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Algebra
Quadratic Equations
(π2βπ2 )=(πβπ)(π+π)
(πβπ)2=π2β2ππ+π2(π+π )2=π2+2ππ+π2
Binomial Expansion
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Algebra
Binomial Theorem
hπ€ πππππΆπ=π !
(πβπ )!Γπ !
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Arithmetic
ππ=πππβπ
π=ππππβπ
Arithmetic Series
π ,π+π ,π+2π ,β¦Geometric Series
π ,ππ ,ππ2 ,β¦
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Arithmetic
Complex Numbers
(ππΒ± ππ )=ππ . ππ
π π=|π|π
|ππ . ππ|=|ππ||ππ|
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Arithmetic
Parametric Complex Numbers
De Moivreβs Theorem
(ππ¨π¬π½+ππ¬π’π§ π½ )π=ππ¨π¬ππ½+ππ¬π’π§ππ½
π=π (ππ¨π¬π½+ππ¬π’π§ π½ )
π=|π|=βππ+ππ
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Analytical Geomtery
Line Coordinates and Gradients
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Analytical Geomtery
Line Equations
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
ππππ½=ππ
πππ π½=ππ
ππππ½=ππ
πππππ π½=ππ
πππ π½=ππ
πππ π½=ππ
Trigonometry
Ratios
x
y
r
ΞΈ
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
cosβ1ππ
=π½
sinβ1ππ
=π½
tanβ1ππ
=π½ cotβ1ππ
=π½
c o se cβ1ππ
=π½
secβ1ππ
=π½
Trigonometry
Inverse of Ratios
x
y
r
ΞΈ
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
tanπ½=ΒΏsinπ½cosπ½
ΒΏ
tan 2π½+1=sec 2π½
sin 2π½+cos2π½=1
cosec π½=πsin π½
Trigonometry
Identities
secπ½=πcosπ½
cot π½=cosπ½sin π½
cot 2π½+1=cosec 2π½
tan π½Γcot π½=1
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Trigonometry
Products
2cos π΄ cosπ΅=cos (π΄βπ΅ )+cos ( π΄+π΅ )
2cos π΄ sinπ΅=sin ( π΄+π΅ )β sin ( π΄βπ΅ )
2sin π΄ cosπ΅=sin ( π΄+π΅ )+sin ( π΄βπ΅ )
2sin π΄sin π΅=cos ( π΄βπ΅ )β cos ( π΄+π΅ )
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Trigonometry
Sums
cosπΆ+cosπ·=2cos(πΆ+π· )2
Γ cos(πΆβπ· )2
sinπΆβsinπ·=2cos(πΆ+π· )2
Γsin(πΆβπ· )2
cosπΆβ cosπ·=β2sin(πΆ+π· )2
Γsin(πΆβπ· )2
sinπΆ+sinπ·=2sin(πΆ+π· )2
Γcos(πΆβπ· )2
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
tan ( π΄βπ΅ )= tan π΄β tanπ΅1+ tan π΄ tanπ΅
sin ( π΄βπ΅ )=sin π΄cos π΅β cos π΄ sinπ΅
cos ( π΄+π΅ )=cos π΄cos π΅β sin π΄sinπ΅
sin ( π΄+π΅ )=sin π΄ cosπ΅+cos π΄sinπ΅
cos ( π΄βπ΅ )=cos π΄ cosπ΅+sin π΄sinπ΅
tan ( π΄+π΅ )= tan π΄+ tanπ΅1β tan π΄ tanπ΅
Trigonometry
Compound Angles
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
π¨=πππππ½
π πππ ππππ=πππΒ°
ππ=ππ+ππβπππcosπ¨
πsin π¨
=π
sinπ©=
πsinπͺ
π=π π½
π¨=ππππsinπͺ
Trigonometry
Rules
Sine Rule
Cosine Rule
Area of a triangle
Radians
Length of arc
Area of sector
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Trigonometry
General Solutions
sin (90βπ)=cosπ
cos (90βπ )=sinπ
tan (90βπ )=cot π
Complementary angles Multiple angles
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
π=2π+2π π΄=ππ
πΆ=2π π π΄=π π2
Geometry
Perimeter AreaShape
a
b
ch
l
b
r
π=π+π+π π΄=12π h
π =12(π+π+π) π΄=βπ (π βπ ) (π βπ) (π βπ )
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Geometry
Surface AreaShape Volume
π=43π π3
π=π π2h
Sphere
Cylinder
Cone
π=13ππ2h
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Geometry
Surface AreaShape Volume
π=π3
π= hππ
π= (π΅π΄ )h
Cube
Cuboid
Prism
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Geometry
Conic Sections
π₯2
π2+ π¦2
π2=1
AlgebraicShape Parametric
Circle
Ellipse
Hyperbolae
π₯2
π2βπ¦ 2
π2=1 π₯=π sec π , π¦=π tan π
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Geometry
Conic Sections
π₯2=4ππ¦
Algebraic EquationShape
Parabola
General Equation to a Conic
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Calculus
Limits
limπ₯β 0
sinππ
=1 limπββ
ππ₯π
=π
Incremental Limits
ππ¦ππ₯
= π β² (π₯ )=limhβ0
π (π₯+h )β π (π₯)h
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Calculus
Differentiation
πΊππ£ππ π¦= π (π₯ )πππ π¦ β²= π β² (π₯ )=ππ¦ππ₯
c 0
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Calculus
Differentiation Rules
πΊππ£πππ’= π (π₯ )πππ π£=π (π₯ )
Product Rule Quotient Rule
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Calculus
Differentiation Rules
πΊππ£πππ’=π (π₯ )πππ π¦= π (π’)
ππ¦ππ₯
=ππ¦ππ’.ππ’ππ₯
Chain Rule or Composite Function Rule
Gradient
ππ¦ππ₯
ππ π (π₯ )ππ‘ πππππ‘ (π₯1 , π¦1 )=π
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Calculus
Integration
k
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Calculus
Integration Rules
β«π
π
π β² (π₯ )β π₯= π (π)β π (π)
β« π (π₯ )π (π₯ )β π₯= π (π₯ )β«π (π₯ )β π₯ββ¬π (π₯ )β π₯ππ (π₯)β π₯
Volume Integral
π=πβ«π
π
π¦2β π₯
FORMULAEFOR STUDENTSMATHEMATICS
Β©2014 MDR www.learningforknowledge.com/glg
Author: M. D. Raghu
Email: [email protected]
Ganit Learning Guides
Thank you
Design-Layout: www.narayanasoftware.com
For exemplars and proofs of formulae
Visit: www.learningforknowledge.com/glg