All the formulas and equations of all the chapters in mathematics class 10 CBSE ?????
Answers
Answer:
Linear Equations
One Variableax+b=0a≠0 and a&b are real numbersTwo variableax+by+c = 0a≠0 & b≠0 and a,b & c are real numbersThree Variableax+by+cz+d=0a≠0 , b≠0, c≠0 and a,b,c,d are real numbers
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Pair of Linear Equations in two variables:
a1x+b1y+c1=0
a2x+b2y+c2=0
Where
a1, b1, c1, a2, b2, and c2 are all real numbers and
a12+b12 ≠ 0 & a22 + b22 ≠ 0
It should be noted that linear equations in two variables can also be represented in graphical form.
Algebra or Algebraic Equations
The standard form of a Quadratic Equation is:
ax2+bx+c=0 where a ≠ 0
And x = [-b ± √(b2 – 4ac)]/2a
Algebraic formulas:
(a+b)2 = a2 + b2 + 2ab
(a-b)2 = a2 + b2 – 2ab
(a+b) (a-b) = a2 – b2
(x + a)(x + b) = x2 + (a + b)x + ab
(x + a)(x – b) = x2 + (a – b)x – ab
(x – a)(x + b) = x2 + (b – a)x – ab
(x – a)(x – b) = x2 – (a + b)x + ab
(a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – b3 – 3ab(a – b)
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
(x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
(x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
(x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
x2 + y2 =½ [(x + y)2 + (x – y)2]
(x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
x3 + y3= (x + y) (x2 – xy + y2)
x3 – y3 = (x – y) (x2 + xy + y2)
x2 + y2 + z2 -xy – yz – zx = ½ [(x-y)2 + (y-z)2 + (z-x)2]
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Basic formulas for powers
pm x pn = pm+n
{pm}⁄{pn} = pm-n
(pm)n = pmn
p-m = 1/pm
p1 = p
P0 = 1
Arithmetic Progression(AP) Formulas
If a1, a2, a3, a4, a5, a6,… are the terms of AP and d is the common difference between each term, then we can write the sequence as; a, a+d, a+2d, a+3d, a+4d, a+5d,….,nth term… where a is the first term. Now, nth term for arithmetic progression is given as;
nth term = a + (n-1) d
Sum of the first n terms in Arithmetic Progression;
Sn = n/2 [2a + (n-1) d]
Trigonometry Formulas For Class 10
Trigonometry maths formulas for Class 10 cover three major functions Sine, Cosine and Tangent for a right-angle triangle. Also, in trigonometry, the functions sec, cosec and cot formulas can be derived with the help of sin, cos and tan formulas.
Let a right-angled triangle ABC is right-angled at point B and have ∠θ.
Sin θ= SideoppositetoangleθHypotenuse=PerpendicularHypotenuse = P/H
Cos θ = AdjacentsidetoangleθHypotenuse = BaseHypotenuse = B/H
Tan θ = SideoppositetoangleθAdjacentsidetoangleθ = P/B
Sec θ = 1cosθ
Cot θ = 1tanθ