class 10 to 12 maths formula
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Linear Equations
One Variable ax+b=0 a≠0 and a&b are real numbers
Two variable ax+by+c = 0 a≠0 & b≠0 and a,b & c are real numbers
Three Variable ax+by+cz+d=0 a≠0 , b≠0, c≠0 and a,b,c,d are real numbers
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
Cosec θ = 1sinθ
Tan θ = SinθCosθ
Trigonometry Table:
Angle 0° 30° 45° 60° 90°
Sinθ 0 1/2 1/√2 √3/2 1
Cosθ 1 √3/2 1/√2 ½ 0
Tanθ 0 1/√3 1 √3 Undefined
Cotθ Undefined √3 1 1/√3 0
Secθ 1 2/√3 √2 2 Undefined
Cosecθ Undefined 2 √2 2/√3 1Swipe left
Other Trigonometric formulas:
sin(90° – θ) = cos θ
cos(90° – θ) = sin θ
tan(90° – θ) = cot θ
cot(90° – θ) = tan θ
sec(90° – θ) = cosecθ
cosec(90° – θ) = secθ
sin2θ + cos2 θ = 1
sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°
Get complete Trigonometry Formulas list here
Circles Formulas For Class 10
Circumference of the circle = 2 π r
Area of the circle = π r2
Area of the sector of angle θ = (θ/360) × π r2
Length of an arc of a sector of angle θ = (θ/360) × 2 π r
(r = radius of the circle)
Surface Area and Volumes Formulas For Class 10
The common formulas from the surface area and volumes chapter in 10th class include the following:
Sphere Formulas
Diameter of sphere 2r
Surface area of sphere 4 π r2
Volume of Sphere 4/3 π r3
Cylinder Formulas
Curved surface area of Cylinder 2 πrh
Area of two circular bases 2 πr2
Total surface area of Cylinder Circumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr2
Volume of Cylinder π r2 h
Cone Formulas
Slant height of cone l = √(r2 + h2)
Curved surface area of cone πrl
Total surface area of cone πr (l + r)
Volume of cone ⅓ π r2 h
Cuboid Formulas
Perimeter of cuboid 4(l + b +h)
Length of the longest diagonal of a cuboid √(l2 + b2 + h2)
Total surface area of cuboid 2(l×b + b×h + l×h)
Volume of Cuboid l × b × h
Here, l = length, b = breadth and h = height In case of Cube, put l = b = h = a, as cube all its sides of equal length, to find the surface area and volumes.