Class 10 Maths Formulas
List of Maths
Formulas for Class 10
The basic maths
class 10 formulas are almost the same for all the boards. The list of maths
formulas are:
- Pair of Linear Equation in Two Variables Formulas
- Algebra and Quadratic Equation Formulas
- Arithmetic Progression Formulas
- Trigonometry Formulas
- Circle Formulas
- Surface Area and Volume Formulas
- Statistics Formulas
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+b1+c1=0 a2x+b2+c2=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 Quadratic
Equations:
Algebraic Formulas
1.
(a+b)2 = a2 + b2 + 2ab
2.
(a-b)2= a2 + b2 – 2ab
3.
(a+b)(a-b) = a2 – b2
4.
(x + a)(x + b) = x2 + (a + b)x + ab
5.
(x + a)(x – b) = x2 + (a – b)x – ab
6.
(x – a)(x + b) = x2 + (b – a)x – ab
7.
(x – a)(x – b) = x2 – (a + b)x + ab
8.
(a + b)3 = a3 + b3 + 3ab(a + b)
9.
(a – b)3 = a3 – b3 – 3ab(a – b)
10.
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
11.
(x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
12.
(x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
13.
(x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
14.
x3 + y3
+ z3 – 3xyz = (x + y + z)(x2 + y2 + z2
– xy – yz -xz)
15.
x2 + y2
= ½ [(x + y)2 + (x – y)2 ]
16.
(x + a)(x + b)(x + c) = x3
+ (a + b +c)x2 + (ab + bc + ca)x +abc
17.
x3 + y3
= (x + y) (x2 - xy + y2 )
18.
x3 – y3
= (x – y) (x2 + xy + y2 )
19. x2 +
y2 + z2 -xy – yz – zx = ½ [(x-y) 2 + (y-z) 2 + (z-x) 2 ]
Basic formulas for powers
Arithmetic Progression(AP) Formulas
|
nth term = a
+ (n-1) d |
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;
Sum of nth term in
Arithmetic Progression;
|
Sn = n/2 [2a + (n-1)d] |
Trigonometry Formulas For Class 10
Trigonometry
maths formulas for Class 10 covers 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.
Other
Trigonometric formulas
sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°
Trigonometry Table
(r = radius
of the circle)
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) × Ï€ r2
Length of an arc of a sector of angle θ=(θ/360) × 2 Ï€ r
(r = radius of the circle)
The common formulas from the surface
area and volumes chapter in
10th class include the following:
Sphere Formulas
|
Diameter of sphere |
2r |
|
Circumference of Sphere |
2 π r |
|
Surface area of sphere |
4 π r2 |
|
Volume of Cylinder |
4/3 π r3 |
|
Circumference of Cylinder |
2 πrh |
|
Curved surface area of Cylinder |
2 πr2 |
|
Total
surface area of Cylinder |
Circumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr2 |
|
Volume of Cylinder |
Ï€ r2 h |
|
Slant height of cone |
L = √(r2 + h2) |
|
Curved surface area of cone |
Ï€rL |
|
Total surface area of cone |
Ï€r (L + r) |
|
Volume of cone |
⅓ Ï€ r2 h |
|
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.
Statistics Formulas for Class 10
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