# Maths Formulas For Class 10

Maths is an important subject for almost all classes. Starting from kindergarten to higher level education, maths have always been a part. Maths formulas for class 10 are the general formulas which you use in various fields. Whether it’s the field of engineering, medical, commerce, finance, computer science, hardware etc., in almost every aspect of different types of industries, the most common formulas are the maths formulas for class 10, which are generally applied.

Maths formulas for Class 10 involves topics based on real numbers, polynomials, quadratic equations, triangles, circles, statistics, probability, etc. These are the basic formulas which we use in our day to day life. Suppose, if we have to find out the volume of a cylindrical jar, then we use the volume of the cylinder formula, where the height and diameter of the cylindrical jar is known to us.

In the same way, we use Class 10 Maths formulas to find multiple entities and also these formulas are very useful for further education and employment purposes. In the competitive exams, questions are usually based on these maths formulas studied in Class 10. Let us learn about Maths formulas for Class 10 here in this article.

## List of Maths Formulas for Class 10

The basic maths formulas for class 10 are almost same for all the Boards. As we learned about various applications of class 10th maths formulas in the above introduction part. Now let us discuss the list of Maths formulas for class 10 standard topic-wise which is commonly used.

### 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

Where a1, b1, c1, a2, b2, and c2 are all real numbers and a12+b12 ≠ 0 & a22 + b22 ≠ 0

These linear equations can also be represented in graphical form.

### Algebra or algebraic equations

The standard form of Quadratic Equations:

 ax2+bx+c=0 where a ≠ 0 And x = $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Algebraic formulae:

• (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]

### 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)

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 nth term in Arithmetic Progression;

 Sn = n/2 [a + (n-1) d]

### Trigonometry Formulae

Trigonometry maths formulas for Class 10 covers three major functions Sine, Cosine and Tangent for a right-angle triangle. Also, 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 $\angle \theta$.

Sinθ= $\frac{Side opposite to angle \theta}{Hypotenuse}$=$\frac{Perpendicular}{Hypotenuse}$ = P/H

Cosθ = $\frac{Adjacent side to angle \theta}{Hypotenuse}$ = $\frac{Adjacent side}{Hypotenuse}$ = B/H

Tanθ = $\frac{Side opposite to angle \theta}{Adjacent side to angle \theta}$ = P/B

Sec θ = $\frac{1}{cos\theta }$

Cot θ = $\frac{1}{tan\theta }$

Cosec θ = $\frac{1}{sin\theta }$

Tan θ = $\frac{Sin\theta }{Cos\theta }$

Trigonometry Table

 Angle 00 300 450 600 900 Sinθ 0 1/2 $1/\sqrt{2}$ $\sqrt{3}/2$ 1 Cosθ 1 $\sqrt{3}/2$ $1/\sqrt{2}$ 1/2 0 Tanθ 0 1/$\sqrt{3}$ 1 $\sqrt{3}$ Undefined Cotθ Undefined $\sqrt{3}$ 1 $\sqrt{3}$/2 0 Secθ 1 2/$\sqrt{3}$ $\sqrt{2}$ 2 Undefined Cosecθ Undefined 2 $\sqrt{2}$ 2/$\sqrt{3}$ 1

Other Trigonometric formulas

• sin(900 – θ) = cos θ
• cos(900 – θ) = sin θ
• tan(900 – θ) = cot θ
• cot(900 – θ) = tan θ
• sec(900 – θ) = cosecθ
• cosec(900 – θ) = secθ
• sin2θ + cos2 θ = 1
• sec2 θ = 1 + tan2θ for 00 ≤ θ < 900
• Cosec2 θ = 1 + cot2 θ for 00 ≤ θ ≤ 900

### Circles

• Circumference of the circle = 2 π r
• Area of the circle = π r2
• Area of the sector of angle θ = $\frac{\theta }{360}$ X π r2
• Length of an arc of a sector of angle θ = $\frac{\theta }{360}$ X 2 π r

(r = radius of the circle)

### Surface Area and Volumes

Sphere

• Diameter of sphere = 2r
• Circumference of Sphere = 2 π r
• Surface area of sphere = 4 π r2
• Volume of Cylinder = 4/3 π r2

Cylinder

• Circumference of Cylinder = 2 π r h
• Curved surface area of Cylinder = 2 π r2
• Total surface area of Cylinder = Circumference of Cylinder + Curved surface area of Cylinder = 2 π r h + 2 π r2
• Volume of Cylinder = π r2 h

Cone

• Slant height of cone(s) = $\sqrt{r^2 + h^2}$
• Curved surface area of cone = π r s
• Total surface area of cone = π r (s + r)
• Volume of cone = ⅓ π r2 h

Cuboid

• Perimeter of cuboid = 4(l + b +h)
• Length of the longest diagonal of a cuboid = $\sqrt{l^2 + b^2 + h^2}$
• Total surface area of cuboid = 2(l*b + b*h + l*h)
• Volume of Cuboid = l*b*h

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

(I) The mean of the grouped data can be found by 3 methods.

1. Direct Method: $\bar{x}$ = $\frac{\sum_{i=1}^{n}fi xi}{\sum_{i=1}^{n}fi}$

Where fi xi is the sum of observations from value i = 1 to n

And fi is the number of observations from value i = 1 to n

1. Assumed mean method : $\bar{x}$ = a + $\frac{\sum_{i=1}^{n}fi di}{\sum_{i=1}^{n}fi}$
2. Step deviation method : $\bar{x}$ = a + $\frac{\sum_{i=1}^{n}fi ui}{\sum_{i=1}^{n}fi}$ X h

(II) The mode of grouped data;

Mode = l + $\frac{f1 – f0}{2f1 – f0 – f2}$ X h

(III) The median for a grouped data;

Median = l + ($\frac{n/2 – cf}{f}$) X h

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#### Practise This Question

If I ask you to construct PQR ~ ABC exactly (when we say exactly, we mean the exact relative positions of the triangles) as given in the figure, (Assuming I give you the dimensions of ABC and the Scale Factor for PQR) what additional information would you ask for?