# List of Maths Formulas for Class 10 (Chapterwise)

### 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=0a2x+b2+c2=0
Where
• a1, b1, c1, a2, b2, and c2 are all real numbers and
• a12+b12 ≠ 0 & a2+ 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 Quadratic Equations:
 ax2+bx+c=0 where a ≠ 0And x = [-b ± √(b2 – 4ac)]/2a

### Algebraic formulas:

• (a+b)= a+ b+ 2ab
• (a-b)= a+ b– 2ab
• (a+b) (a-b) = a– 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)
• x+ 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

• px p= pm+n
• {pm}⁄{pn} = pm-n
• (pm)= pmn
• p-m = 1/pm
• p1 = p
• P= 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; aa+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 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.
Let a right-angled triangle ABC is right-angled at point B and have Î¸.
Sin Î¸= SideoppositetoangleÎ¸Hypotenuse=PerpendicularHypotenuse = P/H
Tan Î¸ = SideoppositetoangleÎ¸AdjacentsidetoangleÎ¸ = P/B
Sec Î¸ = 1cosÎ¸
Cot Î¸ = 1tanÎ¸
Cosec Î¸ = 1sinÎ¸
Tan Î¸ = SinÎ¸CosÎ¸
Trigonometry Table:
 Angle 0° 30° 45° 60° 90° SinÎ¸ 0 1/2 1/√2 √3/2 1 CosÎ¸ 1 √3/2 1/√2 ½ 0 TanÎ¸ 0 1/√3 1 √3 Undefined CotÎ¸ Undefined √3 1 1/√3 0 SecÎ¸ 1 2/√3 √2 2 Undefined CosecÎ¸ Undefined 2 √2 2/√3 1
Other Trigonometric formulas:
• sin(90° – Î¸) = cos Î¸
• cos(90° – Î¸) = sin Î¸
• tan(90° – Î¸) = cot Î¸
• cot(90° – Î¸) = tan Î¸
• sec(90° – Î¸) = cosecÎ¸
• cosec(90° – Î¸) = secÎ¸
• sin2Î¸ + cos2 Î¸ = 1
• secÎ¸ = 1 + tan2Î¸ for 0° ≤ Î¸ < 90°
• CosecÎ¸ = 1 + cot2 Î¸ for 0° ≤ Î¸ ≤ 90°

### Circles Formulas For Class 10

• Circumference of the circle = 2 Ï€ r
• Area of the circle = Ï€ r2
• Area of the sector of angle Î¸ = (Î¸/360) × Ï€ r2
• Length of an arc of a sector of angle Î¸ = (Î¸/360) × 2 Ï€ 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 Circumference of Sphere 2 Ï€ r Surface area of sphere 4 Ï€ r2 Volume of Cylinder 4/3 Ï€ r2
• Cylinder Formulas
 Circumference of Cylinder 2 Ï€rh Curved surface area of Cylinder 2 Ï€r2 Total surface area of Cylinder Circumference of Cylinder + Curved surface area of Cylinder = 2 Ï€rh + 2 Ï€r2 Volume of Cylinder Ï€ r2 h
• Cone Formulas
 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
• 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.

### Statistics Formulas for Class 10

In class 10, the chapter statistics mostly deals with finding the mean median and standard deviation of grouped data.
(I) The mean of the grouped data can be found by 3 methods.
1. Direct Method: x̅ = ni=1fixini=1fi, where fxis the sum of observations from value i = 1 to n And fis the number of observations from value i = 1 to n
2. Assumed mean method :  = a+ni=1fidini=1fi
3. Step deviation method : x̅ = a+ni=1fiuini=1fi×h
(II) The mode of grouped data:
Mode = l+f1f02f1f0f2×h
(III) The median for a grouped data:

Median = l+n2cff×h

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