Saturday, May 2, 2020

List of Maths Formulas for Class 10 (Chapterwise)

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 Variableax+b=0a≠0 and a&b are real numbers
Two variableax+by+c = 0a≠0 & b≠0 and a,b & c are real numbers
Three Variableax+by+cz+d=0a≠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 & 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 ≠ 0
And 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 θ.
Sin θ= SideoppositetoangleθHypotenuse=PerpendicularHypotenuse = P/H
Cos θ = AdjacentsidetoangleθHypotenuse = AdjacentsideHypotenuse = B/H
Tan θ = SideoppositetoangleθAdjacentsidetoangleθ = P/B
Sec θ = 1cosθ
Cot θ = 1tanθ
Cosec θ = 1sinθ
Tan θ = SinθCosθ
Trigonometry Table:
Angle30°45°60°90°
Sinθ01/21/√2√3/21
Cosθ1√3/21/√2½0
Tanθ01/√31√3Undefined
CotθUndefined√311/√30
Secθ12/√3√22Undefined
CosecθUndefined2√22/√31
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
  • secθ = 1 + tan2θ for 0° ≤ θ < 90°
  • Cosecθ = 1 + cot2 θ for 0° ≤ θ ≤ 90°

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 sphere2r
Circumference of Sphere2 π r
Surface area of sphere4 π r2
Volume of Cylinder4/3 π r2
  • Cylinder Formulas
Circumference of Cylinder2 πrh
Curved surface area of Cylinder2 πr2
Total surface area of CylinderCircumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr2
Volume of Cylinderπ rh
  • Cone Formulas
Slant height of conel = √(r2 + h2)
Curved surface area of coneπrl
Total surface area of coneπr (l + r)
Volume of cone⅓ π rh
  • Cuboid Formulas
Perimeter of cuboid4(l + b +h)
Length of the longest diagonal of a cuboid√(l2 + b2 + h2)
Total surface area of cuboid2(l×b + b×h + l×h)
Volume of Cuboidl × 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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