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
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Linear Equations
[vc_table vc_table_theme=”classic”]One%20Variable,ax%2Bb%3D0,a%E2%89%A00%20and%20a%26b%20are%20real%20numbers|Two%20variable,ax%2Bby%2Bc%20%3D%200,a%E2%89%A00%20%26%20b%E2%89%A00%20and%20a%2Cb%20%26%20c%20are%20real%20numbers|Three%20Variable,ax%2Bby%2Bc%20%3D%200,a%E2%89%A00%20%2C%20b%E2%89%A00%2C%20c%E2%89%A00%20and%20a%2Cb%2Cc%2Cd%20are%20real%20numbers[/vc_table]Pair of Linear Equations in two variables:
[vc_table vc_table_theme=”classic”]a1x%2Bb1%2Bc1%3D0|a2x%2Bb2%2Bc2%3D0[/vc_table]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 Quadratic Equations:
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]
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;
Sum of nth term in Arithmetic Progression;
Trigonometry Formulas
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.
Trigonometry Table:
[vc_table vc_table_theme=”classic”][]Angle,[]0%C2%B0,[]30%C2%B0,[]45%C2%B0,[]60%C2%B0,[]90%C2%B0|[]Sin%CE%B8,[]0,[]1%2F2,[]1%2F%E2%88%9A2,[]%E2%88%9A3%2F2,[]1|[]Cos%CE%B8,[]1,[]%E2%88%9A3%2F2,[]1%2F%E2%88%9A2,[]%C2%BD,[]0|[]Tan%CE%B8,[]0,[]1%2F%E2%88%9A3,[]1,[]%E2%88%9A3,[]Undefined|[]Cot%CE%B8,[]Undefined,[]%E2%88%9A3,[]1,[]1%2F%E2%88%9A3,[]0|[]Sec%CE%B8,[]1,[]2%2F%E2%88%9A3,[]%E2%88%9A2,[]2,[]Undefined|[]Cosec%CE%B8,[]Undefined,[]2,[]%E2%88%9A2,[]2%2F%E2%88%9A3,[]1[/vc_table]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°
Circles Formulas
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.
- 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
The common formulas from the surface area and volumes chapter in 10th class include the following:
- Sphere Formulas
- Cylinder Formulas
- Cone Formulas
- Cuboid Formulas
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.