Math formulas for class 10 | Here’s everything you need to know about math formulas (2024)

Linear equations in one, two, and three variables have the following forms:
Linear Equation in one Variable ax + b=0 Where a ≠ 0 and a & b are real numbers
Linear Equation in Two Variables ax + by + c = 0 Where a ≠ 0 & b ≠ 0 and a, b & c are real numbers
Linear Equation in Three Variables ax + by + cz + d = 0 Where a ≠ 0, b ≠ 0, c ≠ 0 and a, b, c, d are real numbers
The pair of linear equations in two variables are given as:
a1x+b1+c1=0 and a2x+b2+c2=0
Where a1, b1, c1, & a2, b2, c2 are real numbers & a12+b12 ≠ 0 & a22 + b22 ≠ 0
Quick Note: Linear equations can also be represented in graphical form.

To know the algebra formulas for Class 10, first, you need to get familiar with Quadratic Equations.
The Quadratic Formula: For a quadratic equation px2 + qx + r = 0, the values of x which are the solutions of the equation are given by:
Now you know the basic quadratic equation.
Let us now go through the list of algebra formulas for Class 10–
(a+b ) = a+ b22 + 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
(a +b)3 = a3+ b3 + 3ab(a + b)
(a-b)3 = a3 – b3 – 3ab(a – b)
(x – a)(x + b) = x2 + (b – a)x – ab
(x – a)(x – b) = x2 – (a + b)x + ab
(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
x2 + y2 + z2 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
y2 + z2 =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]
Quick Note: These formulas will be important in higher classes and various competitive examinations. So, memorize them and understand them well.

Circle formulas act as a base for Mensuration.
The Class 10 Maths Circle formulas for a circle of radius r are given below:
1. Circumference of the circle = 2 π r2. Area of the circle = π r23. Area of the sector of angle θ = (θ/360) × π r24. Length of an arc of a sector of angle θ = (θ/360) × 2 π r

The Trigonometry Formulas for Class 10 covers the basic trigonometric functions for a right-angled triangle i.e. Sine (sin), Cosine (cos), and Tangent (tan) which can be used to derive Cosecant (cos), Secant (sec), and Cotangent (cot).
Let a right-angled triangle ABC is right-angled at point B and have is one of the other two angles.

Some other trigonometric formulas are given below–
sin (90° – θ) = cos θcos (90° – θ) = sin θtan (90° – θ) = cot θcot (90° – θ) = tan θsec (90° – θ) = cosecθcosec (90° – θ) = secθsin2θ + cos2 θ = 1sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°