Here you will find all the maths formulas for class 10. You can also download these formulas of class 10 in a PDF file and take the printout for fast practice. There are fifteen chapters in NCERT class 10 Maths book. We have provided all the formulas for these chapters, including Real Numbers, Polynomials, Linear Equations, Arithmetic Progressions, Quadratic Equations, Trigonometry, Area & Volume, and other important formulas.

Maths formulas for class 10 are the basic formulas that you will need to prepare for the mathematics exam and improve your mathematical skills for higher classes. These basic maths formulas are crucial for every student. We suggest you note down all the important maths formulas for class 10 or take the printout to save your time while studying.

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## Real Numbers

Real number maths formulas include important theorems, algorithms, and Euclid’s division lemma to learn more about real numbers.

### Euclid’s Division Lemma

**Theorem**: For given positive integers a and b, there exist unique integers q and r satisfying,

*a = bq + r, 0 ≤ r < b.*

**Algorithm**: Series of well-defined steps which gives a procedure for solving a type of problem**Lemma:**Proven statement used for proving another statement

### HCF using Euclid’s Division Algorithm

Finding HCF of two number **c** and **d** where **c > d**

**Step 1**: Apply division lemma to get the whole numbers (q and r) such that, c=dq+r, 0≤r**Step 2**: If r=0, d is the HCF of c and d. If r ≠0, apply division lemma to d and r.**Step 3**: Continue the process till the remainder is zero. The divisor at the final stage will be HFC.

### Theorem of Arithmetic

Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

- The prime factorisation of a natural number is unique, except for the order of its factors.
- For any two positive number p and q,
**HCF (p,q) x LCM (p,q) = p x q**

### Rational Number Theorems

- If p is a prime number and a is a positive integer, then if p divides a
^{2}, the p also divides a. - √2 is irrational
- If x is a rational number whose decimal expansion terminates, then x can be expressed in the form of p/q, where p and q are coprime, and the prime factorisation of q is in the form 2
^{n}5^{m}, when n,m are non-negative integers.

LCM (p,q,r) = p.q.r HCF(p,q,r) / HCF(p,q) . HCF(q,r) . HCF(p,r)

HCF (p,q,r) = p.q.r LCM(p,q,r) / LCM(p,q) . LCM(q,r) . LCM(p,r)

## Polynomials

### Degree of polynomials

Highest power of x in a polynomial p(x) is the degree of polynomial.

**Linear polynomials**: Polynomials of degree 1, i.e., 2x-3**Quadric Polynomials:**Polynomials of degree 2, i.e., 3x^{2}-4x+7**Cubic Polynomials:**Polynomials of degree 3, i.e., 4x^{3}+3x^{2}+2x+9

If k is zero of polynomial p(x) = 2x-3, then p(k) = 2x-3 = 0.

Zero of the lineal polynomial ax+b is -b/a = -(constant term)/coefficient of x

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