# Maths Formulas for Class 9 PDF

Here you will find all the maths formulas for class 9. You can also download these formulas of class 9 in a PDF file and take the printout for fast practice. There are fifteen chapters in NCERT class 9 Maths book. We have included all the formulas for these chapters, including Numbers Systems, Polynomials, Linear Equations, Triangles & Quadrilaterals, Area & Volume, and other vital formulas.

The syllabus of maths for class 9 and class 10 is the same in most topics. But, you will learn the basics in class 9, and things will get a bit complex in class 10. If you are preparing for NTSE or STSE examination, you should clarify the basic concepts in mathematics. So, get all the maths formulas for the class 9 PDF from the download link below and start your preparation today.

Page Contents

## Number Systems Formulas for Class 9

You have already studied about number system in previous classes. Number systems Maths formulas for class 9 include important properties and formulas for Rational Numbers and Real Numbers. You have studied the rational numbers in class 8.

### Rational Number (r)

r = $$\frac{p}{q}$$

where p and q are integers and q≠0.

### Equivalent Rational Number (Fractions)

$$\frac{p}{q}$$ = $$\frac{1}{2}$$ = $$\frac{4}{8}$$ = $$\frac{5}{10}$$ = $$\frac{10}{20}$$ = $$\frac{26}{52}$$ , every number is equivalent fraction of $$\frac{1}{2}$$.
• Every integer is a rational number
• Not all rational numbers are integers
• There can be unlimited (infinite) numbers of rational number between any two given rational numbers.

### Irrational Number (s)

s ≠ $$\frac{p}{q}$$ where, p and q are integers and q≠0. e.g., $$\sqrt{2}$$ is not rational number as it cannot be expressed into p/q form.

### Real Numbers (R)

• Collection of rational numbers and irrational numbers
• Every point on the number line represents a unique real number

#### Decimal Expansion of Real Numbers

• A number is rational number if its decimal expansion is terminating or non-terminating recurring.
• A number is irrational number if its decimal expansion is non-terminating non-recurring.

### Real Number Properties

If r is rational and s is irrational, then r+s and r-s are irrational, and rs and r/s are irrational r≠0.

For the positive real numbers a and b:

1. $$\sqrt{\text{ab}}$$ = $$\sqrt{a}\sqrt{b}$$
2. $$\sqrt{\frac{a}{b}}$$ = $$\frac{\sqrt{a}}{\sqrt{b}}$$
3.$$\left( \sqrt{a} – \sqrt{b} \right)\left( \sqrt{a} + \sqrt{b} \right)\$$= $$a – b$$
4.$$\left( a + \sqrt{b} \right)\left( a – \sqrt{b} \right)$$ = $$a^{2} – b$$
5.$$\left( \sqrt{a} + \sqrt{b} \right)$$^{2} = $$a + 2\sqrt{\text{ab}} + b$$

Let a > 0 be a real number and p and q be rational numbers. Then,

• ap.aq = ap+q
• (ap)q = apq
• apbp = (ab)p
• ap / aq = ap-q
To rationalize the denominators of $$\frac{1}{\sqrt{a} + b}$$ we multiply this by $$\frac{\sqrt{a} – b}{\sqrt{a} – b}$$ , where a and b are integers.

## Polynomials Formulas For Class 9

Here you will find Polynomials maths formulas for class 9 and learn about different types of polynomials. You should know how to solve the polynomials and find the zeroes and degree of these polynomials. You will also find algebraic identities in this section.