Number Systems Class 9 Important Questions Free PDF Download

Mathematics is full of fascinating concepts, and one of the most essential chapters in Class 9 is Number Systems. This chapter lays the groundwork for understanding different types of numbers and their properties, which are crucial for solving complex problems in later topics. From Natural Numbers to Rational and Irrational Numbers, this chapter helps us explore the vast world of numbers and their relationships.

As you prepare for exams, it's important to focus on understanding the core concepts and practising key questions. In this blog, we will explore the Number System Important Questions from Chapter 1, which will not only help you revise efficiently but also build a strong foundation for future topics. These questions will cover all the essential types of numbers, their operations, and how to work with them on a number line.

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In the table given below, we have provided the links to Class 9 Maths Number System extra Questions with Solutions. You can download them without having to share any login info.

Chapter 1 Number Systems Important Questions

1. If the decimal representation of a number is non-terminating, non-repeating then the number is:

a. a natural number                                               b. a rational number

c. a whole number                       d. an irrational number

Answer:

(d) an irrational number

Explanation:

A number with a non-terminating, non-repeating decimal representation is an irrational number. These numbers cannot be expressed as a simple fraction (ratio of two integers). Examples include numbers like π and √2​.

2. Rationalize the denominator: 1/(3+√3+√2)

Answer:

‍1/(3+√3+√2)

Multiple Numerator and denominator by (3-√3-√2)

(1/(3+√3+√2)) x (3-√3-√2)/(3-√3-√2)   

(a+b+c)(a−b−c)=a²−(b+c)²

^‍(3-√3-√2)/ 9−5−2√6  

(3-√3-√2)/ 4−2√6 

3. If x = (√3-√2)/(√3+√2) and y = (√3+√2)/(√3-√2) , then find the value of x² + y² + xy

Answer:

x² = ((√3-√2)/(√3+√2))²

x² = (3 + √6 -√6 - 2 )²

x² = (3 - 2 )²

x² = (1 )²

x² = 1

Same way

y² = 1

xy= ((√3-√2)/(√3+√2)) ((√3+√2)/(√3-√2))

xy= 1

Now substituting values

= 1+1+1

= 3

4. The rational numbers between √2 and √3 are:

a. √2 × √3                                          b. √5

c. √4                       d. 6^1/4

Answer:

‍(d) 6^1/4

Explanation:

√2≈ 1.414

√3≈ 1.732

a. √2 × √3   = √6

√6 ≈ 2.449 

b. √5

√6 ≈ 2.236

b. √5

√5 ≈ 2.236

c. √4

√4 ≈ 2

d. 6^1/4

⁴√6 ≈1.565

5. If x = 2+√3, then the value of 1/x is:

Answer: 

1/x = 1/(2+√3)

Rationalize with (2-√3)

(1/(2+√3))((2-√3) / (2-√3))

(a + b)(a – b) = (a² – b²)

(2-√3) / (4-3)

(2-√3)

Chapter 1 Number Systems Important Formulas

• 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
• (1² + 2² + 3² + ….. + n²) = n ( n + 1 ) (2n + 1)/6
• (1³ + 2³ + 3³ + ….. + n³) = (n(n + 1)/2)²
• Entirety of first n odd numbers = n²
• Entirety of first n even numbers = n(n + 1)
• (a + b)(a – b) = (a² – b²)
• (a + b)² = (a² + b² + 2ab)
• (a – b)² = (a² + b² – 2ab)
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• (a³ + b³) = (a + b)(a² – ab + b²)
• (a³ – b³) = (a – b)(a² + ab + b²)
• (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)
• when a + b + c = 0, then a³ + b³ + c³ = 3abc

Chapter 1 Number Systems Important Questions Concepts

In this chapter, we learn about different types of numbers used in mathematics, how they are related to each other, and how to express them in different forms.

Natural Numbers (N): These are the numbers we use for counting: 1, 2, 3, 4, and so on. Natural numbers do not include zero or any negative numbers.

Whole Numbers (W): Whole numbers include all the natural numbers plus zero. So, the set is: 0, 1, 2, 3, 4, and so on.

Integers (Z): Integers include all whole numbers as well as their negative counterparts. So, the set of integers looks like this: ... -3, -2, -1, 0, 1, 2, 3, ...

Rational Numbers (Q): Rational numbers are numbers that can be written as fractions or ratios of two integers. For example, 1/2, 3/4, 7, and -2 are rational numbers. They include both positive and negative numbers and also numbers that are repeating or terminating decimals.

Irrational Numbers: These are numbers that cannot be written as a simple fraction. Their decimal form goes on forever without repeating. Examples include √2, π (pi), and e. These numbers are not rational because they cannot be expressed as fractions.

Real Numbers (R): Real numbers include both rational and irrational numbers. They form the complete set of numbers that we use in everyday life.

Representation on a Number Line: All real numbers can be represented on a number line, with rational numbers placed at specific points. Irrational numbers, like √2, are also placed on the number line, though they cannot be written exactly in fractional form.

Operations on Numbers: The chapter also explains how to perform operations like addition, subtraction, multiplication, and division on different types of numbers, and how these operations help in solving problems.

Chapter 1 Number Systems Important Questions: Why

Chapter 1: Number Systems is one of the foundational topics in Class 9 Maths. It serves as the building block for many mathematical concepts you will encounter in later grades. Understanding the different types of numbers – like Natural Numbers, Integers, Rational and Irrational Numbers – is crucial for solving real-life problems and advancing in mathematics.

But why are important questions from this chapter so critical? Here are a few reasons:

Clarifies Core Concepts: Important questions help reinforce key ideas such as the classification of numbers, their properties, and how they relate to each other. By practising these questions, you gain a deeper understanding of the concepts, which is essential for tackling more complex topics in the future.

Helps in Exam Preparation: Teachers often focus on certain types of questions that are more likely to appear in exams. By working through important questions, you can get a sense of what the exam may look like, which boosts your confidence and preparation.

Builds Problem-Solving Skills: This chapter involves not only theoretical understanding but also problem-solving. Practicing important questions will help you develop logical thinking and the ability to apply formulas and concepts in various scenarios.

Reinforces Operations on Numbers: One of the key skills in this chapter is performing operations like addition, subtraction, multiplication, and division with different types of numbers. By working on important questions, you improve your ability to perform these operations accurately.

Enhances Time Management: Practicing important questions helps you get used to the structure of math problems and manage your time better during exams. You’ll know how to approach problems efficiently, saving time for other sections.

In conclusion, important questions from the Number Systems chapter are not just about passing exams, but also about developing a solid understanding of how numbers work. By focusing on these key questions, you’ll be well-equipped to tackle any math problem that comes your way! We hope that you practise the above Chapter 1 Maths Class 9 Important Questions and achieve your dream marks.

All the Best!