CBSE Class 9 Maths Important Questions

Below are 10 important questions from Class 9 Maths chapters that are important for preparing well and understanding concepts easily.

1. What is the standard form of a number?

Ans: The standard form, or scientific notation, expresses numbers as a product of a number between 1 and 10 and a power of 10. For example, the number 5000 can be written as $5 \times 10^3$. To convert to standard form, move the decimal point to create a number between 1 and 10, then count how many places you moved it to determine the exponent of 10.

2. Explain the properties of rational numbers.

Ans: Rational numbers are numbers that can be expressed as the ratio of two integers, $ \dfrac{p}{q}$, where $q \neq 0$. Important properties include: (1) Closure under addition, subtraction, multiplication, and division (except by zero), (2) The existence of additive and multiplicative identities (0 and 1), and (3) The existence of additive inverses (e.g., a and -a).

3. Solve the linear equation: 3x + 5 = 20.

Ans: To solve for x, first subtract 5 from both sides:  

3x = 15.  

Then, divide both sides by 3:  

x = 5.  

Therefore, the solution to the equation is x = 5.

4. Find the area of a triangle with a base of 10 cm and height of 5 cm.

Ans: The area of a triangle is given by the formula:  

$\text{Area} = \dfrac{1}{2} \times \text{base} \times \text{height}$  

Substituting the values:  

$\text{Area} = \dfrac{1}{2} \times 10 \times 5 = 25  \text{cm}^2$.  

So, the area of the triangle is 25 $\text{cm}^2$.

5. What are the types of angles? Explain.

Ans: Angles can be classified into several types: 

(1) Acute angle (less than 90°), 

(2) Right angle (exactly 90°), 

(3) Obtuse angle (more than 90° but less than 180°), 

(4) Straight angle (exactly 180°), and 

(5) Reflex angle (more than 180°). 

Understanding these types helps in solving geometric problems effectively.

6. Calculate the volume of a cylinder with a radius of 3 cm and height of 7 cm.

Ans: The formula for the volume of a cylinder is:  

$[\text{Volume} = \pi r^2 h]$  

Substituting the values:  

$\text{Volume} = \pi \times (3)^2 \times 7 = 63\pi \text{cm}^3$.  

Thus, the volume of the cylinder is approximately 197.82 $ \text{cm}^3$ when $\pi$ is approximated as 3.14.

7. Prove that the sum of angles in a triangle is 180°.

Ans: To prove this, consider a triangle ABC. Draw a line parallel to BC through point A. The angles formed at point A and along the line are alternate interior angles. The angles at A, B, and C will then form a straight line. Since a straight line is 180°, the sum of angles in triangle ABC is 180°.

8. What is the Pythagorean theorem? Give an example.

Ans: The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):  

$c^2 = a^2 + b^2$.  

For example, if a triangle has sides of length 3 cm and 4 cm, the hypotenuse would be:  

$c^2 = 3^2 + 4^2 = 9 + 16 = 25$ 

So, c = 5 cm.

9. Find the mean of the following numbers: 4, 8, 6, 10, 12.

Ans: The mean is calculated by adding all the numbers and dividing by the total count.  

$\text{Mean} = \dfrac{4 + 8 + 6 + 10 + 12}{5} $=$ \dfrac{40}{5} = 8$.  

Therefore, the mean of these numbers is 8.

10. What is the formula for the circumference of a circle?

Ans: The circumference (C) of a circle is given by the formula:  

C = 2$\pi$ r,  

where r is the radius. For example, if the radius is 5 cm, then:  

C = 2$ \times \pi \times$ 5 = 10$\pi$ cm.  

Thus, the circumference is approximately 31.42 cm when $\pi$ is taken as 3.14. 

Here are some key questions for Class 9 Maths. To improve your understanding of each chapter, refer to the Chapter-wise Important Questions table. This resource will help you to understand the main concepts and prepare effectively for your exams.

How do Maths Important Questions Class 9 Help You with Exams?

• Practising important questions helps students focus on key concepts that are frequently tested in exams. This targeted preparation makes studying more efficient and boosts confidence.

• Working through these questions enhances problem-solving skills, allowing students to tackle various maths problems with ease. Familiarity with different formats reduces anxiety on exam day.

• Important questions reinforce essential formulas and methods, ensuring students understand how to apply maths principles. This knowledge helps improve performance and scores.

• Reviewing these questions provides a structured way to revise all chapters, covering everything needed before the exam. This comprehensive review boosts overall readiness and confidence.

Vedantu's Class 9 Maths Important Questions offer students a valuable resource for effective exam preparation. By focusing on key concepts and problem-solving techniques, these questions help students build a strong foundation in mathematics. Regular practice not only enhances understanding but also gives confidence when facing various types of problems in exams. Additionally, the structured approach to revision ensures that all essential topics are covered, making study sessions more efficient. With Vedantu's support, students can navigate their Class 9 Maths syllabus with ease, ultimately leading to improved performance and higher scores.

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