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If you’re in Class 9, you already know Maths can be either your best friend or your biggest headache. The difference? Smart preparation. That’s where these CBSE Class 9 Maths Important Questions step in - they’re like a secret map that tells you which topics are worth extra attention before exams.
Think about it:
And the best part is whether you’re looking for Important Questions Class 9 Maths to practise chapter-wise or a Class 9 Maths Important Questions PDF to keep offline, this guide covers it all. So, if you’re aiming for better marks without drowning in endless problems, you’re in the right place.
Instead of getting lost in random notes, here’s a one-stop table for all Class 9 Maths Important Questions - neatly arranged chapter-wise so you can revise smartly.
Just having a list of Class 9 Maths Important Questions isn’t enough - the real magic happens when you use them the right way. Follow these steps:
Your NCERT is the base for all CBSE exams. Make sure you understand each concept before moving to extra questions.
Pick one chapter at a time - for example, Number Systems, Polynomials, or Triangles - and solve all related important questions.
Don’t just stick to long questions. Solve MCQs, short answer questions, and HOTS (Higher Order Thinking Skills) for balanced preparation.
Whenever you get a question wrong, note the chapter and topic. Revise that part before attempting similar questions again.
If you like studying without distractions, get a Class 9 Maths Important Questions PDF and keep solving even when you’re away from your phone or laptop.
Practising the right CBSE Class 9 Maths Important Questions can make a huge difference in how well you perform in exams. Here’s why these questions matter:
These questions help you apply formulas and theorems, which makes tough topics easier to grasp than just reading theory from your textbook.
The CBSE Class 9 Maths Question Bank includes a variety of questions, from simple to challenging. This helps you prepare for all kinds of problems you might face in exams.
Regularly solving these questions makes you comfortable with the question style and format used by CBSE, so there are no surprises during the exam.
Practising with a timer teaches you how to pace yourself, helping you complete the exam within the allotted time while minimizing mistakes.
As you solve more important questions, you build confidence in your problem-solving abilities, reducing exam anxiety and boosting your performance.
Here are some practical tips to help you improve your marks in Class 9 Maths, along with practising the CBSE Class 9 Maths Important Questions:
This shows you the kind of questions that come in exams and helps you get used to the exam pattern and marking scheme.
Make a list of important formulas and review them every day so you don’t waste time recalling them during the exam.
Set a timer while solving questions to learn how to finish your paper within the exam time and avoid last-minute rush.
Identify which chapters or topics you find difficult and solve extra questions on those to improve your overall score.
Don’t wait to clear your confusion - ask your teacher, classmates, or use trusted resources to stay on track and avoid gaps in learning.
Here are some of the most important questions you must have to know for your Class 9 Maths exam. These questions cover key concepts and will help you prepare effectively for CBSE.
Q1. What is a rational number? Give an example.
Ans. A rational number is any number that can be written as a fraction p/q, where p and q are integers and q ≠ 0. It includes integers, fractions, and finite or repeating decimals. For example, 3/4 and −5 are rational numbers.
Q2. Define an irrational number.
Ans. An irrational number cannot be written as a fraction of two integers. Its decimal form neither ends nor repeats. Examples include √3 and π, which have infinite, non-repeating decimals.
Q3. Explain the difference between rational and irrational numbers.
Ans. Rational numbers can be expressed as fractions where numerator and denominator are integers, and their decimal expansions either terminate or repeat. Irrational numbers cannot be written as fractions and have decimals that go on forever without any pattern, like √2 or π.
Q4. How can you prove that √2 is irrational?
Ans. Suppose √2 = p/q, where p and q are integers with no common factors. Squaring both sides gives 2q² = p², so p² is even, implying p is even. Then, p = 2k for some integer k. Substituting back shows q is even as well, which contradicts that p/q is in simplest form. Thus, √2 is irrational.
Q5. State and explain the Remainder Theorem with an example.
Ans. The Remainder Theorem states that when a polynomial f(x) is divided by (x − a), the remainder is equal to f(a). For example, for f(x) = x³ − 4x² + 5x − 2, dividing by (x − 2), substitute x = 2: f(2) = 8 − 16 + 10 − 2 = 0. Since the remainder is 0, (x − 2) is a factor of f(x).
Q6. How do you check whether (x − 3) is a factor of a polynomial f(x)?
Ans. To check if (x − 3) is a factor, substitute x = 3 in f(x). If the result is zero, then (x − 3) divides f(x) completely. Otherwise, it is not a factor. This method avoids the need for polynomial division.
Q7. Write the distance formula between two points (x₁, y₁) and (x₂, y₂).
Ans. The distance formula is √[(x₂ − x₁)² + (y₂ − y₁)²], which comes from applying the Pythagorean theorem to the difference in x and y coordinates.
Q8. Find the distance between points (3, 4) and (7, 1).
Ans. Distance = √[(7 − 3)² + (1 − 4)²] = √[4² + (−3)²] = √[16 + 9] = √25 = 5 units. So, the two points are 5 units apart.
Q9. What is the slope of a line passing through points (2, 3) and (6, 11)?
Ans. Slope (m) = (11 − 3)/(6 − 2) = 8/4 = 2. This means for every 1 unit increase in x, y increases by 2 units, showing the steepness of the line.
Q10. Write the general form of a linear equation in two variables and explain.
Ans. A linear equation in two variables x and y is expressed as ax + by + c = 0, where a and b are not both zero. This form represents all straight lines in the coordinate plane. The coefficients a and b determine the slope, while c affects the line’s position relative to the origin.
Q11. What is Euclid’s fifth postulate?
Ans. It states that through a point not on a given line, there exists exactly one line parallel to the given line.
Q12. Define corresponding angles when two parallel lines are cut by a transversal.
Ans. Corresponding angles are pairs of angles located at the same relative position at each intersection where the transversal crosses the parallel lines. These angles are equal in measure.
Q13. Explain how to prove two triangles are congruent by SAS criterion.
Ans. Two triangles are congruent by the SAS criterion if two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle. This ensures the triangles are identical in size and shape.
Q14. In triangle ABC, AB = 5 cm, AC = 7 cm, and angle BAC = 60°. Find BC using the cosine rule.
Ans. Using the cosine rule: BC² = AB² + AC² − 2 × AB × AC × cos(angle BAC)
= 5² + 7² − 2 × 5 × 7 × cos 60°
= 25 + 49 − 70 × 0.5 = 74 − 35 = 39
Therefore, BC = √39 ≈ 6.24 cm.
Q15. What is the area of a triangle with base 8 cm and height 6 cm?
Ans. Area = ½ × base × height = ½ × 8 × 6 = 24 cm².
Q16. State Heron’s formula for the area of a triangle.
Ans. If a triangle has sides a, b, and c, and semi-perimeter s = (a + b + c)/2, then its area is √[s(s − a)(s − b)(s − c)]. This formula helps find area when height is unknown.
Q17. How to find the area of a parallelogram?
Ans. The area is calculated by multiplying the base with the perpendicular height between the bases: Area = base × height.
Q18. Explain the relation between the angle subtended by an arc at the center and at the circumference of a circle.
Ans. The angle subtended at the center of a circle by an arc is always twice the angle subtended at any point on the circumference by the same arc. This relationship helps in solving problems related to circle angles.
Q19. Write the formula for the total surface area of a right circular cylinder.
Ans. Total surface area = 2πr(h + r), where r is the radius and h is the height.
Q20. Calculate the volume of a cone with radius 4 cm and height 9 cm.
Ans. Volume of cone = (1/3)πr²h = (1/3) × π × 16 × 9 = 48π ≈ 150.8 cm³.
Q21. Explain how to calculate the mean from a frequency distribution.
Ans. Multiply each data value by its frequency, sum all these products, then divide by the total frequency. This weighted average gives the mean value of the data.
Q22. Describe how to find the median from grouped data.
Ans. First, find the median class where the cumulative frequency exceeds half the total frequency. Use the formula: Median = L + [(N/2 − CF)/f] × h, where L is the lower boundary of the median class, N is total frequency, CF is cumulative frequency before median class, f is frequency of median class, and h is class width.
Q23. What is the difference between perimeter and area?
Ans. Perimeter is the total length around a figure, while area is the amount of surface covered within its boundaries.
Q24. Define the term ‘linear equation in two variables’.
Ans. An equation of the form ax + by + c = 0, where a and b are not zero, representing a straight line on a graph.
Q25. Explain the steps to construct the perpendicular bisector of a line segment using compass and ruler.
Ans. Place the compass at one endpoint and draw arcs above and below the segment wider than half its length. Repeat from the other endpoint. The two arcs intersect at two points; joining these points gives the perpendicular bisector, which divides the segment into two equal parts at 90°.
Q26. Find the midpoint of the line segment joining points A(1, 2) and B(5, 6).
Ans. Midpoint M = ((1 + 5)/2, (2 + 6)/2) = (3, 4).
Q27. Explain how to verify if a quadrilateral is a parallelogram using coordinates.
Ans. Calculate lengths of opposite sides using the distance formula. If both pairs of opposite sides are equal, the quadrilateral is a parallelogram. To confirm, check if diagonals bisect each other by calculating midpoints; equal midpoints indicate bisection.
Q28. How do you find the volume and surface area of a sphere?
Ans. The volume of a sphere is given by (4/3)πr³, and the surface area is 4πr², where r is the radius. These formulas allow calculation of space occupied by the sphere and the area covering its surface.
Q1. What types of questions are asked in Class 9 Maths exams?
Ans. The exam includes very short answers, short answer, long answer, and application-based questions that test understanding of concepts and problem-solving skills.
Q2. How can I improve my problem-solving speed in Maths?
Ans. Regular practice, learning shortcuts, and understanding concepts deeply help improve speed and accuracy in solving problems.
Q3. Is it necessary to memorize all formulas for Class 9 Maths?
Ans. Yes, memorizing key formulas is important, but understanding when and how to apply them is equally crucial for solving problems correctly.
Q4. Will geometry questions be asked in the Class 9 Maths exam 2025-26?
Ans. Yes, geometry is a significant part of the syllabus, including topics like lines, angles, triangles, and quadrilaterals.
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