CBSE Class 10 Maths Important Questions 2025-26

Mathematics is one of the most important subjects for Class 10 students. In the CBSE Class 10 board exams, maths not only helps in scoring good marks but also builds a strong base for higher studies. Many students feel that maths is a difficult subject, but the truth is that with the right practice and preparation, it becomes one of the easiest subjects to score high.

The best way to prepare for exams is to focus on CBSE Class 10 Maths Important Questions 2025–26. These questions are carefully chosen from each chapter of the NCERT textbook and cover the most expected and frequently asked topics in board exams. By solving these, students can revise the whole syllabus in less time and understand the key areas where they need more practice.

Class 10 Important questions also help in building confidence. Since they are based on previous year papers, sample papers, and exam trends, they give students an idea of the type of problems that may come in the actual exam. Regular practice of these class 10 maths important questions improves accuracy, speed, and problem-solving ability.

In the 2025–26 session, CBSE has continued to focus on application-based learning. This means that solving important questions will not only help students prepare for direct problems but also for word problems and case study-based questions. Each chapter, from Real Numbers to Probability, has its own set of important problems that should not be skipped.

So, if you are aiming to score full marks in maths, make sure to solve all the important questions for class 10 maths 2025–26. They are the perfect tool to revise smartly, practice effectively, and walk into the exam hall with confidence.

CBSE Class 10 Maths Important Questions

Class 10 Maths Chapter 1 Important Questions – Real Numbers

1. Use Euclid’s Division Lemma to find the HCF of 867 and 255.
2. Prove that √5 is irrational.
3. Express 3825 as a product of its prime factors.
4. Find the LCM and HCF of 336 and 54 by prime factorization method and verify that LCM × HCF = product of the numbers.
5. Show that every positive integer can be expressed as the product of its prime factors in a unique way.
6. Find the largest number that exactly divides 504 and 980.
7. Without actual division, find whether 7ⁿ can end with the digit 0 for any natural number n.

Do Check: CBSE Class 10 Maths Syllabus

Class 10 Maths Chapter 2 Important Questions – Polynomials

1. Find the zeros of the polynomial x² – 5x + 6 and verify the relationship between zeros and coefficients.
2. Divide p(x) = x³ – 3x² + x + 2 by (x – 2) and verify the division algorithm.
3. If α and β are the zeros of the quadratic polynomial f(x) = 2x² – 5x + k, find k if α + β = 5/2.
4. Find a quadratic polynomial whose zeros are –3 and 4.
5. If one zero of the polynomial 3x² – 10x + k is 5/3, find the value of k and the other zero.
6. Find the remainder when x³ + 3x² + 3x + 1 is divided by (x + 1).
7. Verify that 2 and –2 are zeros of the polynomial p(x) = x⁴ – 4x² + 4.

Class 10 Maths Chapter 3 Important Questions – Pair of Linear Equations in Two Variables

1. Solve the following system of equations using elimination method:
   2x + 3y = 13, x – y = 1.
2. Solve for x and y:
   7x – 15y = 2, x + 2y = 3.
3. The sum of a two-digit number and the number obtained by reversing its digits is 66. If the digits differ by 2, find the number.
4. Two years later, a father’s age will be twice the age of his son. Two years ago, the father’s age was three times that of his son. Find their present ages.
5. Solve graphically: x – y = 1 and 3x + 2y = 12.
6. A boat goes 16 km downstream in 2 hours and returns the same distance upstream in 4 hours. Find the speed of the boat in still water and the speed of the stream.
7. A fraction becomes 1/3 when 1 is subtracted from the numerator and 1 is added to the denominator. If we add 1 to the numerator and subtract 1 from the denominator, the fraction becomes 3/2. Find the fraction.

Class 10 Maths Chapter 4 Important Questions – Quadratic Equations

1. Solve the quadratic equation by factorization: x² – 5x + 6 = 0.
2. Solve 2x² – 7x + 3 = 0 using the quadratic formula.
3. The sum of the squares of two consecutive odd integers is 290. Find the integers.
4. The product of two consecutive positive integers is 306. Find the integers.
5. A train travels 120 km at a uniform speed. If the speed had been 10 km/h more, it would have taken 36 minutes less. Find the speed of the train.
6. The difference of squares of two numbers is 180. If the difference of the numbers is 6, find the numbers.
7. A motorboat, whose speed is 18 km/h in still water, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Class 10 Maths Chapter 5 Important Questions – Arithmetic Progression (AP)

1. Which term of the AP: 7, 13, 19, … is 205?
2. Find the sum of first 25 terms of the AP: 7, 10, 13, …
3. The 17th term of an AP is 5 more than twice its 8th term. If the 11th term is 43, find the AP.
4. If the sum of the first n terms of an AP is 3n² + 5n, find the AP.
5. The sum of first 14 terms of an AP is 1050 and its first term is 10. Find the 14th term.
6. How many terms of the AP: 9, 17, 25, … must be taken to give a sum of 636?
7. Find the sum of first 20 multiples of 7.

Class 10 Maths Chapter 6 Important Questions – Triangles

1. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
2. In ∆ABC, DE || BC and D, E are points on AB and AC respectively. Prove that AD/AB = AE/AC.
3. Using Pythagoras theorem, prove that in a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.
4. Two poles of heights 6 m and 11 m stand on a level ground. If the distance between the poles is 12 m, find the distance between their tops.
5. A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.

Do Check: CBSE Class 10 Maths Notes

Class 10 Maths Chapter 7 Important Questions – Coordinate Geometry

1. Find the distance between the points (3, –4) and (–1, 2).
2. If P(–3, 2) and Q(7, 8), find the coordinates of the point dividing PQ in the ratio 3:2 internally.
3. The vertices of a triangle are A(1, 1), B(4, 5), and C(–3, 7). Find the area of the triangle.
4. Show that the points A(1, 2), B(3, 6), C(5, 10) are collinear.
5. Find the coordinates of the centroid of a triangle whose vertices are (2, –1), (–3, 4), and (–1, –6).

Class 10 Maths Chapter 8 Important Questions – Introduction to Trigonometry

1. Evaluate: sin²30° + cos²30°.
2. Find the value of: 2tan²45° + cos²60° – sin²90°.
3. Prove that: (1 + cot²A) = cosec²A.
4. If cos θ = 3/5, find the values of sin θ and tan θ.
5. Prove: (sinA + cosA)² + (sinA – cosA)² = 2.

Class 10 Maths Chapter 9 Important Questions – Applications of Trigonometry

1. A balloon is tied to a rope that makes an angle of 60° with the ground. If the length of the rope is 20 m, find the height of the balloon above the ground.
2. From the top of a 12 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of its base is 30°. Find the height of the tower.
3. A man is standing at a distance of 40 m from the foot of a tower. The angle of elevation of the top of the tower is 30°. Find the height of the tower.
4. A kite is flying at a height of 50 m. If the string attached to the kite makes an angle of 60° with the ground, find the length of the string (ignoring slack).
5. The angle of elevation of the top of a hill at a point on the ground is 30°. On walking 100 m towards the hill, the angle of elevation becomes 60°. Find the height of the hill.

Class 10 Maths Chapter 10 Important Questions – Circles

1. Prove that the tangent to a circle is perpendicular to the radius through the point of contact.
2. Two tangents are drawn from an external point to a circle. Prove that they are equal in length.
3. A tangent to a circle of radius 5 cm meets a line through the centre at a point P so that the line is perpendicular to the tangent. If OP = 13 cm, find the length of the tangent.
4. If tangents PA and PB are drawn to a circle with centre O from an external point P, prove that ∆OAP ≅ ∆OBP.
5. From an external point 10 cm away from the centre of a circle of radius 6 cm, find the length of the tangent drawn to the circle.

Class 10 Maths Chapter 11 Important Questions – Areas Related to Circles

1. Find the area of a sector of a circle with radius 7 cm and angle 60°.
2. The wheel of a car has a radius of 21 cm. How many revolutions will it make in covering 1.32 km?
3. A horse is tied to a pole with 7 m long rope. Find the area it can graze.
4. The perimeter of a semicircular protractor is 36 cm. Find its diameter.
5. Find the area of a segment of a circle with radius 14 cm if the angle of the corresponding sector is 90°.

Class 10 Maths Chapter 12 Important Questions – Surface Areas and Volumes

1. A metallic sphere of radius 4.2 cm is melted and recast into small spherical balls, each of radius 0.7 cm. Find the number of balls formed.
2. The height of a cone is 24 cm and the diameter of its base is 14 cm. Find its curved surface area.
3. A solid sphere of radius 7 cm is melted to make 44 identical spherical balls. Find the radius of each.
4. Find the total surface area of a solid right circular cone with slant height 25 cm and base diameter 14 cm.
5. A bucket is in the form of a frustum of a cone with height 16 cm, top radius 20 cm, and bottom radius 12 cm. Find its capacity.

Do Check: CBSE Class 10 Maths Sample Papers

Class 10 Maths Chapter 13 Important Questions – Statistics

This chapter focuses on mean, median, and mode of grouped data, along with cumulative frequency distribution.

Short Answer Questions (1–2 Marks)

1. Find the mean of the following data using the direct method:

2. The marks obtained by 30 students of a class in a test (out of 50) are given below. Find the modal marks.

3. The mean of 5 observations is 18. If one observation is excluded, the mean becomes 16. Find the excluded observation.

Long Answer Questions (3–5 Marks)

4. The following distribution table shows the ages of people in a town. Find the mean age using:
   (i) Direct method
   (ii) Assumed mean method

5. The distribution of daily wages of workers in a factory is given below. Find the median.

| Daily Wages (₹) | 100–120 | 120–140 | 140–160 | 160–180 | 180–200 | 200–220 | 220–240 |
|-----------------|---------|---------|---------|---------|---------|---------|
| No. of Workers | 12 | 14 | 8 | 6 | 10 | 4 | 6 |

6. The marks obtained by 50 students in a Mathematics test are as follows. Draw a cumulative frequency curve (less than type).

Class 10 Maths Chapter 14 Important Questions – Probability

This chapter is based on finding the probability of simple events like cards, dice, coins, and word problems.

Short Answer Questions (1–2 Marks)

1. A card is drawn at random from a pack of 52 playing cards. Find the probability of getting:
   (i) A black queen
   (ii) A red card
   (iii) Neither a king nor a queen
2. A die is thrown once. Find the probability of getting:
   (i) An even number
   (ii) A number greater than 4
   (iii) A prime number less than 6
3. A coin is tossed twice. Find the probability of getting:
   (i) Two heads
   (ii) One head
   (iii) No head

Do Check: NCERT Solutions for Class 10 Maths

Long Answer Questions (3–5 Marks)

4. A bag contains 5 red balls and 7 black balls. A ball is drawn at random. Find the probability that the ball drawn is:
   (i) Red
   (ii) Black
   (iii) Not red
5. Two dice are thrown together. Find the probability of getting:
   (i) A sum of 10
   (ii) A doublet
   (iii) A number greater than 8
6. A box contains 12 balls out of which x are black. If one black ball is drawn, the probability of this event is 1/3. Find the value of x.
7. From a group of 3 girls and 2 boys, a student is selected at random. Find the probability that the student selected is a girl.

Benefits of Solving Class 10 Maths Important Questions

Many students spend hours reading the NCERT textbook but still struggle during exams. The secret to success lies in practicing problems. Here’s why solving class 10 maths important questions is useful:

1. Focused Revision – Instead of revising the whole book, students can focus on the most expected and repeated questions.
2. Improves Speed – By solving maths important questions class 10 regularly, students can complete their exam within the time limit.
3. Clear Understanding – Important questions are designed to test concepts, not just formulas. This helps in better understanding.
4. Boosts Confidence – When students solve 10th maths important questions correctly, they feel confident about attempting any question in the exam.
5. Exam Ready – Most of the questions in board exams are either directly from NCERT or based on these important patterns.

Tips to Prepare for Class 10 Maths Exam

1. Practice Daily – Solve at least 5-10 maths important questions class 10 daily.
2. Revise Formulas – Keep a formula sheet handy.
3. Solve Sample Papers – Time yourself while solving.
4. Focus on Weak Chapters – Give extra time to chapters like Trigonometry and Statistics.
5. Do Previous Year Papers – Most 10th maths important questions are repeated.

Conclusion

Mathematics is not just about memorizing formulas, it is about practice and application. By solving important questions for class 10 maths, students can revise the complete syllabus smartly. The chapter-wise maths important questions class 10 given above will help students focus on exam-relevant topics.

Remember, success in Class 10 board exams comes from consistent practice. Solve the 10th maths important questions daily, manage your time well, and stay confident. With the right strategy, scoring full marks in maths is definitely possible.