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Important Four Marks Questions for CBSE Class 10 Maths

Last updated date: 25th Feb 2024
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Four Marks Questions for CBSE Class 10 Maths

Class 10 Maths paper is designed to test the mathematical aptitude in students of Class 10. The entire syllabus is designed to improve the understanding and application of the subject. Class 10 exams hold much importance in a student's life. It is based on this score that students are admitted into different streams. Also, it will help you in making an informed decision about your future.

Mathematics is a subject which requires regular practice and demands constant effort from the students. With only regular practice can you score well in your Maths paper. Students should have an in-depth understanding of every chapter. An important tool is your Class 10 NCERT textbook. It would be best if you used your NCERT book as a base for your preparations. If you are comfortable with all the questions in your textbook, you will score better in your exams.

List of Important Four Marks Questions

  1. For any integer  n ≥ 0, Prove that n3 - n  is divisible by 6.

  2. There are 49 houses numbered in a row. Find the number of the house whose value will be the sum of all preceding values. 

  3. A boat can travel at a speed of 24 km/hr. When going upstream it takes 1 extra hour more than when going downstream to cover the distance of 32 km.

  4. Two taps take 40/3 hours to fill up a tank. The first tap takes 3 hours more than the second tap to fill the tank. Calculate how much time it will take for each tap to fill the entire tank individually?

  5. Prove that two chords, if equidistant from the centre of the circle are of the same length.

  6. A point A is at a distance of 17cm from a circle of radius 8cm. Find the length of the tangent from point A on the circle.

  7. Using the substitution method, solve the following linear equations:

2x - y = 2

x = 3y = 15

  1. A rectangular sheet has length and breadth 40 cm and 28cm respectively. A semicircle with the breadth as the diameter is cut from one of its sides. Find the area of the remaining sheet of paper?

  2. Find the first three terms of an arithmetic progression in which,

The sum of 4th and 8th terms = 24

The sum of 6th and 10th terms = 44

Important Four Marks Questions CBSE Class 10 Weightage

The exam consists of a total of 80 marks to test a student's knowledge in Calculus, Algebra, Probability, Linear programming, vectors, Three-dimensional geometry, relation and functions.

These are to gauge the students of Class 10 in application, understanding, and remembering of mathematical concepts. Students need to put in consistent effort to grasp the subject. Maths is about practice. If you are comfortable with the subject, only then can you score well. Given below is the marks-wise distribution as per CBSE guidelines. This is to give you a fair picture of how the exam pattern is set up so that you can tackle the questions with better confidence. The marks-wise distribution of the question paper is given below.

Marks-Wise Distribution

  • Objective Type Question (20 Questions × 1 Marks): Each question is to test quick thinking ability in students. If you are well versed with the basics of every chapter, these will be rather easy to attempt.

  • Very Short Answer Type Questions (6 question × 2 Marks): These questions require you to find the answer using mathematical concepts. These can be a bit tricky to attempt, and sometimes students lose marks here because of it.

  • Short Answer Type Questions (8 Questions × 3 Marks): Each question test formulation of complex mathematical problems. With regular practice, you can solve these questions quickly, but these will take up the majority of your time.

  • Long Answer Type Questions (5 Questions × 4 Marks): These are application-based questions. The problems are not complex but require time to formulate. Should pay attention here because it is the most scoring section because of step marking, and these involve the most number of steps.

FAQs on Important Four Marks Questions for CBSE Class 10 Maths

1. The Common Difference of an Arithmetic Progression is 9. Find the Number of Terms and Their Sum if the First and Last Terms of the Progression are 10 and 361 Respectively.

Ans: It is a very basic arithmetic problem that the students can find in their question paper.  In order to solve this students should be aware of the formulas for the nth term and sum of all terms. If you know both of these the only thing left is to calculate the problem mathematically.


first term, a = 10

last term, l = 361

common difference, d = 9

l = a + (n - 1)d

On solving the number of terms of the AP comes out to be:

361 = 10 + (n - 1)9

360 = 9n

n = 40

Formula for the sum of n number of terms in an arithmetic progression is

S = n/2 (2a+(n-1)d)

S = 40/2 (20+399)

S = 20(20+351)

S = 20(371)

S = 7420

2. What is the Class 10 Maths Syllabus?

Ans: Class 10 Maths exam is designed to test the mathematical knowledge of students. The question paper consists of 80 marks. There are four different types of questions you will face in your exam paper. Each chapter is important for your preparation, and you should dedicate enough time during your preparations to prepare yourself for your examinations Given below is the list of each chapter to help you plan your Maths syllabus into your preparations:

  • Chapter 1: Real numbers

  • Chapter 2: Polynomials 

  • Chapter 3: Linear equations

  • Chapter 4: Quadratic equation

  • Chapter 5: Arithmetic progressions

  • Chapter 6: Lines

  • Chapter 7: Triangle

  • Chapter 8: Circles

  • Chapter 9: Construction

  • Chapter 10: Introduction to geometry

  • Chapter 11: Trigonometric identities

  • Chapter 12: Heights and distances

  • Chapter 13: Areas related to circles

  • Chapter 14: Surface Areas and volumes

  • Chapter 15: Statistics

  • Chapter 16: Probability