CBSE Class 10 Maths Four Marks Questions with Stepwise Solutions and Important Topics
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
For any integer n ≥ 0, Prove that n3 - n is divisible by 6.
There are 49 houses numbered in a row. Find the number of the house whose value will be the sum of all preceding values.
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.
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?
Prove that two chords, if equidistant from the centre of the circle are of the same length.
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.
Using the substitution method, solve the following linear equations:
2x - y = 2
x = 3y = 15
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?
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 in CBSE Class 10 Maths with Solutions
1. What are the most important four marks questions for CBSE Class 10 Maths?
The most important four marks questions in CBSE Class 10 Maths usually come from chapters that require step-by-step solutions and application of formulas. These commonly include:
- Quadratic Equations (finding roots using formula)
- Arithmetic Progressions (AP) (finding nth term or sum)
- Triangles (proofs and similarity)
- Trigonometric Identities (proving identities)
- Surface Areas and Volumes (word problems)
- Statistics (mean, median, mode)
2. How do you solve a quadratic equation for 4 marks in Class 10 Maths?
To solve a quadratic equation for 4 marks, use the quadratic formula and show all calculation steps clearly. The formula is x = [-b ± √(b² − 4ac)] / 2a for ax² + bx + c = 0.
- Step 1: Identify a, b, and c.
- Step 2: Find the discriminant D = b² − 4ac.
- Step 3: Substitute values into the formula.
- Step 4: Simplify and write both roots clearly.
3. What is the formula for the nth term of an Arithmetic Progression?
The formula for the nth term of an Arithmetic Progression (AP) is an = a + (n − 1)d. Here:
- a = first term
- d = common difference
- n = term number
4. How do you prove trigonometric identities in Class 10 Maths?
To prove a trigonometric identity, start with one side and simplify it until it becomes equal to the other side. Follow these steps:
- Use standard identities like sin²θ + cos²θ = 1
- Convert tan, cot, sec, cosec into sin and cos
- Simplify step by step without skipping steps
5. What type of questions come for 4 marks from Triangles chapter?
Four-mark questions from the Triangles chapter usually involve proofs based on similarity or Pythagoras theorem. Common types include:
- Proving two triangles are similar using AA, SAS, or SSS
- Using Basic Proportionality Theorem (BPT)
- Applying Pythagoras theorem to find a side
6. How do you find the mean in Statistics for 4 marks?
To find the mean in Statistics, use the direct method formula: Mean (x̄) = Σfixi / Σfi. Steps include:
- Find class marks (xi)
- Multiply frequency and class mark (fi × xi)
- Calculate Σfi and Σfixi
- Substitute in the formula
7. What are important formulas from Surface Areas and Volumes for 4 marks?
Important formulas from Surface Areas and Volumes frequently used in 4-mark questions include:
- Volume of sphere = (4/3)πr³
- Volume of cylinder = πr²h
- CSA of cylinder = 2πrh
- Volume of cone = (1/3)πr²h
8. How do you solve word problems based on Arithmetic Progressions?
To solve AP word problems, first identify the first term, common difference, and required term or sum. Steps include:
- Write given values of a, d, and n
- Use an = a + (n − 1)d or Sn = n/2 [2a + (n − 1)d]
- Substitute carefully and simplify
9. What is the discriminant in a quadratic equation and why is it important?
The discriminant of a quadratic equation is D = b² − 4ac, and it determines the nature of roots. Based on D:
- If D > 0, roots are real and distinct
- If D = 0, roots are real and equal
- If D < 0, roots are not real
10. How should I write a 4 marks answer in CBSE Class 10 Maths to get full marks?
To score full marks in a 4-mark Maths question, write complete steps with correct formulas and final answers clearly highlighted. Follow this structure:
- Write the given data
- Mention the correct formula
- Show step-by-step substitution and simplification
- Box or clearly state the final answer
