Mathematics can be a scoring subject if you have clarity in concepts and regular practice. If you’re a Class 10 student preparing for board exams, this article will provide you with Class 10 Maths important questions with answers – chapter-wise, detailed, and completely exam-oriented.
These questions are selected based on previous year trends, CBSE sample papers, and expert analysis. Practice them regularly to improve accuracy and speed.
Table of Contents
- Real Numbers
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Arithmetic Progression (AP)
- Triangles
- Coordinate Geometry
- Introduction to Trigonometry
- Circles, Surface Areas and Volumes
- Statistics and Probability
1. Real Numbers
Question: Find the HCF of 60 and 72 using Euclid’s division algorithm.
Answer:
72 = 60 × 1 + 12
60 = 12 × 5 + 0
So, HCF = 12
2. Polynomials
Question: If α and β are the zeroes of the quadratic polynomial x² + 5x + 6, find α + β and αβ.
Answer:
α + β = -coefficient of x / coefficient of x² = -5/1 = -5
αβ = constant term / coefficient of x² = 6/1 = 6
3. Pair of Linear Equations in Two Variables
Question: Solve the following pair of equations:
2x + 3y = 12,
x – y = 1
Answer:
From the second equation, x = y + 1
Substitute into the first: 2(y+1) + 3y = 12 → 2y + 2 + 3y = 12 → 5y = 10 → y = 2
Then x = 3
Solution: x = 3, y = 2
4. Quadratic Equations
Question: Solve the equation x² – 5x + 6 = 0 by factorization.
Answer:
x² – 5x + 6 = (x – 2)(x – 3) = 0
⇒ x = 2 or x = 3
5. Arithmetic Progression (AP)
Question: Find the sum of the first 10 terms of the AP: 2, 5, 8, …
Answer:
a = 2, d = 3, n = 10
Sum = n/2 × [2a + (n – 1)d] = 10/2 × [4 + 27] = 5 × 31 = 155
6. Triangles
Question: In ΔABC, if DE || BC and AD/DB = AE/EC, prove that triangle ADE ~ triangle ABC.
Answer:
By Basic Proportionality Theorem (Thales), if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides them in the same ratio. Hence, ΔADE ~ ΔABC.
7. Coordinate Geometry
Question: Find the distance between points A(3, 4) and B(7, 1).
Answer:
Distance = √[(7 – 3)² + (1 – 4)²] = √[16 + 9] = √25 = 5 units
8. Introduction to Trigonometry
Question: If sin θ = 3/5, find cos θ and tan θ.
Answer:
Let triangle sides be opposite = 3, hypotenuse = 5. Using Pythagoras theorem: adjacent = √(25 – 9) = 4
cos θ = adjacent/hypotenuse = 4/5
tan θ = opposite/adjacent = 3/4
9. Circles, Surface Areas and Volumes
Question: Find the surface area of a sphere of radius 7 cm.
Answer:
Surface Area = 4πr² = 4 × 22/7 × 7 × 7 = 616 cm²
10. Statistics and Probability
Question: Find the mean of the following data:
Marks: 10, 20, 30, 40, 50
Frequency: 2, 3, 5, 4, 1
Answer:
Mean = (Σfx) / (Σf) = (10×2 + 20×3 + 30×5 + 40×4 + 50×1) / (2+3+5+4+1) = 470 / 15 = 31.33
How to Practice Maths Effectively for Class 10
- Practice questions daily from each chapter
- Focus on formulas and understand how to derive them
- Revise important theorems and construction steps
- Solve previous year CBSE board papers
- Time yourself while solving mock tests
Download Free Class 10 Maths Sample Papers
Math is Not Tough – It’s Practice-Based
Remember, no one is born a maths genius. It’s just practice, patterns, and patience. If you revise these important maths questions for Class 10 regularly, you’ll gain confidence and speed.
Even if you’re starting late, focus on high-weightage chapters like Quadratic Equations, Trigonometry, Statistics, and Circles.
Final Words
We hope this chapter-wise list of Class 10 Maths important questions with answers helps you plan your preparation better. Bookmark this page for daily revision, and share it with your classmates.
Keep solving, keep learning, and you’ll score high in your maths board exam. All the best!