Introduction
Preparing for Class 10 Maths is all about practice, pattern recognition, and concept clarity. Based on deep analysis of previous year papers, these questions are among the most important and frequently repeated ones. Practicing them will help you confidently tackle similar questions in the board exam.
To fully understand the concepts, detailed explanations, and step-by-step solving of all 33 important questions, make sure to watch the complete video. It will help you build deeper conceptual clarity and perform better in your board exams.
Most Important Topics for Class 10 Maths Boards
Real Numbers
- HCF and LCM relationship
- Euclid’s Division Lemma
- Proof of irrational numbers
Polynomials
- Relationship between zeros and coefficients
- Finding zeros of quadratic polynomials
- Expressions like α² + β², α³ + β³
Pair of Linear Equations
- Graphical method of solving equations
- Conditions for infinite solutions
- Algebraic methods (substitution/elimination)
Quadratic Equations
- Nature of roots using discriminant
- Word problems (speed, pipes)
- Finding roots using factorization
Arithmetic Progression
- Finding nth term using Sn
- Sum of terms problems
- Word problems on AP
Triangles
- Basic Proportionality Theorem (BPT)
- Similar triangles proofs
- Ratio-based problems
Coordinate Geometry
- Section formula
- Midpoint formula
- Finding missing vertices
Trigonometry
- Trigonometric identities
- Standard values
- Expression simplification
Applications of Trigonometry
- Height and distance problems
- Diagram-based questions
Circles
- Theorems related to tangents
- Secant-tangent properties
Areas Related to Circles
- Sector and segment area
- Shaded region problems
Surface Areas & Volumes
- Combination solids
- Scooped out solids
- Total surface area problems
Statistics
- Mean, median, mode relationship
- Missing frequency problems
Probability
- Finding probability using outcomes
- Cards and coins problems
33 Most Important Questions Are
Real Numbers
Q1. HCF = 14, LCM = 1680, one number = 84. Find the other.
Answer: 280
Explanation: Product of two numbers = HCF × LCM.
Q2. Prove that 3 + √5 is irrational.
Answer: Irrational
Explanation: Use contradiction method.
Polynomials
Q3. Find α² + β² if α, β are zeros.
Answer: (α + β)² − 2αβ
Explanation: Use identity and coefficient relations.
Q4. Find zeros and verify relations.
Answer: Solve using factorization.
Explanation: Use sum and product of roots.
Linear Equations
Q5. Solve graphically.
Answer: Intersection point
Explanation: Solution is intersection of lines.
Q6. Condition for infinite solutions.
Answer: a1/a2 = b1/b2 = c1/c2
Explanation: Same line condition.
Quadratic Equations
Q7. Find k for equal roots.
Answer: D = 0
Explanation: b² − 4ac = 0
Q8. Aircraft speed problem.
Answer: Solve quadratic
Explanation: Use speed-distance relation.
Q9. Pipe problem.
Answer: Solve using quadratic equation
Explanation: Time-based equation formation.
Arithmetic Progression
Q10. Find nth term from Sn.
Answer: an = Sn − Sn−1
Explanation: Use formula relation.
Q11. Ratio of sums of APs.
Answer: Use Sn formula
Explanation: Compare two AP sums.
Q12. Sum of 4 consecutive terms.
Answer: a−3d, a−d, a+d, a+3d
Explanation: Standard representation.
Triangles
Q13. Find x using BPT.
Answer: Solve ratio
Explanation: AD/DB = AE/EC
Q14. Prove similarity using medians.
Answer: Triangles similar
Explanation: Corresponding sides proportional.
Coordinate Geometry
Q15. Ratio using y-axis.
Answer: Use section formula (x=0)
Explanation: y-axis implies x=0.
Q16. Find fourth vertex of parallelogram.
Answer: Use midpoint formula
Explanation: Diagonals bisect each other.
Q17. Find ratio dividing line.
Answer: Use section formula
Explanation: Point satisfies given line.
Trigonometry
Q18. Given tan θ = 1/√3, find expression.
Answer: Use triangle method
Explanation: Use standard ratios.
Q19. Prove identity.
Answer: LHS = RHS
Explanation: Expand and simplify.
Q20. Prove expression using squares.
Answer: Square and add
Explanation: Convert to known identity.
Q21. Simplify trigonometric expression.
Answer: Convert to sin/cos
Explanation: Replace sec and tan.
Applications of Trigonometry
Q22. Height and distance problem.
Answer: Use tan θ
Explanation: Draw diagram and apply ratios.
Q23. Balloon/height problem.
Answer: Solve using triangle
Explanation: Use right triangle concept.
Circles
Q24. Theorem-based proof.
Answer: Use circle theorems
Explanation: Apply tangent/secant rules.
Areas Related to Circles
Q25. Find shaded region area.
Answer: Sector − triangle
Explanation: Use formula.
Q26. Find perimeter of shaded region.
Answer: Add arc lengths
Explanation: Use circumference relations.
Surface Areas & Volumes
Q27. Cylinder with cone removed.
Answer: Add exposed area
Explanation: Include curved surface of cone.
Q28. Cone on hemisphere.
Answer: Add surface areas
Explanation: Combined solid.
Statistics
Q29. Mean, mode, median relation.
Answer: Mode = 3Median − 2Mean
Explanation: Empirical formula.
Q30. Missing frequency problem.
Answer: Solve using median formula
Explanation: Use cumulative frequency.
Probability
Q31. 3 coins, exactly 2 heads.
Answer: 3/8
Explanation: Favorable outcomes / total outcomes.
Q32. Card probability.
Answer: Based on 52 cards
Explanation: Use total outcomes.
Q33. Basic probability question.
Answer: Favorable/total
Explanation: Use definition.
Key Preparation Tips for Maths Boards
- Practice important questions daily
- Focus on formulas and identities
- Solve previous year papers
- Work on speed and accuracy
Common Mistakes to Avoid
- Skipping steps in solutions
- Not revising formulas
- Poor diagram representation
- Calculation mistakes
Smart Study Strategy for CBSE Maths
- Prioritize high-weightage chapters
- Practice mixed problems
- Revise daily using short notes
- Attempt mock tests regularly
FAQs
Q1. Which chapter is most important in Maths?
Quadratic Equations, Trigonometry, and Geometry.
Q2. How to score 100 in Maths?
Practice regularly and revise formulas.
Q3. Are previous year questions enough?
They are very important for pattern understanding.
Q4. Is NCERT enough for Maths?
Yes, if practiced thoroughly.
Conclusion
Maths is all about precision, speed, and confidence – and all three come from practice. In these final days, don’t try to solve everything. Instead, focus on these most important questions, revise formulas daily, and avoid calculation mistakes.
One wrong step can cost marks, so practice with full concentration. For better clarity and step-by-step understanding, watch the complete video and solve each question along with it. This focused revision can be the difference between losing marks and scoring full marks.
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