Half Yearly Exam 2025: Class 10 Maths Solved Paper & Key Strategies

Comprehensive Solutions for Class 10 Half Yearly Maths 2025

Thousands of students preparing for Class 10 Half Yearly Maths 2025 need verified solutions to practice effectively. After analyzing an educator’s live problem-solving session, I’ve compiled accurate answers with strategic explanations. This article combines the video’s methodology with curriculum-aligned insights to help you master key concepts before exams.

Section A: Objective Questions Solved

Question 1: HCF of 26 and 91

Solution: 26 = 13 × 2, 91 = 13 × 7. Common factor is 13.
Answer: 13

Question 2: Sum of roots of x² + 7x + 10 = 0

Expert Insight: General quadratic ax² + bx + c = 0 has sum of roots = -b/a.
Calculation: Here, a=1, b=7 → Sum = -7.
Answer: -7

Question 6: Thales Theorem application

Problem: In ΔABC, DE || BC, AD=?, DB=9, AE=2, EC=6.
Method: AD/DB = AE/EC → x/9 = 2/6 → x=3.
Why students err: Misidentifying parallel line ratios. Always verify DE || BC condition first.

Question 15: Mean of 3,5,7,9,11,13,15

Formula: Mean = Sum of observations / Number of observations
Calculation: 63 ÷ 7 = 9

Key Formulas and Concepts Tested

Discriminant of Quadratic Equation:

Standard Formula: D = b² - 4ac (Question 4)
Application: Determines nature of roots—real/distinct if D>0.

Trigonometric Values:

Memorization Tip: sin60° = √3/2, cos30° = √3/2, sin30° = 1/2, cos60° = 1/2 (Used in Q12)

Coordinate Geometry:

Midpoint Formula: ((x₁+x₂)/2, (y₁+y₂)/2)
Example: Center of circle with diameter endpoints (3,-10) and (1,4) = ((3+1)/2, (-10+4)/2) = (2, -3)

High-Value Topics for Exam Success

Arithmetic Progression (AP) Patterns:

nᵗʰ term: aₙ = a + (n-1)d
2025 Trend: 3+ mark problems often combine AP with real-life scenarios.
Q Solution: For AP 7,13,19,25... find a₁₂ → a=7, d=6 → a₁₂ = 7 + (11×6) = 73

Circle Theorems:

Critical Rules:
- Two tangents from an external point are equal (Q10).
- Tangent is perpendicular to radius at point of contact.
Exam Tip: Diagrams often hide alternate segment theorem applications.

Height and Distance Problems:

Framework: tanθ = Opposite/Adjacent
Q Solved: Tower height when θ=30°, distance=30m → tan30°=1/√3 = h/30 → h=10√3m

Revision Checklist for Top Scores

Verify HCF/LCM calculations through prime factorization.
Practice 5+ quadratic equations covering all root types (real/complex).
Memorize trigonometric ratios for 0°, 30°, 45°, 60°, 90°.
Solve 3 AP problems using aₙ and Sₙ formulas.
Draw circle theorem diagrams labeling angles and tangents.

Recommended Resources

NCERT Exemplar Problems: Essential for 2025 exam patterns.
RD Sharma Class 10: Builds advanced problem-solving speed.
Online Quiz: Practice MCQ speed tests on Khan Academy.

Final Thought: Which concept do you find most challenging—quadratic equations or circle theorems? Share in comments for personalized tips!

Important Notice: Physics (Class 12) and Hindi (Class 10) important questions releasing today at 6 PM and 7 PM. Stay tuned!