Class 10th Math Most important question top question for board 2026

📐 Class 10th Maths: Most Important Questions for Boards (CBSE & UP Board)

💡 Board exam 2025 – Real questions, zero answers. A smart question bank to practice smartly.

📷 Unsplash | Focus, practice, repeat – board prep in full swing

Are you a CBSE or UP Board Class 10 student? Maths can feel like a mountain, but with the right set of important questions, you can turn it into a stepping stone. In this post, we’ve handpicked high-weightage & most likely questions from past 10 years and latest sample papers. No answers—just pure brain-churning practice. Let’s crack the code!

🎯 Why Class 10th matters – CBSE & UP Board both

Class 10 is not just another exam – it’s the foundation of your future. Here’s why both CBSE and UP Board students gain massively:

• 📌 Stream decision: Your marks decide Science/Commerce/Humanities in +2.
• 📌 Board exam temperament: First real board exam builds confidence for competitive exams (JEE/NEET/NDA).
• 📌 Universal recognition: CBSE and UP Board certificates are accepted nationwide for scholarships and entrance tests.
• 📌 Maths sharpens logic: Real-life problem solving, data analysis, and even future income potential increase with maths proficiency.
• 📌 Safety net: A good percentage (above 75%) opens doors to NIOS, diploma courses, and early college admissions.

Whether you’re in UP Board (Hindi medium or English) or CBSE, the core maths concepts are similar – only paper pattern differs slightly. Our questions cover both.

📷 Unsplash | Equations can be beautiful – master them

🔥 MOST IMPORTANT QUESTIONS (topic-wise) – Practice these!

👇 These are actual board questions (CBSE & UP Board high frequency). Solve them step-by-step in a separate notebook. No answers given – struggle = strong memory.

🔹 1. Real Numbers

❓ Prove that √3 is irrational, given that √5 is irrational. (CBSE 2024, UP 2023)

❓ Find the HCF and LCM of 96 and 120 using prime factorization method. (CBSE 2023)

❓ Explain why 7×11×13+13 is a composite number. (UP 2022)

🔹 2. Polynomials

❓ If α and β are zeroes of polynomial x² – 3x + 2, find a polynomial whose zeroes are 2α+1 and 2β+1. (CBSE 2024)

❓ Find the zeroes of quadratic polynomial 4√3x² + 5x – 2√3 and verify relationship. (UP 2023)

❓ Divide 3x³ + x² + 2x + 5 by 1 + 2x + x² and verify division algorithm. (CBSE sample)

🔹 3. Pair of Linear Equations

❓ Solve graphically: 2x + y = 6 and 4x – 2y = 4. Shade the triangular region. (CBSE 2023)

❓ A fraction becomes 1/3 when 1 is subtracted from numerator. It becomes 1/4 when 8 is added to denominator. Find fraction. (UP 2024)

❓ For what value of k will equations x + 2y = 5 and 3x + ky – 15 = 0 have no solution? (CBSE 2022)

🔹 4. Quadratic Equations

❓ Find the roots of 2x² – 7x + 3 = 0 by factorization. (UP 2023)

❓ The diagonal of a rectangular field is 60 m more than the shorter side. If longer side is 30 m more than shorter side, find sides. (CBSE 2024)

❓ Solve for x: 4x² – 4a²x + (a⁴ – b⁴) = 0 (CBSE sample)

🔹 5. Arithmetic Progressions

❓ How many two-digit numbers are divisible by 3? (CBSE 2023)

❓ Find the sum of first 40 positive integers divisible by 6. (UP 2024)

❓ If the 3rd and 9th term of an AP are 4 and –8 respectively, which term is zero? (CBSE 2022)

🔹 6. Triangles & Coordinate Geometry

❓ In an equilateral triangle, prove that three times the square of one side equals four times the square of its altitude. (UP 2023)

❓ Find the ratio in which the line 3x + y – 9 = 0 divides the segment joining (1,3) and (2,7). (CBSE 2024)

❓ If A(–5,7), B(–4,5), C(4,5), D(5,7) are vertices of a quadrilateral, find area. (CBSE sample)

🔹 7. Trigonometry

❓ Prove that (cosec θ – cot θ)² = (1 – cos θ)/(1 + cos θ). (CBSE 2023, UP 2024)

❓ If sin A = 3/4, calculate cos A and tan A. (UP 2022)

❓ Evaluate: (5 cos² 60° + 4 sec² 30° – tan² 45°) / (sin² 30° + cos² 30°) (CBSE 2024)

🔹 8. Circles & Construction

❓ Prove that the tangents drawn at the ends of a diameter of a circle are parallel. (CBSE 2023)

❓ Two concentric circles radii 5cm and 3cm. Find length of chord of larger circle which touches the smaller. (UP 2023)

🔹 9. Surface Areas & Statistics

❓ A toy is in form of cone mounted on hemisphere radius 3.5 cm, total height 15.5 cm. Find volume. (CBSE 2024)

❓ Find mean of the following data (grouped) using step deviation method. (data table) – UP 2023

❓ The median of distribution is 28.5, find missing frequencies. (CBSE sample)

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🧠 Top 7 tips to score 95+ in Maths (CBSE / UP Board)

• Master NCERT first: 80% paper comes directly from NCERT. Solve every example and exercise.
• Write steps clearly: Even if the answer is wrong, stepwise marking can fetch half marks.
• Previous year questions are gold: Practice at least 5 years of both CBSE and UP board papers.
• Time management: In exam, attempt 1-markers first (within 15 min) then section-wise.
• Use sticky notes: Memorize all formulas daily – make a formula wall.
• Practice diagrams: For construction, graphs, and figures – use sharp pencil and ruler; they carry marks.
• Revise with question bank: Revise only questions (like above) without looking at solutions.

📷 Unsplash | Consistency beats intensity

⚠️ 5 common mistakes students make in board exam

1. Skipping rough work: Always use rough column – half marks are lost by direct jumps.
2. Forgetting units: In mensuration, probability, statistics – ₹, cm², % – don’t leave them.
3. Overwriting/cutting: Use one line cut; overwriting makes answer sheets messy.
4. Not attempting all questions: Even if unsure, write formula or steps – you’ll get partial marks.
5. Mixing concepts: In trigonometry, using wrong identities. Write which identity you’re using.

🚀 Pro tip: Use the 15 minutes reading time to mark the questions you know best. Attack them first!

📈 Extra edge – CBSE vs UP Board : what’s same?

Both boards now follow NCERT syllabus 90%+ and conceptual questions. UP board papers have more theoretical and direct questions, but they also include high-order thinking slowly. CBSE focuses on application. By practicing the questions above, you cover both patterns. Students from both boards have topped using these very questions.

✍️ Written by VIVEK TIWARI — Ed-tech enthusiast & mentor for board exams. I’ve helped 500+ students score 90+ in maths.

📌 For more important questions, sample papers, and topic-wise mock tests, visit Forgeq.in – a growing platform for smart learning.

🔍 Explore Forgeq for more free resources

📷 Unsplash | Your exam, your victory – every question counts

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🎯 Remember: the more you practice without answers, the sharper your brain becomes. Bookmark this page, solve all questions, and you’ll enter the exam hall with confidence.
— Best of luck for your Boards! 💪

Images source: Unsplash (free to use, no attribution required). All questions are for practice and based on past board papers.