CBSE Maths Pre-Board Exam 2026: Top 50 MCQs with Interactive Test

 

About This Practice Quiz

This collection covers essential topics from the CBSE Class 10 Maths syllabus, including Number Systems, Polynomials, Coordinate Geometry, Trigonometry, Circles, Probability, and more. The questions have been carefully selected to reflect the types of problems you'll encounter in your board examination.

📊 Quiz Features:

• 50 carefully curated MCQs

• Instant scoring and feedback

• Progress saving (your answers are saved automatically)

• Performance analysis after submission

• No login required

Additional Resources for Preparation

• NCERT Solutions: Solve all NCERT exercises thoroughly

• Sample Papers: Practice with CBSE sample papers

• Formula Sheets: Create topic-wise formula revision sheets

• Important Questions: Focus on frequently asked questions from each chapter

Remember: The key to scoring well in Mathematics is consistent practice and clear conceptual understanding. Use this quiz as a tool to identify your strengths and weaknesses, then focus your study efforts accordingly.

Happy studying and all the best for your pre-board exams!

Maths Pre-Board 2026 Quiz

Test your knowledge with these 50 MCQs ©PRIME MATHS

Instructions: Select one answer per question. Click "Submit" at the end to see your score.

Questions: 50 Pass Score: 60%

Question 1 of 50

Results

Score: 0/50 (0%)

Practice quiz for CBSE Class 10 Maths Pre-Board Exam 2026. © PRIME MATHS

Trigonometry, Probability and Statistics 90 Difficult Problems CBSE, ICSE Class X

 

📘 Mastering Trigonometry, Probability & Statistics for Class X CBSE & ICSE Boards

Board exams are around the corner, and three chapters that always carry high weightage in Class X Mathematics are Trigonometry, Probability, and Statistics. These topics not only appear every year but also form the base for higher classes.

To help you practice effectively, here’s a comprehensive 90-question problem sheet covering all major types of problems that can be asked in your board exams.

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🔹 Why Focus on These Topics?

• Trigonometry: Around 8–10 marks every year (Identities, Heights & Distances).

• Probability: 4–6 marks, usually simple but tricky MCQ-type.

• Statistics: 8–10 marks (Mean, Median, Mode, Graphs, Ogive, Histogram).

That means almost 25% of your math exam comes directly from these three chapters!

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🟦 1. Trigonometry Section (Q.1–30, 71–90)

This section begins with basic identities and proofs like:

• Proving trigonometric identities (Q.1–20).

• Higher-level simplifications involving sec, tan, and cot (Q.21–30).

• Word problems on Heights & Distances (Q.71–90), including angles of elevation, depression, aeroplane problems, and applications with towers and buildings.

👉 Tip: Always draw a rough figure in height & distance problems; 50% of the solution comes just from a correct diagram.

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🟩 2. Probability Section (Q.31–50)

The probability section has a mix of dice, coins, cards, and real-life examples:

• Simple dice problems (Q.31–33, 37–38).

• Coin toss problems (Q.39–40).

• Playing cards (Q.35, Q.48).

• Real-world word problems with marbles, ice creams, tickets, etc.

👉 Tip: Always remember

$$P(E) = \frac{\text{Favourable Outcomes}}{\text{Total Outcomes}}$$

and carefully check whether the problem is "or" (union) or "and" (intersection) type.

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🟥 3. Statistics Section (Q.51–70)

This section covers:

• Mean, Median, Mode (Q.51–59, Q.67–69).

• Ogives & Histograms (Q.60–64).

• Word problems with real-life data (Q.65–70).

👉 Tip:

• Use step-deviation method for quicker calculation of mean.

• Median = value of $\frac{N}{2}$-th observation (learn how to locate it correctly in cumulative frequency tables).

• For graphs, label your axis neatly—marks are often lost for presentation.

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📌 How to Use This Problem Sheet?

1. Start with Trigonometric Identities → They sharpen algebraic manipulation skills.

2. Move to Probability → These are quick, scoring questions.

3. Finish with Statistics → Practice graphs separately for neatness and accuracy.

4. Solve at least 10 questions daily from the sheet.

5. Time yourself as if in an exam.

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🌟 Final Words

This 90-question sheet is a perfect revision package for Class X boards. If you can solve these confidently, you’ll be exam-ready for all tricky variations.

📌 Pro Tip: Practice without looking at the answers first, then cross-check.

💡 Consistency is the key—solve 3–5 questions every day and revise formulas daily.

CHAPTER TEST - ICSE MATHEMATICS - Probability, Quadratic Equations, Factorisation, and Trigonometry:

 "TEST – ICSE MATHEMATICS - X", which covers topics in Probability, Quadratic Equations, Factorisation, and Trigonometry:

🧮 Topics Covered

• Probability:

  • Calculating probabilities based on card draws and coin tosses.
  • Real-life scenarios like games and playing cards used to frame questions.

• Quadratic Equations:

  • Solving quadratic equations.
  • Finding conditions for real and equal roots.
  • Application-based problems involving area and tile dimensions.

• Factorisation:

  • Using factor theorem to find unknown coefficients.
  • Polynomial division and complete factorisation.

• Trigonometry:

  • Proving identities involving cotangent, tangent, sine, cosine, secant, and cosecant.
  • Complex expressions simplified to standard trigonometric identities.

📝 Sample Questions

• Probability of winning different prizes based on number card properties.
• Proving trigonometric identities like: [ \frac{(\cot A + \tan A - 1)(\sin A + \cos A)}{\sin^3 A + \cos^3 A} = \sec A \cdot \csc A ]
• Solving and factorising polynomials such as: [ 2x^3 - 7x^2 + kx - 2 \quad \text{(given that } x - 2 \text{ is a factor)} ]
• Finding the value of ( x ) in a tile-based floor problem.
• Probability of drawing a specific card from a reduced deck.

⏱️ Format

• Total Marks: 40
• Duration: 1 hour 30 minutes
• Each question is marked individually, ranging from 1 to 4 marks.

HARDER PROBLEMS FOR CLASSES VIII- X Algebra

This collection is designed for secondary school students (Classes VIII–X) preparing for Math Olympiads and competitive exams. It brings together a variety of challenging algebra problems that go beyond routine textbook exercises and test deeper understanding, creativity, and problem-solving skills.

👉 Key Features of the Set

• Classical Identities – Problems based on famous results such as Sophie Germain’s identity.

• Equation Manipulation – Creative use of algebraic transformations and substitutions.

• Inequalities & Rationalization – Strengthening algebraic reasoning with proofs and simplifications.

• Number Theory Links – Problems connecting algebra with concepts of divisibility and composite numbers.

• Summations & Series – Telescoping series and rational number expansions.

• Olympiad Flavor – Each problem is selected to stimulate lateral thinking and develop advanced techniques.

This set not only sharpens algebraic manipulation but also trains students to recognize patterns, symmetry, and hidden structures in problems—an essential skill for Olympiads and higher-level mathematics.

CHAPTER TEST – ICSE Mathematics – Class X - Inequality, Ratio and Proportion, Section Formula, and Banking

Title: TEST – ICSE Mathematics – Class X

Chapters Covered: Inequality, Ratio and Proportion, Section Formula, and Banking
Full Marks: 40
Time: 1 hour 30 minutes

Structure:

• Total Questions: 15

• Marks Distribution:

  • Questions 1–6: Short answer, 1 mark each (concept recall and direct application).

  • Questions 7–8: Short problems, 3 marks each (multi-step reasoning).

  • Questions 9–15: Long problems, 4 marks each (detailed computation or proof).

Topics Tested:

• Solving and representing inequalities on a number line

• Ratios, continued proportion, fourth proportion

• Coordinate geometry: section formula, trisection points, centroid

• Proportion and algebraic identities (Componendo and Dividendo)

• Banking applications: recurring deposit calculations

• Determining numbers to make quantities proportional

Format:

• Mix of fill-in-the-blank, solve-and-show, and prove type questions

• Some require graphical representation of inequalities on a number line

• Involves both theoretical proofs and practical application problems

Madhyamik WBSSE Board Mathematics Question Paper

 Are you preparing for the Madhyamik Mathematics Board Exam? We've got you covered! 🎯 In this video, we provide a complete step-by-step solution to the official board question papers. This will help you understand the best methods to solve tricky problems, manage time effectively, and score higher in your exams.

🔹 What you'll learn in this video: ✅ Full solutions to all questions ✅ Easy and shortcut methods for quick solving ✅ Important formulas and concepts ✅ Common mistakes to avoid ✅ Time management strategies for the exam 🚀 Boost your confidence and ace the exam! Don't forget to like, share, and subscribe for more educational content. 🎓📚 🔔 Stay tuned for more board exam tips & solution

CLICK ON THE LINK BELOW

Madyamik Mathematics Board Paper 2025

Madyamik Mathematics Board Paper 2024

Madyamik Mathematics Board Paper 2023

Madyamik Mathematics Board Paper 2022

#Madhyamik2025 #MathematicsBoardExam #QuestionPaperSolved #ExamPreparation #MATH #Solution #WestBengal #WBBSE2025 #MadhyamikMaths #MathsTricks #BoardExamSuccess #TopperStrategy #TimeManagementTip #FullPaperSolution #MathForStudents #Education2025 #StudyWithMe

ICSE MATHEMATICS BOARD QUESTION PAPER 2025

ICSE Mathematics 2025 Board Exam with our detailed analysis of the question paper! This blog provides step-by-step solutions, expert tips, and strategic insights to help you tackle every section of the exam with confidence. Whether you're looking to master quadratic equations, understand probability, or solve complex geometry problems, we’ve got you covered. Stay updated with the latest trends, important topics, and frequently asked questions to ensure you’re fully prepared for the big day. Ace your ICSE Mathematics 2026 exam with our expert guidance and practice resources!

Analysis of the ICSE Mathematics 2025 Board Question Paper:

The ICSE Mathematics 2025 question paper is divided into two sections: Section A (40 marks) and Section B (40 marks). Students are required to attempt all questions from Section A and any four questions from Section B. The paper is designed to test a wide range of mathematical concepts, including algebra, geometry, trigonometry, probability, and statistics.

Key Features of the Paper:

1. Section A (Compulsory):

   • Question 1 consists of 15 multiple-choice questions (MCQs) covering topics like quadratic equations, probability, matrices, geometry, and arithmetic progressions. These questions test fundamental concepts and require quick, accurate responses.

   • Question 2 and Question 3 involve problem-solving and application-based questions, including solving quadratic equations, calculating interest in recurring deposits, and proving geometric theorems. These questions require clear working steps and logical reasoning.

2. Section B (Optional - Attempt any 4 questions):

   • This section includes higher-order thinking questions that test deeper understanding and application of concepts. Topics include:

     • Algebra: Solving inequalities, arithmetic progressions, and polynomial factorization.

     • Geometry: Constructions, similarity of triangles, and properties of circles.

     • Trigonometry: Proving trigonometric identities and solving problems using trigonometric ratios.

     • Mensuration: Calculating surface areas and volumes of composite shapes like capsules.

     • Statistics and Probability: Drawing histograms, finding mean and median, and calculating probabilities.

     • Graphical Problems: Plotting points, reflecting shapes, and analyzing graphs.

3. Difficulty Level:

   • The paper is moderately challenging, with a mix of straightforward MCQs and complex problem-solving questions.

   • Section A is relatively easier, focusing on basic concepts, while Section B requires more analytical thinking and application of concepts.

4. Marking Scheme:

   • Marks are allocated based on the complexity of the questions, with detailed working required for full credit.

   • Rough work must be shown clearly, and omission of essential steps can lead to loss of marks.

5. Key Topics to Focus On:

   • Algebra: Quadratic equations, polynomials, and arithmetic progressions.

   • Geometry: Circle theorems, similarity of triangles, and constructions.

   • Trigonometry: Identities and angle calculations.

   • Mensuration: Surface areas and volumes of 3D shapes.

   • Statistics and Probability: Mean, median, histograms, and probability calculations.

6. Time Management:

   • Students should allocate 15 minutes to read the paper and plan their approach.

   • Section A should be completed within 60-75 minutes, leaving the remaining time for Section B.

Conclusion:

The ICSE Mathematics 2025 paper is well-balanced, testing both conceptual understanding and problem-solving skills. Students should focus on practicing a variety of problems, especially in algebra, geometry, and trigonometry, to perform well. Time management and clear presentation of working steps are crucial for scoring high marks.

ICSE Mathematics Competency Based Questions Detailed Solution

Struggling with ICSE Mathematics Competency-Based Questions? Don't worry, we've got you covered! In this video, we break down some of the most challenging competency-based questions from the ICSE Mathematics syllabus, providing step-by-step solutions to help you understand the concepts and ace your exams. 📚✅

What You'll Learn:

• Key strategies to approach competency-based questions.
• Detailed explanations for solving complex problems.
• Tips and tricks to save time and avoid common mistakes.
• Clear understanding of important mathematical concepts.
• How to approach competency-based questions that test understanding, application, analysis, creation, and evaluation.
• Step-by-step solutions to the latest questions released by the ICSE board.
• Tips to develop critical thinking and problem-solving skills for higher-order questions.
• Strategies to tackle real-life application-based problems effectively.

Topics Covered:

• Algebra
• Geometry
• Trigonometry
• Mensuration
• Statistics and Probability

Whether you're preparing for your board exams or just want to strengthen your math skills, this video is perfect for you! Hit the like button if you find this video helpful, and don't forget to subscribe for more educational content. Share this video with your friends who might need some extra help with their math studies. Let's conquer ICSE Mathematics together! 🚀📖

Why Watch This Video?

• These questions are directly from the board and reflect the latest exam patterns.
• Perfect for students aiming to score high by mastering competency-based learning.
• Clear explanations to help you build confidence and improve your problem-solving skills.

Or download the pdf

50 Important Questions for CBSE and ICSE

 "50 Important Questions for ICSE and CBSE - All Chapters" contains a collection of important mathematics problems for Class 10 students. It includes a variety of questions covering different topics from the ICSE and CBSE syllabus.

Key Topics Covered:

1. Algebra:

   • Arithmetic Progression (AP) and Geometric Progression (GP)
   • Quadratic equations
   • Polynomials and factorization
   • Matrices and determinants

2. Geometry:

   • Triangles (Similarity and Congruence)
   • Circles (Tangents, Chords, and Theorems)
   • Coordinate Geometry (Finding slopes, equations of lines, midpoints, etc.)

3. Trigonometry:

   • Trigonometric identities and proofs
   • Heights and distances problems
   • Simplification of trigonometric expressions

4. Mensuration:

   • Volume and surface area of solids (cones, spheres, and cylinders)
   • Problems involving melting and reshaping of solids

5. Statistics & Probability:

   • Mean, mode, and median
   • Probability of drawing cards, marbles, or coin tosses

6. Commercial Mathematics:

   • Shares and dividends
   • Simple and compound interest
   • Recurring deposits

Types of Questions Included:

• Proof-based questions
• Numerical problem-solving
• Conceptual and application-based problems
• Word problems involving real-life scenarios
• Questions requiring graphical representation

The document is a good resource for exam preparation, covering both theoretical and practical aspects of mathematics for ICSE and CBSE Class 10 students. Let me know if you need detailed solutions or explanations for any specific questions! 

National Means-cum-Merit Scholarship Examination (NMMSE)

The National Means-cum-Merit Scholarship Examination (NMMSE) in India is a prestigious scholarship program conducted by the Ministry of Education, Government of India, aimed at identifying and supporting economically disadvantaged but academically talented students. The examination is typically held at the state/UT level for students studying in Class 8, and successful candidates receive financial assistance to continue their education until Class 12. The NMMSE assesses students' mental ability, scholastic aptitude, and proficiency in subjects like Mathematics and Science. By providing scholarships, the program aims to reduce dropout rates at the secondary level and encourage meritorious students to pursue higher education, thereby contributing to the nation's educational and socio-economic development.

The National Means-cum-Merit Scholarship Examination (NMMSE) in India is a significant initiative by the Ministry of Education to support economically underprivileged students who demonstrate exceptional academic potential. Conducted annually at the state/UT level for Class 8 students, the exam evaluates candidates through two tests: the Mental Ability Test (MAT), which assesses logical and analytical thinking, and the Scholastic Aptitude Test (SAT), which focuses on subjects like Mathematics, Science, and Social Science. Students who qualify are awarded a scholarship of Rs. 12,000 per annum to continue their education from Class 9 to Class 12, provided they maintain a minimum academic performance. The NMMSE not only alleviates financial burdens for deserving students but also motivates them to excel academically, thereby fostering a culture of merit and reducing dropout rates at the secondary school level. This initiative plays a crucial role in empowering young minds and contributing to the nation's educational and socio-economic progress.

A blog post featuring the last five years' solved NMMSE (National Means-cum-Merit Scholarship Examination) Maths papers is an invaluable resource for students preparing for this competitive scholarship exam. Such a post would provide detailed, step-by-step solutions to the Mathematics sections of previous years' question papers, helping students understand the problem-solving techniques, concepts, and patterns frequently tested in the exam. By analyzing these solved papers, students can identify important topics, improve their time management skills, and build confidence in tackling challenging problems. Additionally, the blog post could include tips and strategies for approaching the Maths section, common mistakes to avoid, and insights into the exam's difficulty level over the years. This comprehensive resource would serve as an essential study tool, enabling students to practice effectively and enhance their chances of qualifying for the prestigious NMMSE scholarship.

Chapter Test : Miscellaneous Mathematics Problems for Class X (ICSE & CBSE)

 Mathematics plays a crucial role in strengthening problem-solving skills and logical reasoning. This set of miscellaneous mathematics problems is designed for Class X students studying under ICSE and CBSE curricula, covering a wide range of important topics. Let’s take a closer look at the types of questions included and how they help in mastering key concepts.

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1. Trigonometry – Identities and Applications

Trigonometry is a core topic in Class X, and this problem set includes challenges like:

• Evaluating expressions involving sin, cos, sec, and cosec functions.
• Proving trigonometric identities and solving equations.
• Finding values of complex trigonometric expressions, such as sin² θ + cos² θ relationships.

Example:

• If sin θ + cos θ = 2, find the value of sin⁷⁶⁸⁵ θ + cos⁷⁶⁸⁵ θ.

These problems test conceptual clarity and the ability to simplify trigonometric functions efficiently.

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2. Algebra – Quadratic Equations, Factorization & Progressions

Algebraic problem-solving is a fundamental skill. This set includes:

• Quadratic Equations: Proving relationships between coefficients and roots.
• Factorization: Completely factorizing polynomials using algebraic identities and theorems.
• Arithmetic and Geometric Progressions (AP & GP): Finding specific terms and their sums.

Example:

• If the pᵗʰ term of an AP is q and the qᵗʰ term is p, find tₚ₊q and Sₚ₊q.

These problems build a strong foundation in algebra and sequence calculations.

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3. Geometry – Triangles, Circles & Coordinate Geometry

Geometry questions test understanding of:

• Triangle Properties: Proving area and ratio relationships in right-angled triangles.
• Circle Theorems: Using tangents, chords, and angle properties to prove identities.
• Coordinate Geometry: Finding slopes and relationships between different line segments.

Example:

• Prove that AF + CE + BD = AE + CD + BF = ½ Perimeter (∆ABC) when a circle touches the sides of a triangle.

Mastering these problems enhances logical reasoning and visualization skills.

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4. Statistics – Mean Transformations

Understanding mean and its transformations is crucial for data interpretation. The given question involves:

• Computing the mean when data points are multiplied by a factor.

Example:

• If x₁, x₂, x₃ … xₙ have a mean x̄, find the mean of (2a/3) * x₁, (2a/3) * x₂, …

Such problems improve conceptual understanding of averages and statistical operations.

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5. Mensuration – Cones & Volume-Surface Area Relations

Mensuration problems focus on:

• The relationship between the volume and curved surface area of a cone.
• Finding values of expressions involving height (h) and radius (r).

Example:

• If the numerical values of volume and curved surface area of a right circular cone are equal, find (1/h² + 1/r²).

These questions refine students’ ability to work with formulas and spatial reasoning.

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6. Financial Mathematics – Shares & Investments

Real-life application of financial mathematics includes:

• Calculating dividends on shares.
• Determining returns on investments after selling shares at different prices.
• Finding the percentage increase in returns.

Example:

• Mr. Ram Gopal invested ₹8000 in 7% shares at ₹80. He later sold them at ₹75 and reinvested in 18% ₹25 shares at ₹41. Find:
  • First-year dividend.
  • Second-year annual income.
  • Percentage increase in return on the original investment.

Such problems build financial literacy and real-world application skills.

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7. Miscellaneous Problem-Solving

Some additional challenges include:

• Solving rational equations.
• Working with sec, tan, and sine transformations.
• Finding values of trigonometric summations like sin²10° + sin²20° + … + sin²90°.
• Proving complex algebraic expressions.

These problems push students to think creatively and develop strong problem-solving abilities.

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Conclusion

This set of miscellaneous problems provides a comprehensive revision of key Class X topics across Algebra, Geometry, Trigonometry, Statistics, and Mensuration. Whether preparing for board exams or sharpening mathematical skills, these questions serve as excellent practice material.

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