📘 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.
🔹 Why Focus on These Topics?
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Trigonometry: Around 8–10 marks every year (Identities, Heights & Distances).
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Probability: 4–6 marks, usually simple but tricky MCQ-type.
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Statistics: 8–10 marks (Mean, Median, Mode, Graphs, Ogive, Histogram).
That means almost 25% of your math exam comes directly from these three chapters!
🟦 1. Trigonometry Section (Q.1–30, 71–90)
This section begins with basic identities and proofs like:
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Proving trigonometric identities (Q.1–20).
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Higher-level simplifications involving sec, tan, and cot (Q.21–30).
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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.
🟩 2. Probability Section (Q.31–50)
The probability section has a mix of dice, coins, cards, and real-life examples:
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Simple dice problems (Q.31–33, 37–38).
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Coin toss problems (Q.39–40).
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Playing cards (Q.35, Q.48).
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Real-world word problems with marbles, ice creams, tickets, etc.
👉 Tip: Always remember
and carefully check whether the problem is "or" (union) or "and" (intersection) type.
🟥 3. Statistics Section (Q.51–70)
This section covers:
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Mean, Median, Mode (Q.51–59, Q.67–69).
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Ogives & Histograms (Q.60–64).
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Word problems with real-life data (Q.65–70).
👉 Tip:
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Use step-deviation method for quicker calculation of mean.
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Median = value of -th observation (learn how to locate it correctly in cumulative frequency tables).
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For graphs, label your axis neatly—marks are often lost for presentation.
📌 How to Use This Problem Sheet?
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Start with Trigonometric Identities → They sharpen algebraic manipulation skills.
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Move to Probability → These are quick, scoring questions.
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Finish with Statistics → Practice graphs separately for neatness and accuracy.
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Solve at least 10 questions daily from the sheet.
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Time yourself as if in an exam.
🌟 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.
