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.